5th International Colloquium on Transformer Research and Asset Management [1st ed.] 9789811555992, 9789811556005

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Lecture Notes in Electrical Engineering 671

Bojan Trkulja Željko Štih Žarko Janić Editors

5th International Colloquium on Transformer Research and Asset Management

Lecture Notes in Electrical Engineering Volume 671

Series Editors Leopoldo Angrisani, Department of Electrical and Information Technologies Engineering, University of Napoli Federico II, Naples, Italy Marco Arteaga, Departament de Control y Robótica, Universidad Nacional Autónoma de México, Coyoacán, Mexico Bijaya Ketan Panigrahi, Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, Delhi, India Samarjit Chakraborty, Fakultät für Elektrotechnik und Informationstechnik, TU München, Munich, Germany Jiming Chen, Zhejiang University, Hangzhou, Zhejiang, China Shanben Chen, Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, China Tan Kay Chen, Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore Rüdiger Dillmann, Humanoids and Intelligent Systems Laboratory, Karlsruhe Institute for Technology, Karlsruhe, Germany Haibin Duan, Beijing University of Aeronautics and Astronautics, Beijing, China Gianluigi Ferrari, Università di Parma, Parma, Italy Manuel Ferre, Centre for Automation and Robotics CAR (UPM-CSIC), Universidad Politécnica de Madrid, Madrid, Spain Sandra Hirche, Department of Electrical Engineering and Information Science, Technische Universität München, Munich, Germany Faryar Jabbari, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA Limin Jia, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Alaa Khamis, German University in Egypt El Tagamoa El Khames, New Cairo City, Egypt Torsten Kroeger, Stanford University, Stanford, CA, USA Qilian Liang, Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA Ferran Martín, Departament d'Enginyeria Electrònica, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain Tan Cher Ming, College of Engineering, Nanyang Technological University, Singapore, Singapore Wolfgang Minker, Institute of Information Technology, University of Ulm, Ulm, Germany Pradeep Misra, Department of Electrical Engineering, Wright State University, Dayton, OH, USA Sebastian Möller, Quality and Usability Laboratory, TU Berlin, Berlin, Germany Subhas Mukhopadhyay, School of Engineering & Advanced Technology, Massey University, Palmerston North, Manawatu-Wanganui, New Zealand Cun-Zheng Ning, Electrical Engineering, Arizona State University, Tempe, AZ, USA Toyoaki Nishida, Graduate School of Informatics, Kyoto University, Kyoto, Japan Federica Pascucci, Dipartimento di Ingegneria, Università degli Studi “Roma Tre”, Rome, Italy Yong Qin, State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China Gan Woon Seng, School of Electrical & Electronic Engineering, Nanyang Technological University, Singapore, Singapore Joachim Speidel, Institute of Telecommunications, Universität Stuttgart, Stuttgart, Germany Germano Veiga, Campus da FEUP, INESC Porto, Porto, Portugal Haitao Wu, Academy of Opto-electronics, Chinese Academy of Sciences, Beijing, China Junjie James Zhang, Charlotte, NC, USA

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Bojan Trkulja Željko Štih Žarko Janić •

•

Editors

5th International Colloquium on Transformer Research and Asset Management

123

Editors Bojan Trkulja Faculty of Electrical Engineering and Co University of Zagreb Zagreb, Croatia

Željko Štih Faculty of Electrical Engineering and Co University of Zagreb Zagreb, Croatia

Žarko Janić Koncar Power Transformers LTD A Joint Venture of Siemens and Koncar Zagreb, Croatia

ISSN 1876-1100 ISSN 1876-1119 (electronic) Lecture Notes in Electrical Engineering ISBN 978-981-15-5599-2 ISBN 978-981-15-5600-5 (eBook) https://doi.org/10.1007/978-981-15-5600-5 © Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

About This Book

This book is a collection of selected papers from the 5th International Colloquium “Transformer Research and Asset Management” held in Opatija, Croatia. The International Colloquium was organized by the Croatian CIGRÉ National Committee in cooperation with the Faculty of Electrical Engineering and Computing in Zagreb and the Centre of Excellence for Transformers in Zagreb with support from CIGRÉ A2 Study committee (Power Transformers and Reactors). In the last ten years, the colloquium established itself as an important event for transformers and gathers regularly more than 200 participants from more than 20 countries. Some of the papers are a result of Cigre working groups which also had their meetings on the colloquium. Papers are selected from all three main topics • Numerical methods • Materials, Components, and New Technologies • Transformer Life Management. All of the papers went under several rounds of review in order to select the more relevant for this publication.

v

Contents

Relative Permittivity Assessment of Oil-Impregnated Cellulose Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mladen Marković and Marijana Majić Renjo

1

Difference Between 50 and 60 Hz Transformer No-Load Noise Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Miha Pirnat

11

Reproducibility Estimation of Sound Power Level of Large Power Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zdenko Godec, Filip Razum, and Davor Švarc

19

Stressed Oil Volume Theory in Transformer Winding Corner Stress Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Petar Gabrić, Ana Orešković, Vjenceslav Kuprešanin, Antun Mikulecky, and Vladimir Podobnik Synthetic Ester Impact on Power Transformer Design, Manufacturing and Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dario Šegović, Ana Orešković, and Žarko Janić Future Trends in Transformer Online Monitoring . . . . . . . . . . . . . . . . . Teemu Auronen, Ivan Murat, Teemu Hanninen, and Samir Keitoue Optimal Cooling and Life Time Management for Power Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luc Paulhiac and Johannes Raith Analysis of Overvoltages on Power Transformer Recorded by Transient Overvoltage Monitoring System . . . . . . . . . . . . . . . . . . . . Bozidar Filipovic-Grcic, Bruno Jurišić, Samir Keitoue, Ivan Murat, Dalibor Filipovic-Grcic, and Alan Zupan

33

45 55

67

85

vii

viii

Contents

Power Transformer Efficiency—Survey Results and Assessment of Efficiency Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Žarko Janić, Anthony Walsh, Adesh Singh, and Yordan Botev Reliable Power Transformer Efficiency Tests . . . . . . . . . . . . . . . . . . . . . 113 Gert Rietveld, Ernest Houtzager, Dennis Hoogenboom, and Gu Ye Verification of Maintenance Intervals for Vacuum On-load Tap-changers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Niklas Gustavsson Prediction Model for the Distribution Transformer Failure Using Correlation of Weather Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Eun Hui Ko, Tatjana Dokic, and Mladen Kezunovic On Site Measurement and Simulation of Transferred Lightning Overvoltages Through Power Transformers . . . . . . . . . . . . . . . . . . . . . 145 Bruno Jurišić, Tomislav Župan, Goran Plišić, Božidar Filipović-Grčić, Goran Levačić, and Alain Xemard Calculation of Circuit Parameters of High Frequency Models for Power Transformers Using FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Álvaro Portillo, Luiz Fernando de Oliveira, and Federico Portillo Small Signal Internal Voltage Transfer Measurements and White-Box Transient Calculations for Non-standard Test Conditions of a Shell-Form Power Transformer . . . . . . . . . . . . . . . . . . 183 Bjørn Gustavsen, Ariana Martins, Carlos A. Sá, Luis Braña, Ricardo Castro Lopes, Pedro Lima, Andrea Soto, and Mário Soares Internal Fault Performance of Instrument Transformers with Sectioned Active Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Igor Žiger, Danijel Krajtner, and Boris Bojanić Simulation of Long-Term Transformer Operation with a Dynamic Thermal, Moisture and Aging Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Johannes Raith, Christian Bonini, and Mario Scala Line Discharge Capability of Inductive Voltage and Combined Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Ivan Konta, Dijana Papić, Dalibor Filipović-Grčić, and Danijel Brezak Influence of Conductor Transposition on Transformer Winding RLC Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 Ana Drandić, Bojan Trkulja, and Željko Štih

Contents

ix

Appropriate Modelling of Transformer High Current Leads in 3D FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 Karlo Petrović, Bruno Jurišić, and Tomislav Župan Calculation of Eddy Current Losses in Iron Core of Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Stjepan Frljić, Bojan Trkulja, and Željko Štih

About the Authors

Bojan Trkulja was born in Bjelovar, Croatia, in 1978. He received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering and computing from the University of Zagreb, Zagreb, Croatia, in 2001, 2004, and 2008, respectively. He is currently an Associate Professor with the University of Zagreb Faculty of electrical engineering and computing working in Laboratory for electromagentic fields. He is teaching on undergraduate, graduate and postgraduate studies at University of Zagreb. For the exellence in research and teaching he got Koncar and Giannini awards. His main research interests include the application of numerical methods in electromagnetic field analysis. Željko Štih was born in 1955 in Krapina, Croatia. He received the Ph.D. degree from the University of Zagreb, Croatia, in 1984. He worked at the Electrical Engineering Institute ‘Rade Koncar’ on research and development within the Transformer division and at the ‘Infosistem’ on development of graphical programming support. Since 1986, he works at the Faculty of Electrical Engineering and Computing, University of Zagreb, where he became a Full Professor in 2002. Professor Stih is the author of more than thirty scientific papers and more than one hundred expert reports. His research interests are computational electromagnetism and its application in power apparatus and systems. He received the J. J. Strossmayer award for his scientific achievements in the field of technical sciences. Žarko Janić was born in 1980 in Pula, Croatia. He got his M.E. on the Faculty of electrical engineering and Computing in the University of Zagreb at the department of Power Systems in 2004 and Ph.D. at the same Faculty in 2008. He was researcher at the Koncar Electrical engineering Institute in the Transformer Department, working on magnetic topics. After that he was Head of Research and Development in Koncar Power Transformers and then Head of Research in the Large Power Transformer segment in Siemens AG. Currently he is heading the Optimisation department in Koncar Power Transformers in Zagreb, Croatia. He is teaching as assistant professor at the Faculty of electrical engineering xi

xii

About the Authors

and Computing in Zagreb both on the undergraduate study and Transformer specialist postgraduate study. Assistant Prof. Janic is observer member, Croatian representative, in Cigre A2 study committee. Since 2016 he is heading Cigre working group A2.56 Power Transformer Efficiency. He got the Koncar award in 2008 for his Ph.D. as the best Ph.D. with application in the industry.

Relative Permittivity Assessment of Oil-Impregnated Cellulose Insulation Mladen Markovi´c and Marijana Maji´c Renjo

Abstract Insulating system of a power transformer consists of an insulating liquid (mineral oil or ester liquid) and cellulose-based materials (paper and pressboard). Dielectric properties of an insulating material may be expressed in terms of relative permittivity and material conductivity. Material conductivity influences electric fields in power transformers exposed to DC voltages (e. g. HVDC transformers), whereas relative permittivity is more relevant in power transformers subjected to power frequency (50 or 60 Hz). It is well known that a higher discrepancy between relative permittivity of liquid-impregnated material and insulating liquid increases electric field in insulating liquid. It is therefore essential to know values of relative permittivity of cellulose-based materials in order to properly evaluate electric field strengths in the transformer. This paper presents both theoretical and practical approach to relative permittivity assessment of two types of cellulose material in two different impregnation states. Keywords Electrochemical impedance spectroscopy · Power transformer · Insulation · Relative permittivity · Impregnation

1 Introduction The main purpose of the insulation system of a power transformer is to dielectrically separate parts of a transformer with different electric potential. Well-designed transformer insulation allows transformer to work properly during its lifetime. Insulating system consists mainly of cellulose based materials (paper and pressboard) and insulating liquid (mineral oil or ester liquids). Combination of liquid and solid insulation enables impregnation of insulating liquid into the porous cellulose material. This new kind of oil-impregnated material has higher value of relative permittivity than the cellulose material alone [1–4]. For the material of angle rings and angle caps in simple disc winding (Fig. 1), Konˇcar D&ST currently uses a wound kraft paper M. Markovi´c (B) · M. Maji´c Renjo Konˇcar D&ST Inc., J. Mokrovi´ca 8, 10090 Zagreb, Croatia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_1

1

2

M. Markovi´c and M. Maji´c Renjo

Fig. 1 Position of angle cap and angle ring inside an HV winding [1]

glued with poly(vinyl)alcohol (PVA) glue, in this work termed ‘material K’. Due to proposal for abandonment of gluing technology, a question was raised if ‘material K’ can be replaced with another kind of cellulose material, namely a pressboard designated as B.4.1 according to IEC 60641-3-1, in this work noted as ‘material S’. Since relative permittivities of both of materials ‘K’ and ‘S’ in oil-impregnated state were unknown, an investigation was conducted in order to quantify the influence of impregnation on relative permittivity of these two materials.

2 Relative Permittivity of Oil-Impregnated Material Relative permittivity εr (also dielectric constant) is a measure of polarization of a material in electric field (the higher the permittivity, the greater is polarization of the material). Polarization occurs when electric field displaces charge carriers in atoms (electron polarization), molecules (atom polarization), molecule groups (molecular polarization) or crystals (lattice polarization) as shown on Fig. 2 [2]. Mineral oil is composed of symmetric, non-polar molecules that give this dielectric material relatively small dielectric constant εoil = 2.2. Cellulose fiber is expected to have relative permittivity 5.1 ≤ εF ≤ 6.1. Due to impregnation process in which

Fig. 2 Polarization in a atoms and molecules b molecule groups c crystals ([2], Fig. 2.4–1)

Relative Permittivity Assessment of Oil-Impregnated Cellulose …

3

porous material (paper) absorbs liquid (mineral oil), a new value of relative permittivity εimp will be established and will depend on apparent density δ P of the paper, as described by the following theory reproduced from [3]. Firstly, relative absorption ‘a’ can be defined as a weight ratio of absorbed oil in the paper a=

Voil · δoil VP · δP

(1)

where: V oil —oil volume, δ oil —oil density = 0.866 g/cm3 (at 20 °C) [3], V P —paper volume, δ P —paper density. In case of unimpregnated paper, weight of paper is equal to weight of fibers, namely VP · δP = VF · δF

(2)

where: V F —fiber volume δ F —fiber density = 1.43 g/cm3 [3] In case of impregnated paper, volume occupied by oil is Voil = VP − VF

(3)

By inserting V P from (2) in (3), this gives  Voil = VF

δF −1 δP

 (4)

and the relative absorption rate ‘a’ from (1) becomes:  a = δoil

1 1 − δP δF

 (5)

giving Voil δP δP =a =1− VP δoil δF

(6)

Secondly, if cellulose material is represented as fiber matrix impregnated with oil, each cell of the matrix structure can be represented with cube volumes as shown on Fig. 3 whose edge ratio K is defined as:

4

M. Markovi´c and M. Maji´c Renjo

Fig. 3 Representation of impregnated cellulose material

 K =

3

 Voil = VP

3

1−

δP δF

(7)

where K is edge ratio of cubes of oil and fiber on Fig. 3, and δ P and δ F are explained in (1) and (2). Thirdly, the capacitance of an impregnated cell C imp can be calculated according to Fig. 4 with equivalent circuit shown on Fig. 5, for which capacitance values C F1 , C F2 and C oil are calculated as simple disk capacitors

Fig. 4 Calculation of C imp

Fig. 5 Equivalent circuit for C imp from Fig. 4

Relative Permittivity Assessment of Oil-Impregnated Cellulose … Table 1 Calculation of capacitance in equivalent circuit on Fig. 5 according to eq. (8)

5

C

εr

A

d

C F1

εF

1−K 2

1

C F2

εF

K2

(1−K)/2

C oil

εoil

K2

K

C = ε0 εr

A d

(8)

where C is capacitance of a disk capacitor with relative permittivity εr , surface A and thickness d, with corresponding values given in Table 1. Therefore, according to (8) and Fig. 5, the equivalent capacitance C imp is equal to Cimp = CF1 +

CF2 Coil CF2 + 2Coil

(9)

where C F1 , C F2 and C oil are capacitances of a disk capacitor (8) with permittivity, area and length according to Table 1. Fourthly and finally, the equivalent permittivity of impregnated cell is calculated from (9) and is equal to:   εimp = εF 1 − K 2 +

εF εoil K 2 εF K + εoil (1 − K )

(10)

where εF = 5.1, εoil = 2.2 [3], and value of K depends on paper and fiber density according to (6). For simplicity of further calculation, function (10) can be linearized for paper density range 0.7 ≤ δ P ≤ 1.3 and expressed as ε(δP ) = a · δP + b

(11)

where ε—relative permittivity of paper, δ P —density of unimpregnated paper, a, b—coefficients determined by impregnation state Coefficients a and b can be calculated for both impregnated (with εoil = 2.2) and unimpregnated state (with εoil = εair = 1), as shown in Table 2 and on Fig. 6. Table 2 Calculation of coefficients in eq. (11) from eq. (10) Paper

εF

εoil

a

b

Impregnated

5.1

2.2

2.137

1.910

Unimpregnated

5.1

1

3.023

0.441

6

M. Markovi´c and M. Maji´c Renjo

Fig. 6 Linearization of function (10) depending on impregnation state

5

permivity ε (δP)

4.5 4 3.5 3 2.5 2 0.5

0.7

0.9

1.1

1.3

1.5

paper density δP [g/cm³] impregnated

unimpregnated

3 Electrochemical Impedance Spectroscopy Electrochemical impedance spectroscopy (EIS) is a non-destructive method for measurement of the electrodes response to the small amplitude sinusoidal change of potential in the wide range of frequencies. It can be used to determine the resistive and capacitive (dielectric) properties of materials. When specimen is placed between the electrodes, this changes interfacial properties of electrodes (namely impedance of the system). The change of impedance is detected and analyzed across multiple frequencies according to Z=

sin(ωt) U0 sin(ωt) Ut = Z0 = It I0 sin(ωt + φ) sin(ωt + φ)

(12)

where U t is excitation signal with amplitude U 0 and frequency ω, whereas I t is response signal shifted in phase φ with same frequency and different amplitude I 0 . The impedance is therefore expressed in terms of a magnitude Z 0 and phase shift φ. Measuring impedance enables measurement of capacitance of an ideal capacitor, namely C=

1 jωZ

(13)

where C is capacitance of a simple disk capacitor (8). Then, relative permittivity εr is expressed as εr = C

d ε0 A

(14)

Relative Permittivity Assessment of Oil-Impregnated Cellulose …

7

where C is measured capacitance, d is capacitor thickness, A is capacitor surface and ε0 is vacuum permittivity [5, 6].

4 Measurement Procedure Two types of cellulose-based materials were tested: (a) material currently used in Konˇcar D&ST (‘material K’), namely kraft paper glued with poly(vinyl)alcohol glue and (b) pressboard type B.4.1 according to IEC 60641-3-1 (‘material S’). Both materials were tested in two conditions: (i) dried and unimpregnated, (ii) dried and impregnated with mineral oil. Samples were cut on mechanical guillotine shears into the 60 mm × 70 mm rectangular shapes (Fig. 7a), appropriate for the testing apparatus. ‘Material K’ samples were 2 mm thick, as used in the Konˇcar D&ST production. ‘Material S’ samples were 1 mm thick, as provided from the supplier. Two samples per each type and condition were prepared. Samples were dried in the vapor-phase drying plant (VPDP), alongside an active part of a transformer. Half of the samples were vacuumed and sealed into PE/PA pouches immediately after drying. The other half of samples were impregnated in the transformer mineral oil for 24 h (Fig. 7b). Afterwards, the impregnated samples were taken out of the oil, strained shortly, then vacuumed and sealed into PE/PA pouches. Samples were unpacked shortly before the permittivity measurement at nominal frequency of 50 Hz.

'material K'

'material S'

(a)

(b)

Fig. 7 Sample preparation: a samples cut to the required size; b impregnation of samples in mineral transformer oil under vacuum

8

M. Markovi´c and M. Maji´c Renjo

Table 3 relative permittivity of tested samples Type ‘Material K’

Material Kraft paper + PVA glue

d (mm) 2

Impregnation No

Yes

‘Material S’

Pressboard B.4.1

1

No

Yes

Measurement of ε r

Calculation of ε r

C a (F)

ε br

εr

δ cP (g/cm3 )

ε dr

1.985 × 10−11

3.37

3.35

0.65–0.75

2.41–2.71

1.962 × 10−11

3.33

2.363 × 10−11

4.01

2.311 × 10−11

3.93

1.985 × 10−11

3.37

1.962 × 10−11

3.35

2.363 × 10−11

3.82

2.311 × 10−11

3.86

3.97

3.36

3.84

3.30–3.51

0.85–1.1

3.01–3.77

3.73–4.26

a Surface of capacitor plates A = 13.32 cm2 ; nominal measurement frequency = 50 Hz b ε is obtained from measured C according to (14) r c Assumed range of δ for kraft paper is taken from IEC 60554-3-1, for Pressboard B.4.1 from IEC P

60641-3-1 d Range for ε is calculated from assumed δ according to (11) r P

5 Measurement Results Relative dielectric permittivity εr of tested samples is obtained from measuring capacitance C according to (14) and is shown in Table 3 for nominal frequency of 50 Hz. Calculated values of εr for impregnated and unimpregnated condition according to (11) are also given.

6 Analysis From Table 3 it can be seen that the average measured value of εr for ‘material S’ corresponds to calculated value for both impregnated and unimpregnated state, whereas a certain discrepancy of measured and calculated values exists in the case of ‘material K’, which could be explained by the influence of glue as shown on Fig. 8.

Relative Permittivity Assessment of Oil-Impregnated Cellulose …

9

Fig. 8 ‘Material K’ represented as a two layer dielectric

Indeed, if ‘material K’ is represented as a two layer dielectric with thickness d = d G + d P , as shown on Fig. 8, then the resulting permittivity εres can be expressed as εres = d

εG εP εG dP + εP dG

(15)

where εres is resulting permittivity, d is thickness of the ‘material K’, d P is thickness of paper and d G is thickness of glue. Since ‘material K’ is composed out of 6 layers of 0.2 mm paper with overall thickness of d = 2 mm, this gives d P = 1.2 mm and d G = 0.8 mm. Using the measurements of average εres for ‘material K’ in impregnated state (εres = εimp - K = 3.97, Table 3) and unimpregnated state (εres = εK = 3.35, Table 3), and assuming that glue is not impregnated with oil (εimp-G = εG ) and also that average permittivity of impregnated paper is εimp-P = 3.41 (Table 3), then the following set of equations can be arranged using (15): εimp-K = d εK = d

εG εimp-P dP εG + dG εimp-P

(16a)

εG εP dP εG + dG εP

(16b)

This set of equations can be solved for εG and εP εimp-K εimp-P = 5.27 dεimp-P − d P εimp-K

(17a)

εK εimp-K εimp-P   = 2, 70 dεimp-P εimp-K − εK + dP εimp-K εK

(17b)

εG = dG εP = dP

where: εG —permittivity of glue, εP —permittivity of unimpregnated paper, εK = 3.35—permittivity of unimpregnated ‘material K’ (average measured value in Table 3), εimp-K = 3.97—permittivity of impregnated ‘material K’ (average measured value in Table 3),

10

M. Markovi´c and M. Maji´c Renjo

εimp-P = 3.41—permittivity of impregnated paper (average calculated value in Table 3), d P = 1.2 mm—nominal thickness of paper in ‘material K’ (=6 layers of 0.2 mm paper), d = 2 mm—nominal thickness of ‘material K’, d G = 0.8 mm—nominal thickness of glue in ‘material K’ (=d − d P ). Thus, the permittivity of unimpregnated paper εP = 2.70 obtained in (17b) lies in the range of calculated εr value in Table 3 obtained from (11).

7 Conclusion Relative permittivity of paper insulation was measured for two types of cellulose material, and it has been shown that lower density material mixed with glue has similar permittivity to commercially available material with higher apparent density. Additionally, measured values of all samples correspond to analytically calculated values (for both impregnated and unimpregnated state), meaning that analytical approach can be used for future assessment of relative permittivity of other types of cellulose materials and insulating liquids.

References 1. Kulkarni SV, Khaparde SA (2004) Transformer engineering: design and practice. CRC Press, New York 2. Küchler A (2018) High voltage engineering. Springer, Berlin Heidelberg, Berlin, Heidelberg 3. Moser HP, Dahinden V (1988) Transformerboard II. Scientia Electrica, Rapperswil, Switzerland 4. Sbravati A, Rapp K, Schmitt P, Krause C (2017) Transformer insulation structure for dielectric liquids with higher permittivity. In: 2017 IEEE 19th international conference on dielectric liquids (ICDL), pp 1–4 5. Gamry Instruments (2010) Basics of electrochemical impedance spectroscopy. Appl. Note Rev. 1.0 6. Fabijan D (2012) Experimental methods in dielectric spectroscopy. Oddelek za fiziko, Faculty of Mathematics and Physics, Ljubljana, Slovenia, p 14

Difference Between 50 and 60 Hz Transformer No-Load Noise Levels Miha Pirnat

Abstract An unexplained difference between noise levels of 50 and 60 Hz transformers was presented in the previous published work of CIGRE workgroup A2.54 titled ‘No-load sound power levels for specification purposes derived from more than 1000 measurements–a representative figure for three-phase transformers’. The purpose of this paper is to provide further explanation of this phenomenon based on predictable and unpredictable effects, which are the source of the observed no-load noise difference between 50 and 60 Hz transformers. Keywords Transformer · No-load noise · Resonance · Radiation efficiency

1 Introduction CIGRE A2.54 working group has a task to study ‘Power transformer audible sound requirements’ in order to facilitate sound level specification for new transformer purchases. For this purpose, a large database was formed from more than 1000 noload sound level measurements. The datasets were collected by 13 independent transformer manufacturers from around the world who are participating in the working group. Results from the joint database analysis were published in [1]. In the latter, also an unexplained trend was presented regarding the difference between 50 and 60 Hz transformer noise levels. After further workgroup analysis of the gathered data, a slightly different trend than the one presented in [1] was found and is shown in Fig. 1. The graph shows that 60 Hz transformers have typically a higher sound power level than 50 Hz transformers with same core mass and induction. The largest difference of 11 dBA in average was found for small transformers with a core weight around 3000 kg. The difference is decreasing with core mass and is 4 dBA for 100000 kg

Paper is written on behalf of CIGRE WG A2.54. M. Pirnat (B) kolektor Etra d.o.o., Šlandrova Ulica 10, Ljubljana, Slovenia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_2

11

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M. Pirnat

Fig. 1 No-load sound power level difference for 50 and 60 Hz excitation at same core induction

cores. The trend is valid in general for liquid-immersed transformers. Different types of transformers may exhibit a different trend. The purpose of this paper is to provide further explanation of this phenomenon. The explanation is based on several effects which are known to affect sound power levels of objects. As it is not possible to exactly quantify the impact of all individual effects, the considered effects are divided into predictable and unpredictable effects. Values of the predictable effects can be quantified for all transformers, but values of unpredictable effects are different for individual transformers and cannot be easily quantified due to missing information or high complexity of the involved phenomena. Additionally, a number of non-standard noise measurements made by different transformer manufacturers are presented and discussed in order to further support the explanations given.

2 Predictable Effects on Sound Power Levels The predictable effects on sound power levels can be quantified and are valid for all transformers regardless of their size, core induction or any other parameter. In general, radiated sound power of a sound source can be written as [2]: W = ρcSω2 x 2 σ

(1)

where W is the radiated sound power, ρ the fluid density, c the speed of sound, S the sound radiating surface area, ω the angular velocity, x the magnitude (r.m.s.) of the surface displacement and σ the radiation efficiency. The observed difference

Difference Between 50 and 60 Hz Transformer …

13

between 50 and 60 Hz transformers is due to parameter changes in this formula, therefore, we will quantify the effect by changing the frequency. A. Surface velocity The vibrating core surface is the source of the no-load noise. If the excitation frequency of the core is changed from 50 to 60 Hz, while keeping the same induction level, the magnitude of the surface displacements remains the same, however, the velocity is higher according to: v = ρx

(2)

Where v is the surface velocity. As radiated sound power is proportional to velocity square, the increase of radiated sound power level due to the frequency change can be written and evaluated as:   f exc = 1.6d B (3) L p,v = 20 log frated Where f exc is 60 Hz and f rated is 50 Hz. The formula (3) gives 1.6 dB as the effect of increased surface velocity. B. Sound radiation efficiency The sound radiation efficiency of a sound source is based on the ratio of radiated sound power and sound power, which would be radiated by a uniformly vibrating baffled piston with same surface velocity [2]. The radiation efficiency or radiation index is then given by reorganizing (1): σ =

W ρcSω2 x2

(4)

However, in (4) the radiated sound power of a transformer cannot be easily obtained. In order to compare 50 and 60 Hz radiation efficiency one would need to solve homogenous Helmholtz equation for a given transformer geometry and known boundary conditions. To estimate the effect of frequency change on radiation efficiency by a first order approach, it is instructive to examine a simply supported rectangular plate. In the subcritical frequency range, the radiation efficiency of the plate is rising for the majority of its low order vibration modes. In this case, we can estimate the increase of radiation efficiency according to [2]:  σ ≈

2L π kc S



k kc

(5)

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M. Pirnat

Table 1 A weights for different noise harmonics Excitation Freq. 50 Hz

Excitation Freq. 60 Hz

Harmonic [Hz]

A-weight [dB]

Harmonic [Hz]

A-weight [dB]

Difference [dB]

100

−19.1

120

−16.7

2.4

200

−10.8

240

−9.1

1.8

300

−7.1

360

−5.6

1.5

400

−4.8

480

−3.5

1.3

500

−3.2

600

−2.2

1.1

600

−2.2

720

−1.3

0.9

where σ is the radiation efficiency, L the plate peripheral length, S the plate surface area, k c the critical wavenumber and k the wavenumber. By evaluating the expression for a typical transformer, the estimated effect due to increased excitation frequency is in the order of 0.5 dB. However, this estimation is valid only in case that the vibration mode shape does not change significantly with the frequency change. When the vibration mode shape does change, a general estimation of sound radiation efficiency is not possible. C. A-weighting All gathered noise measurements are A-weighted. Because the weighting values are frequency dependent, the average A-weighting is different for 50 and 60 Hz transformers. Differences of individual weighting values are given in Table 1 for the first six main noise harmonics. The average difference for the first three harmonics in Table 1 is 1.9 dB and average for the first six harmonics is 1.5 dB. Hence the contribution of the A-weighting on the difference between 50 and 60 Hz noise levels should be in the range of 1.5 to 1.9 dB depending on the dominance of the different harmonics.

3 Sum of Predictable Effects on Sound Power Levels By combining the presented predictable effects, an A-weighted no-load sound power level difference in the range of 3.6–4 dBA is expected between 50 and 60 Hz transformers. However, the analysis based on gathered no-load noise measurements shown in Fig. 1 gives a range between 4 and 11 dBA. The lower value is in line with the presented sum of predictable effects, but the higher value is left unexplained.

Difference Between 50 and 60 Hz Transformer …

15

4 Additional Noise Measurements at Different Supply Frequencies In order to obtain further insight into the phenomena, a series of additional noise measurements were done by different manufacturers within workgroup. The measurements were executed as standard sound level measurements, they were however done while the transformer was energized at different induction levels and frequencies. A. Noise measurements at 50 and 60 Hz supply frequency In this case sound power level measurements were done at three different core inductions 1.3, 1.5 and 1.7 T. At each induction level the sound power level of the transformer was measured using 50 and 60 Hz supply frequency. Transformer parameters and measurement results are presented in Table 2. From Table 2 one can observe that the average value of dL50/60 is around 4 dBA, which is in line with the estimated difference of the predictable effects. Further worth to note is the average value being largely unaffected by different core induction levels. Table 2 Measured differences in noise levels between 50 and 60 Hz supply frequency at different core inductions dL50/60 [dBA] Power [MVA]

Type

Rated supply frequency [Hz]

Core type

Core mass [kg] Core induction @ 1.3 T

Core induction @ 1.5 T

Core induction @ 1.7 T

21

Network

50

3/0

9472

7

6.1

5.4

18.75

Network

50

3/0

36

Network

50

3/0

11600

1.3

1.7

1.9

13042

5.5

8.3

50

Network

60

6.7

3/0

17969

0.8

0.1

3.1

52.5

Network

40

Network

50

3/0

18903

3.8

4.7

4.7

50

3/0

20941

5.5

2.5

290

3.2

GSU

60

3/0

57500

2.5

2.8

4.7

112

GSU

60

3/0

64253

6.4

3.2

2.2

470

GSU

60

3/0

84700

3.7

3.6

2.9

240

Network

50

3/0

88846

/

2.3

2.2

450

GSU

60

3/0

150411

4.6

1.6

0.5

300

GSU

50

3/2

125020

6.1

6.1

7.2

40

Network

50

3/0

21770

0.4

2.3

4.3

160

Auto

50

3/0

29871

6.5

6.4

7.8

4.2

3.7

4.1

Average dL50/60 [dBA]

16

M. Pirnat

Fig. 2 No-load noise levels at a range of supply frequencies, while keeping the core induction at the same level

B. Noise measurements at several different supply frequencies The dataset contains four noise measurements at rated core induction, while the supply frequency is varied in multiple steps. A trendline can be cast over the measured data points in order to obtain the overall effect while changing the supply frequency– see Fig. 2. The average value for slope is 0.4 dBA/Hz, which means 4 dBA per 10 Hz change in supply frequency. This is again in line with the estimated difference of the sum of the predictable effects.

5 Unpredictable Effects on Sound Power Levels Based on previous sections a difference between 50 and 60 Hz transformer in the order of 4 dBA is explainable, however, the slope shown in Fig. 1 with the 11 dBA difference for transformers with low core mass is yet to be explained. The analysis so far is based on transformers designed for one particular frequency that are subjected to different supply frequencies. It must however also be considered that transformer designs for 50 and 60 Hz differ, although the electrical specification may

Difference Between 50 and 60 Hz Transformer …

17

be comparable. It appears, additional effects arise from the designs for the 50 and 60 Hz world, which could have an impact on acoustic performance of the transformer. A number of these effects are gathered in this section, although their impact is not quantified due to complexity and the list considered of being not complete. A. Resonances Resonance of any of the main transformer parts, such as core, windings, tank and in part also accessories can substantially raise the measured noise levels over expectation. This can also be observed in Fig. 2, where Transformer 4 has a substantial peak at 50 Hz. It is however anticipated that in a large database some transformers are in resonance while others are not, and therefore, the effect of resonances to the average noise level derived by the statistical analysis of the collected database being small. B. Magnetostriction Magnetostriction of the electrical steel is a highly nonlinear phenomenon and there is so far no standardized measurement procedure. The magnetostriction harmonics vary with supply frequency. The elongations of electrical steel sheets at 50 Hz may not be simply proportional to elongations at 60 Hz. C. Sound radiation efficiency In general, it is valid to say that the sound radiation efficiency is rising with rising frequency. However, the vibration mode shape of a transformer tank and other radiating structures can be significantly different for designs made for different supply frequencies. Consequently, the radiation efficiency may change significantly and therefore the radiated sound power. This effect in conjunction with the effect described in the following section D. is considered to be the main reason for the up to 11 dBA difference observed in Fig. 1. It is obvious that more investigation is required in this field. D. Modal density Modal density represents the number of natural frequencies in a specified frequency range. In a given frequency range, smaller transformer will have typically fewer natural frequencies than a larger transformer. By an increased excitation frequency, we move towards higher modal density, which can cause noise levels to increase due to a much greater chance of resonances. However, this effect is difficult to quantify and also difficult to distinguish from other effects. More investigations are also necessary on this topic. E. Miscellaneous Small differences between transformer manufacturers and their noise level measurements could have introduced some uncertainty to the collected database and affected the 50/60 Hz conversion analysis. These differences could be:

18

a. b. c. d. e. f. g.

M. Pirnat

Excitation waveform quality Transformer support structure type Laboratory room acoustics Measurement equipment Noise level measurement execution Magnetic shunt design …

6 Conclusions The analysis of a large database of transformer no-load noise measurements from a survey of CIGRE working group A2.54 yielded an unexplained difference between 50 and 60 Hz transformers, which is presented in this paper in Fig. 1. The observed difference was further analyzed and is in part explained based on a number of predictable but also a number of unpredictable effects. The difference due to the predictable effects was theoretically derived to be in the range of 3.6–4 dBA. This range was confirmed by the average of a number of non-standard noise measurements from several manufacturers. The remainder of the difference is explained by a number of unpredictable effects, which could not be quantified due to their complexity. The changes in radiation efficiency due to different design requirements and features are considered as main reasons for the remainder of the observed noise level difference between 50 and 60 Hz transformers. More investigation is required in this field.

References 1. Ploetner C (2017) No-load sound power levels for specification purposes derived from more than 1000 measurements–a representative figure for three phase transformers. In: Proceedings from CIGRE study committee A2 colloquium. Cracow, 1st–6th, Oct 2017 2. Fahy F, Gardonio P (2007) Sound and structural vibration: radiation, transmission and response. Elsevier

Reproducibility Estimation of Sound Power Level of Large Power Transformers Zdenko Godec, Filip Razum, and Davor Švarc

Abstract Sound power level is a unique feature of large power transformers used to estimate noise effects on the environment. It is determined from the direct measurement of the sound pressure level or sound intensity level. In the paper, procedures for reproducibility estimation of sound power level and procedures for estimation of uncertainty of sound pressure level and sound intensity level are given for point-to-point and walk-around test procedures. Keywords Sound power level · Sound pressure level · Sound intensity level · Estimation of measurement uncertainty · Estimation of reproducibility

1 Introduction Sound power is a unique feature of large power transformers used to estimate their noise effects on the environment. The transformer manufacturer specifies and guarantees the limit value of the sound power level. The measurement result of the transformer noise level determines whether the noise level meets the guaranteed value or not. For correct and reliable decisions with a known risk of error, it is necessary to know uncertainty of the measurement result [1]. Sound power level L W cannot be directly measured. It is determined based on the direct measurement of the sound pressure L p , or sound intensity L I [2]:   S dB, = L p + 10 · lg S0 

L Wp

(1)

Z. Godec · F. Razum (B) Konˇcar - Electrical Engineering Institute, Fallerovo Šetalište 22, 10000 Zagreb, Croatia e-mail: [email protected] D. Švarc Konˇcar Power Transformers Ltd., a Joint Venture of Siemens and Konˇcar, Josipa Mokrovi´ca 12, 10090 Zagreb, Croatia © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_3

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Z. Godec et al.

   S dB L WI = L I + 10 · lg S0

(2)

where S is measurement surface area in m2 and S 0 is the reference surface area (1 m2 ). The standard [2] describes in detail measurement procedures for the sound pressure level L p , sound intensity level L I , and gives expressions (1) and (2) for determination of the sound power level based on the standards [3–5], but gives no procedure for estimation of measurement uncertainty of these quantities. Referring to standard [3] for sound pressure method, and to [4, 5] for sound intensity method, it is only stated in standard [2]: “…measurements made in conformity with this standard tend to result in standard deviations of reproducibility between determinations made in different laboratories which are less than or equal to 3 dB”. In fact, in standards [3–5] is specified typical upper bound value of reproducibility taking into consideration the great variety of machines and equipment obtained by the round robin tests. This large standard deviation of reproducibility (3 dB) mentioned in standard [2] motivated us to estimate more realistic uncertainty and reproducibility of sound measurements of large power transformers in specific test environments and conditions that are pre-set in the standard [2]. The round robin test in the field of measuring the noise level of large power transformers is expensive and difficult to carry out. It is more appropriate to use the approach of estimating the components of measurement uncertainty based on the mathematical model of measurement according to the generally accepted method described in GUM [6]. In the paper, procedures for reproducibility estimation of sound power level, and procedures for estimation of uncertainty of sound pressure level and sound intensity level are given for both test procedures described in [2]: point-to-point and walk-around.

2 Total Standard Measurement Uncertainty Versus Total Standard Deviation of Reproducibility Measurement uncertainty is defined in [6] as: “parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand”, and reproducibility as “closeness of the agreement between the results of measurements of the same measurand carried out under changed conditions of measurement”. In large power transformer sound level measurements “changed conditions of measurement” include location, conditions of environment, measuring instrument, observer and time. In the context of [3] uncertainties of sound levels are expressed by the total standard deviation σtot : σtot =



2 + σ2 σomc R0

(3)

Reproducibility Estimation of Sound Power …

21

σR0 is standard deviation of reproducibility of the method, and σomc is the standard deviation of repeatability (due to the instability of the operating and mounting conditions). However, total measurement uncertainty can only be estimated for metrologically traceable measurements. Metrological traceability is defined as “the property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations, each contributing to the measurement uncertainty” [7]. Sound pressure and sound intensity measurement results are metrologically traceable, but sound power determination is not, because of no reference and because of approximations and assumptions incorporated in the measurement method and procedure [2, 8]. Consequently, it is possible to estimate total measurement uncertainty for sound pressure and sound intensity levels, but for sound power level only total standard deviation of reproducibility (including standard deviation of repeatability, see (3)). Fortunately, this quantity can be used for correct and reliable decision making equally as measurement uncertainty and is according to [9] allowed as such.

3 Measurement Uncertainty of Sound Pressure Level, Point-to-Point Procedure According to [3], the total standard measurement uncertainty of the sound pressure level is expressed by the standard deviation and consists of two components: u tot = σtot =



2 + σ2 σomc R0

(4)

1. σomc is standard deviation of repeatability, which describes the uncertainty associated with the instability of the operating and mounting conditions of particular source under test. This component is determined experimentally from repeated measurements (at least six according to [3]) carried out on the same source at the same location by the same person, using the same measuring instruments and the same measurement positions. For each of these repeated measurements, the mounting of the test object and its operating conditions should be readjusted. It is recommended to repeat the measurement at the location where the highest sound pressure level of transformer is measured.   n  2  1

L p, j − L¯ p (5) σomc = n − 1 j=1 where L p, j is sound pressure level (uncorrected) measured at location j

22  L¯ p

Z. Godec et al.

is the average of the measured L p, j values.

2. σR0 is the standard deviation of reproducibility of the measurement results obtained for the same transformer, but under different conditions (different persons carrying out measurements at different laboratories with different measuring instruments). This component includes the acoustic characteristics of the noise source (transformer) and various environmental conditions but excludes short-term instabilities covered by the standard deviation of repeatability σomc . Standard deviation of reproducibility is determined experimentally on the basis of comparative inter-laboratory measurements [10]. Since we don’t have such measurements, measurement uncertainty will be evaluated on the basis of a mathematical model [6]. It should be emphasized that measurement methods according to the procedures described in standard [2] provide a standard uncertainty of sound pressure level equal to or less than 3 dB. For a more accurate estimation of measurement uncertainty, measurement uncertainty should be determined experimentally or on the basis of a mathematical measurement model. Mathematical model of sound pressure level measurement is given by a (modified) expression from [3]: L p = L¯ p − K 1 − K 2 + δmethod + δomc + δslm

(6)

where is the averaged sound pressure level measured over prescribed contour, with L¯ p  standard uncertainty u L¯ p is the background noise correction with standard uncertainty σ K 1 = u(K 1 ) K1 is the environmental correction with standard uncertainty σ K 2 = u(K 2 ) K2 δmethod is an input quantity to allow for any uncertainty due to the measurement method; it is assumed that the value is equal to zero with a standard uncertainty σmethod [3] is an input quantity to allow for any uncertainty due to operating and δomc mounting conditions, it is assumed that the value is equal to zero with a standard uncertainty σomc δslm is an input quantity to allow for any error in the measuring instrumentation (according to [1] including: δmet δmic δangle δimp

input quantity to allow for any error in the meteorological conditions, input quantity to allow for any error in the finite number of microphone positions an input quantity to allow for any difference of angle an input quantity to allow for any error in the impedance of the surroundings into which the source is emitting sound energy, and 11 more different input quantities).

All quantities δi are expressed in decibels (dB) and the expected values are zero with standard uncertainty σi .

Reproducibility Estimation of Sound Power …

23

Table 1 Uncertainty budget for determination total measurement uncertainty of sound pressure level σR0 Quantity

Estimate/dB

Standard uncertainty, u i /dB 



Probability distribution

Sensitivity

Normal

1+

coefficient,

L¯ p averaged sound pressure level

L¯ p

u L¯ p

K 1 background noise correction

K1

u(K 1 )

Normal

1 100.1L p −1

K 2 environmental correction

K2

K2 4

Normal

1

δmethod method

0

0.6

Normal

1

δomc repeatability

0

σomc

Normal

1

δslm sound level meter

0

0.5 (according to [11])

Normal

1

∂ Lp ∂ xi

1 100.1L p −1

Total measurement uncertainty is calculated on the basis of the mathematical model (6) according to expression for combined measurement uncertainty [6]:

u tot

   2  ∂ L p = · ui ∂ xi i

(7)

where ∂ Lp ∂ xi ui

is the sensitivity coefficient, standard uncertainty.

In Table 1 are given values of parameters, typical values of standard uncertainties, assumed distributions and sensitivity coefficients in accordance with our knowledge. Some of the components of measurement uncertainty are calculated for each measurement (u L¯ p , u(K 1 ) and σomc ), and some are estimated based on the current level of knowledge [3, 11]. Measurement uncertainty of the average A-weighted sound pressure level is: 

u L¯ pA



  N 2 1   1  =√ L pA,i − L¯ pA N N − 1 i=1

(8)

where N is the number of measurement point on prescribed contour, L pA,i is measured (uncorrected) A-weighted value of sound pressure at i-th point, L¯ pA is averaged A-weighted sound pressure level (uncorrected).

24

Z. Godec et al.

The sensitivity coefficient depends on the difference between the measured sound pressure level of the transformer and the measured sound pressure level of background noise: L pA = L¯ pA − L¯ bgA

(9)

where L¯ pA L¯ bgA

is averaged A-weighted sound pressure level (uncorrected), is averaged A-weighted background sound pressure level:

L¯ bgA

M 1 0.1·L bgA,i = 10 · lg 10 M i=1

 (10)

where M is a number of measuring points (M can be less than N, but not less than 10). Correction of K 1 due to the sound pressure level of background noise is neglected according to [2] (equals to zero), but the standard uncertainty of correction u(K 1 ) is determined experimentally by repeating the measurement (at least six times according to [3]) of uncorrected background noise levels at the point on the prescribed contour where the background noise is highest:   nK  2 1

1  L bgA,i − L¯ bgA u(K 1 ) = √ n K n K − 1 i=1

(11)

where, nK is the number of repeated measurements (usually nK = 10), L bgA,i is a measured A-weighted value of the background noise at i-th point, L¯ bgA is averaged A-weighted sound pressure level of the background noise. The environmental correction K 2 accounts for the influence of undesired sound reflections from room boundaries and/or reflecting objects within the test area. The magnitude of K 2 depends principally on the ratio of the sound absorption area of the test room, A, to the area of the measurement surface, S. Expression for environmental correction is:   4S dB K 2 = 10 · lg 1 + A

(12)

Expression for measurement surface S is given in [2], Eq. (8). The measurement uncertainty of the correction u(K 2 ) is according to experience [3] approximately equal:

Reproducibility Estimation of Sound Power …

u(K 2 ) ≈

25

K2 4

(13)

The measurement uncertainty of reproducibility σomc is calculated by the expression (5). The measurement uncertainty caused by different sound pressure meters (class 1) and conditions of application has been estimated to 0.5 dB according to [11]. The total measurement uncertainty of A-weighted sound pressure level measurement is:    2  2  2   u L¯ pA 1 + 100.1L1 pA −1 + [u(K 1 )]2 100.1L1 pA −1 + u tot (pA) =  2 (14) 2 + 0.61 + K42 + σomc

4 Measurement Uncertainty of Sound Pressure Level, Walk-Around Procedure Walk around procedure is a modification of scanning procedure along prescribed contour [2]. The instrument automatically provides the spatially averaged measurement data. Measurement is faster in comparison to point-to-point measurement, and total standard measurement uncertainty is estimated using Eq. (14) with number of measurements (n, N, M and nK ) equal to time in seconds of each scan.

5 Measurement Uncertainty of Sound Intensity Level, Point-to-Point Procedure The sound power level can be determined by measuring the sound intensity level L I according to standard [2]. The sound intensity method is, within certain limits, insensitive to steady-state background noise and reflections. Therefore corrections need not be applied. Mathematical model for measuring the sound intensity level is: L IA = L¯ IA + δmethod + δomc + δslm + δdir

(15)

where L¯ IA is the averaged A-weighted sound intensity level with standard uncertainty u L¯ IA δdir is an input quantity to allow for any uncertainty due to microphone directivity (sound intensity is a vector quantity so it depends more on the microphone

26

Z. Godec et al.

orientation); measurement uncertainty of this component is estimated based on several experiments where the microphone was directed to transformer tank at 0° and at 30°, udir = 0.4 dB. Description of other quantities in mathematical model (15) are given in Sect. 3. All components of the measurement uncertainty are same as in Table 1 except u(K 1 ) and u(K 2 ), which are equal to 0 dB. The total standard measurement uncertainty of sound intensity is: u tot (IA) =

   2 2 + 0.77dB u L¯ IA + σomc

(16)

6 Measurement Uncertainty of Sound Intensity Level, Walk-Around Procedure With walk-around procedure the instrument automatically provides the spatially averaged measurement data. Measurement is faster in comparison to point-to-point measurement, and total measurement uncertainty is estimated using Eq. (16) with number of measurements (n, and N), equal to the time in seconds of each scan.

7 Total Standard Deviation of Reproducibility of Sound Power Level The total A-weighted sound power level of the test object should be calculated from either the corrected total spatially averaged A-weighted sound pressure level, or the corrected total spatially averaged A-weighted normal sound intensity level, according to Eq. (1) or (2). Total standard deviation of reproducibility of sound power level is equal to the total measurement uncertainty of the sound pressure level (14) when is calculated by expression (1). Also, total standard deviation of reproducibility of sound power level is equal to total measurement uncertainty of the sound intensity level (16) when is calculated by expression (2). In expressions (1) and (2) measurement uncertainty  is negligible for most measurements in power of second component 10 · lg SS0 transformer test fields (about 0.1 dB).

Reproducibility Estimation of Sound Power …

27

8 Total Standard Deviation of Reproducibility of Sound Power Level in Short-Circuit Condition at I t  = I n The sound power level at a current different from the rated current (I T ≥ 70% I N ), can be calculated by Eq. (17) according to [2]:   IN dB L WA, IN = L WA, IT + 40 · lg IT

(17)

In this case, the total standard deviation of reproducibility is increased: 



u L WA, IN =



  2  2 u L WA, IT + 0.1737 · u(IT )% dB

(18)

Generally, this increase is very small and can be neglected.

9 Measurement Uncertainty or Reproducibility in Decision-Making and Conformity Assessment According to [3], decision of conformity of sound level of the transformer with a guaranteed limit is based on complete measurement result. Therefore, total measurement uncertainty (of sound pressure level and sound intensity level) or total expanded reproducibility of sound power level should be considered. According to [3], the coverage factor for a one-sided normal distribution should be applied. Coverage factor k = 1.6, corresponds to 95% confidence level. In electrical engineering, according to [12], decision of conformity is based on the measured value.

10 Results and Discussion On the 400 MVA transformer with ONAN and ONAF cooling, the sound intensity and sound pressure levels were measured simultaneously with point-to-point and walk-around procedures at short circuit with rated current, according to [2]. All measurements were repeated three times. In Tables 2 and 3 (ONAN cooling) and Tables 4 and 5 (ONAF cooling) are given mean values of repeated measurements. Total standard measurement uncertainties were also estimated at the end of Tables 2, 3, 4 and 5. Comments on the results. In Konˇcar Power Transformer test field, the differences between the sound pressure level and the sound intensity level (ΔL) of large power transformers are always

28 Table 2 Sound pressure measurement results and estimation of measurement uncertainty—ONAN cooling

Table 3 Sound intensity measurement results and estimation of measurement uncertainty—ONAN cooling

Table 4 Sound pressure measurement results and estimation of measurement uncertainty—ONAF cooling

Z. Godec et al. Values

ONAN; 1 m Point-to-point procedure

ONAN; 1 m Walk around procedure 1 m/s

ONAN; 1 m Walk around procedure 0.5 m/s

L¯ pA /dB   u L¯ pA /dB

59.0

59.3

59.0

0.26

–

–

N L¯ bgA /dB

70

142

264

34.0

34.2

34.1

u(K 1 )/dB

1.9

1.7

1.8

L pA /dB

25.0

25.1

24.9

K 2 /dB

1.4

1.4

1.4

σomc /dB

0.39

0.37

0.41

utot (pA)/dB

0.98

–

–

Values

ONAN; 1 m Point-to-point procedure

ONAN; 1 m Walk around procedure 1 m/s

ONAN; 1 m Walk around procedure 0.5 m/s

L¯ IA /dB   u L¯ IA /dB

56.0

58.4

57.8

0.37

–

–

N L¯ bgA /dB

70

142

264

21.6

21.9

22.2

L/dB

3.0

0.9

1.2

σomc /dB

0.20

0.16

0.19

utot (IA)/dB

0.94

–

–

Values

ONAF; 2 m point-to-point procedure

ONAF; 2 m walk-around procedure 1 m/s

ONAF; 2 m walk-around procedure 0.5 m/s

L¯ pA /dB   u L¯ pA /dB

60.9

61.5

61.5

0.26

–

–

N L¯ bgA /dB

84

180

306

33.9

34.2

34.4

u(K 1 )/dB

2.0

1.8

1.5

L pA /dB

27.0

27.3

27.1

K 2 /dB

1.4

1.4

1.4

σomc /dB

0.25

0.20

0.27

utot (pA)/dB

0.93

–

–

Reproducibility Estimation of Sound Power … Table 5 Sound intensity measurement results and estimation of measurement uncertainty—ONAF cooling

29

Values

ONAF; 2 m point-to-point procedure

ONAF; 2 m walk-around procedure 1 m/s

ONAF; 2 m walk-around procedure 0.5 m/s

L¯ IA /dB   u L¯ IA /dB

58.0

59.1

59.2

0.34

–

–

N L¯ bgA /dB

84

180

306

21.6

21.4

22.0

L/dB

2.9

2.4

2.3

σomc /dB

0.20

0.26

0.23

utot (IA)/dB

0.96

–

–

less than 4 dB, consequently, no correction of the sound intensity level according to point 11.3 in [2] is necessary. With walk-around procedure, generally, sound pressure levels and sound intensity levels were measured slightly higher. The probable reason for this is the operator’s influence, which is greater with the point-to-point procedure than with the walkaround procedure, where the operator’s influence can be neglected. The repeatability σomc varied greatly from measurement to measurement, but never exceeded 0.5 dB and can be classified as stable according to [3]. Maximal differences between three repeated measurements are given in Table 6 (ONAN cooling) and Table 7 (ONAF cooling). According to [2] maximum walking (constant) speed for the walk around procedure is specified at 1 m/s. Operators may favor slower speeds of about 0.5 m/s [8] because the results are more reliable as can be seen from our measurements. Table 6 Maximal differences between tree repeated measurements—ONAN cooling

Table 7 Maximal differences between three repeated measurements—ONAF cooling

Values

ONAN; 1 m point-to-point procedure

ONAN; 1 m walk-around procedure 1 m/s

ONAN; 1 m walk-around procedure 0.5 m/s

L¯ pA /dB L¯ IA /dB

0.5

1.0

0.1

0.3

2.8

0.2

Values

ONAF; 2 m Point-to-point procedure

ONAF; 2 m Walk around procedure 1 m/s

ONAF; 2 m Walk around procedure 0.5 m/s

L¯ pA /dB L¯ IA /dB

0.1

0.4

0.3

0.1

0.7

0.4

30

Z. Godec et al.

The dominant uncertainty components are σslm = 0.5 dB and σmethod = 0.6 dB, while the uncertainty component u(K 1 ) slightly affects total measurement uncertainty of the sound pressure level because L pA in Konˇcar Power Transformer test field (and also other large power transformers manufacturers test fields) is regularly greater than 10 dB. Measurement uncertainties of sound intensity level and sound pressure level obtained by the walk around procedure could not be estimated because we were      ¯ ¯ not able to get data about standard deviation u L IA and u L pA from the instrument (B&K 2270)—even after communication with the sound meter manufacturer. If measurement uncertainty of sound intensity estimation is demanded, it is necessary to measure with point-to-point procedure or walk-around procedure in several segments [5]. Complete measurement result of the sound pressure level of the transformer at ONAF cooling measured by point-to-point procedure and expressed with an expanded uncertainty at the 95% confidence level is (60.9 ± 1.9) dB. Since, 60.9 + 1.6 · 0.93 = 62.4 dB, the transformer does not meet the guaranteed sound pressure level limit of 62.0 dB according to [3], but does meet guaranteed value according to [12]. According to measurements, there are true differences between sound power level determined by sound intensity measurement and sound power level determined by sound pressure measurement. Consequently, sound power level determined by (1) is not equal to the sound power level determined by (2). These are two different quantities! The purpose of a sound measurement is to enable the estimation of the sound power emitted by the power transformer. Per definition, sound power is sound intensity integrated over the measuring surface enclosing the transformer. Another method to determine sound power is to measure sound pressure (with more simple measuring instruments) which assumes the sound pressure and particle velocity being in phase (free field condition). When assumption is not fulfilled, that is in practical test environment, method requires corrections [2]. In sound near field acoustic zone sound field is complex and there are reflective components of sound pressure that do not propagate to the sound far field. The sound pressure measurements in the sound near field tend to overestimate the sound power emission levels of power transformers because it cannot distinguish between active and reactive sound fields. Experience revealed that sound power estimations based on sound intensity measurements represent the true value of sound power more accurately than sound power estimations based on corrected sound pressure measurements [8].

Reproducibility Estimation of Sound Power …

31

11 Conclusion Methods for determining sound power levels by measuring sound pressure levels or sound intensity levels, described in standard [2], generally provide a standard deviation of reproducibility equal to or less than 3 dB. If one wants that the total standard deviation of sound power level measurement of power transformers be estimated more realistically, it must be determined experimentally, or on the basis of a mathematical measurement model—as described in this paper. The realistic estimate of the standard deviation of the reproducibility of the sound power level of large power transformers is approximately 1 dB in Konˇcar Power Transformer test field. Sound meters on the market provide all the necessary data for estimation the uncertainty of sound pressure level measured by walk around procedure, but for the sound intensity level they give only the mean value without standard deviation. Standard deviation of the sound intensity level of a single scan should also be incorporated into sound meters. According to [3], the decision of conformity of sound level of transformer with the guaranteed limit is based on complete measurement result. Therefore, total measurement uncertainty (of sound pressure level and sound intensity level) or total expanded reproducibility of sound power level should be considered. According to [3], coverage factor for a one-sided normal distribution should be applied. Coverage factor k = 1.6, corresponds to 95% confidence level. However, in electrical engineering, according to [12], decision of conformity is based on the measured value. To avoid misunderstandings between manufacturer and purchaser, it is necessary to define the decision rule of conformity as well as the method of determining the sound power level, based on sound pressure or sound intensity measurement. If the conformity assessment rule and method of determining sound power level are not contracted, according to [2] the manufacturer has the right to choose. As a rule, the manufacturer will choose the determination of sound power by sound intensity method with walk-around procedure and decision based on measured value [12].

References 1. Godec Z, Kuprešanin V (2014) Temperature rise of power transformers: comments and proposals to IEC 60076-2:2011. In: 3rd international colloquium transformer research and asset management, Split, Croatia, October 15–17, 2014 2. IEC 60076-10: 2016, Power transformers—Part 10: Determination of sound levels 3. ISO 3746: 2010, Acoustics—determination of sound power levels of noise sources using sound pressure—survey method using an enveloping measurement surface over a reflecting plane 4. ISO 9614-1: 1996, Acoustics—determination of sound power levels of noise sources using sound intensity—Part 1: Measurement and distance points 5. ISO 9614-2: 1996, Acoustics—determination of sound power levels of noise sources using sound intensity—Part 2: Measurement by scanning 6. Evaluation of measurement data—guide to the expression of uncertainty in measurement (GUM), JCGM 100:2008

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7. International vocabulary of metrology—basic and general concepts and associated terms (VIM), JCGM 200:2012 8. IEC 60076-10-1: 2016, Power transformers—Part 10-1: Determination of sound levels—application guide 9. ILAC G17:2002, Introducing the concept of uncertainty of measurement in testing in association with the application of the standard ISO/IEC 17025 10. ISO 5725 (all parts), Accuracy (trueness and precision) of measurement methods and results 11. Payne R (2004) Uncertainties associated with the use of a sound level meter, NPL Report DQL-AC 002 12. IEC Guide 115: 2007, Application of uncertainty of measurement to conformity assessment activities in the electrotechnical sector

Stressed Oil Volume Theory in Transformer Winding Corner Stress Analysis Petar Gabri´c, Ana Oreškovi´c, Vjenceslav Kuprešanin, Antun Mikulecky, and Vladimir Podobnik

Abstract The aim of this paper is to demonstrate how stressed oil volume (SOV) theory can be used in experimental research to obtain better reliability of transformer insulation design criteria. For this purpose, combined stress research is taken as an example. In combined stress research winding edge geometry is investigated, where at the same time winding edge is exposed to axial lightning impulse stress due to potential difference between discs/coils and radial LI stress due to potential difference between windings. Transformer designers usually consider this axial and radial stress as two independent manifestations, evaluating each with its own design criteria. Combining the radial and axial stress into a single design criterion should lead to a more reliable insulation design. This paper shows how SOV theory can be used to analyse the influence of radial electric field on axial oil gap LI withstand stress, which is an essential step in combined stress design criteria development. Keywords Transformer winding · Corner stress · Stressed oil volume · Insulation design

1 Introduction Published studies of transformer insulation breakdown show that initiation and propagation of partial discharges and breakdown in mineral oil are very complicated processes, influenced by physical and chemical properties of mineral oil, pressure and temperature, test voltage waveshape and polarity, electrode geometry, etc. [1]. Since there is no coherent physical theory of breakdown in oil, permissible stresses of different transformer insulation segments are in practice derived through experimental research on insulation models and experience. Experimental research is P. Gabri´c (B) · A. Oreškovi´c · V. Kuprešanin · A. Mikulecky Konˇcar Electrical Engineering Institute, Fallerovo šetalište 22, 10000 Zagreb, Croatia e-mail: [email protected] V. Podobnik Konˇcar Power Transformers, A Joint Venture of Siemens and Konˇcar, J. Mokrovi´ca 10, 10090 Zagreb, Croatia © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_4

33

34

P. Gabri´c et al.

focused on statistical nature of breakdown process and the limitation of this approach is the fact that, even with large number of experiments performed, obtained results are usually valid only in the range of specific geometry and electrode configuration. Many experimental studies in the past have been performed to overcome this problem by applying a general idea to correlate experimental results obtained using different geometries (homogeneous, quasi-homogeneous and non-homogeneous) [2–4]. Although this problem has been investigated by a number of authors, using a variety of electrode sizes and configurations, at different test voltages, some important questions in this field still remain unanswered. This is mostly due to unclear breakdown mechanisms in oil, complex geometry and voltage distribution, as well as large expenses of experimental research. Majority of these studies have shown that the breakdown strength of transformer oil decreases with the “size” of an insulation segment for both power frequency and impulse voltages [5]. “Size effect”, according to different authors, can be interpreted in different ways—as a stressed oil volume (SOV) effect, as a stressed electrode area (SEA) effect or as an oil gap length effect which can also be interpreted as SOV. SOV and SEA effects are theoretically explained with weak-link theory, which assumes that the oil breakdown is initiated by the weakest links in oil or on the surface of electrode (particles and other impurities, dissolved water, dissolved gases, etc.). According to this theory, a larger stressed oil volume (SOV) or a larger stressed electrode area (SEA) increases the probability of a weak spot in insulation which then initiates partial discharges (PD) or breakdown [5]. Besides different approaches in the interpretation of “size effect”, another problem with “size effect” theory is the definition of stressed volume/area. It has been shown that electric field must be large enough to allow the propagation of partial discharges, so in non-homogeneous structures a point is reached at which further increase in size has a very small influence on PD initiation and propagation, [2, 5]. For this reason, early studies suggested that SOV/SEA should be defined as a region where electric field strength is ≥90% of maximum electric field magnitude (E max ). Some later studies of SOV theory have shown that ≥90% of E max is not adequate and space with electric stress ≥80% of E max should be considered as SOV/SEA. Furthermore, it has been shown that the definition of SOV should be modified depending on particular insulation system characteristics [6]. As far it is known, SOV is rarely used as a design criterion in practice. Usually, a simplified approach with gap-dependent curves (which can be interpreted as a simplification of SOV theory under certain conditions), is applied where possible, e.g. Kappeler curves reported in [7]. On the other hand, according to the authors’ knowledge, SEA is never used in transformer insulation design practice. Therefore, SEA is not in the scope of this work. In spite of mentioned problems, “size effect” is recognized in transformer society and is taken into account in transformer design stage indirectly (through the use of safety factors), as well as in experimental research of insulation withstand stress (SOV in models should be comparable to actual SOV in analysed transformer insulation segment).

Stressed Oil Volume Theory in Transformer Winding Corner …

35

The aim of this paper is to demonstrate how SOV theory, although rarely applied in transformer design practice, can be used in experimental research to obtain better reliability of transformer winding edge stress design. For this purpose, combined stress research (chapter “Difference between 50 Hz and 60 Hz transformer no-load noise levels”), reported in [8], is taken as an example. It will be shown how SOV theory can be used to analyse the influence of radial electric field (E rad ) on axial oil gap LI withstand stress, which is an essential step in design criteria development in this case. A short description of combined stress research is given in chapter “Difference between 50 Hz and 60 Hz transformer no-load noise levels”, then electric field calculation and application of SOV theory is explained in chapter “Difference between 50 Hz and 60 Hz transformer no-load noise levels” and, finally, the influence of E rad on axial oil gap LI withstand stress on a transformer winding edge (for simplicity marked as U 1% in this paper) is analysed with SOV theory in chapter “Difference between 50 Hz and 60 Hz transformer no-load noise levels”.

2 Combined Stress Research A characteristic of transformer winding edge exposed to LI stress is a simultaneous combination of axial LI stress due to potential difference between discs/coils and radial LI stress due to potential difference between windings [8]. Transformer designers usually consider this axial and radial stress as two independent manifestations, evaluating each with its own design criteria. Such practice has historical reasons—withstand voltages between discs and withstand voltages between windings were investigated on two separate and essentially independent models. Combining the axial and radial stress into a single design criterion should lead to a more reliable insulation design. The goal of combined stress experimental research was to qualify and quantify the influence of radial electric stress E rad on permissible axial stress U 1% of transformer coil insulation during lightning impulse test [8]. Combined electric field was investigated using insulation models simulating winding edge geometry, as shown in Fig. 1. Two basic types of models were produced and tested, “main” and “control” models, with a significant difference in E rad magnitude. E rad was negligible in “control” models, while in “main” models the magnitude of E rad corresponded to design electric field value in transformer main duct during LI testing. Combined stress models consist of four electrodes, each made of two connected flat wires, where three electrodes are connected and grounded (Fig. 1). Research was performed for conductor insulation thickness (δ 1 ) in the range from 0,4 mm to 0,8 mm and axial spacer thickness (hpl ) from 0 mm (no spacer) to 6 mm. Six identical models were placed in an insulating frame which enabled axial and radial tightening (Fig. 2). After completing high voltage testing, electric field distribution was found and analysed for each tested model [8, 9]. Several different methods were applied, but the

36

P. Gabri´c et al.

Fig. 1 Combined stress model: cross-section (left), 3D view (right) [8]

Fig. 2 Manufactured combined stress models

influence of E rad on U 1% was not completely clarified. The extent of E rad influence on U 1% was shown to depend on model geometry, but the nature of this relation was not explained. A single method which fitts well to all tested models was not found. More details about combined stress research can be found in [8]. In the following, it is shown how SOV theory can be used to subdivide tested geometries into groups with a comparable E rad influence on U 1% in order to simplify design criteria development.

Stressed Oil Volume Theory in Transformer Winding Corner …

37

3 Electric Field Distribution Calculations and Stressed Oil Volume Definition 2D FEM simulations and experimental testing results are used to define the following parameters: stressed oil volume, electric field inhomogeneity factor (η), maximum electric field magnitude (E max ) and LI withstand voltage in axial oil gap (U 1% ). This is done for each tested combined stress model type. Taking account for missing consensus on stressed oil volume definition in relation to E max , different scenarios are examined. SOV is given as 90, 80 and 70% of E max . Figure 3 shows a 2D FEM simulation of combined stress model (model parameters are shown in Fig. 1—δ 1 , δ 2 , d r , hpl ). With E rad raised from negligible to a typical value in transformer design, a relative change in SOV, η, E max and U 1% (ΔX % in Eq. (1)) is found for each combined stress model type as: X % = (X main −X contr ol )/ X contr ol ∗ 100%

Fig. 3 2D FEM simulation of combined stress model

(1)

38

P. Gabri´c et al.

Table 1 Average relative change X % in SOV, η, E max and U 1% Axial oil gap

Average relative change X % in SOV, η, E max and U 1% SOV

SOV

SOV

90% of E max

80% of E max

70% of E max

η

E max

U 1%

0 mm (Fig. 4)

Oil wedge

0.4%

0.3%

Small (Fig. 5)

−96.1%

−8.8%

−4.5%

3.9%

6.5%

2.1%

Medium (Fig. 6)

−11.1%

−95.0%

−87.9%

12.2%

6.8%

−5.8%

Large (Fig. 8)

−4.1%

−56.7%

−92.1%

17.1%

13.6%

−5.3%

Model types are arranged in 4 groups according to axial oil gap width (0 mm oil gap, small, medium and large oil gap—as explained below). The basic difference between models of the same group is the insulation thickness (δ 1 ). Table 1 shows average relative change values X % in SOV, η, E max and U 1% (calculated according to (2)) for each group of models. Inhomogeneity η in Table 1 is calculated as a ratio of E max and average electric field in quasi-homogeneous oil gap. X % =

 n 

 X %,i /n

(2)

i=1

n … the number of model types in a group Figures 4, 5, 6 show electric field distribution in models without axial oil gap (Fig. 4), in models with small axial oil gap (corresponding to the smallest axial oil gaps used in transformer windings, Fig. 5) and in models with the most common axial oil gap width (the middle of the oil gap width range in transformer windings, Fig. 6). Figures 4a, 5a and 6a show “control” models with negligible E rad , while Figs. 4b, 5b and 6b show “main” combined stress models with typical E rad values in actual transformers. All parameters in both “control” and “main” model types are equal,

Fig. 4 Electric field distribution in models without oil gap (a—“control” model, b—“main” model)

Stressed Oil Volume Theory in Transformer Winding Corner …

39

Fig. 5 Electric field distribution in models with small oil gap (a—“control” model, b—“main” model)

except d r (which defines the value of E rad ). Graphical representation of electric field in Figs. 4, 5, 6 is given in shaded plot with five different colours, each representing 20% change of electric field value (i.e. red colour represents the space with electric stress ≥80% of E max , yellow 60 to 80% of E max ). Different scenarios regarding E rad influence on U 1% are analysed in chapter 4 and SOV definition problem is illustrated below. As stated in the introduction, it is still a matter of debate whether SOV should be defined as space where electric stress is ≥90% of E max , ≥80% of E max or as a function of insulation system properties. SOV definition is an important topic in this research because the breakdown strength of transformer oil decreases with the size of SOV, [5]. Figure 7 shows the same electric field distribution as in Fig. 5b, but here each colour represents 10% change of electric field magnitude (red: electric stress is ≥90% of E max , orange: electric stress is 8–90% of E max , …). If SOV in Fig. 7 is defined as ≥90% of E max , it seems that stressed space is concentrated at the conductor edge, while for SOV defined as ≥80% of E max stressed space is concentrated in the quasihomogeneous axial oil gap. Since the size and location of SOV in analysed models indicate the influence of E rad on U 1% (see chapter “Stressed Oil Volume Theory in Transformer Winding Corner Stress Analysis”), it is obvious that one of these two different SOV definitions can give a wrong impression about the E rad influence on U 1% . Experimental results in Table 1 are in line with the second case where SOV is defined as ≥80% of E max . The relative change of SOV defined as ≥90% of E max is in contradiction with experimental results (U 1% ). This example shows that for this specific geometry SOV should be defined as space where electric stress is at least ≥80% of E max . Furthermore, some examples in this research show that even 80% of E max is not always an appropriate definition of SOV. Figure 8 shows a combined stress model with large axial oil gap (“control” model is on Fig. 8a, while “main” model is on Fig. 8b). Each colour represents 10% change of electric stress magnitude starting

40

P. Gabri´c et al.

Fig. 6 Electric field distribution in models with medium size oil gap (a—“control” model, b— “main” model)

from E max . Although experimental results in Table 1 show that withstand voltage of the model from Fig. 8 is influenced by E rad , this cannot be observed from SOV change if SOV is defined as ≥80% of E max . But, if SOV is defined as ≥70% of E max than a good correlation can be made between SOV change and U 1% change. Examples from Figs. 7, 8 show that a unique definition of SOV probably doesn’t exist. One possible approach to solve this problem is to define SOV as a function of E max and electric field inhomogeneity as well. Further research in this direction will be performed but lies beyond the scope of this paper. For the purpose of this paper, SOV defined as ≥80% of E max can be used with acceptable accuracy, except for large oil gaps where SOV should be defined as ≥70% of E max .

Stressed Oil Volume Theory in Transformer Winding Corner …

41

Fig. 7 Electric field distribution in models with small oil gap—“main” model

Fig. 8 Electric field distribution in models with large oil gap (a—“control” model, b—“main” model)

4 Analysis of Radial Electric Field Influence on Withstand LI Voltage E rad influence on U 1% is estimated for all analysed oil gap widths using SOV theory and performed estimation is verified with experimental results. From Figs. 4, 5, 6 and 8 SOV analysis shows that 3 possible scenarios exist regarding the influence of E rad on U 1% —negligible influence (Fig. 4—axial oil gap 0 mm, Fig. 5—the smallest axial oil gaps commonly used in transformer windings), significant influence

42

P. Gabri´c et al.

(Figs. 6, 7, 8, medium and large axial oil gaps in transformer windings) and a transition between previous two cases. In models without axial oil gap (Fig. 4), there is no E rad influence on SOV because stressed oil volume remains practically unchanged when radial electric field is raised from negligible to a typical value in actual transformers. Therefore, the influence of E rad on U 1% should be negligible as well. This is confirmed with experimental results (Table 1) where no significant change of E max and U 1% is found. In models with small axial oil gap (Fig. 5), the influence of E rad on SOV position and size can be neglected. SOV change is relatively small (size difference 75

>70

DC resistivity @ 90 °C (Gm)

>20

>1000

Biodegradability (% after 27 days)

Readily biodegradable (>85%)

No biodegradability

5 Built in Material and Components Compatibility Esters are solvents for a broad array of plastics, resins and rubbers, materials with well-known compatibility with mineral oil and commonly used in transformer production. With ester design, materials should be properly chosen and combined in order not to dissolve or to contaminate the insulation fluid [9]. Special considerations must be made regarding paint and glues used inside transformer as well, as today they are mainly resin based. All gaskets on tank and built in transformer accessories (bushings, OLTCs, pressure relief device, etc.) must be compatible with synthetic esters, as insulating liquid represents around one fifth of the mass of large power transformer and for safe operation must be kept inside tank. Generally, NBR rubber is used as gasket material in transformers for economic reasons, but certain grades of NBR are incompatible with synthetic esters, thus FVMQ or FKM rubbers are preferred. In case of retro filled prototype transformer non compatible materials were easily recognized, but certain delays arose from additional testing of different chemicals used during manufacturing process such as lubricants, thread lockers and markers. All built in components of power transformer must be compatible with synthetic esters from chemical as well electrical point of view, and their compatibility should be approved by supplier or by third party testing. Theoretically OIP bushing can be mounted on ester filled transformer, but mineral oil used as impregnating media in bushing compromises higher fire safety of the whole unit, thus RIP or RIS technology bushings are preferred. Same logic applies on OLTCs, as there are ester compatible tap changers with mineral oil insulated diverter switches. In case of ester filled power transformers vacuum type tap changers should be used. All above mentioned material compatibility issues have to be taken into account also for equipment used for oil processing during transformer filling as well.

52

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6 Process and Manufacture Manufacturing process of ester filled transformer does not differ from manufacturing process of mineral oil filled transformer up to the moment of filling the transformer tank with insulation liquid, provided that all built in materials and components are compatible with ester. Mineral oil impregnation of certain insulation components or windings early on in assembly process is not a problem, if prior the tanking and filling active part of the transformer is dried out, and de-oiled in vapor phase oven. As previously mentioned, higher viscosity of esters in comparison with mineral oil results in a longer impregnation time of transformer solid insulation. Impregnation time of ester filled transformer can be reduced if heated filling equipment is used, but with limited fluid velocity due to higher electrostatic charging tendency of liquid. In case of our prototype 31.5 MVA, Um 245 (170) kV transformer, impregnation and resting time prior to testing was 10 days longer when retro filled with synthetic ester.

7 Conclusion While the cost of ester fluid is more expensive compared to mineral oil, the extra cost of a transformer is an additional 8–12% in distribution transformers and around 20% for power transformers depending on the design. The cost of an ester transformer substation would greatly benefit from the reduced civil costs due to containment and fire suppression system simplification. Ester biodegradability is also an important feature turning power transformer into a “green” and environmentally friendly piece of equipment. Having a prototype transformer that could be tested up to the breakdown, proved not only to be very important for testing the design limits, but also for identifying non compatible material built in transformer and critical points during manufacturing process.

References 1. Massala G, Lesaint O (1998) Positive streamer propagation in large oil gaps: electrical properties of streamers. IEEE Trans Dielectr Electr Insul 5:371–381 2. Wang X (2011) Partial discharge behaviours and breakdown mechanisms of ester transformer liquids under ac stress. PhD thesis, The University of Manchester 3. Liu Q (2011) Electrical performance of ester liquids under impulse voltage for application in power transformers. PhD thesis, The University of Manchester 4. IEC 60076-3 (2013) Power transformers part 3: insulation levels, dielectric tests and external clearances in air. International Electrotechnical Commission 5. Lead exit insulated with natural ester liquid. IEEE Electr Insul Conf (IEC), Montreal, Canada, 129–133 (2016)

Synthetic Ester Impact on Power Transformer Design …

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6. Sima W, Sun P, Yang M, Yang Q, Wu J (2014) Study on the accumulative effect of repeated lightning impulses on insulation characteristics of transformer oil impregnated paper. IEEE Trans Dielectr Electr Insul 21(4):1933–1941 7. Rapp KJ, Corkran J, McShane CP (2009) Lightning impulse testing of natural ester fluid gaps and insulation surface. IEEE Trans Dielectr Electr Insul 16(6):1595–1603 8. Fritsche R, Rimmele U, Trautmann F, Schafer M, Clerk Maxwell J Prototype 420 kV power transformer using natural ester dielectric fluid. Siemens AG 9. Experiences in service with new insulation liquids. CIGRE working group A2. 35, Oct 2010 10. Haramija V, Vrsaljko D, Ðurina V (2014) Thermal properties of synthetic ester-based transformer oil during ageing in laboratory conditions. In: 2014 IEEE international conference on liquid dielectrics, Bled, Slovenia

Future Trends in Transformer Online Monitoring Teemu Auronen, Ivan Murat, Teemu Hanninen, and Samir Keitoue

Abstract The application of online monitoring systems has been intensified over the past two decades and they are now frequently installed with new transformers or retrofitted to the existing ones. A lack of standardization, different asset management strategies and practices between utilities, as well as certain economic factors resulted in systems made to the user’s specifications having different level of complexity: from basic units which monitor only a few parameters, to more comprehensive systems that are monitoring a wide range of parameters and are delivering various diagnostic information related to the transformer’s health. Nowadays data from monitoring systems is in most cases available only in the substation, where data is shown using a locally installed computer, or directly on monitoring devices installed on the transformer where the user can analyze the status of the transformer unit. This makes use of the data impractical and thus prevents the value of the systems to be utilized for a fleet wide asset management. In this paper, future trends in the transformer online monitoring will be presented, based on the previous development of such systems, and according to the concept of the condition-based maintenance of power transformers. As a key functionality, the status of the power transformer will be presented using either a numeric or graphical representation, which will represent the general status of the equipment (health index). This will give the user guidance on how to rank transformers in their network, in order to decide on the schedule and to pinpoint the transformer component which needs to be maintained. For this purpose, the system will need to consider other available information such as results from off-line diagnostic tests, transformer design data and history of known faults. Such approach will enable asset management strategy where the user can implement condition-based maintenance, which will lead to the cost reduction and improvement of reliability and safety with regard to power transformers.

T. Auronen (B) · T. Hanninen Vaisala Oyj, Vanha Nurmijärventie 21, 01670 Vantaa, Finland e-mail: [email protected] I. Murat · S. Keitoue Konˇcar – Electrical Engineering Institute Inc, Fallerovo šetalište 22, 10000 Zagreb, Croatia © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_6

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Keywords Transformer monitoring system · Online DGA · Condition-based maintenance · Centralized monitoring · Health index

1 Introduction Currently, in the market there are vast options for implementing transformer online monitoring—from various sensors, Intelligent Electronic Devices (IEDs), custom made solutions to the numerous specifications, developed by different utilities around the world. Since most utilities that own power transformers are already implementing transformer monitoring, or have plans to implement it, the market growth has been strong in recent years and there is a lot of accumulated experience in this field. But almost every utility is developing its own specification, often seeking advice from different vendors and consultants (based on experience) and incorporating this knowledge into the specification they find useful. We’ve come to the point where each implementation is specific and it is not easy to integrate the solutions provided by different vendors into one common system. A common system would be able to give more information about the transformer status and to compare it to the information received by the monitoring systems implemented under different specification with different sensors. The current state of the practice differs on several levels—specification level, sensors development level, user access implementation level and data analysis level. Each of them needs to be analyzed to provide the framework on establishing the future trends in the transformer online monitoring. A. Specification difference by utilities—brief overview on the different approach to the monitoring Different utilities employ different maintenance strategies regarding their assets. Some utilities have recognized the benefits of the continuous online monitoring which provides the most data needed to plan their activities in accordance to the actual status of their assets, other decide that they would need just some basic input from the monitoring system or some alarms available in the substation control system, while some completely rely on the offline measurement in estimating the status of their assets. Such differences in complexity can be seen in the Table 1, where the major differences in the requirements are noted. This is just the high-level illustration of the requirements, but once we start digging deeper into each type of monitoring level, there are different specifications that need to built and maintained. Some companies are very professional in their approach to specifying the equipment whereas some are just starting and desperately need assistance. Guidance can be sought from the standards, industry working groups or maybe from peer companies who have experienced it already.

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Table 1 Comparison of different transformer monitoring requirements Advanced monitoring Mid-level monitoring Low level monitoring DGA

8 gasses

3-5 gasses

Single gas

Moisture

Yes

Yes

Yes

Load current

Yes

Yes

Yes

Top oil temperature

Yes

Yes

Yes

Bottom oil temperature

Yes

No

No

Winding temperature using fiber optic probes

Yes

No

No

Core temperature using fiber optic probes

Yes

No

No

Cooling system status

Yes

Yes

No

Oil temperature at cooler Yes inlets and outlets

No

No

Oil level in the main tank conservator

Yes

No

No

Partial discharge

Yes

No

No

Bushing capacitance and Yes tan delta on HV side

Yes

No

Bushing capacitance and Yes tan delta on LV side

No

No

Transient overvoltage waveform recording

Yes

No

No

OLTC tap position

Yes

Yes

No

OLTC oil temperature

Yes

No

No

OLTC motor drive power Yes

No

No

Oil level in the OLTC conservator

Yes

No

No

Ambient temperature

Yes

Yes

Yes

Sending alarms to SCADA

Yes

Yes

No

Sending analog and Yes digital values to SCADA

No

No

B. Status of the sensor development To implement the transformer online monitoring system, it is necessary to monitor various quantities. While for monitoring certain quantities the general and already developed sensors can be used (for example CT for the load current monitoring), monitoring some specific quantities requires development of the special sensors. Since many companies decided to implement transformer monitoring, the sensors that are used for the same purpose have been developed differently. In the Table 2, there is a list of the commonly used sensors in the transformer online monitoring.

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Table 2 Common and special sensors used for transformer monitoring

Common sensors

Special sensors

Current transformer

Dissolved gas analyzer

WTI

Partial discharge sensor

Pt100 probes

Bushing sensors for capacitance and tan delta monitoring

Oil level indicator

Sensors for transient overvoltage recording

Pressure relays/relief devices Sensors for oil breakdown voltage Gas relays

Moisture in oil sensors

Leakage detector

In-tank inspection robot

They are grouped into two groups, general sensors and specific sensors, that are used only for transformer monitoring: The most important special sensors used in the transformer monitoring are: • DGA monitoring, including moisture in oil – The state of the development of the DGA sensors is such that there are commonly two sensor tiers—single-gas sensors and multi-gas sensors. Single gas sensors are mostly used in distribution and medium power transformers. Multi-gas sensors are used for more critical and usually large power transformers that are seen in power generation and power transmission or heavy industry. Technology itself is not a limiting factor to deploy the sensors in any size transformer, but it is rather the decision of the end-user to determine which type of solution he is looking for. Will it be an early warning type of solution with the single gas hydrogen (H2) indication or a more comprehensive system with analytics through measuring more parameters. H2 is often referred as the mother of fault gasses due to its appearance at very low energy discharge and temperature. Since it is also present with several fault types it can be used as universal indicator of developing fault. As H2 is present with many fault types the identification of the fault in question is impossible. That is why the other key gasses are used to give further guidance. This is illustrated in Fig. 1 [1]. With the information from online DGA monitoring teams can identify which transformers are developing faults much earlier and prioritize maintenance for those assets, fitting it into operational windows to minimize costs and reduce revenue losses. While number of online DGA monitors are available to transformer owners and operators, these are not all created equally. Reliable measurement of long-term gas trends is of course a must, but other key considerations when selecting a monitoring device will include its ability to operate in a variety of climatic conditions, a robust design that can be easily fitted to operational transformers, and little need to maintain or monitor the unit itself to ensure its effective operation.

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Fig. 1 Relative gas generation of DGA gasses in oil, IEEE and CIGRE

Cost will of course be another significant factor, but here it is important to consider not just the upfront price of an online DGA monitor, but also the costs associated with its installation and operation over its entire active lifetime. Some online DGA techniques require consumables, such as carrier gases, or have moving parts that require maintenance. Alternatives technologies, such as fully optical non-dispersive infrared (NDIR) measurement, mean no additional installation or maintenance costs, offering operators significant cost savings over the lifetime of the technology. Online DGA has led to a sea change in how transformers are monitored and serviced. It offers a more practical and effective approach to transformer monitoring, giving owners and operators greater peace of mind in the knowledge that these vital links in the energy network are operating in peak condition. Development in the DGA field has been very rapid and we have seen many new players enter the market of online DGA solution providing. Seems that technologies that are leaner in terms of end-user involvement to keep the measurements ongoing and valid are getting more popular based in the selected technologies to enter the market. Making the measurement leaner usually means minimizing the moving parts that cause wear and tear and further reducing the lifetime. An example of this are the optical measurement technologies NDIR and Fourier-transform infrared spectroscopy (FTIR). Besides the measurement technology development, we have seen new parameters being introduced in the field of DGA that were earlier more difficult to measure. One example of new measurement parameter could be alcohol like Ethanol. This new parameter could offer additional value by complementing the already known paper ageing parameters that are sometimes difficult to measure without having the piece of paper physically cut from the transformer insulation. This is something you cannot do without having an outage and removing the transformer cover to access the active part (Fig. 2). • Bushing monitoring – Bushing monitoring has seen significant development in recent years and is now a common request in the transformer online monitoring implementation.

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Fig. 2 Illustration of fully optical NDIR DGA measurement technology, Vaisala

There are two main methods to implement the bushing monitoring—the first one is to use sum of currents and the second one requires voltage reference. The sum of currents method is most commonly used method for several reasons— the installation procedure is simple (three cables connected to the sensors at transformer bushing test taps) and it provides reliable data to determine which bushing is potentially developing fault. The same method also has its drawbacks. It only provides the info on the change of the capacitance and tan delta of the bushing, not the actual value and is susceptible to the unbalance occurrence in the grid, which can be wrongly interpreted as the bushing problem. The second method, voltage reference method, compares the voltage measured at the transformer test tap with the voltage measured at the reference voltage transformer and measures the actual value of the capacitance and tan delta. The issue with using the voltage reference method is that it requires extensive cabling (usually several hundred meters) and it requires a voltage transformer to be used for this purpose. • Partial discharge monitoring – Partial discharge monitoring is a polarizing topic, where there is no consensus on what the most efficient way would be to monitor the partial discharge, so the different sensors have been developed: Electrical sensors—these sensors monitor the voltage from the bushing test tap, measured at high frequency in order to detect the discharges at high frequency range, which corresponds to the partial discharge occurrence. There are multiple challenges when implementing the electrical partial discharge monitoring, such as the filtering the noise at the correct frequencies, without compromising signal quality, detecting the location of the

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partial discharge (inside or outside of the transformer) and ensuring the safe operation of the transformer (connection to the test tap). But, also, there are multiple benefits in using the electrical partial discharge monitoring like measuring the apparent charge in pC and determining the nature of PD activity with possible location based on pattern recognition. Ultra-high frequency sensors—the UHF sensors used to monitor the PD data also offer several challenges and several benefits. The biggest downsides to using UHF sensors are: installation procedure—the sensors are not standardized, so the manufacturers use valve sensors, flange sensors and window sensors. Out of these types only valve sensor can be installed while the transformer is filled with oil, while for other types transformer has to be empty., Proper installation of the valve sensor must not interfere with the design of the transformer (the tip of the sensor has to reach the edge of the tank wall). Determining the number of sensors needed for proper monitoring of the partial discharge, as well as the optimal locations for the sensor installation are debatable. The biggest benefits are those that the location of the partial discharge data is always from within the transformer and that this method enables the user to determine the exact location of the partial discharge source using triangulation. Acoustic sensors—the benefits of using the acoustic sensors to detect the partial discharge activity is that partial discharges produce acoustic signals which travel through the insulating oil of the transformer, and they are almost immune to interference caused by corona and other external sources [2]. This method can easily detect partial discharges when sources are located in the insulating oil, but if they are located in the solid insulation system, the signals can be so attenuated that they do not have enough magnitude to reach the sensors. The main advantage in using the acoustic sensors is that enables locating the partial discharge source using triangulation method. Of course, there are some additional drawbacks, like the inability to detect several locations or causes using the triangulation method and that it is possible that environment noise can produce false alarms (like rain or sand). C. Status of the software implementation and the data analysis The software that supports the transformer online monitoring has gone through several generations, where the recent trend has been that the user interface has been developed using web technologies, where the user would access the information using web browser. This has enabled the flexibility to access the data from anywhere, if there is a network access to the transformer monitoring system, additionally, since the user interface is web based, it is also platform independent, what means that the user can access the data using its Windows PC, smartphone or Linux workstation, without any impact on the user experience. The software itself, currently, is mostly based in the representation of data, which means that all the data that is gathered by the transformer monitoring system is collected into the database, online data is displayed on the main screens, along with

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Fig. 3 Transformer monitoring system user interface

the alarms and warnings. All the stored data can be analyzed using trending tools, but the advanced analytics tools are still lacking in advanced features, where the user can get some guidance on the status of the device (advanced DGA analytic tools, health index used for ranking the transformers and trending tools), but the implementation level is still not at the point where the condition based maintenance is fully possible, where the requirement for maintenance and maintenance schedule would come directly from the monitoring system, without any need for the user to analyze the data and to draw conclusion from the data. In the Fig. 3, there is a user interface from the online transformer monitoring system which shows the general transformer data using web page.

2 Development Trends Challenges that we are facing are several and are discussed below: A. Sensor development There is a need to develop additional sensors that would monitor additional parameters (online FRA for example) but the main challenges to the existing sensors are to make them more reliable, where the user would not need to monitor the monitors, to make them smaller and easier to manufacture (which would reduce the cost), to implement wireless communication between sensors and the data processing unit using standardized protocols, so that the sensors from different manufacturers could communicate effortlessly, to implement the sensors using low power electronics, so

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they could use energy harvesting from the transformer itself, which would enable simple and low effort installation and reduce the number of cables being installed on the transformer. Sometimes we are limited by the available outlets in existing transformers. Even if you have the technology at hand there are no available valves, or the installation would take too much effort. In the case of new transformers, things are developing into right direction with manufacturers preparing for the further need of sensors with provisional valves and other support systems. This preparation might seem as something that adds cost but when thinking about the long lifetime of the transformer and the pace of sensor development it is a highly recommendable action. B. Software functionality development and the data analysis The development in the software segment would focus on the implementation of the software support for the decision making in the operation and maintenance field. The software would no longer be just the tool to gather and present data, but the facility which would be cloud based (on premise cloud or using commercial cloud) which would service all the transformers for the same utility (transformer fleet monitoring [3]), compare their health based on the data gathered, data received by the offline measurement and recorded through the entire lifetime of the transformer and provide different conclusions based on all the info received but supported by the advanced computer science technologies like high level artificial intelligence (deep learning neural networks, artificial intelligence models that mimic the expert flow of though when reaching the decision). Looking around it is clear that the presence of transformer experts is getting less. Simultaneously the amount of information is more, which is somehow balancing the equation. The big question is how we capture the expertise of the people today so we can operate with the data in our hands in the future. C. Condition based maintenance The development in the sensor technology and at the software front would enable the biggest advance that the online transformer monitoring can provide—a reliable option to implement the condition-based maintenance. The need for the smarter and more reliable way to implement the operation and maintenance strategy in the field of power transformers would bring several benefits—it would reduce the maintenance cost since the personnel that does the maintenance would focus on the most critical assets, there would be the reduced number of unexpected outages since the utility would have a reliable way to quantify the health of the transformers and to detect the emerging faults. It would enable optimum transformer management and utilization, based on its health and would also improve the personnel and environment safety. It would also provide the tool to decide on the optimal procurement strategy needed to ensure the availability of the spare parts at the optimal time to avoid any unnecessary cost. Using continuous data to plan condition-based maintenance not only makes managing resources simpler and cost effective but can also extend asset lifetimes by allowing operations managers to manage transformer loading until an appropriate maintenance window can be reached. The alternative, a time-based maintenance

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program, uses resource to carry out maintenance that may not be needed, and forces assets offline when it is not necessary. To implement such strategy all the data from all transformer units would need to be stored at the data center and analyzed by the high level transformer monitoring system with the implemented artificial intelligence algorithms which would be able to compare different transformers with even the different sensors installed on them and to conclude what is the optimal strategy for the utilization of the transformers and give propositions regarding the operation and maintenance strategy. Besides this the total cost of asset ownership is increasingly an important measure for owners of power transformers. And while operational budgets become tighter, the industry faces a competing need to manage large capital expenditures for new equipment. This puts the onus back on maintenance teams to extend an asset’s useful life, while controlling and preventing unexpected repair and replacement costs that would stretch budgets. Having a clear and well-planned approach to operations and maintenance can help owners of power transformers manage costs properly over the lifetime of their asset. A proper plan should broadly outline its purpose and goals, as well as consider the best approaches to monitoring assets and maintaining them, as there can be significant cost differences between various approaches.

3 Future of Transformer Monitoring Naturally even if you fit your transformer with all possible sensors out there it would not bring you too far. The basic question remains: What is it that you want to achieve with monitoring in the first place? Whether that is optimizing performance or maintenance or simply add insurance coverage is essential to find out. Once that is clear you also need to know who will act and what that action is, depending on the findings of course. If your sensor is giving alerts and it is only then when you start planning actions. At that point it’s too late. A proper plan needs to be made well in advance and supporting structure created around the plan. Standards to build online monitoring systems are virtually non-existing so it’s up to every customer to determine it by themselves. Suggestions and recommendations from standards today are largely based on off-line measurements and their interpretations. Data accumulated to online systems should be consolidated and new standards to be written. Knowing what happens to a transformer every hour of its lifetime versus once a year is something transformer manufacturers are also interested in. Imagine the possibilities to design a unit in a totally different manner based on the real operation condition findings. The system implemented in near future would be fitted with the updated already available sensors (Table 2) and the new sensors that are being developed, but equipped with wireless, low power, communication protocol which would send all the data to the cloud where the entire transformer fleet would be monitored. All that data would be analyzed by the advanced artificial intelligence system (Fig. 4) which would give suggestions on what are the proper operation and maintenance actions that need to be done [4].

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Fig. 4 Monitoring system support by artificial intelligence application

The system would get the feedback from the utility whether the analysis outcome is correct and improve itself after each iteration. By monitoring a large fleet of transformers such system would, over time, gather more experience than a person and would support the utility experts in making the decisions which would lead to a safer, more economical and more carefree future.

4 Conclusion Possibilities to perform reliable transformer online monitoring already exist, but there are several limitations to achieve true purpose of it—fully autonomous transformer monitoring that supports condition-based maintenance. Biggest obstacles are that standards are nonexistent. The sensor technology is still developing, and the interpretation of the data is still lacking. But, since the number of experienced professionals within utilities is decreasing and the maintenance resources are limited, the requests for the implementation of the transformer online monitoring are increasing in volume and the span of the measured values. This drives the rapid technology development. With such development, the expectations are that in the near future the available transformer monitoring systems will be supported by advanced artificial intelligence and will process all the data collected from the fleet of transformers, analyze it in real time, provide the transformer health assessment and recommend maintenance action. This will not only reduce the operation and maintenance cost and increase the transformer and the grid reliability but also provide feedback to the transformer manufacturers to build even better and more reliable transformers in the future.

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References 1. IEEE C57.104 D3.2, April 2017 relative gas generation CIGRE and IEEEE 2. Ramirez-Nino J, Pascacio A (2009) Acoustic measuring of partial discharge in power transformers. Meas Sci Technol 20(11):115108. IOP Publishing 3. Jakovi´c T, Murat I, Klari´c F, Keitoue S (2017) Transformer fleet monitoring. In: 4th international colloquium transformer research and asset management, Pula, Croatia, May 2017 4. Poole DL, Mackworth AK (2017) Artificial intelligence, foundations of computational agents, 2 nd edn. Cambridge University Press. ISBN: 9781107195394

Optimal Cooling and Life Time Management for Power Transformers Luc Paulhiac and Johannes Raith

Abstract This paper demonstrates how to find optimal threshold values for the cooling system of power transformers in respect to minimize the total loss consumption and maximise the life span without adding extra maintenance costs. To reach this ambition the transient thermal behaviour of a power transformer is studied for different ambient temperature scenarios together with the moisture behaviour over a complete life cycle, an essential parameter to determine the aging condition of the cellulosic insulation. Keywords Cooling control · Life time management · Power transformer · Loss minimization · Ambient temperature

1 Introduction A good thermal design and manufacturing process are one of the key aspects for the lifespan of a power transformer. The heat run test in factory is normally only realized at full cooling capacity and total losses. However, once installed, the transformer is operated with coolers whose efficiency is regulated with regard to temperature and load. There is no known methodology for estimating the optimum character of a setting for the cooling equipment with regard to the losses generated, and cellulosic aging. The purpose of this paper is to give some aspects and methods to better find optimal threshold values with regard to the operating conditions (climate, load profile) and to show the effects on the resulting aging and moisture behaviour.

L. Paulhiac (B) Electricite de France, Saint-Denis, France e-mail: [email protected] J. Raith Siemens AG, Weiz, Austria © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_7

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2 Transformer Modeling 2.1 Thermal Modelling Based on Standards Dynamic Top-Oil models for online monitoring systems can be found in IEC 600767:2018 [1] and IEEE C57.91-2011 [2] loading guides as well as numerous publications like [3–6]. Most of these models are based on the thermal-electrical analogy and heat transfer theory. They are easy to implement and present sufficient accuracy for the global optimization approach on the ODAF unit shown in the case study in Chap. 5.

2.2 Cooling Regulation and Effect on Top Oil and Hot-Spot Rise The 420 kV/20 kV step-up transformer for the case study in Chap. 5 is made with three single 360 MVA phases, each equipped with four independent oil-to-air coolers (Fig. 1). The main transformer parameters, described in Table 1 and used for thermal modelling, were identified by a heat run during the factory acceptance test (FAT) at maximal loss tap position (III). The thermal regulation consists in switching ON and OFF half of the coolers in order to adapt the efficiency of the heat exchanger. The difference between Tup and Tdown (bandwidth) is also called hysteresis in this paper. Operating stage effect on oil-to-air heat exchange: Since the amount of oil that is in each cooler is very low when compared to the total amount of oil in the transformer, the thermal capacity (Cth = τor /Rth .) of the transformer is considered as being constant whatever the operating cooling stage. Using a linear approach, the thermal resistance from oil to air (Rth,stage2 = θor/ (PNL+ PLL )) for any desired cooling stage can be assumed to be proportional to the total number of coolers divided by the number of operating coolers at the considered stage. Therefore in the present case:

Fig. 1 Principle of cooling regulation

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Table 1 Main transformer parameters identified during FAT Parameter

Value

Cooling Mode • Stage 1: From a low oil temperature to “Tup ” • Stage 2: From a high oil temperature to “Tdown ”

ODAF 2 coolers (pump & fans consumption = 15.5 kW) 4 coolers (pump & fans consumption = 31.0 kW)

Rated Power Sn (MVA)

360

PNL : No Load Losses (kW)

108

PLL : Load Losses (kW)

785

θor : Top Oil rise at rated losses (K)

38.9

θhr : Hot Spot to Top Oil (in tank) gradient at rated current (K)

24.7

gr : Average winding to average oil (in tank) temperature gradient at rated current (K)

15.4

τor : Oil Time Constant (min)

66 min

τWr: Winding Time Constant (min)

7 min

Rth,stage1 =

Ncooler s,stage2 · Rth,stage2 Ncooler s,stage1

(1)

It is worth mentioning that it has been found in several occasions by the authors that due to a potential non-linear behavior of oil-to-air coolers, the thermal resistance is “better” represented with the following expression:  Rth,stage1 =

Ncooler s,stage2 Ncooler s,stage1

n · Rth,stage2

(2)

With “n” as an exponent factor, that must be identified either during FAT or while the transformer is operating. For the presented case study in Chap. 5, the “n” value is set to 1. Operating stage effect on winding-to-oil heat exchange: For a given geometrical shape of winding, the forced convection heat transfer [7] is proportional to Rem , where “Re” is the Reynolds Number directly linked to the oil velocity, and “m” an experimental exponent value depending on the type of flow (laminar vs. turbulent). In first approach the local oil flow is considered laminar with a very low Re number. Hilpert [8] correlation for forced convection over a cylinder in cross flow give m ≈ 0.33. On several occasion it has been identified on measured data’s that “m” exponent can even be lower than this value. The oil flow (and therefore the oil velocity) is imposed by the oil pumps and directly proportional to the number of coolers in use. The effect of the cooling stage on Hot Spot to Top Oil gradient (hr ) is therefore given with:

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 θhr,stage1 =

Ncooler s,stage2 Ncooler s,stage1

0.33 × θhr,stage2

(3)

2.3 Losses Modeling For each calculation step [i] of a dynamic thermal simulation, the losses to be evacuated by the cooling equipment of the transformer can be calculated using the following expression:  T otal Losses = PN L + PL L

S[i] Sn

2

     θ [i] + 235 θe + 235 × 0.85 × + 0.15 × θe + 235 θ [i] + 235 (4)

With • PNL • PLL • θe • θ [i] • S[i] • Sn • 0.85 • 0.15 • 235

No-load losses Total load losses 75 °C represent the temperature at which the losses are calculated and should be equal to the average temperature of both high and low voltage windings Average winding temperature at calculation step [i] (Average oil + Average gradient copper-oil) Operating power at calculation step [i] Rated power represent the load losses proportion of winding DC losses (Joule losses) represent the load losses proportion of eddy and stray losses in the metal parts represent the temperature factor for the loss correction for copper (it should be 225 for aluminum).

In addition to these transformer losses, the energy consumption by the oil pumps and the fans of the coolers (Table 1) must be considered.

2.4 Ageing Rate Modelling When the winding insulation being made with Thermally Upgraded Kraft paper (TUK), the relative ageing rate V is defined according to Eq. (5) which is given in [1] and previous versions of IEC 60076-7 standard. (The paper is supposed to be “well dried” in this formula). 

V =e

15000 15000 110+273 − θh +273



(5)

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Equation (6) from the annex of [1] is valid for non-upgraded and thermally upgraded papers and allows the user to consider different oxidation and moisture content conditions. 

A R1 × k = e V = kr Ar

Er E θh,r +273 − θh +273



(6)

where •A •E •R • h,r • h

Environment factor (pre-exponential factor in 1/h) for oxidation and hydrolysis Activation Energy (J/mol) for oxidation and hydrolysis Gas constant in J/(K.mol) = 8.3144621 Reference Temperature (98 °C for non-upgraded paper and 110 °C for upgraded paper) Winding hot-spot temperature.

The Ar , Er coefficients can be found in [1] and A, E coefficients values are identified via table A.4 in [1]. However, [1] give only values for three constant different moisture levels (0.5, 1.5 and 3.5%) and a method how to calculate the moisture is missing. To consider such questions, a transient moisture model is needed as shown in Chap. 4 and [9].

3 Ambient Air Temperature Modeling In addition to yearly load profiles, it is essential to either dispose of measured daily weather records (not always easy), or to generate a realistic representation of the instantaneous ambient temperature in order to perform dynamic thermal calculations. In Chap. 8 of IEC 60076-7_2018 [1] are given guidelines for estimating the ambient temperature to be used for calculation. However, the above mentioned procedure include a number of rough assumptions. Consequently, in the following paragraph, a more precise approach of ambient temperature modeling is proposed.

3.1 Annual Temperature Evolution/Ombrothermic Diagrams and Modeling The main types of climates are defined by the following main parameters: average annual temperatures, annual thermal amplitude, total annual rainfall, dry season. A good starting point is to use realistic data from the meteorological statistics of the place where the transformer is/will be located. These data exist in a form called “ombrothermic diagrams” (also known as Walter Lieth diagram). For example, the following Table 2 gives the ombrothermic values for a French town called Lyon,

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Table 2 “Ombrothermic” values for the town of Lyon Month

1

2

3

4

5

6

7

8

9

10

11

12

Tmin (°C)

0.3

1.1

3.8

6.5

10.7

14.1

16.6

16

12.5 9.3

4.3

1.6

Tmean (°C)

3.34 4.75 8.4

11.4 15.75 19.35 22.15 21.6 17.6 13.35 7.55 4.35

Tmax (°C)

6.4

16.3 20.8

8.4

13

24.6

27.7

27.2 22.7 17.4

10.8 7.1

Rain (mm & 57.1 54.2 60.4 73.3 90 days) 9 d 8 d 9 d 8 d 10 d

78 8d

66.5 6d

72.8 85.7 93.9 7d 7d 9d

85.9 63.1 8d 9d

Av Sunshine 9 (h/day)

15.5

15.5

14

9.5

10.5 12

13.5 15

12.5 11

9

which benefits of a semi-continental climate with Mediterranean influences: For the sake of simplicity it is assumed that the moisture in air (RH%) has no impact on the cooling power of the transformer (i.e. the efficiency of the oil-to-air cooler). In first approach, the minimal, maximal as well as the mean temperatures can be represented and identified by a sinus representation: T

◦



Nday





  2 · π · Nday − 1 − ϕ = Tav + A · cos 365

(7)

where • Tav •A • • Nday

Average temperatures over year (min, mean, max) (°C) Yearly amplitude (min, mean, max) (°C) Phase expressed in days Number of the day (from 1 to 365).

With the values in Table 2, the parameters for the minimal, mean and maximal envelopes can be identified. Results are given in Table 3 and shown in Fig. 2 where points represent values given in the ombrothermic diagram (Table 2) and lines the representation via Eq. (7). Table 3 “Ombrothermic” values

Parameters identified for Lyon Ombrothermic data Envelopes (°C)

Tav (°C)

ϕ (days) 188

Yearly amplitude (°C)

Tmin

8.1

Tmean

12.5

8.2 9.4

Tmax

16.9

10.7

Temperatures °C

Optimal Cooling and Life Time Management for Power Transformers 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

73

Envelope-T°min Envelope-T°moy Envelope-T°max min Average max Moy_Ave_Max

Months 01

01

02

03

04

05

06

07

08

09

10

11

12

12

Fig. 2 “Ombrothermic” values versus sinus identification

3.2 Daily Temperatures Evolutions Modeling A first order representation of a daily temperature evolution can also be obtained with the following sinus equation: ◦ Tair (t) = Tmean (t) +

(Tmax (t) − Tmin (t)) · cos(2 · π · (t − ϕd )) 2

(8)

where • Tmin, Tmean , Tmax Values identified via Eq. (7) depending on the climate modeling Phase/time where the maximum temperature is reached during. • ϕd This representation implicitly relies on the assumption that the weather is considered being always sunny (otherwise there is very little temperature variation during the day) and for ϕd values are not modelled taking into account the season and let constant (this later parameter has very little to no effect on calculation results).

4 Transient Moisture Modeling Table A.4 in [1] demonstrates that the moisture content influences significantly the properties of solid insulation components. Equation (6) considers this influence of the moisture on the aging rate, but literature [1] gives no assistance how the moisture level should be determined as already mentioned above. Furthermore the moisture content in a power transformer is not constant during its lifetime what affects again the aging. That means to determine e.g. the aging rate of the hotspot winding paper (or another insulation component) over the complete lifetime, the moisture behavior during this time period must be known. This can be simulated with a transient moisture model

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which is briefly discussed in the following. Consequently realistic aging rates can be determined. The moisture in a power transformer can increase during its lifetime, because moisture is generated in insulation components by chemical mechanisms during the aging process of the insulation [10]. Furthermore must be considered, that the solid insulation moisture depends always on the temperature of the insulation material and that an interchange of moisture between different insulation parts in the transformer via the oil by the oil flow is possible. This means due to the temperature distribution during the operation some insulation parts will absorb more moisture than others. For instance the hotspot regions in the windings will have significant lower moisture contents than colder parts like the pressure ring or the mounting plate of the power transformer. Based on these circumstances a simulation model for the transient moisture behavior of the insulation system in a transformer must fulfill some requirements. They are: • The transient temperature behavior of the major insulation parts must be considered, depending on the transformer loading, ambient temperature and the performance of the cooling system • An exchange of moisture between different insulation parts via the oil due to the oil flow and the temperature distribution in the transformer must be possible • The generation of moisture in insulation components due to their aging must be considered. The left part of Fig. 3 demonstrates a sketch of such a transient moisture model for transformers. A selection of insulations parts which have different temperature

Fig. 4 Schematic overview of moisture simulation in a power transformer

Optimal Cooling and Life Time Management for Power Transformers

75

levels are modeled in combination with a thermo-hydraulic model. The right section of the graphic shows a schematic overview of the moisture determination for a single insulation part. Based on the temperature and moisture content of each insulation part the decrease of its DP-value is calculated. This can be done with aging models as discussed in [1] or [11]. By the help of this aging information the resulting moisture increase in the insulation part can be calculated. The formula for this moisture-increment due to aging is derived from laboratory measurements shown in [10]. However, not only the aging determines the moisture content of the next time step. A possible difference between the vapor pressure in the insulation and the adjacent oil causes an exchange of moisture. This effect is also determined by the temperature and moisture of oil and insulation. To model the moisture behavior of a power transformer with these basic functions, a network structure is needed where different insulation components are linked with the corresponding local oil and where the moisture transport within the transformer is considered by the oil flow. Such a thermo hydraulic aging model (THAM) is discussed in [9]. This knowledge about moisture in transformers represents the missing information in [1] in order to determine the aging of different insulation parts in a realistic way.

5 Case Study 5.1 Calculation Cases and Main Findings For the 360 MVA transformer defined in Table 1, and for the ombrothermic diagram of Lyon (Table 2) modeled with the Eqs. (7) and (8), different settings (Cases n°1 to 6 defined in Table 4 hereafter) for the heat exchanger temperature control parameters (threshold levels, hysteresis set to 10 K) are evaluated for different load scenarios. The main evaluation criteria are calculated for one year. They are: • Number of transitions/cycles between cooling stages (i.e. stage 1 to stage 2 and stage 2 to stage 1) in order to assess the risk of premature aging and extra maintenance of pumps and fans due to too many starts and stops • Hotspot cellulose aging for different moisture hypothesis in a sealed transformer (“well-dried”, 0.5, 1.5 and 3.5% moisture) according to Eqs. (5) and (6) • Total losses of transformer and fraction of cooler consumption (expressed in percent) using Eq. (4). The main findings for the studied transformer are: • Case 1 (half of coolers) and Case 6 are the worst thermal regulation options since they lead to premature aging and higher total losses. • Case 2 (all coolers always ON) is the best option in terms of global losses and aging, except that it can generate risks during low temperature periods and/or

0.2 353.5 2705.8 6029.8

Tup = 30 °C Tdown = 20 °C 1

Tup = 40 °C Tdown = 30 °C 573

Tup = 50° C Tdown = 40 °C 2982

Tup = 60 °C Tdown = 50 °C 3196

3

4

5

6

2510.8 5320.7

Tup = 50 °C Tdown = 40 °C 2648

Tup = 60 °C Tdown = 50 °C 4148

5

6

0.0 0.2 0.2 62.7 1543.8

0

2 coolers always ON

4 coolers always ON

Tup = 30 °C Tdown = 20 °C 1

Tup = 40 °C Tdown = 30 °C 1

Tup = 50 °C Tdown = 40 °C 151

Tup = 60 °C Tdown = 50 °C 3321

1

2

3

4

5

6

8760.0

757.3

Tup = 40 °C Tdown = 30 °C 78

4

0

0.2

Tup = 30 °C Tdown = 20 °C 1

3

Load = 100% all year long

0.0

8760.0

0

4 coolers always ON

2

0

2 coolers always ON

1

Load = 85% all year long except June where load = 20%

0.0

8760.0

0

4 coolers always ON

0

2 coolers always ON

2

7216.2

8697.3

8759.8

8759.8

8760.0

0.0

3439.3

6249.2

8002.7

8759.8

8760.0

0.0

2730.2

6054.2

8406.5

8759.8

8760.0

0.0

35.9

19.56

12.29

12.18

12.18

12.18

1438

8.16

2.13

1.31

1.31

1.31

74.03

7.17

1.68

0.87

0.84

0.84

46.36

32.37

32.08

32.08

32.08

894.7

24.79

9.76

6.65

6.60

6.60

110.62

23.43

8.52

5.16

4.96

4.96

68.40

87.91

61.45

60.90

60.90

60.90

1681.1

47.09

18.59

12.68

12.58

12.58

209.11

44.54

16.25

9.85

9.47

9.47

129.5

176.12

122.97

121.87

121.87

121.87

3408.3

94.13

37.02

25.22

25.03

25.03

420.63

88.98

32.34

19.57

18.82

18.82

260.0

8016.2 (3.1%)

7973.4 (3.4%)

7971.9 (3.4%)

7971.9 (3.4%)

7971.9 (3.4%)

8448.4 (1.6%)

5669.2 (3.3%)

5620.6 (4.1%)

5603.3 (4.6%)

5613.9 (4.8%)

5613.9 (4.8%)

5779.3 (2.3%)

5483.5 (3.2%)

5437.7 (4.2%)

5421.6 (4.9%)

5420.6 (5.0%)

5420.6 (5.0%)

5546.2 (2.4%)

Total Losses (MW) & cooler Well dry 0.5% H2 O 1.5% H2 O 3.5% H2 O consumption (%)

No. cycles Stage 1 (h) Stage 2 (h) Aging (days)

1

Load = 80% all year long

Case Operating condition

Table 4 Calculation cases and results for one year (8760 h)

76 L. Paulhiac and J. Raith

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77

low load periods and/or cold starts. Extra modeling (not described in the present paper) considering the oil viscosity on heat exchange clearly shows that it is not a safe operating choice. • Except for case 1 and 6, the total losses tend to be similar whatever the settings, meaning that the energy that is injected into the operation of the coolers is recovered through lower losses in the transformer. However, energy savings up to about 1% (or 55 MW) are possible, e.g. when case 4 is used instead of case 6. • Finally, case 4 (Tup = 40 °C and Tdown = 30 °C) seems to be the most appropriate for the different load scenarios since it gives aging and losses very close to Case 2 without generating any risk for low oil temperatures.

5.2 Hysteresis Bandwidth Adjustment

T°_HotSpot Air Free "well dried" Air Free 3.5% moisture

T°air Tup Air Free 0.5% moisture

T°_HotSpot Air Free "well dried" Air Free 3.5% moisture

15 10 5

T°air Tup Air Free 0.5% moisture

T°_TopOil Tdown Air Free 1.5% moisture

0

365

337

309

281

253

225

197

169

Num Day 85

Temp (°C)

Temp (°C)

Cumulative Aging (days)

20

113

365

337

309

281

253

225

T°_TopOil Tdown Air Free 1.5% moisture

0

25

141

5 Num Day

35 30

57

0.5% H2O « well dried »

One year of Temperature history & aging / Tup=40°C ΔT = 15K

29

10

Ambient T°

Cumulative Aging (days)

15

1.5% H2O

Tdown

85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5

1

20

Tup

197

309

365

337

225

281

197

T°_TopOil Tdown Air Free 1.5% moisture

253

169

141

85

113

57

T°air Tup Air Free 0.5% moisture

0

25

169

5 Num Day

30

3.5% H2O

85

10

35

Aging curves

141

15

Hot-Spot Top Oil

57

20

One year of Temperature history & aging / Tup=40°C ΔT = 10K

113

25

85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5

1

30

Cumulative Aging (days)

35

29

One year of Temperature history & aging / Tup=40°C ΔT = 5K

29

85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 -5

1

Temp (°C)

The hysteresis bandwidth adjustment prevents too many ON/OFF switches to occur close to the set points, which is not necessarily good for the materials inside the transformer, although no study addressing the risk of fatigue and/or damage of thermal cycles on solid/liquid insulation, and on the mechanical tightening of the inner structures (windings, core etc.) is known to the authors. Laboratory tests in Siemens showed no significant influence of cycling temperatures on the insulation aging of small samples. Other damages that might occur if the bandwidth of the hysteresis is too low, is that the electrical motors (for pumps and fans) will experience an increased number of starts which can lead to overheating of their windings (inrush or starting current is 4–6 times the rated current). If repeated too many times, the higher temperature of the motor windings insulation will cause higher aging of the motors and subsequently failures. Studies show that the normal insulation lifespan of motors designed according to IEC standards is not impacted if the number of starts per hour is less or equal to 6. In order to better figure the influence of the hysteresis adjustment, simulations (Fig. 4 and Table 5) with three bandwidth values (5, 10, 15 °C) for the chosen setup (Tup = 40 °C) are performed on the 360 MVA case study transformer operated with a constant 85% load (Fig. 5).

T°_HotSpot Air Free "well dried" Air Free 3.5% moisture

Fig. 5 Simulation (Top Oil, Hot Spot and aging for different moisture hypothesis “well dried”, 0.5, 1.5 and 3.5%) for Tup = 40 °C and hysteresis bandwidth = 5, 10 and 15 K/Load = 85% Sn all year long

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Table 5 Hysteresis adjustment results number of cycles and aging with respect to a given set point, bandwidth and moisture content

Number of cycles for set point Tup = 40 °C 5 °C

10 °C

15 °C

Jan

537

49

1

Feb

326

0

0

Mar

78

0

0 0

Apr to Sep

0

0

Oct

10

0

0

Nov

242

0

0

Dec

496

27

0

Total

1689

76

1

Moisture %

Aging (days) 1.6

“well dried”

1.7

1.6

0.5%

8.2

7.8

7.8

1.5%

15.6

14.8

14.8

3.5%

31.1

29.6

29.5

Losses (MW)

5996.2

5993.4

5993.2

Temperature history for Tup=40°C ΔT = 5K

65

Temp (°C)

Month

60 55 50 45 Tup

40 35

Tdown

30 25 20

Stage 1 and Stage 2 cycles

Stage 2 only

15 10 5 0

Num Day

T°air

T°_TopOil

63

62

60

61

-5

T°_HotSpot

Tup

Tdown

Fig. 6 Example of thermal behaviour for Tup = 40 °C and hysteresis set to 5 K for day n°60 to day n°63

For the considered set point, the hysteresis width has almost no effect on losses and aging, but a high influence on the number of cycles (However, even for a 5 K bandwidth, the number of cycles is below the “6 starts/h” criteria). It can easily be shown that for a given set point (Tup ), the larger the bandwidth (Tup –Tdown ), the

Optimal Cooling and Life Time Management for Power Transformers

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lower the cellulose aging and the number of cycles. Again, the best thermal regulation strategy (minimizing both cellulose and electrical motors aging) would be to have no regulation at all. This result is somehow quite logical, since a higher hysteresis will drag down the average hot-spot temperature in addition to lengthening the duration of each thermal cycle. Nevertheless, this may cause problems at very low ambient temperatures as mentioned above.

5.3 Moisture Content for Two Different Settings and Evolution During Transformer’s Lifespan Figure 7 shows simulation results based on the moisture model of Chap. 4 and [9]. The behavior of the moisture content in three different insulation components over 40 years is shown for two different loading conditions (80 and 100% all year long) and two different cooler settings (case 6: Tup = 60 °C and case 4: Tup = 40 °C). One observation of Fig. 7 is that the moisture levels of various insulation components in a power transformer are significant different. E.g. the investigated transformer shows in the new condition about 0.2% moisture in the paper of the hotspot region, about 0.45% in the pressure ring and more than 0.6% in the mounting plate. The reason for these moisture differences is that all these insulation components have different temperature levels. Furthermore an increase of the moisture levels over the lifetime can be seen which depends on the loading and on the used cooler setting. The values for the increase of moisture after 40 years are summarized in Table 6. In general the moisture investigation indicates the higher the temperatures in the transformer during the operation, the

Fig. 7 Moisture in insulations components during the transformer lifetime (initial average moisture content = 0.5%)

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Table 6 Increase of moisture within 40 years of operation at different insulation components Insulation part

Moisture increase in 40 years 80% Load threshold: 40/30 °C

80% Load threshold: 60/50 °C

100% Load threshold: 40/30 °C

100% Load threshold: 60/50 °C

Mounting plate

0.04

0.27

0.26

0.38

Pressure ring

0.02

0.21

0.19

0.27

Winding paper in hotspot

0.02

0.12

0.08

0.11

higher the increase of the moisture level within the lifetime. These results bring two main aspects which should be considered for the operation of a power transformer. On the one hand the moisture in different insulation components should be known during the transformer life in order to determine their aging condition in a realistic way. It may not be always true that the paper in the hotspot region shows the highest aging rate. The second aspect concerns the design of the transformer. The results show that by the help of a suitable design of the active part and with a reasonable cooler setting, the increase of the moisture during the transformer lifetime can be minimized near to zero for sealed transformers. Such a design shows advantages in the overload capability, the dielectric strength and in the aging behavior of the insulation system itself, because moisture influences all these mechanisms in a power transformer significantly. In addition to the increase of the moisture during the lifetime and the differences between different insulation components, an interesting phenomenon can be seen which is caused by the transient behavior of the moisture. This phenomenon is shown in Fig. 7. The left part of the graphic shows temperatures, moisture levels and switchings over a complete year and the right part a zoom into two days where several switches occur. It can be seen, that in periods during the year without switchings the moisture behavior in the insulation is much smoother than in periods where the pumps and fans switches from ON to OFF and reverse. The reason for this transient effect is given by fast temperature changes of the winding insulation (hotspot) due to the switchings. During the fast heating of the winding the moisture in the paper decreases and submits it to the oil.1 Also other insulation components, e.g. the mounting plate, want to submit moisture during a heating process. However, the moisture transition from winding paper to oil is much bigger than the transition from the mounting plate to oil (due to temperature and geometry differences). This leads to a temporary moistening of the mounting plate up to this moment where also such insulation part starts to submit moisture to the oil. That means during switching periods a moisture exchange between different insulation elements via the oil occurs. This is not the case in time periods during the year where no switchings happen, because in these periods the moisture levels in oil and insulation are close to equilibrium. 1 It

can be also seen in the right part of the figure, that a moisture decrease during a heating process is faster than the moisture increase during a cooling process.

Optimal Cooling and Life Time Management for Power Transformers

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Fig. 8 Transient moisture behavior due to cooler switchings (80% load, cooler setting = 60/50 °C)

6 Conclusion This paper points out that the settings of the cooling equipment of a transformer can be optimized in order to reach an optimal energy efficiency and minimal aging without extra maintenance costs. The demonstrated cooling and life time optimization requires: • A relevant yearly ambient temperature representation for a certain location of a transformer • A transient thermal model of the transformer and correction factors to take into account the influence of the cooling stage on the thermal resistance to be used for top oil and hot spot calculation • A moisture model of the transformer [9] to get reasonable aging rates • Aging laws for cellulosic insulation • Different scenarios for the load of the transformer. For these reasons the paper discusses briefly both simulation models which are used for the demonstrated case study. The temperature and moisture behavior of a 360 MVA, ODAF power transformer is studied for a certain ambient temperature scenario. This implies that the paper illustrates also a new method to describe a yearly ambient temperature profile for a certain climate. The main optimization rules in the paper are:

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• Set two extreme cases corresponding to the two operating stages of the coolers (Case n°1 where only half of the coolers are operating and Case n°2 where all coolers are operating) to serve as a framework for intermediate choices (Cases n°3 to 6). • Calculation for each case of: – the global losses in the transformer including the required power consumption for the coolers – the solid insulation aging – the use of oil pumps and fans, including the number of switches in order to avoid operating conditions that could generate extra maintenance costs (pumps and fans replacement). • Optimization consists in finding the best thresholds in order to minimize aging (Case n°2 is the reference, since the minimization of aging is obtained when the cooler is always operated at its maximum efficiency) without generating any risk during low loads and/or cold starts and/or low ambient temperatures. The main findings are: • The worst cooling strategy would be to use only half of the coolers: not only this choice leads to extra aging but is also generating more losses than any other option • The energy injected into the refrigeration is “compensated” by lower losses in the transformer due to a lower operating temperature • Optimization of aging is not in contradiction with optimization of total losses.

References 1. IEC 60076-7: 2018, IEC Loading guide for oil-immersed power transformers 2. IEEE standard C57.91:2011, IEEE guide for loading mineral-oil-immersed transformers and step-voltage regulators 3. Swift G, Molinski TS, Lehn W (2001) A fundamental approach to transformer thermal modelling-I. Theory and equivalent circuit. IEEE Trans Power Deliv 16(2):171–175 4. Swift G, Molinski TS, Bray R, Menzies R (2001) A fundamental approach to transformer thermal modelling-II. Field verification. IEEE Trans Power Deliv 16(2):176–180 5. Susa D Dynamic thermal modeling of power transformers: Doctoral dissertation. June 2005. ISBN 951-22-7742-5. Publisher: Helsinki University of Technology, Power Systems and High Voltage Engineering 6. Vilaithong R, Tenbohlen S, Stirl T (2005) Improved top-oil temperature model for unsteadystate conditions of power transformers. In: Proceedings of the XIVth international symposium on high voltage engineering, Tsinghua University, Beijing, China, 25–29 Aug 2005 7. Incropera FP, DeWitt DP, Bergman TL (2007) Fundamentals of heat and mass transfer, 6th edn, p 594. Wiley, Hoboken, USA 8. Hilpert R (1933) Heat transfer from cylinder. Forsch Geb Ingenieurwes 4:215 9. Raith J, Bonini C, Scala M (2018) Simulation of long-term transformer operation with a dynamic thermal, moisture and aging model. In: 5th international colloquium transformer research and asset management, Oct 2018, Opatjia, Croatia

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10. CIGRE Brochure 349 (2008) Moisture equilibrium and moisture migration within transformer insulation systems 11. Scala M (2014) Measurement results and calculation model of thermally aged cellulose, including non-constant moisture levels. CPRI, New Delhi

Analysis of Overvoltages on Power Transformer Recorded by Transient Overvoltage Monitoring System Bozidar Filipovic-Grcic, Bruno Juriši´c, Samir Keitoue, Ivan Murat, Dalibor Filipovic-Grcic, and Alan Zupan

Abstract In this paper, an on-line transient overvoltage monitoring system (TOMS) for power transformers is used for measurement of overvoltages on the transformer bushing tap. The focus of the paper is on the analysis of transient overvoltages caused by lightning strikes recorded at the terminals of power transformer. Several recorded overvoltages are analyzed and their amplitudes and frequency spectrum are presented and compared with those referring to standard impulse voltages from IEC standard. Collected data include number, peak and duration of recorded transient overvoltages and can be used for the assessment of the transformer insulation condition and estimation of health index. Data recorded by TOMS are also of significant importance since the insulation system of power transformer and other equipment in the substation can be damaged by lightning or switching overvoltages. Keywords Monitoring system · Power transformer · Lightning overvoltages · Frequency spectrum · Insulation

1 Introduction Power transformers are subjected to various transients often caused by lightning or switching operations. Transformer insulation is tested with the standard lighting and switching impulses in high voltage laboratory. However, in the operation various non-standard waveforms stress insulation. Front and tail time of the overvoltages at transformer terminals measured in operation differ from the standard ones, and the waveshapes can be oscillatory contrary to the standard unidirectional double B. Filipovic-Grcic (B) Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia e-mail: [email protected] B. Juriši´c · S. Keitoue · I. Murat · D. Filipovic-Grcic Konˇcar - Electrical Engineering Institute Inc., Zagreb, Croatia A. Zupan Croatian Transmission System Operator Ltd., Kupska 4, Zagreb, Croatia © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_8

85

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exponentials [1]. Standard lightning impulse and switching impulse test voltages have been questioned as they should be based on the actual overvoltages measured in service [2, 3] which can be acquired via appropriate monitoring system. Many investigations have been carried out to study the electric aging of oil-paper insulation, including the research on the accumulative effect of repeated lightning impulses in power transformers [4–11]. The work presented in [11] reveals that the accumulation of repeated lightning impulses may lead to the breakdown of insulation and thus threaten the safe operation of power system. Although many studies have been focused on the influence of accumulative effect, the basic mechanism still has not been clearly clarified, hence it’s necessary to study the influence of accumulative effect on property of oil impregnated paper (OIP) insulation and explore its mechanisms. In [12], the research shows significant influence of repeated lightning impulses on OIP samples and confirmed the existence of accumulative effect. The repeated application of lightning impulses will weaken performance of OIP insulation and could eventually lead to breakdown. During the tests, translucent gelatinous substance was detected and the colour of OIP changed on the sample surface, which can be attributed to the variation of cellulose paper itself. With the accumulation of repeated lightning impulses, the dielectric parameters of OIP increase significantly in the lower frequency range, including relative permittivity, volume conductivity and dielectric loss angle. The generation of polar products and translucent gelatinous substance on the sample surface and the variation of cellulose fiber itself are the main factors. In [13], statistics of amplitudes and time parameters of the intrusive lightning overvoltages into the substation have been investigated based on the measured data, which were monitored at the HV bushings of the power transformers in a 110 kV air-insulated substation. Measured data indicated bidirectional oscillatory lightning waveforms. Considering the lightning stroke characteristics, structure of power system and observation conditions, the majority of induced lightning surges, the surge arresters, and the winding resonance in the transformer, resulted in the relatively long time parameters of the recorded overvoltages on transformers. For the front time and tail time obtained in [13], the 50% values of the cumulative frequency are 20.8 and 198 µs, respectively. In real operating conditions, lightning overvoltage at transformer terminals can be an oscillatory waveform, due to multiple reflections at the points where the impedance significantly changed. It is important to know the frequency spectrum of lightning overvoltages at transformer terminals, since in case when dominant frequency of lightning overvoltage is close to the natural frequency of the transformer winding, resonance overvoltages can occur. These overvoltages may cause transformer failure, such as the cases of transformer failures described in [14]. In this paper, an on-line TOMS for power transformers is presented. Overvoltages are measured on the transformer bushing tap. The focus of the paper is on the analysis of transient overvoltages caused by lightning strikes recorded at the terminals of power transformer. To determine the origin of the recorded transient overvoltages, data from TOMS are correlated with data from the lightning location system (LLS) and SCADA system. Several recorded overvoltages are analysed and their frequency

Analysis of Overvoltages on Power Transformer …

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spectrum is presented and compared with those referring to the standard impulse voltages from the IEC standard [15]. Collected data include number, peak and duration of recorded transient overvoltages and can be used as the basis for the assessment of the transformer insulation condition and estimation of health index. Data recorded by TOMS are also of significant importance since the insulation system of power transformer and other equipment in the substation can be damaged by lightning or switching overvoltages.

2 On-line Transient Overvoltage Monitoring System Overvoltages, as well as service voltage, are measured on a measuring tap of corresponding bushing. The connection with the measuring tap is accomplished with a specially designed adaptor while the link between the adaptor and the impedance matching circuit is carried out with a coaxial cable. The inbuilt acquisition card is fast enough to capture transients containing frequency components up to 1 MHz. It is important to note that the capacitive voltage divider used for the measurements does not change the shape of the measured signal (the calibration range of frequencies extends up to 500 kHz) which allows monitoring of fast front and slow front overvoltages. In Croatia, the TOMS is currently installed in eight power transformer units and one shunt-reactor located in four 220/110 kV substations, one 400/110 kV and one 400/220/110 kV substation. More details about TOMS measuring system, matching circuit and triggering of overvoltage acquisition can be found in [16]. TOMS is installed in two substations which are managed by the Croatian transmission system operator. The brief layout of the 110/220 kV substations and transmission lines are shown in Fig. 1. Measurements are performed simultaneously at 220 and 110 kV side of two 150 MVA autotransformers located in two 110/220 kV substations as shown in Fig. 1. Surge arresters are installed in all transformer and transmission line bays (surge arresters with rated voltage U r = 198 kV are installed at 220 kV level and with U r = 108 kV at 110 kV level). Double circuit 220 kV transmission line is connecting substations 1, 2 and 3. Transmission line is equipped with a single shield wire and it is situated in the area with relatively high lightning activity. Also, transmission line is crossing over the rocky terrain with relatively high soil resistivity, passing through mountainous area with relatively high tower grounding resistance. Therefore, flashovers on transmission line often occur due to lightning strikes, leading to short circuit and automatic reclosing of circuit breakers located in transmission line bays. Three cases of faults caused by lightning strikes to 220 kV double circuit transmission line are analyzed in this paper, as shown in Fig. 1. TOMS successfully recorded transient overvoltages in substations 1 and 2.

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B. Filipovic-Grcic et al. SUBSTATION 1 110 kV busbars

TOMS

220 kV busbars 245 MVA 220/13.8 kV

AT1 150 MVA 220±12x1.25%/115 kV YNa0d5

110 kV 7 transmission lines 240/40 mm2 Al/St 150/25 mm2 Al/St

G

AT2 150 MVA 220±12x1.25%/115 kV, YNa0d5

Fault 2

150 MVA 13.8/110 kV

Fault 3 AT3 150/150/50 MVA 220±12x1.25%/115/10.5 kV, YNy0d5

G

220 kV double circuit transmission line l=46 km

SUBSTATION 2 110 kV busbars

TOMS

220 kV busbars

220 kV double circuit transmission line l=18.2 km

Fault 1 SF6 subsation 9 bays with cables and transmission lines

AT1 150 MVA 220±12x1.25%/115 kV YNa0d5

SUBSTATION 3

220 kV transmission line l=13.7 km 220 kV transmission line

AT2 150 MVA 220±12x1.25%/115 kV YNa0d5

Fig. 1 Layout of 110/220 kV substations which are connected with 220 kV transmission lines

3 Lightning Location System At the end of 2008, a LLS was established as part of the LINET network, covering a wide area of the Croatian territory. LINET is a modern LLS with a network of more than 125 sensors covering most of Europe. LLS measures the VLF/LF frequency spectrum of electromagnetic waves which lightning strikes emit. The measurement of magnetic flux is carried out through highly sensitive sensors which are arranged across the area with spacing of around 150–250 km. Since the electromagnetic emission of the lightning spreads at the speed of light, it reaches the sensors at different

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points in time. Although the difference is in the order of micro-seconds, the relatively accurate calculation of the original emission location of the lightning strike is possible. The data measured by every single sensor is transmitted to a central server. The exact geographical position for all the lightning strikes measured is calculated and stored in a database. This measurement method is also known as the “time-of-arrival” method. Application of LLS in power system control of Croatian transmission system operator enables lightning activity tracking and time-spatial correlation with incidences (faults, automatic re-closures, outages) registered by the relay protection system [16].

4 Transient Overvoltages Recorded on Power Transformers Overvoltages in power network can be caused by lightning strikes to overhead transmission lines, circuit breaker switching operations and faults. Power transformers can be exposed to such transient overvoltages during the operation. Transient overvoltages with steep wave front have an impact on dielectric stresses of the insulation of the first few winding turns or in the case of the resonance voltage built up locally inside the winding. The number and amplitudes of overvoltages which stress the insulation depend on various parameters such as the lightning strike density in the considered area, since it determines how often the transformer is stressed by lightning overvoltages. Since the overvoltage amplitudes at transformer terminals are usually unknown, an on-line overvoltage transient recorder is used with the ability to sample, analyze and store transients in real-time. Three cases of faults (Fig. 1) caused by lightning strikes are analysed in more detail to investigate amplitude and frequency characteristics of lightning overvoltages recorded at power transformer terminals.

4.1 Case 1—Lightning Strike to 220 kV Transmission Line Connecting Substations 2 and 3 Causing Insulator Flashover in Two Phases Transients recorded by TOMS installed in substations 1 and 2 are shown in Figs. 2 and 3. The recorded transients were time-correlated with a lightning strike which was detected by LLS. Lightning strike with current amplitude 115 kA occurred hit tower of 220 kV transmission line connecting substations 2 and 3, at a distance of 11.2 km from substation 2 (7 km from substation 3). At the same time, SCADA system detected double phase to ground fault in phases A and C, following the autoreclosure operation of circuit breakers in the line bays in substations 2 and 3. Although substation 2 is closer to the fault location compared to substation 1, overvoltages in substation 2 are lower due to network topology and reflections of traveling waves,

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Fig. 2 Transient overvoltages recorded in substation 1

Fig. 3 Transient overvoltages recorded in substation 2

coming simultaneously from both circuits of transmission line (induced and direct overvoltages) and entering substation 1. It is possible to extract the transient overvoltage waveforms from the recorder data using the high-pass FIR filter. High-pass filter is used to obtain only high-frequency components caused by lightning overvoltages and to remove low-frequency and power frequency components from measured waveforms. Lightning overvoltage waveforms obtained after filtering out low frequency components from measurements are shown in Figs. 4 and 5. Waveforms from Figs. 4 and 5 were transformed to the frequency domain using the fast Fourier transform (FFT) and calculated frequency spectrum is shown in Figs. 6 and 7.

Analysis of Overvoltages on Power Transformer … Fig. 4 Lightning overvoltages recorded in substation 1 (after filtering out low frequency components)

Fig. 5 Lightning overvoltages recorded in substation 2 (after filtering out low frequency components)

Fig. 6 Frequency spectrum of lightning overvoltages recorded in substation 1

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Fig. 7 Frequency spectrum of lightning overvoltages recorded in substation 2

4.2 Case 2—Lightning Strike to 220 kV Transmission Line Connecting Substations 1 and 2 Causing Insulator Flashover in Two Phases Transients recorded by TOMS in substations 1 and 2 are shown in Figs. 8 and 9. Recorded transients were time-correlated with a lightning strike which was detected by LLS. Lightning strike with current amplitude −75.3 kA occurred on the 220 kV transmission line connecting substations 1 and 2 at a distance of 2.9 km from the substation 1. At the same time, SCADA system detected double phase to ground fault in phases A and B, following the auto-reclosure operation of circuit breakers in the line bays in substation 1 and 2. Transient overvoltages after filtering out low frequency components and their frequency spectrum is shown in Figs. 10, 11, 12 and 13. Fig. 8 Transient overvoltages recorded in substation 1

Analysis of Overvoltages on Power Transformer … Fig. 9 Transient overvoltages recorded in substation 2

Fig. 10 Lightning overvoltages recorded in substation 1 (after filtering out low frequency components)

Fig. 11 Lightning overvoltages recorded in substation 2 (after filtering out low frequency components)

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Fig. 12 Frequency spectrum of lightning overvoltages recorded in substation 1

Fig. 13 Frequency spectrum of lightning overvoltages recorded in substation 2

4.3 Case 3—Multiple Lightning Strike to 220 kV Transmission Line Connecting Substations 1 and 2 Causing Insulator Flashover in Three Phases Another interesting event recorded by TOMS was caused by multiple lightning strike which occurred on the 220 kV transmission line route, at a distance of 16 km from the substation 1 (30 km from substation 2). Parameters of multiple lightning strikes are given in Table 1. Recorded transients were time-correlated with a lightning flash consisting of seven subsequent lightning strikes which were detected by LLS. Three lightning strikes marked in Table 1 were selected as the ones that probably caused recorded transients. This was done by matching the time difference between the successive lightning strikes detected by LLS with the time difference between the events recorded by TOMS.

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Transients recorded by TOMS which were caused by strike no. 2 (current amplitude −80.2 kA) and corresponding frequency spectrums are shown in Figs. 14, 15, 16, 17, 18 and 19. At the same time, SCADA system detected line to ground fault in all phases, following the auto-reclosure operation of circuit breakers in the line bays in substations 1 and 2. Circuit breakers interrupted short-circuit current firstly in substation 2. While short-circuit current was still supplied from substation 1, two successive lightning strikes 13 ms apart (no. 6 and 7 from Table 1) hit transmission line, and overvoltages were recorded by TOMS at power transformer terminals in substation 1 (Figs. 20 and 21). These two lightning overvoltages can be clearly seen in Fig. 20, while at the end of recording (around 25 ms) switching overvoltages occur due to opening of circuit breaker in substation 1. Fig. 14 Transient overvoltages recorded in substation 1

Fig. 15 Transient overvoltages recorded in substation 2

96 Fig. 16 Lightning overvoltages recorded in substation 1 (after filtering out low frequency components)

Fig. 17 Lightning overvoltages recorded in substation 2 (after filtering out low frequency components)

Fig. 18 Frequency spectrum of lightning overvoltages recorded in substation 1

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Fig. 19 Frequency spectrum of lightning overvoltages recorded in substation 2

Table 1 Parameters of multiple lightning strikes detected by LLS Lightning strike number

Time (h:min:s.ms)

Lightning current amplitude (kA)

1

01:02:12.257

15.5

–

2

01:02:12.261

−80.2

4

3

01:02:12.274

−20

13

4

01:02:12.293

−8

19

5

01:02:12.294

−30.3

1

6

01:02:12.306

−19

12

7

01:02:12.319

−12.7

13

Fig. 20 Transient overvoltages recorded in substation 1 (continued)

13 ms

Time difference between subsequent lightning strikes t (ms)

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Fig. 21 Frequency spectrum of lightning overvoltages recorded in substation 1 (continued)

5 Discussion and Future Work The wide variety of lightning stroke characteristics and the modifying effects of power system components result in a diversity of intrusive lightning voltage waveshapes that stress transformers. These are not the traditional standard lightning impulses with a waveshape of 1.2/50 µs which are used according to IEC [15]. Therefore, the applicability of the standard lightning impulse voltage to power transformer testing has been questioned, and the overvoltage used in the test on transformers should be as close as possible to the lightning overvoltages measured in service [13]. Analysis of measurement results indicated that bidirectional oscillatory overvoltage waveforms caused by lightning strikes appear at terminals of power transformer. Oscillatory character of recorded overvoltages is caused by multiple reflections of travelling waves in the substations and at the points where the system impedance significantly changed. Considering the lightning strike characteristics, structure of power system and observation conditions, the operation of surge arresters in transformer and line bays, and the winding resonance in the transformer, resulted in the relatively long-time parameters of overvoltages recorded on power transformers. Recorded lightning overvoltages are bidirectional oscillatory with duration of several milliseconds (5–6 ms), which is quite different from standard lightning impulse waveform used for testing of power transformers. Maximum recorded amplitude of overvoltages is 371 kV (Fig. 10) causing the operation of surge arresters installed in line and transformer bay. It is also important to investigate the frequency spectrum of lightning overvoltages at transformer terminals, since in case when dominant frequency of overvoltage is close to the natural frequency of the transformer winding, resonance overvoltages can occur which in some cases may cause transformer failure. FFT analysis of recorded overvoltages showed that dominant frequency components are in range 1–30 kHz. Frequency spectrum of measured overvoltages differs from the frequency spectrum of standard impulse waveforms. Figure 22 shows comparison between spectral densi-

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Fig. 22 Spectral density of measured overvoltage and standard lightning impulse waveform 1.2/50 µs, 1050 kV

ties of measured overvoltage (from case 2, Fig. 10, phase A) and standard lightning impulse waveform 1.2/50 µs with amplitude 1050 kV. According to the method described in [17], Frequency Domain Severity Factor (FDSF) can be determined which is defined as the ratio between the spectral density of the measured overvoltage and the spectral density of the standard lightning waveform used for testing transformers. It considers the frequency content of the overvoltages measured in the substation and compares it to the frequency content of voltage waveforms for which the transformer had been tested. The FDSF factor should be less than 1 to ensure that the stresses arising from a particular event occurring in the system will be adequately covered by dielectric tests performed in the HV laboratory. Figure 23 shows calculated FSDF factor which was greater than 1 at frequency ranges 2.5–6.1 kHz and 9.3–10.4 kHz, meaning that at these frequencies the highest electrical stress on the transformer insulation is expected. It also means that transformer tests performed with lightning waveforms do not cover adequately low frequency stresses. Therefore, overvoltages measured in a substation can excite a Fig. 23 FSDF of measured overvoltage versus frequency

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resonance throughout the windings of transformer which is often found in the 5– 30 kHz range. The FDSF approach can thus be used both for design review upon incoming transients and in analysis of failures. When combined with online monitoring, it can also be used as indicator of increased transient risks for a power transformer. Some investigations presented in [12, 18] show negative accumulative effect of multiple lightning impulses on insulation properties of oil-paper insulation systems. The repeated application of lightning impulses will weaken the insulation performance of insulation system and can eventually lead to breakdown. Lightning discharges (flashes) that transfer to ground both positive and negative charges are termed bipolar lightning discharges. In case 3 presented in the previous section, bipolar lightning flash consisting of seven subsequent lightning strikes caused transient overvoltages on power transformer terminals. As can be seen from this case, time difference between subsequent lightning strikes varies from 1 to 19 ms. Therefore, in a relatively short time period multiple transient overvoltages of different polarity may occur on transformer terminals. Experimental investigations confirm that degradation of transformer insulation system increases significantly as time difference between successive transient overvoltages decrease. Therefore, it is very important to measure transient overvoltages on transformer terminals and to record such events in order to assess an overall condition of transformer insulation system and to include this effect in estimation of health index. The future investigations will consider: – Automatic grouping of overvoltage types (temporary, switching, lightning) based on correlation with SCADA and LLS. – Statistical analysis of amplitudes, frequency spectrum and FDSF based on a larger number of transient overvoltages registered on a power transformer (for example data collected over several years). – Comparison of the measured oscillatory non-standard voltage waveforms with the standard one using energy method in which oscillatory waveforms are equivalented by double exponential waveforms with the same energy. Afterwards, front time, crest voltage and tail time of equivalent waveforms can be determined and compared to standard impulse waveforms. – Simulation of electromagnetic transients and comparison with measurements. Such analysis can be used for example for validation of high-frequency power transformer models or to study the interaction between power transformers and network. – Development of method for assessment of the transformer insulation degradation caused by transient overvoltages based on measured data from TOMS. This will be used for estimation of power transformer health index. – Use an existing TOMS for measurement of transient currents through station surge arresters caused by lightning or switching overvoltages. This will enable to determine energy stress of station arresters directly from measurements.

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6 Conclusions In this paper, an on-line transient overvoltage monitoring system for power transformers is used for measurement of overvoltages on the transformer bushing tap. The focus of the paper is on the analysis of transient overvoltages caused by lightning strikes recorded at the terminals of power transformer. Three cases of faults caused by lightning strikes to 220 kV double circuit transmission line are presented. Measured overvoltages and faults were correlated with SCADA system and LLS data. Recorded lightning overvoltages are bidirectional oscillatory with duration of several milliseconds, which is quite different from standard lightning impulse waveforms used for testing of power transformers. FFT analysis of recorded overvoltages showed that dominant frequency components are in range 1–30 kHz. Frequency spectrum of measured overvoltages differs from the frequency spectrum of standard lightning impulse waveforms. Analysis of FSDF factor showed that transformer tests performed with lightning waveforms do not cover adequately low frequency phenomena which are present in recorded overvoltages. Bipolar lightning flash consisting of seven subsequent lightning strikes caused transient overvoltages on power transformer terminals. Therefore, in a relatively short time period multiple transient overvoltages of different polarity may occur on transformer terminals. Experimental investigations confirm that degradation of transformer insulation system increases significantly as time difference between successive transient overvoltages decrease. Therefore, it is very important to measure transient overvoltages on transformer terminals and to record such events in order to assess an overall condition of transformer insulation system and to include this effect in estimation of health index.

References 1. Darveniza M (1988) The generalized integration method for predicting impulse volt-time characteristics for non-standard wave shapes-a theoretical basis. IEEE Trans Electr Insul 23(3):373–381 2. Okabe S, Takami J (2008) Evaluation of breakdown characteristics of oil-immersed transformers under non-standard lightning impulse waveforms—method for converting nonstandard lightning impulse waveforms into standard lightning impulse waveforms. IEEE Trans Dielectr Electr Insul 15(5):1288–1296 3. Berlijn S, Garnacho F, Gockenbach E (1999) Today’s problems with the evaluation methods of full lightning impulse parameters as described in engineering. In: Proceedings of the international conference on high-voltage engineering, London, UK, 1999, pp 49–52 4. Standring WG, Hughes RC (1956) Breakdown under impulse voltages of solid and liquid dielectrics in combination. IEE Proc Power Eng 103:583–597 5. Liu Q, Wang ZD (2011) Streamer characteristic and breakdown in synthetic and natural éster transformer liquids under standard lightning impulse voltage. IEEE Trans Dielectr Electr Insul 18:285–294 6. Kaufhold M, Borner G, Eberhardt M, Speck J (1996) Failure mechanism of the interturn insulation of low voltage electric machines fed by pulse-controlled inverters. IEEE Electr Insul Mag 12(5):9–16

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7. Yin W (1997) Failure mechanism of winding insulations in inverter-fed motors. IEEE Electr Insul Mag 13(6):18–23 8. Bellomo JP, Lebey T, Oraison JM, Peltier F (1996) Electrical aging of stator insulation of low voltage rotating machines supplied by inverters. In: IEEE international symposium on electrical insulation, pp 210–213 9. Vandermaar AJ, Wang M, Neilson JB, Srivastava KD (1994) The electrical breakdown characteristics of oil-paper insulation under steep front impulse voltages. IEEE Trans Power Del 9:1926–1935 10. Balaji SP, Merin Sheema IP, Krithika G, Usa S (2011) Effect of repeated impulses on transformer insulation. IEEE Trans Dielectr Electr Insul 18:2069–2073 11. Okabe S (2006) Voltage-time and voltage-number characteristics of insulation elements with oil-filled transformers in EHV and UHV classes. IEEE Trans Dielectr Electr Insul 13:436–444 12. Sima W, Sun P, Yang Q, Yuan T, Lu C, Yang M (2014) Study on the accumulative effect of repeated lightning impulses on insulation characteristics of transformer oil impregnated paper. IEEE Trans Dielectr Electr Insul 21(4) 13. Sima W, Lan X, Yang Q, Yuan T (2015) Statistical analysis on measured lightning overvoltage surges in a 110 kV air-insulated substation. IET Sci Measur Technol 9(1):28–36. https://doi. org/10.1049/iet-smt.2013.0235 14. CIGRE Joint Working Group A2/C4.39, “Electrical transient interaction between transformers and the power system, Part 2: Case studies”, CIGRE brochure 577B, April 2014 15. IEC 60060-1 (2010) High voltage test techniques, Part I: General definitions and test requirements 16. Filipovi´c-Grˇci´c B, Franc B, Ugleši´c I, Pavi´c I, Keitoue S, Murat I, Ivankovi´c I (2017) Monitoring of transient overvoltages on the power transformers and shunt reactors—field experience in the Croatian power transmission system. Procedia Eng 202:29–42 17. CIGRE technical brochure, “Electrical transient interaction between transformers and the power system, Part 1—Expertise”, Joint Working Group A2/C4.39, April 2014 18. Sun P, Sima W, Yang Q, Yuan T, Lan X, Lu C (2013) Accumulative effect of oil-paper insulation system under multiple lightning impulse voltage. In: 2013 annual report conference on electrical insulation and dielectric phenomena, Shenzhen, pp 202–205

Power Transformer Efficiency—Survey Results and Assessment of Efficiency Implementation Žarko Jani´c, Anthony Walsh, Adesh Singh, and Yordan Botev

Abstract Cigre working group A2.56 Power Transformer Efficiency conducted a survey among utilities worldwide to determine how maximum allowed losses are managed in their existing specifications of transformers—whether the losses are capitalized and how the load and no load, loss factors are calculated etc. Findings of that survey will be presented in the paper. Keywords Power transformer · Efficiency · Capitalization · Power loss

1 Introduction Globally, policy makers are trying to influence transformer specifications by introducing specific rules on minimum transformer efficiency. A survey conducted by the Cigre working group A2.56 Power Transformer Efficiency gives insight on how efficiency is defined in the procurement process in utilities around the world, with the aim to understand how loss levels are defined and what is the actual state. In the survey, distributed through the Cigre organization, 30 completed answers were received from 22 countries from 5 continents. Unfortunately, a majority of feedbacks (18 responses; 60%), were coming from EU countries. Most of the companies (23)

Ž. Jani´c (B) Koncar Power Transformers LTD, A Joint Venture of Siemens and Koncar, J. Mokrovi´ca 12, Zagreb, Croatia e-mail: [email protected] A. Walsh ESB Networks, Dublin, Ireland A. Singh Total Transformer Consulting, Johannesburg, South Africa Y. Botev Hyundai Heavy Industries, Sofia, Bulgaria © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_9

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indicated that they are transmission operators or vertically integrated companies. Most of the text below is taken from the preparatory work for the technical brochure [1].

2 Capitalisation One of the key conclusions from the working group, that will be published in the upcoming Technical brochure, is that capitalization of losses is the key to ensure that overall lifecycle costs are minimised. This also applies to any other network component. Capitalisation is not used to minimise transformer losses, it is used to minimise the investment required to obtain the greatest energy savings for the least cost, arising from lower loss transformers. This in turn results in the selection of transformers whose losses are economically optimal, but not necessarily minimal. In essence the process of capitalisation involves the calculation of the value today of the savings from losses over the lifetime of the transformer. This involves considerable uncertainty in the volume of kWh savings, the value of each kWh saved (which will vary over time) the discount rate used over the 30–50 years period, all of which must be estimated in order to arrive at the present value of the losses saved. It is generally recognized that the most economic result will arise when the Total Costs of Ownership (TCO) is evaluated, where the initial cost of the transformer plus the associated losses are considered together. In this manner savings in initial purchase costs from buying an inefficient transformer are balanced by the higher level of losses incurred, and vice versa, with increased savings in losses by the higher initial purchase price. The principles of capitalization are well explained in the literature and were covered extensively in Eurelectic submissions to the EU EcoDesign Transformer groups [2] and also [3–5], also there are a lot of works where practical analysis using capitalization are made e.g. [6, 7]. A very simplified information is given below to simplify the understanding of further reading. TCO = Initial cost + Capitalised Losses

(1)

Capitalised losses = A ∗ NoLoadLoss + B ∗ LoadLoss

(2)

A = PVn ∗ C2 ∗ 8760 h

(3)

B = PVn ∗ C2 ∗ TLLF ∗ 8, 760 h

(4)

PVn = f(n, d, . . .)

(5)

A—capitalized price of kW of no load losses e/kW B—capitalized price of kW of load losses e/kW

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PVn—Present value factor over n years at a particular real discount rate (including growth) C0 —price of electric energy (EUR/kWh) TLLF—Transformer Loss Load Factor n—capitalization period (years) d—discount rate—typically WACC (but can be modified to allow for load growth)

3 Survey Results Obviously, the capitalization depends on a number of factors and the aim of the survey was to understand if and how these principles are used, or which other approach is used in defining transformers. As the results are collected via an excel file and not by interview it is possible to have some misunderstandings and wrong answers, but hopefully that is a minor part that should not have much influence on the overall picture. Out of the 30 responses 15 responded that they are giving maximum loss levels and 19 responded that they are giving capitalization values (several use both). It has to be said that all combinations exist—with use of maximum levels or capitalization, or both. The period for which the capitalization is being calculated is important as it defines the period for which the cost of losses is being taken into consideration. The problem with defining this period is that it is the period over which a saving in losses will be accrued, which is not necessarily the lifetime of the transformer, it is the duration for which this transformer will be energized and save losses. Obviously one limit will be the expected ‘manufactured’ lifetime of the transformer but there is also the possibility that the transformer will be replaced before it’s ‘manufactured’ lifetime expires either due to an uprating to cope with increased load, replacement initiated by a change of system voltage (e.g. from 10 to 20 kV), deterioration (e.g. rusting) where due to the advance of technology it is cheaper to replace by new unit with lower losses and which has a full potential lifetime on installation. or other. Results gathered from the survey are presented in Fig. 1. One of the responses, 10 years, is for a special project where this is the investment horizon, so it should be looked at as an exception. There is quite a variety of results, varying from 20 to 50 years. However, as the impact of savings which are made in the far future is very small due to the impact of counting the actual impact on loss evaluation is much less significant. This can best be appreciated by comparing the PV factors for 25 and 50 year capitalizations as shown in Table 1. It can be seen that whilst the 50 year period is twice as long as the 25 year period the actual ratio between the losses included is much less- 18% extra—which is the ratio of the PV factors i.e. 13.8 for 50 years and 11.65 for 25 years (at 7%,) giving an 18% increase in capitalized losses. The price of energy used to calculate the capitalization values is also one of key factors. There the results differ significantly. Obviously, the prices are very different in different countries, but the range is from as low as 10e/MWh up to 80 e/MWh,

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Fig. 1 Period used in the capitalization calculation

Table 1 Influence of period and discount rate on present value of annual losses savings

Capitalisation period (years)

Discount rate 3%

5%

7%

20

14.88

12.46

10.59

25

17.41

14.09

11.65

30

19.60

15.37

12.41

35

21.49

16.37

12.95

40

23.11

17.16

13.33

50

25.73

18.26

13.80

although most of the results are in the range of e30–e40/MWh which would be in the expected range for gas fired marginal plant. However on closer examination it is apparent that the lower end prices are from countries using Hydro or Coal, and those where gas is marginal fuel tend to use e40–e50/MWh. Some other factors also play a major role, particularly the discount rate and assumptions on load growth rates. In Table 1 the impact of varying capitalization periods and discount rates on the Present Value factor (PVn) are shown. The Table shows that if the capitalization period is 20 years and discount rate is 3%, then a cost generated by energy losses of 1 EUR per year, will be worth 14,88 EUR in today’s money over this period. Simplified, this is the capitalised value of the cash flow over the period at the interest rate chosen and based on this the value of future loss savings can be calculated in today’s money. The survey responses are shown in Fig. 2, sorted in an ascending order. As it can be seen the rates vary from 3% up to 11%. In general, South America has high

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Fig. 2 Discount rate used

discount rates (10–11%) and EU rates are around 5% with Australia/Oceania at 9%. However one EU country is using 3%. The discount rate has a very significant impact on the calculation of capitalization factors (e/kW) due to it’s large influence on the annuity factor PV e.g. for a 40 year period using 3% gives an annuity factor of 23.11 versus 13.33 for 7%, a near doubling, as the annuity factors are very sensitive to the discount rate used, although relatively insensitive to the capitalization period. Whilst there is scope for several PhD’s in the consideration of the appropriate discount rate to be used the following criteria are pertinent: (a) The losses saved are a societal benefit, persist for long numbers of years, are fairly certain and if being produced by a Government. would be evaluated at a ‘societal discount rate’. (b) A ‘societal discount rate’ is a low discount rate which has no inbuilt finance risk (as Government is assumed to be able to fund investment by tax and without risk) and the value of the discount rate used is supposed to reflect the long term opportunity cost of the capital employed. In the UK a figure of 3.5% is used, and in the EU EcoDesign Directive a figure of 4% was used, and this is meant to represent the long-term opportunity cost society of an investment in this project. Developing countries typically have greater opportunity costs so discount rates in South America will be greater than in EU. In using societal discount rates for discounting losses saved no allowance for risk of the expected benefits being achieved is included. Accordingly there is a requirement to include the expected uncertainties in the cash flows of the estimated losses being discounted, as there is significant uncertainty over the valuation of the losses saved—essentially this is a prediction over 40 years of what loading and loss will occur on the transformer, what the future price of

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electricity will be, how long these savings will persist and what discount rate is applicable. As the investment in the transformer is being made by a utility which has different opportunity costs and carries financial risk the investment costs should be discounted at the companies cost of capital (WACC), which is a much higher rate than the societal discount rate. This approach is probably the most ‘pure’ approach but requires a lot of work to estimate the uncertainties in the cash flows being discounted, as ignoring this area will result in an overvaluation of the losses. (c) Alternatively a cruder approach is to use a larger discount rate for both savings and investment and assume the uncertainties are included—typically the company WACC as set by the regulator is used e.g. 5% (d) This is a simple approach but assumes that the risk of an investment in reducing losses carries the same level of risk as other typical risks borne by the company, which is incorrect as investment in loss reduction is significantly riskier than typical utility investments. So a premium (1–2%) should be added to the utility WACC to more correctly reflect extra risk. Additionally, as less developed economies have higher opportunity costs they should use higher discount rates, even within the EU. Occasionally load growth rates can be accounted for by adjusting the financial discount rate, so that the rate used is a combination of load growth rates and financial discount rates e.g. a 5% discount rate combined with a 1% load growth rate would result in an effective composite rate of 4%. However it can be seen that the rates used by utilities in the survey can be justified–less developed economies had higher discount rates, more developed economies lower. A small difference in choosing discount rate, energy demand increase or similar can have a considerable impact on the capitalization factors. The value of the capitalization of losses can easily be of a similar magnitude as the initial cost of the transformer, so a difference of 1% in the discount rate can have a considerable impact on the optimum design. This is one thing to look for when such processes are handled by a third party (EPC or similar). Where the EPC may use a high discount rate as capital is scarce whereas the final user may have a much lower WACC and would benefit from the return on reduced losses. Additionally, a new factor to take into account is the availability of ‘Green Bonds’ whereby the financing of certain energy efficiency investments can be funded through the use of ‘Green Bonds’ which are available at a slight discount if the environmental criteria are met. In the second part of the survey examples were requested to assess typical losses levels/efficiency. Data from a total of 109 transformers was received. One of the data items requested was the transformer load factor and transformer loss load factor used to calculate the capitalization factor. Data on the load factor for 55 units was received, but loss load factors for only 42 units.

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Fig. 3 Load and load loss factors used for capitalisation

The transformer load factor is the average of the loading of the transformer in terms of the transformer rating. Transformer loss load factor is the average value of the loss factor, which can vary between the extremes of being equal to the transformer load factor and the transformer load factor squared. Typically it is taken as the square of the transformer load but is sometimes estimated more exactly as a linear combination of the transformer load factor and the square of the transformer load factor e.g. 0.85* TLF2 + (1−0,85)*TLF. In Fig. 3 the collected factors are shown. In the VITO report [8] there is an overview of available data on the loading factors. For smaller transformers loading factors are typically from 30 to 40%, while for transmission transformers it is lower and is about 20%. Transmission transformers formed the majority of the transformers in this study. The loading factors in Fig. 3 seem rather high and where levels of around 70% are encountered disagree with the load factor inferred from the capitalization rates, which is about 40–50% (Sqrt (eLL/eNLL) = Load Factor). It is possible that there was confusion between the terms load factor and transformer load factor. The load factor is simply the ratio of the average load to the peak load, but is unrelated to the transformer rating. To establish losses the Load Factor must be related to the transformer rating as transformer losses are quoted at full load. So a 100kVA load with a load factor of 90% on a 200kVA transformer would have a transformer load factor of 45% based on the transformer utilization factor being 50% (=100kVA/200kVA) and the Transformer Load Factor then being 45% (= 0.9*0.5). Use of peak efficiency index (PEI) on power transformers means that the ratio of copper to iron losses can be optimized to match the transformer load factor encountered. So higher loading factors increase the importance of load losses and decreases the importance of no load losses. As a result of that it is optimum for the manufacturer to use more copper in order to lower the load losses instead of decreasing losses in the core. If only the PEI value as provided in the EU Directive is used the manufacturer

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Fig. 4 Peak efficiency index (PEI)

will manufacture the cheapest transformer which meets the Regulation but which will not be matched to the load usage and hence minimize overall losses. Providing the load factor as well as the PEI overcomes this issue (- similarly providing the capitalization factors is even better because not alone do the capitalization factors infer the load factor they also provide guidance as to how far in advance of the PEI it is worthwhile to optimized the transformer.) One of the obvious questions is whether the transformer specified with maximum losses have higher or lower losses than the ones specified by capitalization factors, as capitalization is searching for an economic optimum not lower losses. In Fig. 4 the gathered data are shown. For an easier understanding of the data EU Tier 1 and Tier 2 are included. Although there is a lot of scatter, it can be seen that efficiency of transformers purchased using capitalization is on average higher than those purchased using maximum losses. This is because use of maximum losses puts a limit on losses for which the transformer will be designed as the manufacturer will not be rewarded in the tender for providing lower losses (- if for no other reason that the benefit of the lower losses cannot be evaluated in the Tender). In contrast the process of capitalization does not provide a lower limit to the losses and the manufacturer is not disadvantaged by optimizing the transformer design and this is rewarded in the tender process. Accordingly, capitalization results in a cost optimal transformer of high efficiency. It is also seen in the survey that some utilities use the EU EcoDesign Regulation as an upper limit to the loss levels, with capitalization factors then used to assess whether lower limits are justified and if so facilitate their inclusion in the tender. Note: Some utilities establish economic loss levels using capitalization prior to tender, and then use the loss levels so established to provide fixed values of losses so as to simplify the tender process. However this is not as good as simply using

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capitalization values in the tender as the establishment of the fixed losses without involving multiple manufacturers is difficult. The remaining factor in the survey is the price of electricity used and this should be the energy component of the wholesale price, excluding any fixed costs but including variable O& M costs and including the cost of carbon. Typically costs in EU are in the range e40–e50 but in countries where coal is predominant costs are significantly lower e.g. e16/MWh, and may not include a premium for carbon. As the cost of electrical energy can vary over time the actual price used should be a discounted average of the forecast price over the duration of the investment. However this is very difficult to establish and in the past the capitalization values are more sensitive to the discount rate and period than the electricity price, so using the current price is the norm. However with increased use of renewables the marginal cost of electrical energy all approaches zero and the value of losses will be defined by the impact on system services and network capcity required due to peak losses. One utility currently includes the cost of the impact of losses at peak on network and generation capacity requirements and this has a significant effect on the capitalization rate used.

4 Regulation Impact In the last part of the survey experience with efficiency regulation was investigated. In most of the countries in the on survey there is a regulation in place. Most of the responders see very small or no impact on Power Transformer purchase costs as they were already close to the EU requirements. However there were significant increases in costs associated with transportation and installation where critical limits on weight or dimension were exceeded. Some of the responses are reporting a change in power transformer dimensions but are not reporting any associated problems other than where critical limits are exceeded. In relation to distribution transformers one utility commented that the use of fixed values for iron and copper losses was less flexible than the use of PEI allowed for power transformers. This lack of flexibility meant that the transformer could not be designed for the load involved and this led to extra losses e.g. Transformer losses were weighted toward a reduction of iron losses yet with Electrification of heat and transport it is copper losses that should have been minimized. Use of PEI would have allowed the transformer design to match the expected load factor which would have been more efficient and economic.

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5 Conclusion The results of the survey show that utilities around the world are putting effort into efficiency of transformers and procuring transformers that meet or exceed efficiency levels defined in Regulations. However the use of PEI provides scope for further reduction in losses as it allows the transformer to be designed to match the load, either minimizing copper or iron losses as appropriate. This in turn suggests that the use of fixed losses for distribution transformers is sub-optimal and efficiency could be further increased using PEI. Many utilities use the regulation as a lower limit on losses and capitalization values to further optimize the transformer, as can be seen from Fig. 4. However utilities have the opportunity to invest in other equipment than transformers. In cases when capitalization suggest that optimum design is a less efficient than the regulation, a larger reduction of losses for the same investment would be available in some other equipment. The main conclusion is that there is still a potential to increase the knowledge of people involved in the procurement process so that by altering the specification the costs can be decreased further and efficiency increased.

References 1. Janic Z, Walsh A, Virtanen E et al Power transformer efficiency, Cigre Technical broschure, in preparation non published 2. Walsh A (2017) Consultation on Tier 2 fixed loss levels on distribution and power transformers implementation. Eurelectric 3. Purchase and operating Cost for Transformers (1996) EEA, New Zealand 4. Guidelines on the Calculation and use of Loss Factors (2013) Electricity authority Te Mana Hiko 5. Harlow J (2004) Electric power transformer engineering. CRC Press 6. Janic Z (2008) Improvement of power transformer design in order to reduce stray losses. Ph.D. thesis, Faculty of electrical engineering and computing, Zagreb, 06 June 2008 7. Janic Z, Sitar R, Pandya M (2014) Use of fem tools for stray loss optimization in transformers. In: The 16th international IGTE symposium on numerical field calculation in electrical engineering, graz, institute for fundamentals and theory in electrical engineering-IGTE, p 35 8. Final Report LOT 2 (2011) Distribution and power transformers Tasks 1–7, VITO, Study for European Commission DG ENTR unit B1

Reliable Power Transformer Efficiency Tests Gert Rietveld, Ernest Houtzager, Dennis Hoogenboom, and Gu Ye

Abstract Power transformer efficiency measurements are a crucial part of the acceptance tests of a power transformer. These tests have increased importance since the EU Ecodesign Directive per 1 July 2015 has put efficiency limits to power transformers that are sold on the European market. In this paper we present a series of measures to assure that power transformer efficiency tests performed by power transformer manufacturers are accurate and reliable. This includes the development of more accurate industrial loss measure-ment systems (LMS), optimized LMS calibration approaches, and a reference system for on-site LMS calibration. Keywords Power transformers · Efficiency · Loss · Loss measurement · Reliability · Calibration · Accuracy · Uncertainty

1 Introduction Power transformer efficiency is a very important parameter, first of all for the utilities that purchase the power transformers, since they have to carry the costs associated to the power transformer losses over the life time of the transformer. These costs are a substantial part of the total cost of ownership to the utility, and can sometimes even exceed the purchase costs. Because of this economic impact of power transformer losses, fines are put on losses exceeding the specified limits, that can be as large as 10,000 e/kW. For a 100-kVA transformer with 1% specified losses, a 3% excess of the losses (i.e. losses of 1.03%) would then result in a fine of 150 ke. Power transformer losses also have a societal impact, since they increase the cost of the electricity grid infrastructure and lead to significant additional CO2 emissions. An EU impact study has estimated that the saving potential of more efficient power transformer designs is 16 TWh/year and 3.7 Mt of CO2 emissions per year [1]. This has brought the EU to put requirements on the efficiency of power transformers that G. Rietveld (B) · E. Houtzager · D. Hoogenboom · G. Ye VSL, Thijsseweg 11, Delft, The Netherlands e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_10

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are sold on the European market after 1 July 2015 as part of the Ecodesign Directive [2]. These social, economic and environmental effects of power transformer losses have increased the need and relevance for power transformer manufacturers to make reliable loss tests of their products, as part of the factory acceptance tests. To achieve reliable loss tests suitable loss measurement system should be available, with sufficient accuracy. In this paper we describe new developments and discuss several aspects that are relevant for accurate, reliable power transformer loss measurements. This includes the development of advanced industrial loss measurement systems (LMS), the different LMS calibration approaches and assurance of the validity of the calibration, and the development of reference setups for on-site LMS calibration at the premises of power transformer manufacturers [3].

2 Power Transformer Loss Measurement Systems Figure 1 gives a schematic of the typical LMS used by power transformers to measure the losses of their products. The LMS has voltage and current scaling devices to scale the large test voltage and test current to values that can be handled by the watt meter (WM). For the current scaling typically conventional current transformers (CTs) are used, whereas the voltage channels either consist of conventional voltage transformers (VTs) or of voltage dividers (VDs) consisting of high-voltage (HV) capacitors (C HV ) in combination with low-voltage electronics. The key challenge for the LMS in loss power measurements is to measure power with good phase accuracy. This can be readily seen given the loss power Ploss for sinusoidal test waveforms is equal to: Ploss = V × I × cos (ϕ)

(1)

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Fig. 1 Single-phase schematic overview of an industrial loss measurement setup for determining the load and no-load losses of power transformers

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with the phase angle ϕ between the voltage V and current I close to 90°. Measuring losses with an accuracy of 3% at a power factor (PF) of 0.01 thus requires measurement of the deviation of the phase ϕ from 90° (corresponding to an ideal transformer with no losses) with an accuracy of 300 μrad or 1 min. With the increased importance of reliable power transformer and reactor loss measurements, the need arose for the advanced LMSs with accuracies of 0.5—1% at PF = 0.01. This approximately is a factor 3 improvement with respect to the typical specifications of present LMSs. An evaluation of the commercial power transformer LMSs available on the market, and power transformer manufacturer experiences with these LMSs, showed that in particular the accuracy of the LMS voltage channels should be improved. Therefore, as part of the TrafoLoss project [3], two new voltage channels have recently been developed with high accuracy and good stability over time. Figure 2 gives photographs of the two dividers. The first divider is a capacitive divider with a buffered output to make the divider output voltage independent of measurement burden [4]. The low-voltage arm consists of ceramic capacitors (290 nF or 3600 nF) on the feedback loop of the buffer amplifier (see schematic in Fig. 2) [5]. This divider has already successfully been used as part of a LMS to measure the losses of an air-core shunt reactor with 0.5% accuracy at PF = 0.01 [4]. The second divider is an improved version of an existing conventional design, where the accuracy improvement has been achieved through passive error compensation [6]. A further improvement is the addition of direct readout of the secondary voltage signal using a time-synchronised digitiser. This direct readout has several advantages. First, it allows for further digital compensation of the remaining ratio errors and phase displace-ments. Second, it removes the long conventional secondary wiring, reducing both the burden on the voltage transformer output and the possible effects of interference.

Fig. 2 Two high-accuracy HV dividers for inclusion in future advanced LMSs. The left hand shows a capacitive divider with buffered output (see schematic). The right hand shows a conventional voltage transformer with passive error compensation and digital readout

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Such direct readout devices have become available via the development of time dissemination equipment based on the white rabbit protocol [7] or derived technologies, together with metrology digitisers that are synchronised to each other using this timing technology [8]. A trend in LMS development is to apply this technology to directly digitise both the voltage and current signals at the output of the voltage and current scaling devices. The time-stamped digital measurement values are subsequently transferred via a fiber connection to a central unit in the test control room, where the loss power is calculated. Apart from the above-mentioned improvement in accuracy and reduction in interference effects, this in practice also allows for more convenient LMS operation.

3 LMS Calibration Aspects Industrial loss measurement systems are used by power transformer manufacturers to test the quality of their products. However, such a test is only useful, and its results are only indisputable, if the loss measurement system is of proven, adequate quality. Specifications are an indication of the expected LMS behaviour, but cannot be taken for granted. The LMS manufacturer might have failed to realise the specifications, or the LMS may have drifted so that following initial accurate operation, over the period of several years the LMS has moved outside its specifications. Calibration of the LMS thus is required to determine the LMS accuracy and to determine whether the LMS meets its specification and/or the user requirements. In turn, the calibration is only useful when it is performed with sufficient accuracy and reliability. This chapter first gives an overview of the LMS accuracy requirements in different standards and legislation. Then several LMS calibration aspects are discussed: the two available calibration approaches, how to assure LMS quality when adjustments have to be made to the LMS, and how often calibration should be performed. Finally, the quality assurance of the LMS calibration is covered. Reference systems suitable for LMS calibration are presented in the next chapter.

3.1 LMS Accuracy Requirements The most explicit requirement on the required LMS accuracy in power transformer loss measurements is given by the IEEE standard C57.12.00-2010 [9]. Table 20 in this standard requires an accuracy of 3.0% in the loss measurements, down to a power factor of 0.01. The IEC 60076 series of standards on power transformers only gives an indication of the required LMS accuracy. Chapter 10 of the IEC 60076-8 [10] mentions that for advanced measuring systems, “the resulting phase angle error for the complete system may be of the order of 100–200 μrad (0,3–0,6 min). With such systems, an overall maxi-mum error of ± 3% may be achieved for the loss determination down

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to a power factor of 0,02 or even lower.” This may be taken as a hint that such uncertainties are preferred for loss measurements, but there is no hard require-ment. Finally, the Ecodesign Directive for power transformers indicates in Annex III that for market surveillance “the measured value shall not be greater than the declared value by more than 5%” for load losses and no-load losses [2]. This is generally interpreted that the measurement uncertainty of the market surveillance test should be better than 5%, and that power transformer manufacturers should reach such accuracy in their loss measurement tests as well. However, the customers of the power transformer manufacturers, the utilities that buy the power transformers and shunt reactors, may set their own accuracy requirements. As already indicated earlier, power transformer losses are a significant part of the total cost of ownership to the utility, sometimes even equaling the acquisition costs. Therefore, the utility may not only set a maximum declared loss value for the power transformer, but also set requirements on the accuracy with which this loss value is measured. Figure 3 illustrates the rationale behind such requirements: loss measurements with good accuracy reduce the risk of incorrect decisions, such as a measurement value that fails to detect compliance of a transformer with the customer or Ecodesign requirements. Or vice versa, a measurement value that fails to detect non-compliance. In general, high-accuracy loss measurements reduce the margin of discussions between manufacturer and customer. Furthermore, they provide the power transformer manufacturer with a tool to design his products closer to the customer limit. This is a competitive advantage, since less expensive materials can be used for a transformer with higher losses. As an extreme example, the authors were once asked on their measurement capability to verify that a transformer, designed to have 0.997% losses, would surely meet the customer requirement of at most 1% losses. This request would require a loss measurement with better than 0.003% accuracy (0.3% at PF = 0.01), and was one of the drivers for development of the high-accuracy reference setup described in the next chapter.

Actual loss Probability

Fig. 3 Visualisation of the risk on obtaining incorrect test results for inaccurate loss measurements. For the accurate test, all test results would prove the compliance of the transformer with the Ecodesign or customer requirements. For the inaccurate test, there is a significant risk (with associated financial consequence) that the test result fails to detect this compliance

Ecodesign or customer limit

Accurate test Inaccurate test

Test result fails to detect compliance

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3.2 LMS Calibration, Adjustment, and Verification To unambiguously prove that an LMS is meeting the imposed accuracy requirements, it must be calibrated. In the calibration, reference instrumentation is used to determine the deviation of the LMS from the ideal nominal measure-ment value. Based on the calibration results a statement can then be made on whether the LMS indeed meets its specification and/or the user requirements. There are two basic approaches in LMS calibration. The first, traditional, method is to calibrate the individual components of the LMS: the voltage scaling, current scaling, and the power meter (see Fig. 1). Subsequently, the individual calibration results must be combined to achieve the total LMS accuracy. A major advantage of the ‘component calibration’ is that it is relatively easy to perform and that each individual LMS component can be calibrated on all its ranges. However, the component calibration does not cover all possible error sources of the system as a whole, such as interference between the three phases of the LMS and other system effects [11]. In the second, more recent, method the LMS is calibrated as a whole [11–14]. Such a ‘system calibration’ has the major advantage that it covers all systematic effects of the LMS, including possible errors in the LMS test software. This calibration is more difficult to perform, but leads to lower final LMS uncertainties than the component calibration. To simplify the calibration, reference setups for LMS system calibration are single phase, so that the LMS voltage and current channels have to be placed in parallel and series respectively during the calibration [11–14]. If the calibration results lead to the conclusion that the LMS is not meeting its specifications or user requirements, either corrections have to made to future test results or the LMS has to be adjusted to bring the LMS back into its required accuracy. However, when the LMS is adjusted, the LMS should be calibrated both before and after the adjustment to maintain an overview of the actual LMS behaviour and drift over the years. Unfortunately, this is not common practice in LMS calibration. If adjustments are made and only the final calibration results are provided that prove the LMS is (again) meeting its specifications, the power transformer manufacturer has no clue on the actual LMS accuracy just before the LMS adjustment. Indeed, if the LMS was outside its accuracy specifications before the adjustment, the loss measurements performed before the adjustments were not meeting the expected accuracy requirements. As Fig. 3 visualises, this has the serious risk that incorrect test results were obtained and subsequently incorrect conclusions were drawn on the question whether a power transformer is compliant with its loss requirements or not. The IEC 60060-2 standard mentions that calibrations “should be repeated annually, but the maximum interval shall not be longer than five years” [15]. The optimal interval between successive calibrations depends on many factors, such as the calibration accuracy, LMS stability, required overall LMS accuracy and the risk that the power transformer manufacturer is willing to take [13]. In practice, many power transformer manufacturers opt for the maximum 5-year interval. This may at first sight seem to save on calibration costs, but increases the risk of significant costs

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brought by possible incorrect loss measurements performed near the end of the 5year period [13]. If that indeed appears to be the case during the LMS calibration, corrective actions should be taken. Next to the costs associated with the corrective actions, they may also significantly damage the reputation of the power transformer manufacturer. It therefore is recommended to follow the precision measurement industry practice of calibrating electronic equipment such as power meters every year. For the current and voltage scaling channels, longer re-calibration periods may be used, depending the stability of the technology used in the current and voltage scaling. Ideally, the actual drift and stability of the LMS components is first determined by relatively frequent calibrations in the first years after the acquisition of the LMS, followed by extended calibration intervals based on the actual LMS drift. The final re-calibration interval has to be determined balancing calibration costs and costs of possible corrective actions and thus may be different for different power transformer manufacturers. However, given the importance and impact of reliable and accurate loss tests, a general re-calibration period of 3 years seems more appropriate than the present frequently chosen 5-year interval. In IEC 60076-8 it is recommended that “the test department shall possess routines for continuously maintaining the quality of measurements. This should be by regular checking and calibration routines for components and for the complete system. It may comprise both in-house functional comparisons between the alternative systems, checking the stability and periodical re-calibration of components” [10]. Cross-check routines indeed are highly valuable for monitoring and verifying the LMS calibration status in between calibrations. They typically are not performed with the same accuracy as a formal calibration, as they serve as a ‘sanity check’ of the calibration status of the LMS.

3.3 Traceability Similar to the performance requirements on LMSs themselves, there are performance requirements posed on the equipment used for calibration of the LMSs. An important requirement according to IEC 60060-2 is that “any calibration shall be traceable to national and/or international standards” [15]. This means that there should be an unbroken chain of measurements linking the LMS calibration to international measurement standards, where each measurement in the chain has a measurement value and uncertainty. Following statements on the LMS specifications, IEEE standard C57.123-2010 explains that “having traceability is a prerequisite to being able to achieve this specification. It provides a means to have documented evidence of the magnitude and phase errors of the various components of the measurement system and their associated uncertainties” [16]. Similarly, IEC 60076-1 requires that “all measuring systems used for the tests shall have certified, traceable accuracy and be subjected to periodic calibration, according to the rules given in ISO 9001. Specific

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requirements on the accuracy and verification of the measuring systems are described in IEC 60060 series and IEC 60076-8” [17]. The IEC 60060-2 standard gives more background on how the traceability can be achieved. This can be either done by the user himself, or “alternatively, any user may choose to have the performance tests made by a National Metrology Institute or by a Calibration Laboratory accredited for the quantity to be calibrated” [15]. The advantage of the latter approach is explained in a note of paragraph 4.1 of this standard, where it is remarked that “calibrations performed by a National Metrology Institute, or by a laboratory accredited for the quantities calibrated and reported under the accreditation, are considered traceable to national and/or international standards” [15]. Formal accreditation of the company performing the LMS calibration is an important guarantee that the LMS calibration is performed by qualified personnel following adequate, independently reviewed, measurement procedures. The accreditation should preferably be done according to the ISO\IEC 17025 standard for test and calibration laboratories [18], which has specific requirements to ensure correct test and measurement values, next to the more general quality requirements as also given in the ISO 9001 standard. Indeed, with the increased relevance of reliable transformer loss measurements, the request for LMS calibrations performed under ISO\IEC 17025 accreditation is increasing as well. Following this trend, power transformer manufacturers might even want to become accredited themselves in the future for the loss tests they are performing, as accreditation gives an undisputed, independent proof of the quality of the tests.

4 Reference Setups for On-Site Lms Calibration LMS calibrations have to be performed on-site at the premises of the power transformer manufacturers, since the equipment is too large to be transported to the calibration laboratory. In addition, it is important to calibrate the LMS with the same secondary cabling as during normal use so that possible errors due to loading of the current and voltage channel by the secondary cabling are included in the calibration. In order to realize a meaningful LMS calibration, the reference setup should be more accurate than the LMS specifications or LMS user accuracy requirements. Typically, a test uncertainty ratio (TUR) of 3–5 is required, meaning that the reference setup should be 3–5 times more accurate than the LMS.

4.1 LMS Component Calibration For the LMS component calibration, conventional calibration equipment can be used. The LMS voltage and current channels for example can be calibrated using a reference voltage divider and current transformer respectively, together with an adequate

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Fig. 4 Pictures of an actual on-site LMS component calibration of the current channels (left) and voltage channels (right), using a sampling current ratio bridge and a high-voltage capacitance bridge [19, 20]

measurement bridge [19, 20]. Figure 4 shows the calibration equipment during an actual on-site LMS component calibration of the current and voltage channels. During a similar calibration campaign, it was found that the power meter formed a significant burden to the current channels, next to the secondary wiring, so that the current channels had to be calibrated with the power meter connected in order to achieve meaningful calibration results. The calibration of the power meter itself does not necessarily have to be performed on-site. In the power meter calibration it crucial to include low power factors, down to at least 0.01. Typical power meter applications relate to energy measurements with power factors close to 1, and therefore most power meter calibrations are performed at these power factors. However, since at power factors near 1 the phase errors of the power meter do not play a significant role, such a calibration is not relevant and meaningful for an application in loss measurements. Following the component calibration, the total LMS uncertainty has to be evaluated. Even though the IEC 60076-19 standard provides extensive guidance in this uncertainty evaluation, including calculation examples [21], this uncertainty calculation is experienced as quite complex. Moreover, as already mentioned in the previous chapter, the component calibration does not cover systematic errors of the system as a whole. Therefore, component calibration is a convenient LMS calibration method, but not suitable if best accuracies are to be achieved, for example in the calibration of advanced LMS with specifications of 0.5—1% accuracy at PF = 0.01 (phase accuracy 50–100 μrad). LMS component calibration may even become obsolete in the case when all LMSs will eventually use direct digital readout. In that case, the voltage and current channels essentially cannot be tested separately, since in such systems only the final loss power value is available to the user and not the individual voltage and current readings. Any attempt to still calibrate the digital outputs of the voltage and current channels will be hampered by the different digital protocols used by the different LMS equipment manufacturers in their communication with the central control unit. Moreover, in the final loss power value the phase (=timing) error of the individual

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digital readout units is not important, but only the difference in this phase error for the two units used to read out a particular LMS voltage and current channel. This means that for an LMS with digital readout, LMS system calibration likely is the only remaining feasible option.

4.2 LMS System Calibration In view of these developments of advanced LMSs, and to assure the highest level of reliability in LMS tests, a reference setup has been developed for ‘system calibration’ of LMS as a whole. The approach in the LMS system calibration is that the reference setup simulates different losses to the LMS system and compares the LMS loss measurement results with those measured by the reference setup, see Fig. 5 [14]. To this end, the reference setup generates a test current with a stable and accurately known phase angle with respect to the applied high voltage. This can either be realized via parallel generation of the voltage and current test signals [22], or via a control loop that generates the current based on the measured phase of the applied high voltage, as depicted in Fig. 5 [12, 14]. Figure 6 gives more details on the VSL reference setup for system calibration of industrial LMS. A current-comparator-based capacitive voltage divider provides a low-voltage copy of the applied high voltage. A digital signal processing (DSP) unit subsequently generates a driving signal for the transconductance amplifier G that generates the high test current. The actual applied current is measured with an active electronically-compensated current transformer (CT). The DSP unit compares the actual phase of the current with the desired setpoint and adjusts the driving signal until the actual current phase matches the setpoint. A second current transformer and a reference watt meter is used to verify the readings from the digital feedback loop.

I V

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Fig. 5 Single-phase schematic overview of system calibration of the industrial LMS of Fig. 1. The reference setup is able to generate currents with different, stable, phase angles with respect to the applied high voltage, thereby simulating a power transformer with different losses to the LMS

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VT (CC-based capacitive divider)

Fig. 6 Detailed schematic of the VSL reference setup for LMS system calibration (left), and its actual components (right)

Such a verification is important in case a deviation of the LMS is detected during the calibration, and the power transformer manufacturer subsequently starts to question the accuracy of the reference system with which the LMS is calibrated. In the final implementation of the reference setup, extensive attention was paid to shielding and grounding to ensure correct operation under the non-ideal and sometimes even harsh conditions of the test site of the power transformer manufacturer. A triax cable is used to connect the HV capacitor with the low-voltage currentcomparator electronics of the reference voltage channel. It was verified that even 20 meters of triax cable does not change the voltage reading by more than 0.05% at PF = 0.01 (5 μrad). Similarly, the CT output cable is a double-shielded twisted pair cable. In both cases, the shielding was on-site verified on its effectiveness. A star ground is strictly used in the measurement circuit, and fiber readout of the DSP ensures that there is no interference with between the analog measurement circuit and the digital readout by the PC in the control room of the test site. The reference setup in the mean time has been used for several on-site LMS system calibrations. The digital approach of the feedback loop together with extensive automation of the data acquisition process proved to be a real advantage. It allows for LMS system calibration at 21 voltage and current combinations for both 50 and 60 Hz, and each at 5 power factors, within the time frame of a single weekend. In each on-site calibration measurement, the readings of the digital DSP and the reference power meter are compared and found to agree with each other well within the reference system accuracy. Table 1 shows the overall accuracy of the reference setup based on careful calibration of all its components. This uncertainty budget proves that the setup achieves an accuracy of better than 0.2% at power factors down to 0.01, for voltages up to 100 kV and currents up to 2 kA. In a recent comparison of the VSL and PTB LMS reference setups this accuracy was independently verified. The measured difference in the VSL and PTB results was less than 12 μW/VA (0.12% loss power at PF = 0.01) for currents up to 1000 A and voltages up to 70 kV [23]. This is well within the measurement accuracies of the VSL and PTB reference setups.

124 Table 1 Uncertainty budget of the VSL reference setup for on-site LMS calibration AT PF = 0.01, for voltages up to 100 kV and currents UP to 2000 A

G. Rietveld et al. Uncertainty source

[%]

Voltage scaling—HV cap

0.05

Voltage scaling—LV unit

0.07

Current scaling

0.05

Power measurement

0.08

Noise

0.05

System effects

0.07

Total uncertainty (k= 2)

0.15

5 Conclusion Reliable loss measurements support the drive for higher efficiency in power transformers and shunt reactors. In order to meet the demand for increased accuracy in these measurements, two new voltage channels with improved accuracy and stability have been developed for inclusion in future advanced LMS: a capacitive divider with buffered low-voltage output, and a conventional voltage transformer with passive and digital compensation techniques. The loss measurement accuracies required according to IEEE and the Ecodesign Directive are 3 and 5% respectively at PF = 0.01. However, utilities already require better accuracies, in order to reduce their total cost of ownership. This can go down to an accuracy of better than 0.5% at PF = 0.01. At these accuracy levels, great care is required in the LMS calibration to correctly verify that this accuracy indeed is achieved. ‘System calibration’ of the LMS as a whole is more complex to perform but covers all possible errors in the LMS and reaches the best accuracies. All LMS calibrations must be traceable to (inter) national reference standards. This is best achieved by a laboratory that is ISO\IEC 17025 accredited for this calibration. A reference setup has been developed for on-site system calibration of LMSs. Here, the reference system simulates a power transformer with different losses to the LMS. A digital feedback loop assures generation of a current with stable and known phase with respect to the applied high voltage. Via optimized feedback loop parameters, and careful calibration of the components in the reference setup, an overall accuracy of better than 0.2% in loss power at PF = 0.01 is achieved. This low uncertainty meets the calibration requirements of even the most advanced industrial LMS. Acknowledgements This research is performed within the “TrafoLoss” EU joint research project, which has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. Additional funding is received from the Dutch Ministry of Economic Affairs and Climate.

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References 1. VITO, ErP study, Final Report, LOT 2: Distribution and power transformers, 2010/ETE/R/106 2011 2. Commission Regulation No 548/2014 On implementing Directive 2009/125/EC of the European Parliament and of the Coun-cil with regard to small, medium and large power transformers. Official J Eur Union L285:10–35 3. TrafoLoss joint research project. https://www.euramet.org/research-innovation/search-res earch-projects/details/project/loss-measurements-on-power-transformers-and-reactors/ 4. Havunen J, Suamalainen EP, Tornberg J, Hällström J, Lehtonen T, Merviö A (2019) Measuring losses of an air-core shunt reactor with an advanced loss measuring system. Springer series lecture notes in electrical engineering, pp 1–12 5. Mohns E, Chunyang J, Badura H, Raether P (2019) A fundamental step-up method for standard voltage transformers based on an active capacitive high-voltage divider. IEEE Trans Instr Meas 68(6):2121–2128 6. EPRO standard voltage transformer. https://www.epro.at/en/products/test-bay-equipment/sta ndard-voltage-transformers/ 7. White rabbit. https://www.ohwr.org/projects/white-rabbit/ 8. Houtzager E, Hornecker R, Rietveld G (2019) Compact distributed digitizers with metrological precision. IEEE Trans Instr Meas 68(6):1653–1658 9. IEEE standard C57.12.00-2010 IEEE standard for general requirements for liquid-immersed distribution, power, and regulating transformers. IEEE Power Energy Soc 10. IEC 60076-8:1997. Power transformers—Part 8: Application Guide 11. Rietveld G, Houtzager E, Zhao D (2015) Impact of the ecodesign directive on traceability in power transformer loss measurements. In: 23rd International conference and exhibition on electricity distribution. Lyon, France, pp 1–4 12. So E, Miljanic PN, Angelo DJ (1995) A computer-controlled load loss standard for calibrating high-voltage power measurement systems. IEEE Trans Instr Meas 44(2):425–428 13. Rietveld G, Houtzager E, Acanski M, Hoogenboom D (2017) Meeting Ecodesign efficiency requirements: ensuring accuracy in power transformer loss tests via TLM system calibrations. In: 24th CIRED conference. Glasgow, UK, pp 1–5 14. Rietveld G, Houtzager E (2017) High-accuracy reference setup for system calibration of transformer loss measurement systems. In: Proceedings of the 20th international symposium on high voltage engineering (ISH 2017), pp 1–6 15. IEC 60060-2:2010 High-voltage test techniques—Part 2: Measuring systems 16. IEEE standard C57.123-2010 17. IEC 60076-1:2011 Power transformers—Part 1: General 18. ISO/IEC 17025:2018 General requirements for the competence of testing and calibration laboratories 19. Van den Brom HE, Rietveld G, So E (2015) Sampling current ratio measurement system for calibration of current transducers up to 10 kA with 5·106 uncertainty. IEEE Trans Instr. Meas 64(6):1685–1691 20. Petersons O, Anderson WE (1975) A wide-range high-voltage capacitance bridge with one ppm accuracy. IEEE Trans Inst Meas 24(4):336–344 21. IEC 60076-19:2013 Power transformers—Part 19: Rules for the determination of uncertainties in the measurement of the losses on power transformers and reactors 22. Mohns E, Räther P, Badura H, Schmidt M (2016) Standard for high-power loss measurement systems for testing power transformers. In: 2016 Workshop on applied measurements for power systems (AMPS), Aachen, Germany, pp 1–6, August 2016 23. Rietveld G, Mohns E, Houtzager E, Badura H, Hoogenboom D (2019) Comparison of two reference setups for calibrating power transformer loss measurement systems. IEEE Trans Instr Meas 68(6):1732–1739

Verification of Maintenance Intervals for Vacuum On-load Tap-changers Niklas Gustavsson

Abstract The long maintenance intervals of vacuum tap-changers require extensive testing. Since resistive vacuum tap-changers where introduced to the market in the 2000s there are very few of these that have been in service 10–15 years without any kind of maintenance and likely no experience at all from installations with longer service intervals. To really verify that a tap-changer can handle 30–40 years in difference load conditions and applications, testing beyond normal type testing is needed. Keywords Tap-changer · Vacuum · Verification · Maintenance

1 Introduction On-load tap-changers with load commutation in oil have been the common technology since the early 1900s. It is well-proven, but with the drawback that the arcing from load commutation breaks down the oil and wears the surface of the contacts. The breaking ability is therefore reduced with increasing number of operations. When the oil decompose, soot is created which can end up on insulating surfaces. If the oil in the tap-changer has been contaminated with moisture, the moisture in combination with soot can become a conducting layer that in time can cause flashovers. All this together makes periodic maintenance of the tap-changer required, which is depending both on the number of operations and the time in service. It may also be needed to fit on-line oil filters to the tap-changer to continuously clean its oil from soot and moisture. A further development is the vacuum technology, where load commutation is performed in vacuum interrupters instead of in the oil. This technology origins from medium voltage switchgear and have been used in reactive tap-changers since the 1960s. It was however not introduced in resistive tap-changers until early 2000s. The advantage of the vacuum technology is that the arcing takes place inside the vacuum N. Gustavsson (B) ABB Components AB, Ludvika, Sweden e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_11

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interrupters instead of in the oil. This means that the oil does not deteriorate and there is no creation of soot in the oil. The absence of soot makes the tap-changer less sensitive to moisture. The breaking ability is also unchanged regardless of number of operations. Compared to traditional tap-changers, the contact wear is much less since the contact material condensates back to the contact surfaces. This together enables longer maintenance intervals which are only set by the number of operations, not time in service. Vacuum tap-changers also have a better breaking capacity than nonvacuum types which is an advantage in challenging applications such as HVDC. Regardless, it is of course important to ensure that the tap-changer oil always is of good quality. There have also been studies and field prototypes of electronic tap-changers, where power electronics such as thyristors, are used to handle load commutation. This means in practice unlimited number of switching operations without need of maintenance. The disadvantage with this technology is the relatively high losses and that the components may be sensitive to their surrounding environment, for instance high temperatures. To add, the price of the components is still relatively high which makes the technology shift even more difficult. By comparing these technologies, the conclusion is that vacuum technology is today the best alternative. It provides long maintenance intervals with very little impact on the insulation fluid. The absence of soot reduces the sensitivity to moisture which removes the need of oil filters which in turn is a component that requires maintenance. These properties also make vacuum tap-changers suitable for applications with alternative insulation fluids, such as natural and synthetic esters, where due to environmental requirements or fire safety mineral oil is not preferred. Besides the longer maintenance intervals, use of ester fluids are the main driver for the need of vacuum technology.

2 Tap-changer Design The tap-changer is the only moving part inside the transformer and statistically also a large source for transformer failures. This is for instance highlighted in the Cigre Technical Broschure 642: “Transformer reliability survey” [1]. A tap-changer failure can in worst case lead to a catastrophic transformer failure with risk of fire and personal damage as consequence. This puts enormous requirements on its design. Resistive tap-changers are operated by a spring battery that is charged from the motor drive unit. When the energy is released, a sequence of contacts must open and close in a very short time, usually 50–100 ms, and with high accuracy. This leads to high mechanic stresses on a design that is required to have a life-time of over 1,000,000 mechanic operations. Besides the mechanic stresses, the tap-changers must commutate high load currents and withstand large dielectric fields which in turn requires good contact materials, low resistance in contact transitions and welldesigned electrode shapes. All this while the tap-changer must be able to operate

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in temperatures between −25 °C and below up to 130 °C which in turn puts tough requirements on materials and material combinations. Besides the technical requirements, the tap-changer must be easy to mount on the transformer and be as compact as possible to reduce its impact on the transformer size. Low need of maintenance is mentioned earlier, but it is also important that it is easy to perform maintenance to avoid causing problems when working with the tap-changer. Vacuum tap-changers enable long maintenance intervals, usually 300,000 operations and no time-based requirements, and no need of oil filter units. Nothing is however maintenance-free. The vacuum interrupter contacts can be regarded maintenance-free but the motor drive unit, the shaft system and the insulating fluid still requires attention. Since resistive vacuum tap-changers were introduced to the market in the 2000s there are very few of these that have been in service 10–15 years without any kind of maintenance and likely no experience at all from installations with longer service intervals. As a manufacturer of tap-changers it is therefore extremely important to verify that the design can handle the promised maintenance intervals and life-time.

3 Verification of Maintenance Intervals Type testing of tap-changers is controlled by international standards such as IEC 60214-1 and IEEE C57.131. The requirements in the standards can be regarded as the lowest acceptable performance that is accepted in the market. To really verify that a tap-changer can handle 30–40 years in difference load conditions and applications, additional testing is needed.

3.1 Mechanic Endurance Testing The international standards usually put 500,000 operations as requirement for the mechanic endurance test. Since the promised life-time is usually more than 1,000,000 operations, more extensive testing is needed. For practical reasons it is also difficult to test several units in parallel which require the test units to be operated even longer to compensate the low statistical support. Figure 1 shows a suggested statistical relation between number of test units and number of operations in relation to the promised lifetime. This method, developed by ABB Components [2], depicts the number of operations to apply on a small sample of test objects to ensure that all test objects can perform the desired number of operations with a confidence level of 95%. Furthermore, no maintenance is performed on the test objects even though the international standards allows maintenance to be performed with the intended intervals for the product that is tested.

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Fig. 1 Number of operations related to promised lifetime versus number of tested units

Table 1 Example of test objects and operations in mechanic endurance test

Number of test objects Operations in mechanic endurance test 1

2 * 1,200,000 = 2,400,000

2

1,71 * 1,200,000 = 2,052,000

3

1,58 * 1,200,000 = 1,896,000

Table 1 shows an example how to verify a life-time of 1,200,000 operations which is common for many vacuum tap-changer models. It shows that three test units is a suitable combination of test objects and number of operations. The test is also performed in different temperatures with regular measurements of the contact sequence to verify the function for different cases. If the timings in the contact sequence remains within the limits set for the tested tap-changer model after the test, the test is considered successful. The evaluation is also consisting of a visual inspection to ensure that there are no damaged or loose parts or undue wear.

3.2 Capacitive Breaking Capacity Winding arrangements like plus/minus and coarse/fine are used to increase the transformers regulating range. This requires the tap-changer to be equipped with a change-over selector. The change-over selector is used to connect the main winding to different parts of the regulating winding or to connect to the coarse regulating winding. This selection is without making or breaking of current but during operation, the moving change-over selector contacts will be electrically floating. This can

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lead to discharges between the fix and moving contacts. The size of these discharges depends on the capacitances between the transformer windings and between the windings and the transformer tank. To handle these discharges so-called tie-in resistors are sometimes needed. These are connected to the change-over selector to ensure that the contact is not on floating potential. To set design values for deciding whether these are needed, the tap-changer’s capacitive breaking capacity needs to be determined. This test is not covered by any international standard, and it is up to the manufacturer of tap-changers to ensure that the stated catalogue values are verified. The test is performed by operating the change-over selector with defined voltage and current levels and measuring arcing time and energy. The discharges also create gases such as acetylene and hydrogen. These gases can disturb the gas analysis of the transformer, since the change-over selector sometimes is placed in the transformer main tank. The capacitive breaking test can therefore also provide input regarding which gas levels that is considered normal when operating the change-over selector.

3.3 Service Duty Test The service duty test is a type test to verify the maintenance interval and shall simulate real service conditions. After completed test, the tap-changer shall be in such condition that continued service is ensured. For vacuum tap-changers, the IEC standard requires the tap-changer to be tested 20% more operations than the maintenance interval. For a typical maintenance interval of 300,000 operations, this means a service duty test of 1.2 * 300,000 = 360,000 operations. A phenomenon that mainly happens in vacuum tap-changers and not in the same way in non-vacuum types is welding of contacts when closing. The pre-arc that occurs when closing contacts with a voltage in between causes the contact surfaces to get welded to each other, which can cause large contact wear if the contact material is not adapted for this. Since the current is only limited by one turn of the transformers regulating winding, the current in this pre-arc rises extremely fast. In non-vacuum types, the impact of this pre-arc is negligible since the contacts are placed in oil which makes welding much more difficult. It has therefore not been relevant to test this, and traditional test circuits have not been designed with this into account. Vacuum interrupters are on the other hand a perfect environment for welding since the contacts are in vacuum. Traditional test circuits can therefore not simulate real service conditions for vacuum tap-changers. ABB has therefore developed a synthetic test circuit for testing of vacuum tapchangers for real service conditions and to verify that the contact material can withstand the promised contact life [3]. The test circuit can simulate both the relevant breaking current as well as the rapidly increasing closing current and have now been included in the latest IEC standard as an alternative test method. It is used for type testing of vacuum tap-changers and to verify tap-changer performance for especially demanding applications, such as HVDC.

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3.4 Electric Aging of Contacts On-load tap-changers are designed to be operated and a common design philosophy is to use sliding contacts in the tap selector or change-over selector. These contacts are self-cleaning since oxides and other layers is wiped away during operation. In some applications however, the tap-changer is seldom operated. This is especially related to the change-over selector in the cases where the tap-changer is not operated over its mid-position. There are also plug-in contacts in a tap-changer that are never operated. Depending on contact material and design, there is then a risk of over-heating and in the end coking of contacts. There are methods to verify the long-time stability of the contacts. One way is during a set time, for instance 30 days, cycle high temperature and high current is accelerate the impact on the contacts. By measuring the contact resistance before and after the test, the performance of the chosen material combination can be verified. Silver material in both fix and moving change-over selector contacts is for instance an efficient way to eliminate a high contact resistance and thereby the risk of overheating.

3.5 Dielectric Aging of Insulating Material Dielectric stress on insulating materials in combination with soot, particles and moisture can lead to serious failures. In vacuum tap-changers, there is no soot from switching, but there are still particles from mechanic wear of the mechanism and moisture can enter the oil at installation, maintenance or from leakage. The particles are typically metallic materials such as silver, aluminum, copper and iron. When the tap-changer is not operating, these particles can sediment on different surfaces by gravitation. Particles that does not sediment directly is influenced by the electric and thermal forces that appears in the tap-changers. After some time, these particles can form on insulating materials. To verify the tap-changers long-time stability, accelerated testing is needed. This is done by placing the tap-changer in dirty oil with high moisture content and particle concentration, for instance from mechanic endurance tests, and during a certain time apply a voltage higher than maximum allowed service voltage. The larger the voltage, the shorter time is required to achieve the requested aging. If the tap-changer withstands the test without any flash-overs, it is shown that the product is welldesigned from a dielectric point of view and that oil filters are not needed. It must however still be stated that it is important to keep a good quality of the tap-changer oil.

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3.6 Summary To summarize, no technical data for a well-designed tap-changer is achieved by a coincidence. Many years of experience in combination with extensive simulations and testing is behind the data. It is also important to have good margins between catalogue values and tested values to handle tolerances in manufacturing and installation. As a manufacturer of tap-changers it is important to understand the different stresses that the product is subjected to during its life-time and to be able to verify that the tap-changer can withstand these. It is also important to be actively involved in development and revision of standards. One example of this is the synthetic test circuit for service duty testing of vacuum interrupters.

4 Maintenance Regardless what technology that is used, the tap-changer will in the end need maintenance. For vacuum tap-changers, recurring oil sampling, with dissolved gas analysis and measurement of the breakdown voltage, a good indication of the tap-changer’s condition. Even if the tap-changers has made relatively few operations, the oil may need to be replaced or filtered to ensure continued service. Since particles may sediment or be attracted to insulating surfaces, particle count from oil samples is not always a reliable method to discover and predict potential problems. Therefore, both the oil and the tap-changer itself may need cleaning depending on application and time in service. Maintenance requires the transformer to be taken out of service, which means that it is important to keep the outage as short as possible. Safety is top priority for all organizations which also impacts tap-changer maintenance. Tap-changers placed inside the transformer, so-called in-tank models, requires access from the transformer cover to the tap-changer. This in turn requires different kind of safety equipment for the service personnel, like scaffolding and personal protection equipment. If the tapchanger is lifted to ground level for maintenance, a crane is usually needed which in turn may cause over-head power lines to be taken out. Despite all safety measures, interviews with service personnel show that some persons still feel somewhat unsafe when working on heights [4]. It is also shown that safety equipment and procedures sometimes are not used correctly due to time-pressure and technician’s attitude. The longer maintenance intervals with vacuum tap-changers do therefore not only add economic advantages but also increases safety. Most optimal is to have access to the tap-changer from ground level. In many parts of the world, tap-changers placed on the outside of the transformer tank (socalled on-tank or bolt-on types) is the preferred solution. These can then be placed on a suitable working height to provide good access from ground level. This usually also means that the motor drive unit is placed directly on the tap-changer with no

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external shaft system, which removes another maintenance aspect. Besides the safety advantages, the maintenance work is easier from ground level which can make the outage shorter. Even if on-tank types have been on the market a very long time, they can still be considered a very modern solution from a safety point of view. On-tank types are however not possible to be used for higher system voltages (>145 kV).

5 Conclusions Vacuum technology is currently the best solution for tap-changers. Long maintenance intervals in combination with proven technology ensures carefree service. But even if the maintenance intervals are longer than for non-vacuum types, maintenance can still not be discarded. For vacuum types, maintenance is in general related to condition assessment, for instance check of oil quality and contact wear, while for non-vacuum types it is focused on restoring the condition of the tap-changer and its contacts. Considering the tough technical requirements and that tap-changers are one of the larger sources of transformer failures, it is important to select a well-designed tap-changer that is carefully tested. Usually it is required to test beyond what is stated in international standards to cover all aspects of a tap-changers life. This is especially important for vacuum types due to their longer maintenance intervals. Many years of experience together with extensive simulations and testing are behind the technical data in the catalogues. It is also important for a manufacturer to be actively involved in development and revision of standards. Vacuum technology is also preferred from a safety perspective, especially for intank types, since it reduces the time spent on heights for the service personnel. To fully minimize the safety risks, on-tank models are recommended.

References 1. Tenbohlen S et al (2015) Transformer reliability survey. Cigre Technical Broschure 642, Working Group A2.37, December 2015 2. ZSC000427-AAX technical guideline mechanical endurance test, ABB Internal document 3. Stenestam B-O, Sundquist P, Andersson G, Jonsson L, Johansson E, Gentsch D (2015) New demands in vacuum interrupters in tap-changer applications. In: TechCon Asia-Pacific 4. Gustafsson H, Gustavsson N. Risks and safety aspects in transformer component maintenance (unpublished)

Prediction Model for the Distribution Transformer Failure Using Correlation of Weather Data Eun Hui Ko, Tatjana Dokic, and Mladen Kezunovic

Abstract Distribution Transformer (DT) is an integral component of a distribution network. Electric utilities have invested efforts in reducing DTs failure rates. This paper presents a method for prediction of probability of DT failure by analyzing a correlation between weather data and historical DT failures data. Logistic regression prediction model is used in order to predict DT failure, and to extract the correlation between parameters of weather and DT failure. Accuracy of prediction is reliable, which is presented using evaluation metrics. This method not only has a vital significance for the maintenance of DTs, but also improves the economic efficiency and reliability of distribution network operation. Keywords Distribution transformer · Failure · Logistic regression · Prediction model · Weather data

1 Introduction The Distribution Transformer (DT) is a vital link in the chain of power apparatus supplying electric power to the customers. DT failures have a major financial impact on both utility company and customers. The utility companies invest large funds annually for maintenance of distribution transformers. Predictions of transformer failure rates is regularly assessed and DTs may be replaced according to set of criteria during the evaluation. However, there is still a limited capability to mitigate DT failures caused by weather. A practical utility example given in Table 1 illustrates that the rate of DT failures caused by weather is still high and presents the second highest cause after aging, also affected by weather. The factors of DT failure consist of aging, weather, overloading, corrosion, out of maintenance, animal contact, installment error, people’s error, etc. Among the causes, aging, corrosion and overloading constitute 47% (Table 1), which combined is the E. H. Ko · T. Dokic · M. Kezunovic (B) Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_12

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136 Table 1 The causes of dt failure in Jeollanam-do of South Korea (2011–2018)

E. H. Ko et al. Cause

The number

Rate [%]

Aging

337

27.2

Weather

333

26.9

Corrosion

155

12.5

Animal contact

145

11.7

Out of maintenance

92

7.4

Overloading

87

7.0

Object contact

25

2.0

Tree

18

1.5

People error

16

1.3

Manufacture error

15

1.2

Flooding

13

1.0

Installment error

3

0.2

Fire

1

0.1

1,240

100

Total

largest reason. In order to decrease this failure rate caused by aging, corrosion and overloading, utility company implements lots of methods including electric measurement methods for electrical insulation tests [1], Dissolved Gas Analysis (DGA) [1], Oil and paper tests and thermography for chemical and physical tests [1]. While there are a quite a few papers that study the causes of DT failure, very limited research is done on prediction of weather-related distribution transformer failures. One of them [2] analyzes the root causes of failure, overvoltage and overloading, as well as the surge affecting the core and winding failure. The other study [3] shows the main causes (Tree, animal, contamination, nature disaster, and human) according to geographical regions. According to study about DT failure root causes in India, the reasons for failure are overload, lighting surge, moisture, and high voltage [4]. However, it does not deal with weather impact as a principal cause. Such analysis focuses on lightning-induced voltages and correlation between LV surge arresters and grounding resistance. The utility companies need a practical method to predict weather-related failures and implement efficient methods for mitigation. Our paper provides such an approach by using logistic regression to analyze weather-related failures. The main advantage is that it can be used as an input to the replacement decision-making hence alleviating the limits of existing maintenance methods. It separates weather parameters causing failure, and expresses them with numerical values. In addition, it has high accuracy evaluated using objective evaluation metric. The paper is organized as follows: Sect. 2 discusses the problem formulation. Section 3 demonstrates the data source and processing. Section 4 explains prediction model, and Sect. 5 describes evaluation. Section 6 analyzes result, and Sect. 7 contains conclusions.

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2 Problem Formulation Power utility company are aware that there is a correlation between weather and DT failure according to their field experiences. However, it is typically not known which weather parameter is most relevant among different parameters, and such correlation is not quantified. In order to verify the correlation between weather parameters and failure, it is necessary to collect historical weather and DT failure data. Extracting DT failure data is the first step. In our case we are considering data from South Korea. The area where failure occurred the most in South Korea is selected and events are sorted by the dates of failure and areas. The next step is matching the areas of failure and area where weather stations are located. The weather stations are selected at one of the closest locations. The last step is extracting the historical weather data according to dates and area of DT failures. The weather station provides weather data about Lightning, Average Temperature [°F] (AT), Highest Temperature [°F] (HT), Relative Humidity [%] (RH), Maximum Wind Speed [m/s] (MWS), Wind Gust [m/s] (WG), and Precipitation (mm) (PT). The information of DT failure and historical weather data is processed by using logistic regression. The goal of the logistic regression implemented in this study is prediction of future failures. We calculate coefficients of correlation between parameters and failure and apply to the test set next. Through this method, the degree of correlation between parameters of weather data and DT failure is measured and the probability of each failure is calculated.

3 Data Source We studied step down transformers (22.9 KV–220 V) used in the distribution sectors in South Korea (see Table 2). The 237 events comprise the data set and the predictor variables (see Table 1) are used for our study for modeling purpose. We also applied preprocessing steps to extract the useful features and prepare data for prediction algorithm. We collected the data for modeling outage events used for prediction and analysis starting from year 2012 up to year 2018. Before applying the logistic regression, let us go through our adjusted modeling data in simple descriptive statistical measures. The historical outages are extracted for five causes; lighting, tree contact, snow, rain, and dust. The region is Jeollanam-do in South Korea and the size of the region is 4,729 mi2 , the population is 1.9 million and there are 842,668 households. It consists of 22 cities Table 2 Distribution facilities in Jeonllanam-do (unit: 1000) [6] Transformer

Protective devices

Bank

Number

Capacity (kVA)

Breaker

Equipment

COS

104

243

9,252

12

1.4

72

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as shown in Fig. 1, which account for 65% of the entire land area. The Jeollanam-do area ranks first in the number of DTs in Korea as shown Fig. 3. The area has more countryside and seaside than other states, therefore it is more vulnerable to weather impacts (Fig. 2). From 1/1/2011 to 11/2/2018 the number of total outages is 1,025 and failures caused by weather account for 237, which constitutes 24%. The causes of all outages include lightning, three contact, snow, aging, overload, bird contact, people fault, installation fault, manufacture fault, corrosion, fire, etc. The data for the logistic regression is extracted from outages caused by weather; lighting, rain, snow, dust. Aging and overload are related to temperature; however,

Fig. 1 Jeollanam-do area [5]

Fig. 2 The comparison of the number of DT in Korea [6]

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Fig. 3 Distribution facilities in Korea [6]

Table 3 Parameters of weather data

Lightning [0/1] (LI)

Average temperature [°F] (AT)

Maximum wind speed [m/s] (MWS)

Highest temperature [˚F] (HT)

Relative humidity [%] (RH)

Wind gust [m/s] (WG)

Precipitation [mm] (PT)

those are not direct causes, thus these are excluded. The weather parameters that are taken into account are shown in Table 3. The dates which have outages caused by weather are selected for Y = 1 and the dates which don’t have any outages are presented as Y = 0 and historical weather are extracted.

4 Prediction Model Logistic regression is used for modeling a binary response (i.e., success/fail) in many applications [7, 8]. This model estimates the probability of the response occurring P(X) = Pr (Y = 1|X) through a linear function of explanatory variables X. In this study, it is natural that the response variable Y is a DT failure, i.e., 1 (failure) and 0 (no failure), and weather predictors like LT, AT, HT, RH, MWS, WG, PT are available for modeling logistic regression. Specifically, X is n × (p + 1) design matrix where n is the number of observations and p is the number of weather predictors. Naturally, the number of coefficients is eight by seven predictors and an intercept. The corresponding coefficients β of predictors designate the effect of the weather predictors on the probability of DT failure. The basic intuition behind using maximum

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likelihood to fit a logistic regression model is as follows: we seek estimates such that the predicted probability of failure for each individual DT is most likely to agree with its observed failure. This intuition can be formalized using the mathematical Eqs. (1), (2), and (3) as follows. T  β = β0 , . . . , β7 (β) =



p(xi )



(1 − p(xi  )

(1) (2)

i  :yi 

i:yi =1 

β = max (β) β

(3)

Once the coefficients in Eq. (3) have been estimated, the probability of failure is given by ex β 1 + exT β T

p(x) =

(4)

The accumulated impact of historical events can be taken into account by generating temporal embeddings that summarize the impact of each parameter over time. Both weather and operation related parameters can be embedded this way. For example accumulated impact of past lightning strikes can be combined into a set of parameters that summarize the number and intensity of past lightning strikes, for an area of a certain radius (such as 100 m, 500 m, 1 km, 10 km, etc.) around the transformer location. As another example, the number of historical transformer failures over a certain period of time can also be embedded as an additional parameter.

5 Evaluation A. Evaluation Metric and Effect of Predictors To evaluate logistic regression, Receiver Operating Characteristics (ROC) [9] graphs are useful for organizing classifiers and visualizing their performance. The Area Under Curve (AUC) [10] is used, and the estimated coefficients quantify the effect of weather on the probability of failure. AUC is the most popular metric for visualizing the performance and analyzing the coefficient serves as intuitive interpretation of the effects of predictors. To distinguish between the actual class and the predicted class, we use the labels Y, N for the class predictions produced by a model as shown Fig. 4. There are four possible cases. If the prediction is failure when real value is failure, it is true positive (tp), and if the prediction is failure when real value is no failure, it is false negative (fp). On the other hand, if the prediction is no failure when real

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Fig. 4 Confusion matrix and common performance metrics [9]

value is no failure, it is true negative, and if the prediction is no failure when real value is failure, it is false positive. The true positive rate of a classifier is estimated as tp rate ≈

Positive corr ectly classi f ied T otal positives

(5)

The false positive (fp) rate of the classifier is estimated as fp rate ≈

N egatives incorr ectly classi f ied T otal negatives

(6)

A ROC graph depicts relative tradeoffs between true positive and false positives. The ROC curve is a popular graphical method for simultaneously displaying the two types of errors for all possible thresholds. The AUC has an important statistical property. The overall performance of a classifier, which summarizes all possible thresholds, is given by the AUC. An ideal ROC curve will approach the top left corner, so the larger the AUC the better the classifier. Coefficients show how the corresponding predictors have an impact on an outcome by describing the magnitude. Seven weather predictors are showed in X-axis and magnitude of the corresponding coefficient values are represented in Y-axis. It shows which weather parameter has the largest effect on DT failure. B. Experimental setup All DT failures have their own failure number and date, and the failure data spans from 2011 to 2018. The weather data is correlated through the date and location of failure [11]. The historical DT failure data is divided into the testing and training sets. The total number of DT failure is 237, and 90% of the total is selected for the training set. The remaining 10% of the data is used for the testing sets for model estimates. There is total of 148 of no failure cases used. The probability of the occurrence of 385 weather data is represented as a result of logistic regression. When a probability of DT failure is lower than 0.5, we show Y = 0, and when a probability is above 0.5, we assign Y = 1. The degree of high temperature (HT) is classified into three temperature thresholds such as 82.4, 86, and 89.6 °F in order to make interpretation of HT coefficient precise. The basic loading of distribution transformer for a

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normal life expectancy is continuous loading under the operating condition in a constant 30 °C (86 °F) ambient temperature as discussed in [12].

6 Results The results are shown in Table 4. For the case of HT 82.4 °F, 113 cases are predicted as no failure (i.e., Y = 0), and 47 cases show prediction that there will be a failure (i.e., Y = 1). For the case of HT 86 and 89.6 °F, 112 events and 111 cases are predicted as no failure respectively. On the other hand, 190 cases and 183 cases have prediction of failure (see Table 4). The accuracy of prediction is 0.7995 by calculating (113 + 190)/384 = 0.789. In the case of HT 86 and 89.6 °F, the accuracy of prediction = 0.786 ((112 + 190)/384) and 0.766 ((111 + 183)/384) respectfully. For HT 82.4 °F, the accuracy of prediction of probability is the highest. The AUC is 0.796, 0.798 and 0.764 respectively as shown Fig. 5, which means the result can be considered as very good. The AUC of HT 86–89.6 °F have the highest values (see Fig. 5b). HT is divided by three groups (0/1) according to the temperature. We assume that probability of DT failure would increase by HT. Three HTs such as Table 4 Event versus prediction of failure

Event

Failure (Y/N)

Y=0 HT 86 °F or below HT 86–89.6 °F HT 89.6 °F or above

a) HT: 86℉ or below

Fig. 5 ROC for classification

Prediction Y=1

Y=0

113

47

Y=1

35

190

Y=0

112

47

Y=1

36

190

Y=0

111

54

Y=1

37

183

b) HT: 86℉ - 89.6℉

c) HT: 89.6℉ or above

Prediction Model for the Distribution Transformer Failure … Table 5 Coefficient values

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Degree of HT

LI

AT

HT

86 °F or below

1.7455

0.003565

0.21771

86–89.6 °F

1.4329

0.007634

0.30125 0.78165

89.6°F or above

1.3649

0.010839

RH

MWS

PT

0.01176

0.13367

0.005994

0.008571

0.0823

0.01289

0.007447

0.060257

0.01922

86 °F or below, 86–89.6 °F, and 89.6 °F or above are selected. For example, for a certain temperature below 86 °F, the probability is 0 and if the temperature is above 86 °F, the value is 1. The positive coefficient of the predictor indicates that the predictor increases the probability of DT failure, while the negative coefficient makes the probability of DT failure decrease. That is, predictor with the positive coefficient is the most relevant contributor to the failure, and predictor with the negative coefficient is the least relevant contributor to the failure. The positive coefficient is likely to have an effect on failure, and on the other hand, negative coefficient is less likely to have an influence on failure. The coefficients for DT failure shown in Table 5 and Fig. 6, which are LI, AT, HT, RH, MWS and PT have all positive values. Lightning is the most influential coefficient, since it is the biggest one and HT is the second. We realize that lightning and higher temperature, especially HT 89.6 °F or above have the biggest effect on DT failure as shown Fig. 6c). For the coefficient value of HT, there is no huge differences between 86 and 89.6 °F from 0.21771 to 0.30125 in Table 5. However, the value increases in 89.6 °F or above as 0.78165. The average Temperature (AT) has low relationship; however, it is positive. Therefore, in case AT is positive, HT coefficient turns into the important factor, which is in turn associated with higher probability of DT failure. On the other hand, RH, NWS, and PT have a low positive correlation.

a)

HT: 86℉ or below

Fig. 6 Coefficients value estimate

b) HT: 86℉ - 89.6℉

c)

HT: 89.6℉ or above

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7 Conclusion The paper describes a logistic regression prediction model of distribution transformers failure by using correlation of weather parameters. The main contribution of our study are as follows: The variety of weather predictors causing DT failure has been identified including Lightning, Average Temperature [°F], Highest Temperature [F], Relative Humidity [%], Maximum Wind Speed [m/s], Wind Gust [m/s], and Precipitation (mm). • The logistic regression model has been used to calculate the probability of DT failure caused by weather. • The prediction model shows high-level accuracy, where the average AUC is 0.78. • The coefficient values estimate show that the weather predictors have positive value indicating the Lightning and HT being the most important factor which affect the DT failure. HT has more effect on failure when it reaches high temperature such as 89.6 °F or above. • The approach is a promising step to predicting not only DT failure but also other outages of power network. Acknowledgements This work has been funded by Nationals Science Foundation under the project titled “BD Spokes: SPOKE: SOUTH: Collaborative: Smart Grids Big Data”.

References 1. Rajotte C et al (2011) Guide for transformer maintenance. CIGRE 2. Marín OJS et al (2014) Causes of failure of distribution transformers in the East Zone of Caldas 3. Tippachon W et al (2006) Failure analysis of power distribution systems in Thailand. In: 2006 international conference on power system technology. IEEE 4. Pandit N, Chakrasali RL (2017) Distribution transformer failure in India root causes and remedies. In: 2017 international conference on innovative mechanisms for industry applications (ICIMIA). IEEE 5. JeollaNamdo, JeollaNam Provincial Government. http://www.jeonnam.go.kr/contentsView. do?menuId=jeonnam0600000000 6. EPSIS, Korea Electric Power Statistics Information System. https://epsis.kpx.or.kr/ 7. Adwere-Boamah J, Hufstedler S (2015) Predicting social trust with binary logistic regression. Res Higher Educ J 27 8. Soule P (2017) Predicting student success: a logistic regression analysis of data from multiple SIU-C courses 9. Fawcett T (2006) An introduction to ROC analysis. Pattern Recogn Lett 27(8):861–874 10. James G, Witten D, Hastie T, Tibshiran R (2013) An introduction to statistical learning 11. Korea Meteorological Administration, KMA. http://www.kma.go.kr/eng/index.jsp 12. B˙içen Y et al (2011) An assessment on aging model of IEEE/IEC standards for natural and mineral oil-immersed transformer. In: 2011 IEEE international conference on dielectric liquids. IEEE

On Site Measurement and Simulation of Transferred Lightning Overvoltages Through Power Transformers Bruno Juriši´c, Tomislav Župan, Goran Pliši´c, Božidar Filipovi´c-Grˇci´c, Goran Levaˇci´c, and Alain Xemard

Abstract High voltage electrical devices such as power transformers are often stressed by the overvoltages that occur during switching operation and atmospheric discharges. Consequently, it is of particular interest to monitor these events in the power network. Nowadays, power transformers can be equipped with transient recorders that measure the voltages at the bushing measurement taps. It is possible to simulate events captured by these recorders, in EMTP. In this process, the crucial element that has to be modelled properly is the power transformer. In this paper, three wideband transformer models are presented: black-box, grey-box and white-box. These models are validated using the transmitted overvoltage measurements at high voltage laboratory. Then, the results of the simulation of the transient event recorded in 220/110 kV substation is presented and compared to the on site measurements results. Keywords Transient recorder · On site measurements · Wideband transformer model · Lightning · EMTP

B. Juriši´c (B) · T. Župan Konˇcar–Electrical Engineering Institute, Inc., Zagreb, Croatia e-mail: [email protected] G. Pliši´c Konˇcar Power Transformers Ltd., Zagreb, Croatia B. Filipovi´c-Grˇci´c Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia G. Levaˇci´c HOPS Croatian Transmission System Operator Ltd., Zagreb, Croatia A. Xemard Electricite de France R&D, Saclay, France © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_13

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1 Introduction In electric power systems, pieces of equipment such as power transformers are often stressed by overvoltages that contain significant amount of energy at the frequencies higher than nominal. Power transformers are usually protected against these overvoltages by surge arresters. However, surge arresters are not always effective in the case of overvoltages that contain high frequencies, resonant overvoltages or multiple overvoltage stresses over period of time [1]. Slow front, fast and very fast overvoltages are most of the time caused by switching operations and/or atmospheric discharges. They are the source of traveling electromagnetic waves that can be monitored on line at the voltage taps of the transformer bushings, using a transient recorder which is part of a commercially available transformer monitoring system (TMS) [2, 3]. To simulate these phenomena in an electromagnetic transient program (such as EMTP), it is necessary to have a proper wide-band transformer model [4–9]. In the scope of this paper, electromagnetic transients due to atmospheric discharges are measured at the primary and secondary side of a real power transformer installed in a substation. These transients are classified as fast front overvoltages and can be numerically simulated with different wide-band transformer models. Three different wideband transformer models are described in the paper: detailed whitebox transformer model, simpler grey-box model, that does not reveal design data which is an industrial secret and black-box model which is constructed only from the measurements without knowing the transformer geometry. The models are validated with transferred overvoltage measurements conducted in a high voltage laboratory. In addition to the model validation a comparison between simulation results and on site real lightning transient measurements recorded using the TMS equipped with transient recorder are shown. The simulations are done in EMTP software. A recent CIGRÉ workgroup (JWG A2/C4.52) is dealing with non-standard waveforms and high-frequency transformer and reactor models with the goal of adequately representing the transformer under such transient overvoltages [10, 11] has been set up recently. The results presented in this paper give a unique insight into the applicability of wideband transformer models by comparing its results with sheer lightning overvoltage transients that were measured on site using a transient recorder and correlated with a Lightning Location System (LLS) system. It is important to note that these wide-band transformer models can be used in a large variety of power systems studies, as they are also valid for power frequency and harmonics simulations. This is important, especially with the introduction of renewable energy sources which are significant sources of high-range harmonics in power network [12]. Furthermore, it is important to continuously monitor these power network transients due to possible component’s insulation degradation as a result of successive voltage stresses. This is one goal of successful transformer asset management. In Sect. 2 of the paper the wideband transformer models are presented: black-box, grey-box and white-box models. Then, in Sect. 3, the system for on site monitoring of transient overvoltages across the transformer’s bushing is described. In Sect. 4,

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the model validation with the transferred overvoltages measured at high voltage laboratory is presented first, following with the real test case that compares detailed simulation results versus transient measurements using the TMS on site. Finally, a conclusion of this work is given.

2 Wideband Transformer Modelling In this section, three different wideband transformer models are described. The first, black-box model, is a model based on the measurements results, conducted at the outside transformer terminals. Such measurements can be conducted for any existing transformer in the power network. This model is often used among power utilities as it does not require any knowledge about the transformer’s inner design. The main drawback of the black-box modelling is that it cannot be used to calculate the overvoltages that occur inside the transformer. Then the grey-box model is presented. This model is used by power utilities as it requires the limited amount of transformer design data, which is usually available to the transformer buyer company. Using this approach, it is possible to calculate the overvoltages that occur inside the transformer. Finally, the white-box model is presented. This model is used inside the power transformer factory to calculate the overvoltage stress that occurs during the factory acceptance test. It requires the detailed transformer geometry and knowledge of material parameters/properties. White-box models are not often used in power system studies to simulate the transferred overvoltages. A. Black-box models Transformer models that can be classified as black-box models are usually based on the fitting of the measured frequency dependent admittance matrix of the transformer and can be determined without any prior knowledge on the transformer geometry. Therefore, they can only be applicable to evaluate external overvoltages, in order to analyse the interactions between a transformer and the network and to study the insulation coordination [8, 13–22]. For the purpose of this paper, a black-box model is calculated from the measurements conducted with the SFRA measuring equipment. This is a standard equipment for measuring the frequency response of a transformer as suggested in the IEC 6007618 Standard [23]. The measurement procedure is similar to the one described in [8]. A frequency response analyzer is capable of measuring the ratio (H) between the input (V in ) and the output (V out ) voltages: H( f ) =

Vout ( f ) Vin ( f )

(1)

In (1) f stands for the frequency. Note that the measurements are done at discrete frequency points. Since the SFRA measurement’s equipment is not normally used for

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measuring Y matrix, a specific procedure for measuring is established. The measuring method stems from the following expression: ⎛

I1 ( f ) I2 ( f ) .. .

⎞

⎛

⎜ ⎟ Y11 ( f ) · · · ⎜ ⎟ ⎜ ⎟ ⎜ .. .. ⎜ ⎟ =⎝ . . ⎜ ⎟ ⎝ I N −1 ( f ) ⎠ YN 1( f ) · · · IN ( f )

⎞ ⎛ U1 ( f ) ⎞ ⎟ Y1N ( f ) ⎜ ⎜ U2 ( f ) ⎟ ⎟ ⎟⎜ .. .. ⎟ ⎠⎜ . . ⎟ ⎜ Y N N ( f ) ⎝ U N −1 ( f ) ⎠

(2)

UN ( f )

Expression (2) is valid for a core-type transformer with N terminals. The measuring procedure includes N*(N + 1)/2 measurements as it is shown in [13, 14]. Note that the measuring methods differ for off-diagonal and diagonal matrix elements. As a results of the measurements one can calculate the transformer frequency dependent admittance matrix, Y(f). B. Grey-box models Transformer models that can be classified as grey-box models are usually derived from limited information about the transformer geometry. In this section the concept of the grey-box model presented in [4] is explained. It is based on a lumped RLCG equivalent network and a segmentation of the transformer geometry. Similar models can be found in [24–26]. In this model the parameter values are calculated from the transformer geometry and properties of the materials. Each RLCG element represents a physical part (segment) of the transformer’s winding. See Fig. 1 for the example of a RLCG network which represents Fig. 1 RLCG network for one phase of a two winding transformer

Ghg/2

Glg/2 Glv,hv/2 Clg/2 + Rlv

Clv,hv/2 +

Chg/2 + Rhv

Rlv,hv Llv,hv

Clv Llv + Clg/2 Glg/2

Glv,hv/2 Clv,hv/2 +

Chv Lhv + Chg/2 Ghg/2

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one phase of a two windings transformer represented with only one segment per winding. From Fig. 1, it can be seen that the transformer is represented with the inductances, resistances and capacitances of the windings itself, the mutual inductance and resistance (related to proximity effect), capacitance and conductance between the windings and the capacitances and conductance to the ground of each winding. The model is valid for wideband frequency range with the upper frequency boundary that depends on the length of the geometry segmentation element. The model assumes that the capacitance parameters are constant while the resistance, inductance and conductance values vary versus frequency, which is correct for most power system transient studies. Therefore, to calculate the model’s parameters, two problems have to be solved: a magnetic one and an electrostatic one. The most efficient way to solve these problems is to build a model in an electromagnetic field software program (i.e. a software program which includes a Finite Element Method (FEM) solver for quasi-static problems such as FEMM [27]). Another possibility would be to use analytical expressions. However, it is not always possible to derive analytical expressions for complex structures such as the transformer’s windings, especially when it comes to the calculation of resistances inside a transformer at high frequencies. This is due to the calculation of the eddy currents effects: skin and proximity effects. To calculate the R and L parameters of the transformer in a reasonable time, a method to approximate eddy currents by substituting the conductive material for a non-conductive hysteretic material described with a complex permeability is implemented. In that way the quasimagnetostatic FEM formulation of a problem can be implemented and solved more efficiently [27–30], which makes the calculation time compatible with the one of an engineering study. By setting the material’s conductivity to zero, the conductors can be observed macroscopically since it is not necessary to calculate eddy currents locally. The physical explanation of the complex permeability behaviour in the conductive material is that the real part of the permeability represents the ability of the conductive material to conduct the magnetic flux while the imaginary part of the permeability represents the losses generated by the eddy currents circulating in the material. Note that only eddy currents due to the proximity effect are taken into account since the only magnetic field that is taken into consideration is the external one [4]. The contribution due to the skin depth has to be added afterwards using analytical formulas [4]. To calculate the C and G parameters of a transformer, the electrostatic problem has to be solved with a FEM software program. For the model, two different types of capacitances (capacitances of the segments to the ground, capacitances between the segments) and conductances are calculated (conductance of the segments to the ground and conductance between two segments). Contrary to the capacitances, the conductances are considered as frequency dependent. Nevertheless, their values can be derived from the values of the capacitances by using the linear approximation of Buckow’s experimental results [31] already used for transformer modelling in [4, 24, 32].

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In order to use the model in a power system studies, when all the RLCG parameters of the model are calculated, it is necessary to compute its frequency dependent admittance matrix. By doing that, one obtains the same matrix as the one in the black-box model. Therefore, the interaction between the model and EMTP software is similar, as explained further in this section. C. White-box model Detailed physical or white-box models are used for calculating the voltage distribution across the transformer windings during standard impulse testing conducted during the factory acceptance tests [1]. Consequently, these models have to be detailed and advanced since overvoltages of very high frequencies (few MHz) can occur inside the transformer windings, caused by the reflections between the parts of the transformer’s windings or resonances inside the transformer. White-box models have been used for several decades, among transformer manufacturing companies, as it can be seen from an overview on transformer design [33]. The parameters of these models are determined from the detailed transformer geometry which is usually the property of the transformer manufacturer and it is not common for power utilities to have access to such data. The parameters are calculated by using analytical expressions or numerical methods, such as the finite element method [24, 34, 35]. The accuracy of these calculations has a direct influence on the accuracy of the model. In some cases, an analytical approach is chosen instead of a numerical approach because it is a good trade-off between calculation time and accuracy. Many transformer manufacturers have their own coefficients, based on experience, to adjust the values of the dumping inside the model. For the purpose of this paper a white-box model based on lumped RLC parameters, calculated using combined analytical expressions and FEM is provided by the transformer manufacturer. Parameters of the model are calculated at a single frequency and are not frequency dependent. Therefore, the interaction with EMTP software is straightforward and does not include as fitting procedure. Since the model is used through RLC matrices export directly in EMTP, the parameters representing damping are somewhat simplified due to the size of the model in EMTP. Finally, this will influence the results and one can expect waveshapes that are slightly less damped than they should be. D. Integration of a frequency dependent transformer model in EMTP To include the frequency dependent nodal admittance matrix of the wideband transformer model, Y(f) in the EMTP software program, the procedure shown in Fig. 2 is used. It consists of fitting the admittance matrix coefficients using the rational approximation and enforcing the passivity of the model. Such approach is widely used when it comes to representing multiple-input, multiple-output systems (MIMO) such as power transformers [36–40]. The fitting of the admittance matrix element Y ij (f) is done using a rational expression [7, 20, 41] of the type given below:

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TRANSFORMER’S ADMITTANCE MATRIX derived from: -SFRA measurements -FEM calculations Ynodal (f) or Y(f)

RATIONAL APPROXIMATION of the matrix parameters of Ynodal (f) or Y(f)

-stable and passive functions STATE SPACE REPRESENTATION

A, B, C, D matrices EMTP-RV STATE SPACE BLOCK Fig. 2 Procedure for inputting transformer models with frequency dependent parameters in EMTP

Yi j (s) ≈ Yi j, f it (s) =

Np  n=1

cn,i j + di j s − an,i j

(3)

In (3) an, ij represents the poles which can be either a real or complex conjugated pair, cn, ij represents the residues which can also be either a real or complex conjugated pair, d ij is a real value constant. s stands for j2π f where f is the frequency. Np is the number of poles used for approximating each matrix element. Prior to rational approximation, the frequency dependent admittance matrix Y(f) or Y nodal (f) should be rewritten to form a function of variable s, Y(s) instead of f . The rational functions have to be both stable and passive since the transformer is a passive component of the power network. The stability is ensured by keeping only the poles which are stable. The passivity is enforced by the perturbation of the residues and the constant values in order to match the passivity criterion [20, 38, 42–47]:

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P = Re u∗ Yfit (s)u > 0

(4)

The rational expression (3) enables the use of the state space equations. The matrices A, B, C, and D for the state space representation can be input directly into the state space block in EMTP. These matrices are obtained by using the values of the poles and the residues from the rational functions (3) to form the function given below:  C∗B + D ∗ U(s) (5) I(s) = Y(s) ∗ U(s) = (s[I] − A) Expression (5) represents the relationship between the terminal currents and the voltages of the transformer. The state space representation is used to describe a linear network. Therefore, it can be used to represent a transformer, since it is a linear system at high frequencies. The main advantage of using these equations is that they can be used both in the frequency and the time domain. For the frequency dependent grey-box and black-box models, a toolbox developed by EDF R&D and compatible with EMTP [48] is used. This toolbox is based on research conducted by EDF R&D, the Faculty of Electrical Engineering and Computing of Zagreb and the University of Clermont-Ferrand [4].

3 Transient Monitoring System In this section, a transient monitoring system that can be installed at a bushing of a power transformer or shunt reactor is presented first. Following, an example of recorded lightning overvoltages is given with the procedure to extract the transient overvoltages from the total recorded event. A. Method for overvoltage measurements at transformer bushings Overvoltages, as well as voltages, can be measured on a measuring tap of the corresponding transformer bushing using TMS. The connection with the measuring tap shown in Fig. 3a is accomplished with a specially designed adaptor while the link between the adaptor and the impedance matching circuit is carried out with a coaxial cable. The inbuilt acquisition card is fast enough to capture data with a time resolution of 0.5 μs, which is enough for transients containing frequency components lower than 1 MHz. The number of points recorded per event is 60000 which leads to a total recording time of 30 ms per event (the equipment starts recording 0.3 ms before the trigger). While overvoltages are acquired occasionally, voltages need to be measured continuously in order to detect changes of bushing capacitance (C, tan δ). It is important to note that the capacitance divider used for the measurements does not change the shape of the measured signal (the calibration range of frequencies

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(a)

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(b)

Fig. 3 a Connection to measuring tap; b Transient overvoltage monitoring system installed on 100 MVAr shunt reactor [2, 3]

extends up to 500 kHz [49]) which allows monitoring of fast front and slow front overvoltages [50]. In Croatia, the TMS system with transient monitoring is currently installed in eight power transformer units and one shunt-reactor located in four 220/110 kV substations, one 400/110 and one 400/220/110 kV substation. B. Transformer monitoring data analysis For the purpose of this paper the overvoltages that occurred due to the atmospheric discharges at the terminals of a 150 MVA 220/110 kV Yna0d5 autotransformer unit are observed, see Fig. 4. Overvoltages are measured both at 220 and 110 kV sides of the autotransformer. It is possible to extract the transient impulse signal from the recorded data, if one is only interested in transient phenomena without taking into account the 50 Hz voltage. The impulse signal is extracted from the original recorded signal using the high pass FIR filter. After the filter application a correction has to be applied on the extracted data in order for the transient to start from 0 V. The extracted impulse, corresponding to the example shown previously, is given in Fig. 5.

4 Application: Comparison Between in Situ Lightning Overvoltage Measurements and Emtp Simulations The final goal of this section is to compare lightning overvoltages, which have been measured in a substation using the equipment presented in the previous paragraph with the simulation results involving the transformer models of Sect. 2.

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Fig. 4 Atmospheric overvoltages recorded using the transformer monitoring system

Fig. 5 Extracted impulse signal from a recorded atmospheric overvoltage

At first, the transformer models are validated using the low voltage measurements of transferred overvoltages conducted at high voltage laboratory. Then a comparison between EMTP simulation results and on site measurements of atmospheric overvoltage transferred through a real 150 MVA 220/110 kV Yna0d5 autotransformer

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unit is presented. Overvoltages are measured on site using the transient recorder unit installed. A. Lightning transferred overvoltages measurements in HV laboratory The test set-up for validating the presented wideband models consists of a 150 MVA 220/110 kV Yna0d5 autotransformer unit, a recurrent surge generator, an oscilloscope and a connection box which allows different low voltage elements such as resistors to be connected to the transformer terminals. In the scope of this paper, the model validation for lightning impulses is presented only for a configuration similar to the one in the power network: all HV and LV winding terminals were connected to 390  resistances while the tertiary winding terminals were connected to 50  resistances, the neutral was solidly grounded. Lightning impulse is generated with a recurrent surge generator, Haefelly type 481, 400 Vpp. The amplitude of the applied signal was around 300 V. The measurement set-up is shown in Fig. 6. Overvoltages were measured at HV and MV transformer terminals as the number of measurements channels was limited. Test set-up was simulated in EMTP for all three transformer models. The comparison between measured and simulated results are shown in Fig. 7. From the results given above, it can be concluded that all three presented transformer wideband models can calculate the overvoltages which are transferred from the HV to the MV side of the transformer in this specific configuration accurately enough. Black-box model is the most accurate one as its main purpose is to simulate transferred overvoltages and it relies on measurements while the other two models are more complex as they represent the interactions inside the transformer; their main

50 Ω 390 Ω

390 Ω

390 Ω

+

390 Ω

N

390 Ω

2U 2V 2W

1U 1V 1W -

50 Ω

50 Ω

3U 3V 3W

Fig. 6 Set-up for measurements of transferred overvoltages in the specific configuration

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Fig. 7 Comparison of simulated and measured results of transferred overvoltages measurements in high voltage laboratory. The results are shown for a black-box, b grey-box and c white-box model

(a)

(b)

(c)

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advantage is that they can be used for a wider area of application than the black-box model. B. Transferred atmospheric overvoltages measured in a real network, when the transformer is operational The transients shown in Figs. 4 and 5 were observed in a 220/110 kV substation at the terminals of a 150 MVA 220/110 kV Yna0d5 autotransformer unit. Due to the rise time of the recorded transient it can be concluded that it arrives to the substation from the 220 kV side. Therefore, to model this event properly in EMTP, it is necessary to represent correctly the 110 kV side of the substation, as well as to include the wideband transformer models into the simulation. In the substation, three autotransformer units operate in parallel. Each unit has been modelled in EMTP using the black-box wideband transformer model based on the similar 150 MVA autotransformer. 7 different overhead lines connected to the 110 kV busbars are simulated using the constant parameter line model. Line lengths are ranging from 7 up to 43 km. Due to the lack of data, surge impedance, Zs for the line models is chosen to be 400 , while the realistic resistances and line lengths data was used. Each line is terminated with the 3.4 nF capacitance representing the capacitance of the neighboring substation. Corona model from standard EMTP library was used to limit the overvoltages while propagating through the overhead lines. Voltage and current measurement transformers were modelled using the capacitance to the ground (400 pF and 750 pf respectively) in each overhead line bay as well as in the autotransformers bay. Surge arrestors are not taken into account in the model as the observed overvoltage level is below the rated voltage of arrestor. The tap position of the transformer at the time of the recorded event is not known and the grounding system of the substation was not modelled. Simulated 110 kV side of the network in EMTP is shown in Fig. 8. Measured voltage impulses were applied to the 220 kV side of the transformers and the voltages at the 110 kV side of the transformer were observed. From the results shown in Figs. 9 and 10, it can be concluded that the recorded overvoltages have been successfully simulated with a high degree of the accuracy taking into account the complexity of the models, both of the autotransformer and the substation. The models are accurate at low frequency as well, which can be seen from the correct 50 Hz voltage ratio in Fig. 9. However, when comparing Figs. 4 and 9, it can be seen that the model is lacking some damping.

5 Conclusions Overvoltages that occur in a power system due to the switching operations or atmospheric discharges can be measured accurately. Nowadays, TMS systems are equipped with transient recorders that can capture these events. In the paper, a test

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Fig. 8 110 kV part of the substation and the connected overhead lines, modelled in EMTP

bed for simulating lightning overvoltages is presented and its results are compared to real on site measurements. To simulate such high-frequency events in EMTP, wideband transformer models are required. In the paper, three different models are presented: black-box, greybox and white-box. Before being used to simulate the transmission of lightning overvoltages from their primary to their secondary side, these models are validated using low voltage measurements results of transferred overvoltages, conducted in a high voltage laboratory. An important aspect regarding wideband transformer models is that each model has to be validated for each transformer unit as these models are quite complex and it is not always easy to get the correct model. In the case shown in the paper, due to its very design, the black-box model showed as the most accurate one and for this reason it was used further in the detailed simulation of the real event on site presented in the paper. The 110 kV side of the substation is modelled as well as the 150 MVA 220/110 kV Yna0d5 autotransformer unit in EMTP to simulate the transient event that arrives from the 220 kV side of the autotransformer. The simulation results show a good agreement with on site measurements.

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Fig. 9 Simulated results of the observed overvoltage together with 50 Hz that occurs on terminals of the autotransformer in 220/110 kV substation

Fig. 10 Comparison between simulated and on site measured overvoltage

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The presented test case is a good starting point to monitor transient events in power networks and to check the models for transient studies. A further work would be to identify the exact lightning that caused the overvoltages and to analyze the propagation of the overvoltages along the line to the substation and through the transformer. Acknowledgements The authors express their thanks to Konˇcar Power Transformers Ltd. for providing the measurement results and data which were used for the development and validation of the models presented in this paper.

References 1. CIGRE WG A2/C4.39 (2013) Electrical transient interaction between transformers and the power systems 2. Filipovi´c-Grˇci´c B et al (2017) Monitoring of transient overvoltages on the power transformers and shunt reactors–Field experience in the Croatian power transmission system. Procedia Eng 202:29–42 3. Keitoue S, Murat I, Filipovi´c-Grˇci´c B, Župan A, Damjanovi´c I, Pavi´c I (2018) Lightning caused overvoltages on power transformers recorded by on-line transient overvoltage monitoring system. In: 2nd South East European regional CIGRE conference 4. Jurisic B (2016) Methods for calculations of high frequency transmitted overvoltages through a power transformer, Ph.D. dissertation. University of Zagreb, University Blaise Pascal 5. Juriši´c B, Poujade P, Xemard A, Uglesic I, Paladian F (2017) Calculation of internal overvoltages using a wide band transformer model based on limited information about transformer design. In: 4th international colloquium “Transformer research and asset management” vol 0, pp 1–9 6. Jurisic B, Uglesic I, Xemard A, Paladian F (2016) Difficulties in high frequency transformer modeling. Electron Power Syst Res 138 7. Gustavsen B (2004) Wide band modeling of power transformers. IEEE Trans Power Deliv 19(1):414–422 8. Holdyk A, Gustavsen B, Arana I, Holboell J, Member S (2014) Wideband modeling of power transformers using commercial sFRA equipment. IEEE Trans Power Deliv 29(3):1–8 9. Plisic G, Capuder K (2014) Influence of winding capacitances to ground modelling on the calculation of transferred voltages in power transformer. In: 3rd international colloquium transformer research and asset management 10. JWG and A2/C4.52, High-frequency transformer and reactor models for network studies 11. Gustavsen B, Portillo A, Høidalen HK (2018) Modelling of transformers and reactors for electromagnetic transient studies. In: CIGRE 2018 12. Levaˇci´c G, Ugleši´c I, Juriši´c B, Filipovi´c-Grˇci´c B (1848) Influence of cables on power transmission network frequency response. Teh Vjesn-Tech Gaz 26, 8 13. Jurisic B, Uglesic I, Xemard A, Paladian F (2016) Difficulties in high frequency transformer modelling. Electron Power Syst Res 138, Special Issue: 11th international conference on power systems transients (IPST), pp. 25–32 14. Jurisic B, Xemard A, Ugleši´c I, Paladian F, Guuinic P (2014) Case study on transformer models for calculation of high frequency transmitted overvoltages. In: 3rd international colloquium transformer research and asset management, pp 1–10 15. Jurisic B, Xemard A, Uglesic I, Paladian F (2014) High frequency transformer model for calculations of transferred overvoltages. CIGRE Int Colloq Light Power Syst pp 1–15

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Calculation of Circuit Parameters of High Frequency Models for Power Transformers Using FEM Álvaro Portillo, Luiz Fernando de Oliveira, and Federico Portillo

Abstract To study the transient interaction between the transformers and the power system is essential use very accurate transformer models considering the dependence of damping with frequency. In this work the fundamentals of transformer parameters calculation for high frequency transients using finite elements method (FEM) are reviewed and a promissory time-domain equivalent circuit is proposed based in the analysis of transient measurements results obtained by the CIGRE JWG A2/C4.52 in two transformers manufactured by WEG in Mexico. Keywords Transformer white-box models · Parameter calculation · Damping in function of frequency · FEM

1 Introduction Transient overvoltages in the power system are one of the root causes of transformer dielectric failures [1]. Such failures can occur even when the transformer was designed to meet the lightning and switching impulse tests and protected by surge arresters. One of the reasons for such failure is that the transformer is exposed to overvoltages with different shapes than found in the lightning and switching impulse tests, e.g. steeper wave fronts and oscillating waveforms. The standard lightning impulse voltage waves used in transformer factory testing does not properly cover all the overvoltage stresses that a transformer can experience while in service. CIGRE formed in 2008 Working Group JWG A2/C4.39 [2, 3] (“Electrical transient interaction between transformers and the power system”) with the objective to clarify the underlying reason for such failures and if possible, recommend procedures for avoiding their occurrence. One of the major conclusions from that work is the Á. Portillo (B) · F. Portillo Transformer Consultant, Brenda 5920, 11400 Montevideo, Uruguay e-mail: [email protected] L. F. de Oliveira WEG – Power Transformers, Blumenau, Brazil © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_14

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observation that oscillating overvoltages of relatively low amplitudes that impinge the transformer terminals, with frequencies close to the natural frequencies of the transformer, can result in excessive overvoltages inside the transformer’s windings by resonance as has also been documented in several past studies [4–12]. The maximum value of the resonance voltages is highly dependent of the damping effect of the core’s and winding’s losses, that are strongly frequency dependent, and therefore, for the determination of the internal transformer voltages during such resonant transients is essential count with transformer models which can represent the frequency dependence of transformer impedances in the range of frequencies involved in the transient. The assessment of internal winding dielectric stresses is in the case of power transformers routinely performed by the manufacturers using in-house calculation programs called white-box models. The white-box models can be categorized as lumped parameters circuit models based on a spatial discretization of the windings, or distributed parameters models based on traveling wave-type approaches. The extraction of the model’s parameters is in all cases based on a detailed description of the transformer’s geometry and materials properties. From this information, the model’s parameters are extracted via formulae and/or finite element method (FEM) computations. Frequency-dependent damping can be obtained using empirical damping factors which are embedded directly in the applied state-space model [13, 14] or with more sophisticated models using equivalent circuits that are capable to model with high precision the damping effects consequence of core losses [15] and proximity and skin losses in winding conductors [16, 17]. All the various modelling approaches have their advantages and disadvantageous regarding accuracy and computational effort. CIGRE JWG A2/C4.52 has in 2016 performed an extensive measurement campaign on a single-phase and a three-phase transformer, manufactured by WEG in Mexico, in order to assess/improve the accuracy of currently applied whitebox models, and to provide input for black-box and grey-box modelling [18]. The measurements involve frequency domain and time domain measurements at the transformer external terminals and at some internal points [19]. To evaluate the accuracy of the existing white-box models the complete design of both transformers measured in México was distributed between the members of the working group that have software able to calculate the internal voltage distribution when applying transient voltages on some of the transformer external terminals. Comparison with measurements shows that the white-box models need improvements for use in system studies which includes oscillating overvoltages on the terminals. In the time domain the results demonstrate a quite good agreement in the prediction of the maximum voltages values that appears in the measured points inside the transformers but a poor agreement in the temporal wave shapes which are dependent on the natural (resonance) frequencies of the transformer. Was also calculated, the admittance matrix in the frequency domain for both transformers, to compare with the admittance matrices measured in the frequency domain in the transformers in México, and the calculated results looks very much better.

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The comparatives shown the importance of take into account in the model the damping variation with frequency to improve the calculated results and the most promissory calculation approach is lumped parameters models [20, 21] based in calculate the transformer impedances using frequency scan with finite elements [22] using the principle of the complex permittivity [23, 24] followed by vector fitting [25–27] and finally synthesis in the time domain of an equivalent constant parameters circuit using magnetic coupled circuits [16] or first order series Foster circuits [17] for each branch of the transformer. We will present the fundamentals of this calculation approach in this paper. It is hoped that this paper can provide a basic information level to the reader already familiar with the subject, so that it is possible for him to analyse in an objective way the quality and accuracy of high-frequency transformer and shunt reactor models for transient studies. The evaluation of such capability is of fundamental importance during the design review process of power transformers and shunt reactors.

2 Calculation Procedure The proposed calculation method consists of the following steps: Step 1: A lumped parameter circuit model will be used, then the transformer windings are divided in n elements or branches. For example, for a disc winding each branch can be a group of discs, a pair of disks, a disk or a turn. The more branches are used to represent the windings in the transformer’s model, better it will be able to represent higher frequency transients accurately. Each branch has two nodes and the nodes belonging to each winding will be connected according to the winding design (continuous disc, interleaved, disc, multi-start winding, etc.). The total number of nodes of the transformer will be q. Step 2: A certain number of logarithmically spaced frequencies f k (k = 1, . . . , p) with p in the order of 14 to 20 are selected in the range of 50 Hz to 1 MHz: 1

f k+1 = f k × 10 nd

(1)

where n d is the number of frequency samples per decade. Example: with n d = 3 and f 1 = 50 Hz we obtain p = 14 frequencies between 50 Hz and 1077.2 kHz and with n d = 4 and f 1 = 10 Hz we obtain p = 17 frequencies between 10 Hz and 1 MHz. Step 3: For each frequency an equivalent anisotropic complex permeability is calculated for each transformer winding strand (strand by strand, not turn by turn, for example each turn of a winding can be a CTC with many strands) according to Moreau equations [23] in function of strand dimensions and frequency. Step 4: Sometimes a homogenization process is applied to reduce the size of the model. Based in the complex permeability of each strand, the geometry of the branch containing the stand and the insulation between strands, an equivalent

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complex permeability is obtained for each branch (group of strands to form a turn and group of turns to form a branch, for example in a disc winding a pair of discs). Step 5: The matrix of inductive transformer impedances (dimension n × n): Z i j ( f k ) = Ri j ( f k ) + j2π f k L i j ( f k ) i = 1, . . . , n j = 1, . . . , n k = 1, . . . , p (2) is calculated for each frequency f k using FEM [22] solving a 2D-axisymmetric complex magnetostatics problem, modelling each branch with an equivalent material with conductivity equal 0 and anisotropic complex permeability calculated in Step 4. This impedance matrix includes proximity effect but not include the skin effect. Step 6: The skin effect impedances: Z iis ( f k ) = Riis ( f k ) + j2π f k L iis ( f k ) i = 1, . . . , n k = 1, . . . , p

(3)

are calculated for each frequency f k using FEM [22] or Stoll [28] formulas and added to diagonal elements of the matrix of inductive transformer impedances. Step 7: Using vector fitting we obtain for the matrix of inductive transformer impedances Z(s), from the values calculated in Step 5 and 6 for the frequencies f k (k = 1, . . . , p), an expression of the type: Z(s) = D + s E +

r =m r =1

Ck s − ak

(4)

The number of stable real poles m must be select as small as possible but enough to obtain a small rms error in the fitting process (less than 4 × 10−3 ). Normally m results between 4 to 6 depending of the complexity of the transformer. Step 8: A topology for the inductive time domain equivalent circuit of each branch is defined. The two most usual approach are using coupled magnetic circuits [16] or first order series Foster circuits [17]. Step 9: Once the topology of the inductive equivalent circuit has been defined, it is possible to calculate the impedance matrix represented by this circuit based on the resistances and self and mutual inductances of the circuit and put them in a format similar to that of the vector fitting (4): ¯ + sE ¯ + Z(s) = D

r =m r =1

C¯ k s − a¯ k

(5)

By matching these expressions (4) and (5), a system of non-linear equations is obtained that allows determining the parameters of the equivalent circuit. Step 10: The capacitances of the transformer are calculated by FEM in a turn-toturn level. The capacitances are assumed constant with frequency and the dielectric losses normally are disregarded. The capacitive impedance matrix is finally reduced

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from turn-to-turn level to branch-to-branch level according to the defined inductive branches to be compatible with the inductive equivalent circuit. Step 11: The calculated capacitances are included in the inductive time domain equivalent circuit to obtain the complete time domain equivalent circuit of the transformer. Step 12: Finally, the total time domain equivalent circuit of the transformer is solved for the transient under investigation using commercial circuit solvers (as SPICE, EMTP, ATP, etc.).

3 Complex Permeability Principle Standard FEM eddy current calculations are not practical in real transformers at high frequencies because is necessary use very huge meshes with at least two finite elements in the skin depth δ which turn the calculation impossible (skin depth for copper at 1 MHz is 0.066 mm). The skin depth is calculated in (6) in function of the angular frequency ω, permeability μ (μ = μ0 for copper or aluminium) and conductivity σ of the conductor material.  δ=

2 ωμσ

(6)

For the calculation of losses in the conductors due to proximity effects the principle of complex permeability is applied. The approach consists in replace the conductors (strands) with a non-conductive ferromagnetic material described by a complex anisotropic permeability μ¯ x and μ¯ y (elliptical hysteresis loop) calculated in such a way that the complex power (active and reactive) in each conductor remains unchanged. The complex permeability μ¯ x and μ¯ y is calculated in function of frequency and strand dimensions (h and e in Fig. 1) using formulas (7), (8), (9) and (10) from Refs. [23, 24].     μδ sinh hδ + sin hδ     Re(μ¯ x ) = h cosh hδ + cos hδ     μδ sinh hδ − sin hδ     Im(μ¯ x ) = − h cosh hδ + cos hδ       μδ sinh δe + sin δe e   Re μ¯ y = e cosh δ + cos δe       μδ sinh δe − sin δe     Im μ¯ y = − e cosh δe + cos δe

(7)

(8)

(9)

(10)

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Fig. 1 Conductor dimensions and coordinates

y

j

h

z

k

i

x

e

Using the complex permeability principle, the FEM problem is reduced to solve a complex magnetostatics problem that allows a coarse mesh.

4 Homogenization Process Since the branches are normally a group of rectangular conductors with his respective insulation a homogenization process, based on reluctance considerations, is sometimes applied to determinate one equivalent anisotropic permeability μ¯ x and μ¯ y for each winding branch or element to reduce the size of the problem to solve. R1x =

a e e R3x =  R2x = μ0 (h + b)l μ0 bl μ¯ x hl

Rx = R1x +

R2x R3x e+a =  R2x + R3x μ¯ x (h + b)l

μ¯ x =

e+a a μ0

+

h+b b h R2y = R3y = μ0 al μ0 el μ¯ x el   R1y R2y + R3y h+b Ry = =  R1y + R2y + R3y μ¯ y (e + a)l =

h+b μ0 a e+a μ0 a

+ 

b μ0 e

b μ0 e

+

+

h μ¯ y e

h μ¯ y e

(12) (13)

e(h+b) μ¯ x h+μ0 b

R1y =

μ¯ y

(11)



(14)

(15)

(16)

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Fig. 2 Homogenization in x direction

2

1

3

1

2

Fig. 3 Homogenization in y direction

2

1

3

1

2

Based in the geometry of Figs. 2 and 3, where l is the length of the branch under consideration, the equivalent reluctances are calculated in direction x (11), (12) to obtain μ¯ x in (13) and the equivalent reluctances are calculated in direction y (14) (15) to obtain μ¯ y in (16). Then, each branch in the FEM model is replaced by a non-conductive material with anisotropic complex permeability μ¯ x and μ¯ y reducing the size of the model from strand by strand to branch by branch.

5 Modelling of Core Influence Transformer cores in power transformers are built using thin cold rolled grain oriented (CRGO) silicon steel laminations stacking together in such a way that the direction of the magnetic flux produced in the core by the windings coincides with the rolling direction of the magnetic steel. There are three different type of core losses: classic eddy current losses or Foucault losses, hysteresis losses and anomalous loss. The Foucault losses increase in higher frequencies and are relatively easy to calculate and the two latter components are not easy to estimate and are normally disregarded. The laminations are subjected to an alternating magnetic flux density and as consequence appears eddy currents that affects the magnetic field distribution as

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well the effective permeability of the laminations and create Foucault losses in the core. This phenomena affects the inductive transformer impedances and is modelled in FEM using for the core a material with a conductivity σ and an anisotropic complex permeability (μ¯ x x and μ¯ yy ) that can be calculated in function of frequency using formulas (17) and (18) from Ref. [15].   tanh (1 + j) 2δbx

μ¯ x x = k F E μ0 μx x

μ¯ yy = k F E μ0 μ yy

(1 + j) 2δbx   tanh (1 + j) 2δby (1 +

j) 2δby

 δx =  δy =

2 ωσ μ0 μx x

(17)

2 ωσ μ0 μ yy

(18)

where x is the rolling direction, b is the laminations thickness, k F E is the core stacking factor (≈ 0.96), and typical values for σ , μx x and μ yy are: σ = 5 × 106

S μx x μx x = 500μ yy = = 16.7 m 30

The influence of the core is highly dependent of the winding terminals connections during the transient under analysis. In factory acceptance tests the transient voltage is applied to one of the transformer terminals and all the other terminals are grounded. In that case the influence of the core in high frequencies is not important and can be disregarded. In service the situation is completely different, and the transformer terminals are connected to surge arresters and eventually to loads and in this case the influence of the core in transients is of paramount importance in the high-frequency behaviour of the transformer and must be considered in the transformer model. There is a tendency in some utilities to make the impulse test with the winding terminals open, connected to the surge arresters, to try to reproduce in the test conditions most similar as possible to service.

6 Calculation of Transformer Inductive Impedances in Function of Frequency Since the elements of the inductive impedance matrix (resistive and inductive) have a very smooth frequency dependence, it is possible use a frequency scan with no more than 20 logarithmically spaced frequencies f k to interpolate such dependence in 5 decades (10 Hz to 1 MHz). The losses in the transformer came from several different contributions: ohmic or DC losses, skin-effect losses and proximity effect losses in the winding conductors and losses in the silicon steel laminated core.

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To calculate the consequence of core and proximity effect in the impedance, FEMM [22] with anisotropic complex permeability μ¯ is used, in the frequency domain, using the potential vector A formulation (19) for determine the distribution of the flux density B (20) in the transformer geometry for each frequency f k , and then the impedances are calculated from the complex fluxes. The winding conductors are modelled using the complex permeability principle followed by homogenization as is described in Sects. 3 and 4, and the core effect is modelled using also an anisotropic complex permeability considering the effect of sheets lamination as is described in Sect. 5. A current Ii is imposed in branch i (Ii = 1A), Eq. (19) is solved, the flux φ¯ j is calculated in branch j (I j = 0 A) using Eqs. (20) and (21), the complex inductance is obtained in (22) and finally the resistance Ri j and inductance L i j of Z i j are calculated in (23) and (24) for frequency f k . To complete the impedance matrix this process is repeated for all the frequencies f k (k = 1, . . . , p) and all the branches (i = 1, . . . , n).  ∇∧

1 ∇ ∧ A = Ji i = 1, . . . , n μ¯

(19)

B = ∇ ∧ A

(20)

0  0 0 − →   ¯ φ j = ∫ B × nd S = ∫ ∇ ∧ A × nd S = A × d P j = 1, . . . , n S

(21)

S

C

φ¯ j i = 1, . . . , n j = 1, . . . , n L¯ i j = Ii

(22)

Ri j ( f k ) = −2π f k Im(φ¯ j )

(23)

L i j ( f k ) = Re(φ¯ j )

(24)

To calculate the ohmic and skin losses effect a self-resistance Rs (25) and a selfinductance L s (26), derived from an analytical 2D magnetic field calculation [28], are calculated for each conductor and added to the diagonal terms of the previous calculated inductance matrix.           1 e sinh hδ + sin hδ h sinh δe + sin δe Ω e + 2 e h h + Rs =  e h 2 2δ 2δ m − cos cosh cosh − cos 4σ + δ δ δ δ 2

2

(25) 



h

h

eδ sinh δ − sin δ μ0     Ls =   2 4 cosh hδ − cos hδ 4 2e + h2



+

e

 e  

hδ sinh δ − sin δ     4 cosh δe − cos δe

H (26) m

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In (25) and (26) h and e are the axial and radial conductor dimensions (Fig. 1) and σ is the conductivity of the conductor material. Then the matrix of inductive transformer impedances (dimension n × n) is calculated for each frequency f k : Z i j ( f k ) = Ri j ( f k ) + j2π f k L i j ( f k ) i = 1, . . . , n j = 1, . . . , n k = 1, . . . , p (27) Finally, using vector fitting [25–27] we obtain a mathematical expression Z(s) for the matrix of inductive impedances from the values calculated in (27) for the frequencies f k (k = 1, . . . , p): Z(s) = D + s E +

r =m r =1

Ck s − ak

(28)

where D, E and C k (k = 1, . . . , r ) are real constant matrices. To represent properly a circuit that contains only resistances and self and mutual inductances the poles ak must be negative real numbers and the number of poles m must be select as small as possible but enough to obtain a small rms error in the fitting process (less than 4 × 10−3 ). Normally for a model with a frequency range of five decades (10 Hz to 1 MHz) m results between 4 to 6 depending of the complexity of the transformer. During the vector fitting process passivity is enforced because having a nonpassive model may result in unstable time-domain simulations.

7 Time Domain Inductive Equivalent Circuit One of the fundamental steps in the development of the model is define a topology for the time domain inductive equivalent circuit. The advantage of having a time domain equivalent circuit is that it can work in combination with models of the power systems in circuits solvers like EMPT, APT, SPICE, etc., is easy to include in the circuit the capacitive effects and can be include in the transformer model non-linear elements, as internal surge arresters, internal air series reactors to limit short-circuit currents and any other external impedance connected to the transformer terminals during factory acceptance tests. The equivalent circuit must be capable of represent the frequency dependent behaviour of the transformer inductance matrix and for that there are two classical approaches to define the circuit topology: the Mombello’s circuit [16] that uses auxiliary circuits magnetically coupled with the winding branches (Fig. 4) and the Eslamian’s circuit [17] that uses first order series Foster circuits to represent each winding branch (Fig. 5).

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Fig. 4 One branch in Mombello’s approach

Fig. 5 One branch in Eslamian’s approach

Both circuits are equivalents, but the circuit parameters determination is directly and very much easy in the Mombello approach than in the Eslamian approach where is necessary to solve iteratively a non-linear equations system that can present convergence problems. The complete Mombello’s circuit for a transformer with n branches is shown in Fig. 6 (the mutual inductances are not indicated in the Figure), where n is the number of winding elements or branches, r is the number of groups of auxiliary or fictitious circuits and m = n × r de total number of auxiliary circuits. The equivalent circuit is based in two hypotheses: 1. It is not considered magnetic coupling between auxiliary coils 2. The resistance and self-inductance of all auxiliary circuits in each group are equal (R f k and L f k for k = 1, . . . , r ).

Fig. 6 Inductive equivalent Mombello’s circuit

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The equations system that represents the inductive equivalent Mombello’s circuit are given in matrix form in (29a). ⎡

ub ⎢ 0 ⎢ ⎢ ⎢ 0 ⎢ ⎣ ... 0

⎤

⎡

Rb ⎥ ⎢ 0 ⎥ ⎢ ⎥ ⎢ ⎥=⎢ 0 ⎥ ⎢ ⎦ ⎣... 0

0 R f1 0 ... 0

0 0 R f2 ... 0

... ... ... ... ...

⎤⎡ 0 ⎢ 0 ⎥ ⎥⎢ ⎥⎢ 0 ⎥⎢ ⎥⎢ . . . ⎦⎣ Rfr

ib i f1 i f2 ... i fr

⎤

⎡

Lb ⎢ Mt ⎥ ⎢ 1 ⎥ ⎢ ⎥ ⎥ + s ⎢ M t2 ⎢ ⎥ ⎣ ... ⎦ M tr

M1 L f1 0 ... 0

M2 0 L f2 ... 0

... ... ... ... ...

⎤⎡ ⎤ ib Mr ⎢ ⎥ 0 ⎥ ⎥⎢ i f 1 ⎥ ⎥⎢ ⎥ 0 ⎥⎢ i f 2 ⎥ ⎥⎢ ⎥ . . . ⎦⎣ . . . ⎦ L fr i fr (29a)

where: u b : vector (n × 1) with the voltages in the main branches i b : vector (n × 1) with the currents in the main branches e f k : vectors (n × 1) with the induced voltages in the auxiliary circuits in group k (k = 1, . . . , r ) i f k : vectors (n × 1) with the currents in the auxiliary circuits in group k (k = 1, . . . , r ) R b : diagonal matrix (n × n) with the resistances of the main branches L b : complete matrix (n×n) with self and mutual inductances of the main branches R f k : diagonal matrices (n × n) with the resistances of the auxiliary circuits of group k (k = 1, . . . , r ) L f k : diagonal matrices (n × n) with the self-inductances of the auxiliary circuits of group k (k = 1, . . . , r ) M k : complete matrices (n × n) with the mutual inductances between main branches and auxiliary circuits of group k (k = 1, . . . , r ) From the previous equations we obtain the inductive impedance of the equivalent circuit Z eq (s) from the relationship between the voltages [u b ] and currents [i b ] in the main branches (29b). k=r  1 M 2k Z eq (s) = R b + s L b − s L f k s + Rfk k=1 L fk 2

(29b)

8 Determination of Inductive Equivalent Circuit Parameters The parameters of the equivalent inductive circuit are obtained matching the know impedance matrix Z(s) with the unknow impedance matrix Z eq (s) representative of the equivalent circuit. In first place the impedance matrix Z(s) is converted in (30) to a format similar to Z eq (s).

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175

Z(s) = R + s L − s 2

k=r  k=1

Kk s + λk

(30)

where:  Ck  Ck Ck R= D− L= E− 2 a ak a2 k=1 k k=1 k k=r

λk = −ak K k = −

k=r

(31)

Finally matching Z eq (s) in (29b) with Z(s) in (30) the parameters of the equivalent circuit are calculated: Rb = D −

k=r  Ck a k=1 k

(32)

Lb = E −

k=r  Ck a2 k=1 k

(33)

Rfk = −ak k = 1, . . . , r L fk

(34)

The equivalent circuit is not unique, in fact there are infinite solutions, and to determine the problem the values of L f k for k = 1, . . . , r are selected arbitrary and then the values of R f k are calculated in (35a) using Eq. (34). R f k = −ak L f k k = 1, . . . , r

(35a)

Finally, the matrices of the mutual inductances between the main branches and the auxiliary circuits are calculated with Eq. (35b).  Mk =

−

L fk C k k = 1, . . . , r ak2

(35b)

If a matrix is positive definite the elements of his square root are real numbers, this means that the matrices M k must be positive defined. This is the only condition that must be fulfilled to obtain the parameters of the Mombello’s equivalent circuit, and the simplicity of the former equations is one of the most remarkable advantages of the Mombello’s approach.

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9 Calculation of Transformer Capacitive Impedances FEM is widely used to accurately calculate the capacitance between two electrodes having any geometrical shape and one of the advantages of FEM are that the fringing effects around the electrodes are automatically calculated. The behaviour of a dielectric material in an electric field is described using a complex frequency-dependent permittivity: ε¯ = ε0 ε¯ r = ε (ω) − jε (ω) = ε (ω)(1 − jtanδ)

(36)

The complex permittivity principle is analogous to complex permeability described in Sect. 3. The capacitive impedance matrix (capacitances and conductances) of the transformer is calculated in a turn-to-turn level (n t ×n t ) solving Eq. (37) with FEMM [22] for the potential V using a complex permittivity ε¯ (36) for each dielectric material for different frequencies f k : ∇ × (¯ε ∇V ) = 0

(37)

A voltage Vi is imposed in turn i (Vi = 1V ), Eq. (37) is solved, the electric charge Q j is calculated on the surface of turn j, and the capacitance Ci j between turns i and j is calculated using Eqs. (38) to (39).  = ε¯ E = ε¯ ∇V D

(38)

0

 × nd S Qj = ∫ D

(39)

Si

Ci j =

Qj i = 1, . . . , n t j = 1, . . . , n t Vi

(40)

To complete the capacitive impedance matrix this process is repeated for all the frequencies (k = 1, . . . , p  ) and all the turns (i = 1, . . . , n t ). The capacitances between each turn and ground Cii are calculated applying the same principle. The capacitive impedance matrix is finally reduced from turn-to-turn level to branch-to-branch level according to the defined inductive branches to be compatible with the inductive equivalent circuit. Typical dependency of complex permittivity with frequency for pressboard, paper and oil [29, 30], shows that the real part has only very weak frequency dependency whereas the imaginary part (representing the dielectric losses) is strongly frequency dependent for paper and pressboard and for oil the imaginary part is almost zero for all frequencies.

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Studies and calculations carried out in the CIGRE working group by several members have shown that dielectric losses and the dependence of capacitance with frequency have a second order effect in the accuracy of high-frequency transformer’s models and can be disregarded.

10 Inclusion of Capacitances in the Inductive Equivalent Circuit The inductive equivalent circuit is obtained connecting the branches of Fig. 6 to represent the transformer windings and then the capacitances are included in the circuit to obtain the total equivalent circuit of the transformer. The series capacitance of each branch is connected in parallel with the respective branch and the parallel capacitance between windings and between windings and ground are connected to the corresponding nodes of the windings. As example, in Fig. 7 is shown a transformer with two windings and each winding is divided in two branches. For this case the number of branches is 4 and the number of nodes is 6. In Fig. 8 is shown the complete equivalent circuit with the series and parallel capacitances included (for simplicity the coupled auxiliary circuits and the mutual inductances are not included in the figure). Fig. 7 Transformer scheme

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Fig. 8 Transformer equivalent circuit

11 Solving the Equivalent Circuit in Time Domain Once the transformer equivalent circuit is ready, the internal connections between windings and the connections of transformer terminals to the applied voltages and to ground are included in the circuit. The internal non-linear elements (surge arresters), series reactors and external circuit elements, if exits, are also included and finally the circuit is solved in the time-domain by any circuit solver like EMTP, ATP, SPICE, etc. It is also possible to solve the model in the time domain in the form of spacestate equations applying the trapezoidal rule for integration. The results presented in Sect. 12 was calculated using this last approach.

12 Comparison Between Calculations and Measurements In this section, the calculated voltages are compared with the measured values for the Cases 6 and 7 of the single-phase transformer, manufactured by WEG in Mexico, and measured by CIGRE JWG A2/C4.52 in 2016, when a standard lighting impulse (1.2/50 us) is applied to terminal H1 of the transformer. In Fig. 9 are shown the connections diagram for Case 6 and in Fig. 10 the calculated and measured voltages in terminals H1, R1, X1 and Y1. This same example was calculated in Ref. [31] using the classical approach with constant L and C matrices (independent of frequency) and using Fergestad approach

Calculation of Circuit Parameters …

Y1

+ 84

179 Case 6 Nom+ (Tap 11+)

X1

+149

-213 -219 HV

+

k

RW

+217

1 2 3 4 5 6 7 8 9 10 11

+182 TV

LV

+181 +216 HV

RW

-214 -1 Y2

- 85 X0

- 150 H1

H0

Fig. 9 Single phase transformer connection diagram for Case 6

Fig. 10 Single phase transformer Case 6 comparatives

[13, 14] to consider damping in function of frequency. The comparison between calculations and measurements are shown in Figs. 10 and 11 of this reference. From the inspection of these figures we can conclude that the classical calculation is acceptable in the prediction of the maximum values of the voltages but is not very accurate in the determination of the oscillation frequencies.

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Y1

+ 84

Case 7 Nom+ (Tap 11+)

X1

+149

-213 -219 HV

+

k

RW

+217

1 2 3 4 5 6 7 8 9 10 11

+182 TV

LV

+181 +216 HV

RW

-214 -1 Y2

- 85 X0

- 150 H1

H0

Fig. 11 Single phase transformer connection diagram for Case 7

Fig. 12 Single phase transformer Case 7 comparatives

Is evident comparing the results showed in Fig. 8 with the results presented in Figs. 10 and 11 of Ref. [31] that the calculated values obtained in this work with the new proposed approach are very much better compared with the measurements. In Fig. 11 are shown the connections diagram for Case 7 and in Fig. 12 the calculated and measured voltages in terminals R1 and X1 (the impulse voltage applied in terminal H1 is the same as in case 6).

13 Conclusions The proposed model is the better approach, in opinion of the authors, considering the comparisons between measurements results and the calculations made in the CIGRE WG A2/C4.52 for the transformers manufactured by WEG in Mexico. The model

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can represent with great precision the effect of the damping dependence with the frequency and the equivalent circuit obtained from the transformer model can be included without problems in the analysis of the interaction of the transformer with the power system in any circuit solver like EMTP, ATP, SPICE, etc. Memorial and Acknowledgements In first place we want to dedicate this work to Robert Degeneff, that passed away this year. Robert was pioneering in developing high-frequency transformer models and shared generously his knowledge and experience with us for more than thirty years. Secondly the authors would like to thank Bjorn Gustavsen, Enrique Mombello, Oliver Sterz, Tobias Röhrl and Anniyappan Palani for their support and many fruitful discussions on transformer modelling in the last years working together in the CIGRE JWG A2/C4.52.

References 1. CIGRE WG A2.37: Transformer reliability surveys. Technical Brochure 642, December 2015 2. CIGRE JWG A2/C4.39: Electrical transient interaction between transformers and the power system. Part 1—Expertise. Technical Brochure 577A, April 2014 3. CIGRE JWG A2/C4.39: Electrical transient interaction between transformers and the power system. Part 2—Case studies. Technical Brochure 577B, April 2014 4. McNutt WJ, Blalock TJ, Hinton RA (1974) Response of transformer windings to system transient voltages. IEEE Trans Power Appar Syst PAS-93(2):457–467 5. Margolis HB, Phelps JDM, Carlomagno AA, McElroy AJ (1975) Experience with part-winding resonance in EHV auto-transformers: diagnosis and corrective measures. IEEE Trans Power Appar Sys PAS-94(4), Pt.1:1294–1300 6. McElroy J (1975) On the significance of recent EHV transformer failures involving winding resonance. IEEE Trans Power Appar Syst PAS-94(4):1301–1307 7. Musil RJ, Preininger G, Schopper E, Wenger S (1981) Voltage stresses produced by aperiodic and oscillating system overvoltages in transformer windings. IEEE Trans Power Appar Sys Vol. PAS-100(1):431–441 8. Musil RJ, Preininger G, Schopper E, Wenger S (1982) The resonance effect of oscillating system overvoltages on transformer windings. IEEE Trans Power Appar Sys PAS-101(10):3703–3711 9. Degeneff RC, McNutt WJ, Neugebauer W, Panek J, McCallum ME, Honey C (1982) Transformer response to system switching voltages. IEEE Trans Power Appar Syst PAS101(6):1457–1470 10. CIGRE WG 12.07: Resonance behaviour of high-voltage transformers. Paper presented in the name of Study Committee 12 (Transformers) by Working Group 12.07, CIGRE 1984 Session, Paper 12–14 11. Henriksen EE (1998) Study of very fast transients overvoltages in transformers (VFTO). CIGRE Working Group 12.11, ELECTRA Nº179, August 1998, pp 12–23 12. Electrical environment of transformers—impact of fast transients. Prepared by CIGRE JWG A2/A3/B3.21, ELECTRA Nº218, February 2005, pp 24–37 13. Fergestad PI (1972) Transient oscillations in transformer windings. Thesis, Oslo Universitetsforlaget 14. Fergestad PI, Henriksen T (1974) Transient oscillations in multiwinding transformers. IEEE Trans Power Appar Sys PAS-93(2):500–509 15. Abeywickrama N, Podoltsev A, Serdyuk Y, Gubanski S (2006) Influence of core characteristics on inductance calculations for modelling of power transformers. In: First international conference on industrial and information systems, ICIIS 2006, 8–11 August 2006, Sri Lanka

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16. Mombello E, Zini H (2007) A novel linear equivalent circuit of a transformer winding considering the frequency-dependence of the impedances. Electric Power Syst Resea 77:885–895, ScienceDirect, Elsevier 17. Eslamian M, Vahidi B (2015) New equivalent circuit of transformer winding for the calculation of resonance transients considering frequency-dependent losses. IEEE Trans Power Delivery 30(4):1743–1751 18. Gustavsen B, Portillo Á, Høidalen HK (2018) Modelling of transformers and reactors for electromagnetic transient studies. Paper A2-213, CIGRE Paris Biennale 2018 19. Gustavsen B, Portillo A, Ronchi R, Mjelve A (2017) Measurements for validation of manufacturer’s white-box transformer models. In: 4th international colloquium transformer research and asset management, May 10–12, 2017, Pula, Croatia. Procedia Eng 202, 2017, pp 240–250 20. CIGRE Technical Brochure JWG A2/C4.52: High-frequency transformer and reactor models for network studies—Part 1: White-Box Models (to be published) 21. Röhrl T (2017) Dämpfungsmodelle für Leistungstransformatoren. Masterarbeit, Ostbayerische Technische Hochschule Regensburg, Fakultät Elektro- und Informationstechnik, Februar 2017 22. Meeker DC (2019) Finite element method magnetics. FEMM 4.2, April 2019. http://www. femm.info 23. Moreau O, Popiel L, Page JL (1998) Proximity losses computation with a 2D complex permeability modelling. IEEE Trans Magnet 34(5):3616–3619 24. Moreau O, Michel R, Chevalier T, Meunier G, Joan M, Delcorix JB (2005) 3-D High Frequency Computation of Transformer R, L Parameters. IEEE Transactions on Magnetics 41(5):1364– 1367 25. Gustavsen B, Semlyen A (1999) Rational approximation of frequency domain responses by vector fitting. IEEE Trans Power Delivery 14(3):1052–1061 26. Gustavsen B (2006) Improving the pole relocating properties of vector fitting. IEEE Trans Power Delivery 21(3):1587–1592 27. Deschrijver D, Mrozowski M, Dhaene T, De Zutter D (2008) Macromodeling of multiport systems using a fast implementation of the vector fitting method. IEEE Microwave Wire Compon Lett 18(6):383–385 28. Stoll RL (1974) The analysis of Eddy currents. Clarendon Press, Oxford 29. Abeywickrama N, Ekanayake C, Serdyuk Y, Gubanski S (2006) Effects of the insulation quality on the frequency response of power transformers. J Electri Eng Tech 1(4):534–542 30. Bjerkan E (2005) High frequency modeling of power transformers. PhD thesis, Norwegian University of Science and Technology, Trondheim 31. Gustavsen B, Portillo Á (2018) A damping factor-based white-box transformer model for network studies. IEEE Trans Power Delivery 33(6):2956–2964

Small Signal Internal Voltage Transfer Measurements and White-Box Transient Calculations for Non-standard Test Conditions of a Shell-Form Power Transformer Bjørn Gustavsen, Ariana Martins, Carlos A. Sá, Luis Braña, Ricardo Castro Lopes, Pedro Lima, Andrea Soto, and Mário Soares Abstract Research tests were performed on a shell-form autotransformer with a more rigorous impulse test methodology than the traditional recurrent surge oscillograph method. These tests included non-standard terminal connections with open terminals, differing from those tests defined by the international standards related with impulse testing of power transformers. The test voltage responses were obtained using voltage transfer frequency sweep measurements that were converted into time domain waveforms. The measurement results were compared against simulations by a white-box model, demonstrating satisfactory accuracy of the transient calculation tool. In addition, the sensitivity of the measurements to measuring probes length was experimentally evaluated. Reducing the lengths with 1.5 m only affected frequency components around 1 MHz. Keywords Shell-form transformer · Transient response measurements · Simulations · White-box model

1 Introduction The dielectric withstand capability of the transformer windings against transient overvoltages is verified by the lightning impulse factory test [1]. In-service voltages impinging the transformer terminals are however very different from the standard B. Gustavsen (B) SINTEF Energy Research, Postboks 4761 Sluppen, 7465 Trondheim, Norway e-mail: [email protected] A. Martins · C. A. Sá Universidade do Porto, Faculdade de Engenharia, Porto, Portugal L. Braña · R. C. Lopes · P. Lima · A. Soto Efacec Energia - Máquinas e Equipamentos Eléctricos, S.A, Matosinhos, Portugal M. Soares REN - Rede Eléctrica Nacional, S.A, Lisbon, Portugal © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_15

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impulse test voltage. The verification against internal stresses due to other voltage wave shapes and terminal conditions can only be calculated using the white-box transformer model available to the transformer designer. It has been found in CIGRE JWG A2/C4.39 [2] and A2/C4.52 (ongoing) that although the white-box models used by manufacturers are well suited for the standard lightning impulse response prediction, their accuracy still needs to be evaluated for the application of nonstandard waveshapes and terminal connections. In order to assess the white-box accuracy limitations, we performed research tests with direct measurements of frequency domain voltage transfer functions, from external terminals to critical internal points in the regulating winding. The time domain voltage response to any time domain excitation could then be determined via rational approximation and convolutions and be compared against simulations by a white-box model. While a similar approach has already been applied to core-form transformers [3], we apply in this work the approach to a shell–form transformer. We also investigate the effect of measurement lead lengths on the measured results.

2 Shell-Form Transformer 2.1 Transformer Main Data The tested transformer is a seven leg, 800 MVA, shell-form, three-phase autotransformer. The nominal phase-to-phase voltages are 500 kV, 161 kV and 34.5 kV, for the high voltage, low voltage and tertiary voltage respectively. Each phase of the series winding was designed with 6 tap leads, for connection to a de-energized tap-changer and were available for testing. At the time of testing, the connections between phases were not done yet (neutral and delta), so all the leads were available as 3 single phase units.

2.2 Transformer Winding Layout Each phase is built with 56 pancake coils (4 for tertiary winding, 24 for common winding, 28 for series winding), and 6 static shields as per Fig. 1. Minimum tap position was chosen for these tests, because it leads to a higher floating portion of tap winding, so higher voltages should be expected at tap leads P5 and P6.

Small Signal Internal Voltage Transfer Measurements … 3.2W

2W

1.1W

185

2.1W

3.1W

8W 3W

3W 8W

4W

7W

7W 4W

5W 6W

6W 5W

P3=3W=8W P4=4W P5=5W P6=6W P7=7W

Fig. 1 Left: Window cutaway for phase W (red: tertiary winding and leads, green: common winding and leads, blue: series winding and leads, black: static shields). Right: Table with the definition of the de-energized tap changer connections referring to the minimum tap position

2.3 Specifics of Shell-Form Versus Core-Form Effect on Voltage Distribution Shell-form transformer coils have a very large surface facing each other and a very small surface facing the ground (magnetic circuit, magnetic shielding and tank walls), which results in a very high series capacitance (CS ) and a very low capacitance to ground (CG ). The higher the ratio between CS and CG the more linear will be the impulse voltage (or of any other high frequency voltage) distribution along the windings. If these voltage distributions were not close to linear, then some localized overvoltages would appear, which means that the insulating structure would have to be reinforced at some spots, and probably overdimensioned at others. As an illustration for this, one can consider the capacitances circuit in Fig. 2 (that is somewhat representative of a winding for high frequencies), where we have five elemental series capacitances and four elemental capacitances to ground. If we consider k as the ratio between CS and CG and apply a high frequency sinusoidal voltage at terminal V1 , we can assess the voltage distribution at V2 , V3 , V4 and V5 as k changes. As we can see in Fig. 3, the higher the k, the more linear will be the voltage distribution. For instance, if we take CS equal to CG (k = 1), the voltage difference between V1 and V2 will be 0.618 p.u., while if CS is one hundred times higher than CG (k = 100) V1

CS

CS

V2 CG

CS

V3 CG

CS

V4 CG

CS

V5 CG

Fig. 2 Example capacitances circuit (CS : elemental series capacitance, CG : elemental capacitance to ground)

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1 k=100 k=10

Voltage [p.u.]

0.8

k=9 k=8 k=7

0.6

k=6 k=5

0.4

k=4 k=3

0.2

k=2 k=1

0 V1

V2

V3

V4

V5

Ground

Node

Fig. 3 Voltage distribution for different k factors (ratio between CS and CG )

the same voltage difference will be 0.212 p.u. This means that for k = 1, the voltage difference will be 2.9 times higher than for k = 100, and thus will result in a higher dielectric stress at the respective series capacitor CS .

3 Voltage Transfer Measurements 3.1 Procedure The basic approach is to measure the voltage transfer function from one transformer terminal to a second terminal, as function of discrete frequency. The voltage transfer function h(ω) is defined as the response voltage V 2 (ω) divided by the excitation voltage V 1 (ω), h(ω) =

V2 (ω) V1 (ω)

(1)

3.2 Measurement Setup The actual measurement of h(ω) is performed using a suitable vector network analyzer (VNA) in combination with two identical passive voltage probes having the same transfer function K(ω), see left part of Fig. 4. We use a VNA setting with

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Fig. 4 Left: Voltage transfer measurement. Red: voltage signal conductors; blue: ground conductors/grounded parts. Right: Test fixture for attaching coaxial cable and grounding shunt

1 M input impedance for the VNA reference (R) and input (T). The signal is brought from the VNA to the transformer terminal using a coaxial cable. The VNA itself is separated galvanically from the power outlet using a separation transformer, to minimize interference. When the two probes are identical (and of equal length), the measured voltage ratio on the VNA (VT /VR ) is exactly equal to V2 /V1 , since we have h(ω) =

K (ω) · V2 (ω) V2 (ω) VT (ω) = = VR (ω) K (ω) · V1 (ω) V1 (ω)

(2)

The measured response is of course dependent on the terminal condition of the other terminals (open, grounded or loaded). In order to connect to the transformer terminals by coaxial cables, prefabricated test fixtures (connections) were used, see right part of Fig. 4. They include an N-type coaxial connection to which a grounding shunt can be screwed for fast grounding or opening of terminals. The voltage probe (tip and grounding clips) are easily connected to the test fixture.

3.3 Measurement Conditions Similarly, as in [3], a ground plane is established on the transformer that is used as a ground reference. The ground reference is made from braided wire that is connected to grounding points on the transformer. Figure 5 shows the terminations used in the measurements as well as the ground reference. In this case, we used two external terminals (H3, X3) while all other external terminals were grounded (left part of Fig. 5). Additionally, we measured voltage transfer to three internal points in the regulating winding (leads marked 3, 5, 6 in Fig. 5).

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Fig. 5 Connections. Voltage transfer measurements from floor level

3.4 Conversion from Frequency Domain to Time Domain Figure 6 (left panel) shows an example of measured voltage transfer functions, from X3 to P3, P5 and P6, with H3 grounded. The left panel shows the magnitude functions (blue traces—“Data”), as well as a rational function approximation calculated by vector fitting (dashed red traces—“FRVF”). The rational function (3) is seen to match the measurement very closely. h(ω) ∼ = r0 +

N  i=1

4.5

V3 V5 V6

1.2 1

3

Voltage [V]

Magnitude

3.5

(3)

Lightning impulse response

1.4 Data FRVF Deviation

4

2.5 2 1.5

0.8 0.6 0.4 0.2

1 0.5 0

ri jω − ai

0 10

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Fig. 6 Left: measured voltage transfer functions and a 60th order rational approximation; right: calculated 1.2/50 µs voltage responses using recursive convolution. Case 3

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2 V3 V5 V6

6

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Voltage [V]

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3 2

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0 -1 -50

0

50

100 150 200 250 300 350 400

-1 -0.5

Time [μs]

0

0.5

1

1.5

2

Time [μs]

Fig. 7 Time domain measurement of voltage responses on P3, P5 and P6 (solid traces). Comparison with simulation (dashed traces) via rational model and recursive convolution

Using the rational approximation (3), which defines an impulse response, the time domain response of any time domain excitation can be calculated using “recursive convolution” via time domain discretization. Details of the rational fitting and time domain convolution is found in [3] and references therein. The right panel in Fig. 6 shows the 1.2/50 µs lightning impulse response as calculated from the rational approximations (3) associated with the frequency responses in the left panel of Fig. 6. The accuracy of the procedure was verified by applying a time domain step voltage to one terminal and measuring the voltage responses using an oscilloscope. The recursive convolution approach was able to reproduce the measured voltage waveforms with excellent agreement. Figure 7 shows one example of comparison. A zoomed view of the response is shown in the right panel.

4 White-Box Calculations Versus Measurements 4.1 Outline of the Simulation Procedure The applied white-box model is a lumped-parameter type equivalent circuit composed of resistances, capacitances, self-inductances and mutual inductances. The model is intended to emulate the transformer response to high frequency transients as close as possible to reality. We start by splitting the coils into the portions of interest, depending on the desired accuracy, not forgetting that the higher the number of lumped parameters the longer it will take to solve the equivalent circuit. The ends of these portions, which feature lumped parameters, will be the nodes of the equivalent circuit. This discretization procedure implies the determination of the self and mutual inductance matrix, the resistive elements between each one of the nodes and the capacitances of the various coils’ portions.

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The capacitances calculations include the following elements: • • • • • •

Between turns; Between coils; Between coils and static plates; Between static plates; Between coils and ground (magnetic circuit, magnetic shielding and tank walls); Between static plates and ground (magnetic circuit, magnetic shielding and tank walls);

The determination of all capacitances and resistances are made by analytical formulae. The self and mutual inductances are determined using a 3D numerical software. The 2D axisymmetric FEM, alone, is not suitable to be used in Shell form transformers because the windings are rectangular and not circular, therefore, we use a third-party 3D software program for the inductances’ matrix calculation. This software program has incorporated two solvers: FEM and BEM. In this work we used the 3D BEM solver. Finally, the RLC circuit is built and solved using a circuit analysis program. This calculation tool is continuously being improved by Efacec and allows to control every circuit parameter and to refine it when necessary. It is also being automated and integrated in Efacec’s information system to accelerate the transient simulations and avoid human errors.

4.2 Leads’ Connections Several test cases were made with alternative leads (terminal) conditions. Table 1 and Fig. 8 define the leads connections, taking Fig. 1 as reference for the nodes’ designation. Table 1 Leads Connections Name Case 01 Case 02 Case 03 Case 04 Case 05 Case 06

H3 Lead (1.1W) Applied Applied Grounded Open Applied Applied

X3 Lead (2.1W) Grounded Open Applied Applied Open Grounded

3.2 Lead (3.2W) Grounded Grounded Grounded Grounded Open Open

3.1 Lead (3.1W) Grounded Grounded Grounded Grounded Grounded Grounded

H0X0 Lead (2W) Grounded Grounded Grounded Grounded Grounded Grounded

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Cases 02 and 04

Case 05

3.1

3.1 3.2

3.2

Fig. 8 Leads (terminals) and grounding conditions for the test cases

4.3 Measurements Versus Simulations Using the measurement procedure described in Sect. 3, a set of time domain responses were obtained via measurement of frequency domain voltage transfer functions, followed by rational approximation and convolution with the ideal lightning impulse voltage waveform. In each measurement, the terminal conditions were imposed by applying the relevant connections on the transformer terminals. One major advantage over a direct time domain measurement is that one obtains the voltage response to the ideal lightning impulse voltage excitation, thereby making the comparison with white-box time domain simulations more easy. In addition, the waveforms are free of noise, unlike a direct time domain measurement. Figures 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18 show the comparison between the calculated values and the measured results. One can in all cases observe a very good agreement between calculated and measured values. 200 0 -200

Voltage (kV)

Fig. 9 Comparison for Case 01, P6 lead, (black: applied waveform, red: measurement, blue: calculation)

-400 -600 -800 -1000 -1200 -1400 -1600 0

20

40

60

80

Time (μs) P6 Measured

6W Calculated

Applied Voltage Waveform

100

192 200 0 -200

Voltage (kV)

Fig. 10 Comparison for Case 02, P6 lead, (black: applied waveform, red: measurement, blue: calculation)

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Time (μs) P6 Measured

Applied Voltage Waveform

200 0 -200

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Fig. 11 Comparison for Case 02, X3 lead, (black: applied waveform, red: measurement, blue: calculation)

6W Calculated

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Time (μs) X3 Measured

Applied Voltage Waveform

0 -100 -200

Voltage (kV)

Fig. 12 Comparison for Case 03, P6 lead, (black: applied waveform, red: measurement, blue: calculation)

2.1W Calculated

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Small Signal Internal Voltage Transfer Measurements … 1000 500 0

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Fig. 13 Comparison for Case 04, P6 lead, (black: applied waveform, red: measurement, blue: calculation)

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Fig. 14 Comparison for Case 04, H3 lead, (black: applied waveform, red: measurement, blue: calculation)

6W Calculated

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Time (μs) H3 Measured

Applied Voltage Waveform

400 200 0 -200

Voltage (kV)

Fig. 15 Comparison for Case 05, P6 lead black: applied waveform, red: measurement, blue: calculation)

1.1W Calculated

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Fig. 16 Comparison for Case 05, X3 lead, (black: applied waveform, red: measurement, blue: calculation)

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Applied Voltage Waveform

200 0 -200

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Fig. 17 Comparison for Case 06, P6 lead (black: applied waveform, red: measurement, blue: calculation)

2.1W Calculated

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Applied Voltage Waveform

200 0 -200

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Fig. 18 Comparison for Case 06, 3.2 lead (black: applied waveform, red: measurement, blue: calculation)

6W Calculated

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Small Signal Internal Voltage Transfer Measurements … Lightning impulse response

1.4

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Fig. 19 Effect of reducing the connection leads lengths by 1.5 m. Results with shorter leads (dashed traces) and with longer leads (solid traces). Right panel: zoomed view of left panel

5 Observations on Measurement Accuracy The measurement points (H3, X3, P3, P5, P6) were brought down from the transformer’s windings to the ground reference using insulated wires, as can be observed in Fig. 5. The presence of such wires can potentially lead to false oscillations which manifest as (false) resonances at high frequencies in the measured transfer functions. In order to clarify this potential problem, a set of duplicate measurements were performed where the measurements were made from a platform. This permitted the lengths of the insulated wires to be reduced by approximately 1.5 m. The ground reference was elevated 1.5 m as well. Figure 19 shows the same result for time domain voltage transfer functions as in Fig. 6. The result with shorter leads is shown with dashed traces, superimposed on the original responses (solid traces). The traces are virtually overlapping, except for the initial response (right panel). It is observed that reducing the lead lengths by 1.5 m affects the high-frequency oscillation component of about 1 MHz. Reducing the length slightly increases the oscillation frequency while the amplitude is reduced.

6 Discussion The accuracy of white-box simulations (Figs. 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18) are in general better than similar simulations obtained for a core-form transformer [3]. One reason can be that shell-form transformers are inherently easier to model than core-form transformers, due to lower complexity and higher series capacitance: • Shell-form transformers have almost no magnetic or capacitive coupling between phases, unlike core-form transformers;

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• Shell-form transformers have normally a reduced number of coils when compared to core-form transformers and have basically two types of windings (continuous coil winding and parallel wound tap coil winding) while in core-form transformers we can find several types of windings (continuous winding, a few types of interleaved discs winding, shielded-conductor winding, layer winding, etc.); • Also, in shell-form transformers one normally finds a more favorable ratio between the series capacitance and the ground capacitance (higher k) than in core-form transformers, which improves the voltage distribution and its predictability. In fact, looking at Fig. 3, one observes that the voltage distribution has higher sensitivity to lower k values than to higher k values. For instance, changing k from 10 to 1 worsens much more the voltage distribution than changing k from 100 to 10.

7 Conclusion A non-standard impulse test procedure was used for obtaining the voltage response at critical positions in the regulating winding, with alternative terminal conditions. The measured responses were compared to simulations by a white-box model, demonstrating a good accuracy between measurements and simulations. The measurements are in general fast and easy to perform. The approach is an excellent means of assessing the accuracy of a manufacturer’s impulse voltage computational tools, thereby enabling further improvements to the model’s parameter determination. Acknowledgements This article is a result of the project GreenEst—Green Ester Transformers, supported by Competitiveness and Internationalisation Operational Programme (POCI), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF). Additional support from Norwegian Research Council, (project “ProTrafo”, no. 269303/E20) is appreciated.

References 1. IEC 60076-3, Power transformers—Part 3: insulation levels, dielectric tests and external clearances in air 2. CIGRE Technical Brochure 577A, Electrical transient interaction between transformers and the power system. Part 1—expertise. CIGRE JWG A2/C4.39, April 2014 3. Gustavsen B, Portillo A, Ronchi R, Mjelve A (2017) Measurements for validation of manufacturer’s white-box transformer models. In: 4th international colloquium transformer research and asset management, May 10–12, 2017, Pula, Croatia. Procedia Eng 202:240–250

Internal Fault Performance of Instrument Transformers with Sectioned Active Part Igor Žiger, Danijel Krajtner, and Boris Bojani´c

Abstract Relevant international instrument transformer standards specify internal arc testing to prove the transformer behavior under internal fault conditions. However, the test is defined in a way that does not recognize that it is possible to limit and reduce the total fault energy. For such instances, currently defined testing is mostly inapplicable. The purpose of this paper is to provide a theoretical background on behavior of units with sectioned active part under fault conditions, aided by numerical analysis of different fault scenarios on a variety of inductive voltage transformers, spanning from 72.5–550 kV. Numerical calculations are verified with several tests performed on a 123 kV inductive voltage transformer. This paper is a part of a continuous broad research with an aim to develop and specify adequate routine, type and special testing sequence for qualifying the paper-oil insulation systems that limit internal arc energy. Furthermore, the idea is to prove performance of such systems by introducing criteria that exceed the practices of current standards and aim to improve the instrument transformer fault statistics. Keywords Instrument transformers · Internal arc testing · Fault performance · Open core concept · Sectioned active part · Finite element analyses

1 Introduction and Background One of the more important performance aspects in recent years is the operational security and safety of high-voltage apparatus. The main driving factor behind it is the fact that a catastrophic failure of equipment that is inherently very reliable, can have significant consequences for the surrounding equipment or in extreme cases even on personnel in the substation. CIGRE technical brochure 512 is the latest source of relevant in-service failure data for instrument transformers [1]. It was conducted over a population of 322,500 single-phase instrument transformers with a service experience of 1,290,335 instrument transformer years. A total of 3179 failures were I. Žiger (B) · D. Krajtner · B. Bojani´c Konˇcar Instrument Transformers. Inc, J. Mokrovi´ca 10, 10090 Zagreb, Croatia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_16

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Table 1 Fire and explosion failures for each instrument transformer type Voltage class

Instrument transformer type Inductive voltage transformer

Combined transformer

Capacitive voltage transformer

Current transformer

60 ≤ U ≤ 100 kV

0

0

0

2

100 ≤ U ≤ 200 kV

8

4

2

32

200 ≤ U ≤ 300 kV

1

4

1

25

300 ≤ U ≤ 500 kV

3

7

1

9

500 ≤ U ≤ 700 kV

0

0

0

0

U ≥ 700 kV

0

0

0

1

12

15

4

69

Total

processed therein. Failures that resulted in fire and explosion (a subset of what is defined a major failure according to the same document) are summarized in Table 1. The data in the table exclusively refers to paper-oil insulated instrument transformers. From the table it is apparent that instrument transformers in general are a very reliable component. However, any such failure on instrument transformers influences the surrounding objects and can have tremendous residual damage and consequences. Moreover, it is outlined that 80% of such faults stem from internal dielectric failures and 70% originate from the main insulation. 65% of those are due to insulation aging and 12% due to design or manufacturing fault [1]. In an attempt to improve the performance in instances that could lead to catastrophic failures, internal arc testing was introduced in relevant international instrument transformers standards during the 2000s [2, 3]. According to [4], the requirements present in current standards were based on experiences accumulated by Électricitié de France (EDF) who have been conducting internal arc tests on current transformers since 1987 and on other types since 1993. These were refined through several years of continuous efforts from members of different working groups within IEC and IEEE and introduced into current standards. Since then, a fair amount of controversy is connected to valid test definitions. Objections were noted outlining inadequate fault current requirements, test duration (leading to an unrealistic energy that the transformer has to withstand) and fault location selection, which is either biased to some transformer constructions or does not represent failure modes that can actually be found in service [4, 5]. Fault current requirements that are valid today are based on system short-time thermal currents, which are not realistic for instrument transformers installed in actual substations. Therefore, in order to qualify, instrument transformers have to be significantly over-dimensioned, which is recognized both in literature and in actual standards [2, 4, 5]. Furthermore, fault levels experienced by both Hydro Quebec and EDF showed lower arc current levels and rarely experienced full asymmetry (asymmetry factor below was 2.5). This issue will be addressed in the upcoming revisions of both relevant standards with introduction of arc-proof current in IEEE

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C57.13.5 (currently in balloting) and basing ratings on system phase-to-earth fault current in IEC 61869-1 (committee draft currently in comment resolution) [6, 7]. The location of the arc inception is even more controversial. Both IEEE and IEC initially specified the location to be at the location where the dielectric stress is the highest. As discussed in [4], the highest dielectric stress in paper-oil insulated instrument transformers is typically located at the edge of capacitive screens in the bushing part of the insulation (i.e. within the insulator, not within the metal enclosure). Incepting an arc with current levels and duration specified in the standards will lead to violent failure of the insulator. To bypass this, some manufacturers are intentionally increasing local dielectric stress to be able to perform the test in the most favorable scenario for pressure relief, which is not representative of actual inservice conditions [5]. This definition is also being updated in [6] and [7] by stating that the arc inception location has to be placed in the location of highest risk based on individual manufacturer design and experience. The final issue with current internal arc performance definition is that it is specified in a way that it assumes a high-energy violent fault. This also means that the test is constructed to guarantee a certain level of safety, and is applicable only when the arc is incepted close to the pressure relief device, which does not cover a variety of failure modes which can appear under various conditions in service (most notably failures in the bushing portion of instrument transformers) [8]. When specified in such way, the test removes all “responsibility” from the transformer insulation system and tests solely the enclosure and pressure relief device, which may be appropriate for gas-filled units, which have a different fault propagation mechanism. In addition, internal arc testing does not really address the main contributors that lead to fire and explosion events, as mentioned above (aging, quality control and design faults) [1, 5]. All these contributors for paper-oil insulated units, where the fault propagation is slower, can be recorded and mitigated in other ways [4]. The described issue is addressed in [6] by recognizing that some transformer constructions are designed specifically to limit the energy of internal faults and that testing according to general requirements is not applicable in such cases. This paper is a part of a continuous broad research with an aim to develop and specify adequate routine, type and special testing sequence for qualifying the paperoil insulation systems that limit internal arc energy. Furthermore, the idea is to prove performance of such systems by introducing criteria that exceed the practices of current standards and aim to improve the statistics presented in [1]. The specific focus of this paper is to demonstrate performance of instrument transformers with sectioned active parts in respect to internal fault inception. The paper is based on experiences with open core inductive voltage transformers. Due to an identical active part concept, all conclusions and information disclosed is applicable to Combined Transformers, Power Voltage (Station Service) Voltage Transformers as well as Star-point Reactors [9, 10].

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2 Basic Theory of Units with Sectioned Active Part A typical example of open-core voltage transformer with a sectioned active part can be seen in Fig. 1a. A simplified representation of the insulation system is shown in Fig. 1b [11]. As it can be seen from Fig. 1, the active part of the unit consists of bushingtype capacitively graded main insulation and a sectioned primary winding. Basic concepts of such insulation systems are presented in papers [9] and [12]. The idea is that each section (coil) of the primary winding is insulated from adjacent sections (coils). Furthermore, as shown in Fig. 1b, each section of the primary winding is connected to its corresponding screen from the main insulation. Therefore, each pair of coil and adjacent screen comprises one segment of the main active part. There are several purposes for such a setup. One purpose is to equalize dielectric stress during different overvoltages, including impulse, switching and very fast transients (VFTO) 0. The other is to localize faults within the active part of the transformer, which is the purpose of this paper and will be expanded on below. There are two possible failure modes for these units; a failure in the main insulation or a failure in the primary winding. Depending on the fault origin, severity and other parameters the fault propagation time is different, but typically long lasting [4, 5]. Fault in the primary winding can originate from excessive stress in turnto-turn or layer insulation, quality deficiencies in either the primary conductor or layer insulation and gross design errors. Similarly, the faults in main insulation can

1

2

1. 2.

3

3. 4 5

4. 5. 6.

6 7

7. 8. 9.

Bellows cover with HV terminal Stainless steel bellows CapaciƟvely graded main insulaƟon Insulator Primary (HV) winding Secondary (LV) winding Open core Base assembly Secondary terminal box

8 9

(a)

(b)

Fig. 1 a Open-core voltage transformer cross-section. b Simplified representation of the active part

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Fig. 2 Possible failure modes of instrument transformers with sectioned active part, a fault originating in the main insulation, b fault originating in the primary winding

originate from local partial discharge, which are typically a consequence of aging, local electric field non-uniformities, high dissipation factor or other reasons [1, 4]. The main interest of this paper is to describe the transformer behavior once the fault propagates to one segment of the active part. Both failure modes are depicted in Fig. 2a, b. It is clear that regardless of the fault origin, once the fault propagates to the entire segment the affected section of the primary winding is short-circuited, either through the galvanic connection to the capacitive screen, or through the coil itself. The primary coil insulation is dimensioned so that it can withstand a theoretical loss of half of the primary winding sections (n/2 criterion, n being the total number of sections) regardless of the voltage class (72.5–550 kV). Such a criterion is imposed to provide a significant safety factor, taking into account faults with extremely low level of probability. This feature effectively localizes the fault on one segment of the active part, with the supply voltage distributed over all remaining sections, preventing a direct phaseto-ground short circuit and limiting the fault current. As seen in Fig. 2, two main variables have to be considered. One is the short-circuit current I CP flowing through the faulted segment of the active part, while the other is the total current I FP , flowing into the ground. As disclosed in [9] and [13], I FP will typically reach the level of 2–4 times the rated current I RP , and barely thermally stress the entire transformer. In addition, I CP will typically reach the level of 10–30 times the I RP , causing local thermal overload, oil gassing and consequent oil volume expansion. This energy limiting insulation concept is conceptually similar to insulation system of Capacitor

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Voltage Transformers, which essentially behave in the same way, as discussed in [12] and [13]. From previous considerations, it is clear that the active part concept is responsible for limiting the internal fault energy. However, the energy generated during the fault has to be contained and safely dissipated. To do so, two components are vital, stainless steel bellows and bellows cover (cap). Both are shown in Fig. 1. (a) for reference. Stainless steel bellows ensure oil volume compensation and hermetic sealing of the entire unit. Due to internal gassing, the bellows will expand and at a point push against the bellows cover. At that moment the pressure, which was constant, will start to increase. This will mechanically strain the bellows cover, which is structurally dimensioned to break off the unit at a design value, several times lower than the mechanical withstand of other structural components. The bellows material has to be strong and flexible enough to allow deformation without losing mechanical integrity and thus allowing controlled pressure relief. Results obtained during internal arc tests presented available literature showcase a gas generation rate of 110 l/MJ [14]. Depending on the energy developed the expected gas formation rate can vary from 0.3 to 13 l/ms [5]. This produces an average liquid pressure rise rate of 0.3–0.5 MPa/ms [15]. This is such generation of energy, that even an equivalent arcless source of pulse pressure can be proposed, which utilizes the combustion of explosive material [15]. In comparison, the results obtained during tests described in references [9, 12, 13] display an average gas formation rate of 4 × 10−5 l/ms, and an average pressure rise of 7.5 × 10−5 –13.3 × 10−5 MPa/ms. These values are drastically lower, which again proves that the internal fault was contained to a low energy, long duration event.

3 Numerical Modelling of Internal Fault Scenarios The aid of numerical modelling of fault occurrences in units with sectioned active parts was first mentioned in [9] and [13] with an aim to conceptually reinforce findings which were obtained by previous tests. The aim in this paper is different. The idea is to use numerical modelling as a tool that can predict exact levels of fault currents I CP and I FP based on the location of the fault. This is vital information in order to assess the fault energy and to determine the worst-case scenario for purposes of further testing. The proposed methodology consists of a 3D model of the active part of the unit under analysis. As shown in Fig. 2, both possible failure modes lead to the same outcome; a short-circuit of one active part segment. This can easily be modelled using Mentor Graphics MagNet version 7.7 [16]. Figure 3a shows geometry of a 123 kV voltage transformer active part including the appropriate finite element mesh, while Fig. 3(b) shows the accompanying circuit with one short-circuited segment. 3D time-harmonic analysis at fundamental frequency was used. To reduce calculation time ¼ symmetry model was used.

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Fig. 3 a Meshed model of the active part, b circuit used in numerical calculations

Initial calculations were performed on the active part without the short-circuited segment, with an objective to obtain the rated current I RP . Fault occurrence was simulated by short-circuiting one section (coil) of the primary winding at a time, as shown in Fig. 3b. The calculation was repeated n times, where n is the total number of sections (coils) in the active part. In each calculation, I CP and I FP were recorded for each calculation thus forming two fault vectors. In order for the calculation results to be comparable across all variants of active part design (different transformer types, voltage levels, coil number, etc.) the obtained results are best expressed as ratios of fault current to the rated current I FP / I RP and I CP / I RP , respectively. Such analysis for a standard 123 kV voltage transformer is given in Table 2. This analysis was performed at rated voltage of the unit; however, the model is proposed to be linear, so the actual applied voltage is irrelevant in respect of obtaining the fault current ratio vectors. There are several takeaways from this analysis. The first is that it is apparent that the total current I FP of the transformer increased 2–4 times, as stipulated in the introductory chapters. The fault current in the short-circuited section (coil) increased Table 2 Results of FEM calculation of fault performance of a standard 123 kV voltage transformer Fault vector

No. of coil under fault 1

I FP /I RP

1.98

I CP /I RP

8.44

2

3 2.40

11.5

4

5

6

7

8

9

10

2.70

3.13

3.61

3.45

2.89

2.56

2.29

1.83

13.64

17.38

21.69

20.40

15.59

12.98

11.40

8.48

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Table 3 Results of FEM calculation of fault performance for the entire inductive voltage transformer product range Highest fault ratio Rated insulation level of the unit 72.5 kV 123 kV 145 kV 170 kV 245 kV 362 kV 420 kV 550 kV I FP /I RP

3.77

I CP /I RP

20.86

E FP [J/s]

4283

3.61 3.35 21.69 5901

3.18

22.24 24.58 7544

5778

2.89

2.52

33.69 40.33 4910

4810

2.18 2.47 33.65

37.27

4967

5446

9–22 times, which is significant enough to cause severe thermal overload of the faulted section, but not enough to cause a sudden overload and consequent energy generation in the entire active part. In comparison, a fault current of the same active part, assuming a complete breach of the insulation system would cause a I CP /I RP ratio of several thousands, which would naturally cause a drastically faster phenomenon. However, due to the reasons disclosed in chapter 2, such an occurrence is not possible. The second takeaway is that the analysis shows the most unfavorable location for the fault, which is in this case coil No. 5. Provided that internal fault performance has to be verified by test, the most unfavorable location for fault inception should be chosen, and numerical analysis can easily disclose where that location is, which is very convenient. The same analysis was performed on all standard inductive voltage transformers from 72.5–550 kV, with an aim to compare worst fault levels across the entire product range. Essentially the same results are obtained for combined units as well. The results of the analysis are shown in Table 3 where results that produced the highest fault current ratios are displayed. Again, several things can be concluded from the analysis. I FP /I RP ratio decreases as the insulation level increases, which is logical as higher voltage units inherently have more sections in the active part. On the other hand, the I CP /I RP ratio increases with the insulation level, which is also logical, as the rated current I RP is typically lower while I CP is of similar magnitude. Total energy potential of the fault is indirectly assessed through generated losses using expression (1) [13], where Rw is the resistance of the entire winding at reference temperature, while RC is the resistance of the short-circuited coil at reference temperature. E F P = I F2 P · Rw + IC2 P · RC

(1)

This once again proves that obtained energy generation rates are much lower than those presented in [5, 14, 15] and insufficient to cause an almost instantaneous pressure accumulation. Furthermore, based on these results and other relevant parameters, such as enclosure size, oil quantity and rated withstand of structural components, a most unfavorable unit to qualify the entire product range can be pinpointed, which is very relevant information.

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4 Experimental Verification One of the main purposes of this paper is to verify the findings obtained through numerical modelling which were presented in the previous chapter. Due to availability, the same 123 kV inductive voltage transformer that was used for numerical analyses presented in Tables 2 and 3 was also used for experimental verification. Initial experimental verification was performed on a dried, oil-impregnated active part. To allow access to all segments of the active part and both currents of interest (i.e. I FP and I CP ), the unit was drained of oil and opened. This naturally means that all tests had to be done at a reduced voltage, which is convenient as it allows for a longer test-time and a simpler test circuit. Diagram of the test circuit is shown in Fig. 4a, while a photograph of the test setup is shown in Fig. 4b. During each test I FP , I CP and capacitive current through the main insulation (shown as I C in Fig. 4a) were recorded. Each current path was closed off by a 1  shunt. Three identical, calibrated FLUKE 179 mulitmeters were used to record the voltage on each shunt. Apart from verifying the numerical calculation, the influence of the fault in the primary winding on the main insulation was analyzed. This was done by measuring capacitive current I C during each test. For comparison, I C can be obtained through analytical calculation, as shown in [11]. The first tests performed were done to verify the linearity of the model. The tests were performed with first coil short-circuited and results are shown in Fig. 5. It is clear that the behavior of the transformer is linear, which has been confirmed by both calculation and measurement. It is also apparent that measured and calculated values are in excellent correlation, with average difference between them under 1% for I FP and around 7% for I C . Since the linearity of the test has been established, further tests can be performed. All of them were performed at approximately 25% of rated voltage. The results are presented in Fig. 6.

Fig. 4 a Diagram of the testing circuit. b Test setup

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(c) Fig. 6 a Comparison of measured and calculated current in relation to short-circuited section a I FP , b I CP , c I C

Again, the comparison of results displays a very good correlation with an average error of 3.3% for I FP , 14% for I CP and 11.7% for I C . Maximal deviations are 8.5%, 29.4% and 29.8%, respectively. This shows the adequacy of numerical modelling for this application. A higher degree of error is expected with I CP and I C , due to several reasons; dependency of I CP on contact resistance, and a lower measurement accuracy due to the magnitude of I C at reduced voltage.

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It is clear that numerical calculation is accurate enough to demonstrate the behavior of the transformer under internal fault conditions. One conclusion that is also confirmed is that if the fault originates in the primary winding the main insulation is unaffected, as conceptually shown in Fig. 2b. This is clear from obtained values of capacitive current I C , which are constant regardless of the incepted fault in the primary winding. This also in line with conclusions of papers [9] and [12]. After initial tests were performed, the unit with coil No. 5 short-circuited (i.e. the one with the highest fault current ratios) was assembled and filled with oil, with an aim to repeat the measurements up to rated voltage. Naturally, as the unit is closed I CP could not be measured since the sections themselves were not accessible. The same general circuit shown in Fig. 4a was used for the repeated test as well. However, the test location and recording equipment was different. Figure 7a shows the test setup, while Fig. 7b shows current waveforms obtained during testing. It is worth mentioning that this test causes gassing and pressure build-up, provided the voltage is applied long enough, thus the testing time was limited to 30 s. The comparison of test results to calculated data is given in Fig. 7b, c.

(a) Measurement

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Once again, the expected behavior was achieved in experimental conditions. The average difference between measured and calculated I FP is approximately 2%, while the average difference for I C is 5.5%. This test unequivocally confirms the adequacy of numerical modelling to accurately represent actual behavior of transformers with a sectioned active part. Apart from calculation and several previously performed tests, it is worth noting that this behavior is also verified in service, which is shown in detail in reference [13].

5 Conclusions This paper presents theoretical background on internal fault performance of instrument transformers with sectioned active parts. The main theoretical considerations are backed up by numerical calculations performed on several representative units, ranging in insulation level from 72.5 to 550 kV. Fault energy generation rates are compared with data available in relevant literature and proved to be significantly lower. Numerical approach was verified with several tests performed on a 123 kV inductive voltage transformer. The correlation of results was very good, which makes numerical modeling the basis to assess critical fault locations, energy generation and expected transformer behavior under said conditions. The findings presented in this paper will be used as a foundation for further testing and calculations. Presented work is a necessary foundation for verifying internal fault performance of units with sectioned active parts. As mentioned in the introductory chapters, the biggest drawbacks of currently specified internal arc testing are that some vital failure modes are excluded and that the quality of insulation system is not qualified in an adequate way. In addition, from a logistic standpoint, internal arc testing is very unpopular. In order to adequately sustain the arc burn-through, a very well equipped testing laboratory is necessary. Furthermore, since residual fire is expected and allowed even if the test is successful, let alone if the arc energy is not sustained, it is perceived as a safety hazard. This is why some laboratories are reluctant to perform the test and the test itself is very expensive. In addition, since the dimension of the arc-incepting element is specified in current standards, it may happen that the arc is not sustained long enough (or the current asymmetry is off), which makes the test invalid, and the test object has to be scrapped [2, 3]. It should be noted that major instrument transformer faults are statistical in nature, and depend on a variety of parameters that are difficult to define and standardize. Furthermore, as instrument transformer production can be labor intensive, guaranteeing its behavior based on one-off special tests may not be enough. This is why a more extensive verification of the insulation system should be specified, and some of it performed routinely. Some ideas and concepts on the matter were presented in [4]. This, along with appropriate maintenance and monitoring is the only viable way to further reduce major faults in instrument transformers, which will be the focus of future work.

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As a final thought, internal-arc testing, as specified by the current standards, is adequate only to prove conformance to a certain degree of operational safety. Moreover, subjecting units that are inherently designed to reduce and limit the fault energy means exposing them to fault propagation mechanisms that are not realistic nor even possible. This makes testing increasingly difficult, leads to an unnecessary overdesign of the unit and, in the end, is of little value for actual in-field fault performance, which is recognized in [6]. Instrument transformer faults are rarely trivial, which is why a more comprehensive approach is crucial, if we are truly keen on reducing them.

References 1. Working Group A3.06 CIGRE (2012) Final report of the 2004–2007 international enquiry on reliability of high voltage equipment. Part 4: Instrument transformers. Cigre Brochure 512 2. IEC 61869-1 (2007) Instrument transformers—part 1: general requirements 3. IEEE Standard C57.13.5 IEEE (2009) Standard for performance and test requirements for instrument transformers of a nominal system voltage of 115 kV and above 4. Poljak M, Bojani´c B (2010) Method for the reduction of in-service instrument transformer explosions. Eur Trans Electr Power 927–937 5. Nogueiras JM (2018) Safety in the operation of oil-paper instrument transformers. 47th Session of Cigre, Paris 6. IEEE Standard C57.13.5 IEEE (2019) Standard for performance and test requirements for instrument transformers of a nominal system voltage of 115 kV and above D3.0. Currently in balloting 7. IEC 61869-1 (2019) Instrument transformers—part 1: general requirements 38/606/CD. Currently in Comment Resolution 8. Yi Z, Hua R, Xu L, Honggang R, Shimin W, Aimin W, Hai W, Jia W (2016) Analysis of a 220 kV current transformer explosion accident. In: 4th international conference on machinery, materials and computing technology (ICMMCT 2016), Hangzhou, China 9. Žiger I, Bojani´c B, Krajtner D (2015) Power voltage transformers: expanding beyond station service. IEEE PES General Meeting, Denver CO, USA 10. Žiger I, Krajtner D, Filipovi´c–Grˇci´c D (2018) DC current capability of high voltage apparatus based on the open-core concept. Electr Power Syst Res 647–654 11. Žiger I, Krajtner D, Ubreki´c Z (2014) Pushing the Boundaries of Inductive Voltage Transformer Design. In: 3rd international colloquium transformer research and asset management, Split, Croatia 12. Žiger I, Bojani´c B, Krajtner D (2014) Open-core power voltage transformers: concept, properties, application. IEEE Energycon 2014, Dubrovnik, Croatia 13. Krajtner D, Bojani´c B, Žiger I, Ubreki´c Z (2015) Instrument transformers safety from explosion—in-service verification. In: 12th HRO Cigre Session, Šibenik, Croatia 14. Darian LA, Dementyev YA, Efremov VP, Shurupov AV, Kozlov AV (2010) A new approach to design of oil-filled transformers with fire and explosion safety. 43rd Session of CIGRE, Paris 15. Darian LA, Polistchook VP, Shurupov AV (2014) Testing of models of explosion protection system for high-voltage oil-filled electrical equipment. J Energy 158–165 16. Mentor Graphics package for magnetic analysis using Finite Elements, Mentor A Siemens Business, Wilsonsville, Oregon, USA

Simulation of Long-Term Transformer Operation with a Dynamic Thermal, Moisture and Aging Model Johannes Raith, Christian Bonini, and Mario Scala

Abstract This paper introduces a dynamic thermo-hydraulic network model for transformer applications. The model includes the dynamic performance of temperatures, moisture levels, oil flows and the temperature dependent losses, separated in individual windings and individual positions. Therefore, interactions between single windings and also the core are covered by this model which is not the case in standard models. The temperature and moisture values are applied to calculate the insulation aging at different positions. In IEC 60076-7 (2018) the influence of moisture and oxygen can be considered roughly for aging calculations while the determination of the local moisture levels is not part of the standard. Here this paper gives assistance to determine such local moisture levels during the life time of a transformer. The thermo-hydraulic model includes also the dynamic properties of moisture transport in solid and liquid insulation to determine the local moisture levels and DP-values in the insulation. Simulations point out the difference between the aging model of IEC and the model developed by the transformer manufacturer. In addition, the moisture generation during cellulose aging and the change of moisture absorption capability by aging are parts of the simulation studies in the paper. Keywords Life time management · Transformers · Aging · Moisture · Overloading

1 Introduction The performance of transformers in operation and their thermal limits is a topic which is as old as transformers themselves. The standards of IEC and IEEE illustrate methods to determine the temperatures also during operating conditions. However, there are restrictions in these methods like the limitation to one winding, etc. The dynamic thermo-hydraulic network model used in this study is based on another approach. Including the oil flow in individual windings, a multi-winding J. Raith (B) · C. Bonini · M. Scala Siemens AG Oesterreich Transformers Weiz Global Technology Centre, Weiz, Austria e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_17

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model is established. The consideration of the buoyancy force in this model approach includes the interaction between individual windings, and other heat sources, like the core, are considered too, which are not driven by the load current. Instead of time constants, heat transfer coefficients are introduced in the model which depend on their physical quantities like the actual heat flux. This avoids the imprecise usage of time constants which do not vary at different conditions. This approach covers transient heating and cooling processes with the same model and allows the recalculation to different tap changer positions and cooling conditions. For long-term simulations the aging condition of the transformer insulation is of interest. Here not only the thermal behavior is essential, but also the moisture content. For the used moisture model in this study many investigations were done including laboratory measurements to describe the properties of the materials applied. An example of such an investigation is shown in [1]. Moisture in the cellulose insulation accelerates aging which is also discussed in the IEC 60076-7 [5], but the determination of the moisture itself is missing in this loading guide. Moreover, the dynamic variation of loading and temperatures and their effect on the moisture is also not covered in the standard. Literature [2, 3] introduce a method which provides information about the initial moisture condition of a new transformer. This initial value is the basis for further aging investigations. Nevertheless, to simulate the long-term aging of a transformer, the knowledge of both temperature distribution and moisture distribution are needed. The complexity increases due to the change of the total moisture content in transformers during operation, and due to the change of material moisture properties (e.g. moisture absorption) which depend on the aging condition. Consequently this study tries to include all these properties and requirements in a complete dynamic thermo-hydraulic aging model for transformers.

2 Overview of Thermo-Hydraulic Aging Model (THAM) 2.1 General This chapter shows a brief overview of the thermo-hydraulic aging model. The oil flow system of a transformer is depicted, with individual windings, the core, the cooling arrangement and the tank. These elements are modeled by different branches with specific properties which are connected by nodes in order to reach a thermal network model [4]. To consider the moisture and the cellulose aging in such a model, different cellulose parts inside the tank are allocated to corresponding branches and nodes. Furthermore the tank with gaskets and conservator with membrane are considered to allow a potential moisture exchange with the atmosphere. An example of such a model setup is indicated in Fig. 1.

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Major transformer elements: 7

8

Node 1-4-9-5: Transformer core Node 3-22-8: Tank bulk oil Node 3-23-8: Tank wall Node 6: Mixed winding top oils (pressure ring) Node 7: Tank Topoil and conservator membrane Node 8: Tank Topoil including the gaskets Node 10 – 21: Transformer windings Node 24-26: Cooler element

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Fig. 1 Thermo-Hydraulic Model (THAM) of a transformer for long-term simulations

The THAM calculates the steady-state and the transient behavior of following quantities based on the loading, respectively the ohmic and eddy current losses considering their temperature characteristic: • Heat flow and temperatures of all transformer components, e.g. top and bottom oil in the tank and coolers, core temperatures, average winding temperatures, hot spots and local oil temperatures in windings. The heat transfer coefficient depends on several parameters: e.g. the temperature rise, absolute temperature, etc. Therefore no time constant is required. Instead of the time constant the change of temperature is directly based on the dissipated heat. • Oil flow in the transformer components (core, windings, tank, etc.) determined by hydraulic resistances, buoyancy force and optional the pump pressure. • The hydraulic resistances restrict the oil flow in the loops and can depend on the viscosity of the liquid with its significant influence on temperature. The oil flow and the dissipated heat of the cooling elements determines the temperature difference between cooler top and bottom temperature. Regarding the moisture and aging behavior the following items are calculated: • The exchange of moisture between solid and liquid insulation including a potential moisture exchange with the atmosphere by diffusion of moisture through the conservator and gaskets • Calculation of local degree of polymerization (DP value) of different cellulose elements considering the: – Influence of moisture and oxygen – Cellulose quality (thermally non-upgraded or upgraded paper) – Moisture generation by the aging itself • Influence of aging (DP value) on moisture absorption of cellulose • Risk of bubbling.

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dmoist = V/Aoil E.g. Pressure ring with a volume V and a surface Aoil

Block of cellulose for a THAM model

Fig. 2 Transformation of transformer cellulose parts into cellulose blocks in the model

2.2 Moisture Model 2.2.1

Modeling of Cellulose Components

The following cellulose components are essential for the calculation of the transient moisture behavior in a transformer and should be considered in a long-term simulation. • Cellulose insulation of windings – Paper insulation of winding conductors (thermally non-upgraded or upgraded) – Spacers between discs – Cylinders around windings • Winding pressure ring (on top) and mounting plate (at bottom), laminated board • Additional insulation in the tank (e.g. insulation to fix lead connections). In the model the cellulose insulation parts are simplified as a block, with the temperature of the associated branches or nodes. The surface area of such a cellulose block (Aoil ) is given by the surface which is in contact with the oil. The effective penetration thickness of the block (dmoist ) is given by the volume of the block divided by the cellulose block surface Aoil (Fig. 2).

2.2.2

Moisture Transport and Moisture Equilibrium in Solid and Liquid Insulation

In the model each cellulose block is divided into several layers with different thicknesses to calculate also the moisture diffusion inside the solid insulation and the balancing between the solid insulation and adjacent oil. As shown in Fig. 3, the exchange of moisture is determined by moisture diffusion within the solid insulation and moisture transport by the oil flow. The local moisture levels in the cellulose insulation and the oil (Wc and Woil ) are determined by the corresponding local moisture vapor pressures (pc and poil ) which are depending on the local temperatures of cellulose and oil (Tc and Toil ). This is described with the formulas (1)–(6). It must be noted that p0 represents the vapor pressure of pure water

Simulation of Long-Term Transformer Operation with a Dynamic … Fig. 3 Moisture exchange in cellulose and to oil

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pc p0

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(1) (2) (3) (4)

(DP value is calculated with formula Eq. 13 or 14). Moisture in oil: Soil = 10

a−

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poil · Soil p0

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The moisture exchange is driven by the geometry of the insulation and the moisture vapor pressure difference p between the layers within the insulation or with the vapor pressure difference of the outermost insulation layer and the local oil (formulas (7)–(9)). Dynamic moisture exchange: dW Aoil · p =K· dt dlayer

(7)

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(K… Factor for dynamic exchange). Moisture exchange inside the cellulose: p = pc,i − pc,i+1

(8)

Moisture exchange between the cellulose surface and adjacent oil: p = pc,i=1 (Tc , Wc ) − poil (Toil , Woil )

2.2.3

(9)

Diffusion of Moisture Between Oil and Atmosphere

In addition, the model includes the aspect to allow a moisture exchange with the ambient air, based on a potential moisture diffusion through the rubber membrane of the drying unit, or through gaskets. Formula (11) shows that this moisture exchange refers also to the moisture vapor pressure difference. The moisture vapor pressure in air (pair ) is determined by the relative humidity in air (rh) as shown in formula (10). pair = r h(Tair ) · p0 (Tair )

(10)

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(11)

The oil temperature in the conservator is modeled with the oil temperature at the top of the tank and the ambient air temperature. The temperature level of the conservator is estimated with formula (12). Tconser vator = 0.67 · Ttopoil + 0.33 · Tair

(12)

It must be noted, that the conservator’s air passes the dryer which reduces the value of the relative humidity to about 6% of its outer value.

2.3 Aging Model 2.3.1

DP Value

Aging causes a degradation of the mechanical strength of cellulose, respectively the paper tensile strength. A reduction of the tensile strength to below 40% of the initial value is often indicated as a risky condition regarding the short circuit withstand strength [5]. Instead of the measured tensile strength, the average length of the cellulose fibers, the degree of polymerization (DP value), is a common quantity to

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describe the condition of cellulose. Tensile strengths of about 40% correlates with DP-values of about 200. New transformers show normally DP values higher than 900. The THAM calculates the decrease of the DP value in each modeled solid insulation part of the transformer (Fig. 1). Two aging formulas are studied in this paper. Formula (13) represents an aging formula developed by Siemens [6], and Eq. (14) illustrates the formula in the IEC loading guide [5]. It is clear, that the temperature, moisture and oxygen levels are always actualized between two calculation time steps in a THAM simulation (from t−1 to t). 1   1− p(T ) 1− p(T ) + Ot · Mt · t · ( p(T ) − 1) D Pt = D Pt−1

(13)

−1  E −1 D Pt = D Pt−1 + t · A · e− R·(T +273)

(14)

In the following only the quanities of formula (13) are explained in more detail, because formula (14) is discussed in the loading guide [5]. It can be seen, that the DP value drop in Eq. (13) is strongly influenced by a moisture factor Mt , a temperature function p(T) and oxygen factor Ot . It must be noted that in the IEC formula, the temperature influence is added with a factor to the time “t” and the exponent p is kept constant ([5, 6]). However, in Eq. (13) the thermal function is applied in the exponent p which includes also the cellulose quality (upgraded vs. non-upgraded). (15, 16)

2.3.2

Moisture Factor Mt

Formula (13) describes the influence of the moisture content on the cellulose insulation aging (DP value). The IEC loading guide shows this influence only for three constant moisture levels of 0.5, 1.5 and 3.5%. However, based on the operation the moisture distribution in the transformer varies and during the lifetime the moisture content in the transformer changes due to a moisture generation by the aging itself and due to a potential exchange of moisture with the atmosphere, depending on the sealing system. Therefore, the information of the loading guide is not enough to perform an aging calculation for a certain transformer operation (Fig. 4).   Mt = 8 · 10−8 · 0.3 + 0.64 · Wc1.7

(17)

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Fig. 4 Influence of moisture on relative aging rate (Mt factor normalized to one at 0.5% moisture)

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The oxygen dissolved in oil accelerates the aging, what is considered with the Ot factor. By the way the aging consumes the oxygen and generates CO and CO2 as degradation products at the end of the chain of chemical reactions. However, a sealed transformer is nearly free of oxygen. The oxygen factor Ot in Eq. (13) depends also on the insulation temperature as shown in Eq. 18 and with the Table 1 below. O(T, ppm) =

1 + (OT − 1) · O ppm /Osat

(18)

Osat = 37000 ppm (< 1000 m sea level, in mineral oil). Oppm …Oxygen concentration measured in transformer.

2.3.4

Moisture Generation by Aging

The total moisture content during the lifetime of a transformer is not constant. Even with a total tight tank arrangement, moisture can be generated by the aging of cellulose itself. Figure 5 shows results of laboratory measurements for such a moisture generation by aging. Based on these measurements from literature, a moisture generation function (Wage ) can be derived as shown in formula (19) which is used in the THAM to calculate the moisture generation by aging. This means, depending on the mass of the individual cellulose elements a certain amount of water is generated based on the DP value drop. The parameter F in formula (19) depends on the paper quality. For non-upgraded paper F is assumed with 0.5. Thermally upgraded paper

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Fig. 5 Moisture generation by aging of non-upgraded paper cellulose according to a [7] and b [8]

generates much less moisture than non-upgraded paper as shown in [6]. In that case F is 0.01.   D P0 −1 (19) Wage = F · D Pt+1

3 Aging Simulation Study 3.1 Overview This chapter discusses results of a case study using the thermo-hydraulic aging model of Chapter 2. The studied unit is a 490 MVA, ODAF transformer with thermally upgraded paper in the windings. The study considers following conditions: • Cooling stage of transformer is kept constant (maximum cooling, ODAF) • Completely tight transformer (no moisture exchange with atmosphere) vs. leaky transformer (with moisture exchange with atmosphere) • Aging (DP value) is calculated according to Siemens formula (Eq. (13)) and IEC formula (Eq. (14)) • Moisture generation by aging is assumed with Eq. (19) and no oxygen in transformer • Fixed loading cycle (up to 110% for each day) to reach temperatures as shown in Fig. 6b • Reasonable yearly ambient temperature profile (Fig. 6a).

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Fig. 6 a Yearly ambient temperature profile, b temperatures and c moisture in 1st year at hottest day

Figure 6a shows the used yearly ambient temperature profile in this study. For each simulated year the same ambient temperature profile is applied. Figure 6b illustrates an example of the occurring temperatures in the transformer for one day in the summer and Fig. 6c the moisture distribution for the same day in the first year of operation.

3.2 Example for DP Value Distribution This chapter shows an example for some simulated DP values over 50 years for the investigated transformer. The average DP value is calculated with formula (19) which makes a higher weighting of low DP values than linear.  avg.D P =

n 1 1 · n i=1 D Pi

−1 (20)

Figure 7 shows the drop of the DP value for different insulation parts. It can be seen, that the lowest DP value in the investigated transformer occurs in the spacers Fig. 7 Simulated DP value drop over 50 years (Wc, initial = 0.5%, completely tight tank)

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of the hotspot region. This means, despite of the higher temperature level of the insulation paper the thermally upgrading effect reduces its aging. This is an important observation at units with thermally upgraded winding paper. Even the winding pressure ring shows a lower DP value than the winding paper in the simulation. This means the winding pressure ring could be more critical than the thermally upgraded paper itself. This is especially of interest, because the pressure ring is essential for the short circuit withstand capability of a transformer.

3.3 Comparison of IEC and Siemens Aging

1000 900 800 700 600 500 400 300 200 100 0

AverageDPValueinTransformer

Average Moisturein Cellulose

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Moisture in %

DP value

Figure 8 compares the calculated average DP value using the Siemens approach, Eq. (13), and the IEC method, Eq. (14). The inputs are the same and shown in III-A. It must be noted, that the moisture generation in the simulations for both, the IEC and the Siemens method, is based on their corresponding drops of the DP values using Eq. (19). Principally it can be seen, that the Siemens approach is much more conservative, resulting in a faster drop of the DP value and consequently also in a faster increase of the moisture content. Moreover, the aging according to IEC after 50 years is very low in Fig. 8 (average DP value of only about 600). One reason for this difference is the used temperature influence in the aging Eqs. (13) and (14). The following table compares relative aging rates using the appendix A.3 and A.4 of the IEC loading guide [5], the IEEE C57.91 loading guide and Eq. (13) of this paper. The table shows the temperature influence for thermally upgraded and non-upgraded paper with a moisture level of 0.5%. In IEC and IEEE both paper types show a very strong reduction of the aging with decreasing temperatures, whereas the Siemens equation lead especially at lower temperatures to a higher relative aging rate. This explains the different aging results in Fig. 8. Therefore, a check of the thermal influence on the

1.5 1.25 1 0.75 0.5 0.25

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Fig. 8 Aging and moisture results according to IEC (blue lines) and Siemens (green lines) with an initial moisture content of 0.5% (transformer assumed as completely tight)

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aging is highly recommended, because these characteristics influence significantly the drop of the DP value and in further consequence the moisture behaviour during the transformer lifetime (Table 2).

3.4 Influence of Initial Moisture Content and Tank Tightness In this chapter the influence of the initial average moisture content is studied together with the effect of the tank tightness. For this reason the long-term simulations are done with two different initial moisture levels (0.5 and 0.8%). New transformers are typically manufactured in this range and a method to determine the initial average moisture content of a transformer is given in [2] and [3]. For the tank tightness two assumptions are studied. The first one assumes a complete tight transformer whereas the second one allows a moisture exchange with the atmosphere. This means a residual diffusion of moisture through gaskets and rubber bag membrane could remain. In general, in the last decades sealed systems with rubber bag conservators are preferred to reduce the influence of oxygen to aging. The characteristic of membrane and the gasket materials are assumed to be equal in the simulation and the moisture of atmospheric air oscillates around 50% relative humidity for each day. Figure 9 illustrates the results of these simulations. With 0.5% initial moisture over the total cellulose, the DP value trends over 50 years are similar between “absolute tight” and a residual rubber moisture diffusion. It can be seen, that the moisture in the “totally tight” simulation starts to increase, whereas the simulation with “moisture diffusion with atmosphere” shows a flattening of the moisture increase. This means that moisture penetrates from the transformer out to the atmosphere. Furthermore is shown that the effects are much more pronounced in the simulations with an initial moisture content of 0.8%. This indicates that the initial moisture content of a transformer is an essential quality parameter. The moisture in the 0.8% tight simulation increases significantly at the end which causes a more or less linear drop of the DP value in this period. This phenomenon is based on the used moisture generation function Wage (Eq. (19)). Therefore a check of this equation seems to be advantageous.

3.5 Influence of Non-Upgraded and Thermally Upgraded Paper This chapter shows the difference in the aging and the moisture behavior when non-upgraded paper is used for the windings. All other design parameters of the transformer remained unchanged. Figure 10 shows that the average DP value of all insulation components decreases faster as when non-upgraded paper is used in the windings. Furthermore it can be seen, that the non-upgraded winding paper becomes

Vnon-upgraded, IEC, Annex A

0.12

0.25

0.50

1.00

1.94

3.67

Temperature

80

86

92

98

104

110

2.41

1.54

1.00

0.66

0.44

0.30

Vnon-upgraded, Siemens

Table 2 Relative aging rates V, depending on temperature and paper quality

1.00

0.65

0.42

0.26

0.16

0.10

Vupgraded, IEC, Annex A

1.00

0.54

0.28

0.15

0.07

0.04

Vupgraded, IEC = IEEE

1.00

0.66

0.44

0.30

0.21

0.14

Vupgraded, Siemens

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1000 900 800 700 600 500 400 300 200 100 0

Average DP Value of Cellulose WC=0,5, tight WC=0,5, moist. difusion WC=0,8, thight WC=0,8, moist. diffusion

0

5

10

15

20

25

30

35

40

45

Avg. moisture in %

DP value

224

50

6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0

Average Moisture in the Transformer WC=0,5, tight WC=0,5, moist. difusion WC=0,8, thight WC=0,8, moist. diffusion

0

5

10

15

20

Time in years

25

30

35

40

45

50

Time in years

Fig. 9 Aging and moisture results with different initial moisture contents and tank tightness

800

700

700

600

600

500 400

400 300

200

200

100

100

0

0

5

10

15

20

25

30

Time in years

35

40

45

50

0

non-thermally upgraded Paper, WC=0,5% thermally upgraded Paper, WC=0,5%

2.5

500

300

Average Moisture in Cellulose

3 2.75

non-thermally upgraded Paper Spacer Pressure Ring thermally upgraded Paper Spacer Pressure Ring

900

DP value

DP value

800

Local DP-Values for initial moisture content 0,5%

1000

non-thermally upgraded Paper, WC=0,5% thermally upgraded Paper, WC=0,5%

900

Avg. moisture in %

Average DP Value in Cellulose

1000

2.25 2 1.75 1.5 1.25 1 0.75 0.5 0.25

0

5

10

15

20

25

30

35

Time in years

40

45

50

0

0

5

10

15

20

25

30

35

40

45

50

Time in years

Fig. 10 Aging and moisture with different paper quality

dominant and shows the lowest DP value. This is not the case when upgraded paper is used. In addition more moisture is generated when non-upgraded paper is used which accelerates again the aging of other transformer insulation parts. This means the usage of upgraded winding paper reduces also the aging of non-upgraded cellulose like the pressure ring. E.g. the difference in years to reach a DP value of 200 is about 10 years for this component.

3.6 Influence of Initial DP Value This chapter shows the influence of the initial DP value on the aging and the moisture generation. A completely tight transformer is assumed in these simulations. The results in Fig. 11 show, that the average DP value after 45 years is nearly the same for all conditions, but the moisture level at the end is significant higher with higher initial DP-values. This is caused by the higher moisture production during the lifetime. At the DP level of 200, the simulated moisture content in the cellulose with an initial DP value of 1100 is about 0.35% higher than in the simulation with an initial DP value of 900. This is an unexpected result but can be explained with the used formulas. The individual insulation parts, e.g. winding paper, spacer and pressure ring, show the same trend. Nevertheless, it must be noted that the mechanical properties of the cellulose with a higher initial DP level are during the lifetime always better than with

Simulation of Long-Term Transformer Operation with a Dynamic …

1000

900

900

800

800

700

700

600 500 400

600 500 400

300

300

200

200

100

100

0

0

5

10

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20

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30

Time in years

35

40

45

50

2.25

DP Spacer (DP 1100) DP Spacer (DP 900) DP Spacer (DP 700) DP Pressure Ring (DP 1100) DP Pressure Ring (DP 900) DP Pressure Ring (DP 700)

Average moisture in cellulose in %

1100

1000

0

Average Moisture in Cellulose

DP-Values in Pressure Ring and Spacer

1100

DP value

Average DP value

Average DP-Value

225

0

5

10

15

20

25

30

Time in years

35

40

45

50

2 1.75 1.5 1.25 1 0.75 0.5 0.25 0

0

5

10

15

20

25

30

35

40

45

50

Time in years

Fig. 11 Aging with different initial DP values (blue lines: DPinit = 1100, green lines: DPinit = 900, red lines: DPinit = 700)

a lower initial DP value. However, it indicates that the initial DP value is not a very critical parameter for a new transformer. The initial moisture content is much more important as shown in Fig. 9.

4 Conclusion This case study indicates a big difference of the temperature influence on the aging between the IEC and the demonstrated Siemens approach, especially at lower temperatures. With decreasing temperatures, in IEC the aging halves per 6 °C temperature step for non-upgraded cellulose, while in the Siemens method this temperature step increases with decreasing temperature as shown in laboratory tests [6]. Consequently the DP value decreases with the Siemens formula much faster than with the IEC approach (Fig. 8). Therefore, due to this big difference, a check of the used temperature influence on the cellulose aging is highly recommended. Furthermore the paper shows how moisture in a transformer must be considered for a suitable aging determination for a transformer. It is shown, that the dynamic moisture distribution within the transformer must be determined. So it is far beyond the methods given in the IEC loading guide, where the aging is only indicated for three different constant moisture levels (0.5, 1.5 and 3.5%). For the comparison with the Siemens approach, a function based on these three values was applied to extent the IEC application to individual values, also below 0.5% moisture. This is essential for aging calculations, because based on an average moisture of 0.5%, the moisture in the hotspot area varies between 0.15 and 0.3% according to the influence of temperature distribution on local moisture. This paper also points out an important quality parameter for a new transformer. It is the initial moisture content in the solid insulation material, which is important to extend the lifetime of a transformer. A realistic simulation shows, that the time to reach an average DP value of 200 is with 0.5% initial moisture about 11 years longer than with 0.8% initial moisture. Therefore, a method to determine the initial moisture content is recommended for new transformers as shown in [2, 3]. Moreover, if the initial moisture content is low, then potential moisture issues can be avoided

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during the complete lifetime of the transformer. Otherwise critical moisture levels can occur after many years of operation (Fig. 9, tight tank simulation). In addition, the paper shows that the initial condition of the solid insulation material, given by its DP value, is not essential to extend the lifetime of a transformer (Fig. 11). All in all a powerful model is shown in this paper which allows a dynamic simulation of the thermal performance of a transformer together with its corresponding moisture behavior. These two aspects, in combination with suitable aging formulas for different transformer insulation components, enable the possibility of long-term simulations for different transformer designs to evaluate their specific aging behaviors already at the beginning of their life in the design stage. Furthermore, the usage of a THAM in monitoring or digital twin applications improves the quality of data to determine the condition of different insulation components in the transformer considering the real loading and ambient conditions.

References 1. Scala M (2008) Moisture assessment in transformers including overloading limits. CIGRE, A2-202, Paris 2. Scala M Bonini C (2019) Bonini, Moisture determination and drying simulation during manufacturing of transformers. Transformator’19 conference, Torun-Poland. http://transformator.ptp iree.pl/konferencje/transformator/2019/po_konf/materialy_trafo_2019.pdf 3. Scala M Bonini C (2019) Direct moisture determination of power transformers. Transformator’ 19 conference, Torun-Poland. http://transformator.ptpiree.pl/konferencje/transformator/ 2019/po_konf/materialy_trafo_2019.pdf 4. Seitlinger W (2000) A thermo-hydraulic transformer model. In: Conference of electrical power supply industry (CEPSI), Manila 5. IEC 60076-7, Loading guide for mineral-oil-immersed power transformers (2018) 6. Scala M, Bonini C (2014) Measurement results and calculation model of thermally aged cellulose, including non-constant moisture levels. CPRI, New Delhi 7. CIGRE Brochure 349, Moisture equilibrium and moisture migration within transformer insulation systems, WG A2.30, (2008) 8. Lundgaard LE, Hansen W, Linhjell D, Painter TJ (2004) Ageing of oil-impregnated paper in power transformer. IEEE Trans Power Delivery 230–239

Line Discharge Capability of Inductive Voltage and Combined Transformers Ivan Konta, Dijana Papi´c, Dalibor Filipovi´c-Grˇci´c, and Danijel Brezak

Abstract Although their primary purpose is not line discharging, inductive voltage and combined transformers are recognized as suitable solution for line discharge due to a typically very fast decay of trapped charge. Discharge capability of instrument transformers is not defined by relevant standards. Instead, it is often specifically defined by technical specifications of individual network utilities. In this paper authors have analysed discharge capability of inductive voltage and combined transformers. The focus of this paper will be placed on two main aspects of line discharge activity: thermal and mechanical capability. The aim of this document is to prove that discharge capability of inductive and combined transformers can be simulated with adequate precision. Furthermore, the proposed approach provides an indispensable tool for determining and optimizing relevant electrical and mechanical transformer parameters in order to achieve requested discharge capability even when technical specifications or project requirements exceed discharge capability of a standard instrument transformer design. Lastly, the paper will present relevant testing procedures, which verify discharge capability of inductive voltage and combined transformers. Keywords Instrument transformers · Line discharge testing · EMTP simulation · Finite element analysis

1 Introduction In case when one end of overhead line or cable stays isolated from ground and from supply side of network, e.g. after circuit-breaker opening, certain DC voltage may stay trapped on the line/cable capacitance, Fig. 1. This could cause dangerous I. Konta (B) · D. Papi´c Konˇcar – Instrument Transformers, Inc., J. Mokrovi´ca 10, 10090 Zagreb, Croatia e-mail: [email protected] D. Filipovi´c-Grˇci´c · D. Brezak Konˇcar – Electrical Engineering Institute, Inc., Fallerovo šetalište 22, 10000 Zagreb, Croatia © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_18

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Fig. 1 Isolated transmission line

overvoltage and transient recovery voltage across the contacts of circuit-breaker in case of an automatic re-closure. Use of inductive voltage or combined transformers for fast discharge of trapped voltage has been verified as an effective solution [1]. Requests on instrument transformers line discharge capability are not defined in relevant IEC and IEEE standards [2–4]. Therefore, instrument transformers manufacturers have to consider performance of voltage transformer design only in case when that is necessary due to the specific project requirements. Usually, discharge capability is defined by: – – – –

line capacitance discharge voltage decay time of residual line voltage and number of consecutive discharges and their intervals.

As a base for actual discharge tests and its simulation, an example of a discharge capability request is given. This specification requests inductive voltage and combined transformers to be able to discharge cables and overhead circuits up to the following capacitance, as shown in Table 1. Proof of discharge capability is to be provided by ten discharges of the capacitance energized to the peak value of the phase to earth voltage. Although this specification does not prescribe decay time rate of the line residual voltage, it will be commented as a part of discharging performance. Full scale discharge tests and corresponding simulations were performed on the following voltage transformers: – inductive voltage transformer type VPU-170 – inductive voltage transformer type VPU-420 and – combined current-voltage transformer type VAU-170. Table 1 Line capacitances

Max rated voltage (kV)

Line capacity (µF)

123

≤5.5

170

≤3.0

245

≤3.0

420

≤6.0

Line Discharge Capability of Inductive Voltage …

229

Table 2 The main electrical parameters Unit designation

Unit 1

Unit 2

Unit 3

Type designation

VPU-170

VPU-420

VAU-170

Transformer type

Inductive voltage

Inductive voltage

Combined (current-voltage)

Highest voltage of equipment (kV)

170

420

170

√ 150/ 3

√ 400/ 3

√ 150/ 3

√ 100/ 3

√ 100/ 3

√ 100/ 3

Rated primary current (A)

–

–

400

Rated secondary current (A)

–

–

1

Rated voltage factor

1.9/8 h

1.9/4 h

1.9/8 h

Rated flux density (T)

0.65

0.82

0.66

Rated primary voltage (kV) Rated secondary voltage (V)

The main transformers electrical parameters relevant for discharge capability are given in Table 2. Inductive voltage and combined transformers are using open-core design shown in cross-section drawings, Figs. 2 and 3. Simulations presented in this article are covering thermal and mechanical aspects of line discharge phenomena [5]. Furthermore, verification of obtained results will be done through laboratory testing of the analysed transformer units.

2 Thermal Capability Analysis During the line discharge through inductive or combined instrument transformer, most of the energy trapped on the line is converted into thermal energy stored in transformer primary windings and represented by copper losses. This assumption is based on the fact that the most of the trapped line charge is dissipated during the first hysteresis loop of the transformer core. Therefore, core losses are negligibly small compared to copper losses of the primary winding [6]. Due to the relatively short discharge time, transfer of thermal energy from primary windings to surrounding paper-oil insulation of transformer is negligible. Line discharge could cause serious temperature rise of primary windings because the value of discharge current could be more than 100 times higher than rated primary current. Energy stored on the line before discharge can be calculated according to expression (1): WC =

C · U2 . 2

(1)

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1 1. Primary (HV) terminal

2

2. Stainless steel bellows 3

3. Capacitively graded main insulation

4

4. Insulator 5

5. Primary (HV) winding 6. Secondary (LV) winding

6

7. Open-type magnetic core 8. Base assembly

7

9. Secondary terminal box 8

10. Oil sampling valve

9 10 Fig. 2 Inductive voltage transformer cross-section

In above equation, C is line capacitance and U is maximum voltage trapped at line. Temperature rise of transformer primary winding caused by line discharge, assuming no heat dissipation from the winding, is shown in expression (2): T =

Q . m·c

(2)

Q is thermal energy stored in primary windings, m mass of copper (primary windings) and c is specific heat capacity of copper.

Line Discharge Capability of Inductive Voltage …

231

1 2 3 4

1. Dilatation bellows 2. CT cores with secondary windings 3. Transformer head

5 6 7

4. CT primary winding 5. Core housing 6. Insulator 7. Capacitive graded insulation

8 9 10 11 12

8. VT primary winding 9. VT secondary winding 10. VT open-type magnetic core 11. Secondary terminal box 12. Base assembly 13. Oil sampling valve

13 Fig. 3 Combined transformer cross-section

Electro Magnetic Transients Program (EMTP) time domain calculation was used for simulation of voltage-current conditions during discharge activity. One phase circuit shown in Fig. 4 is supplied by a 50 Hz AC voltage source, connected via a controlled switch that disconnects the source at voltage maximum value equal to the peak value of the phase to earth voltage. After opening of the switch, discharge of the voltage from the capacitor representing line capacitance begins. Inductive and combined transformers discussed in this article are modelled in two ways. The first model, shown in Fig. 4, uses saturable EMTP transformer model, having all elements of its equivalent diagram: magnetizing branch with non-linear characteristics, primary and secondary resistances and leakage inductance [7]. Secondary

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Fig. 4 EMTP full simulation circuit

Fig. 5 EMTP simplified simulation circuit

winding of the voltage transformer is left unloaded due to the fact that typical instrument transformer burden has little effect on primary voltage and current [6]. The second EMTP model, shown in Fig. 5, is used for simplified discharge calculation. It is based on two assumptions: due to the fast increase of current through primary windings, transformer magnetic core becomes completely saturated and secondary side burden has negligible effect on primary side voltage and current. Therefore, saturable EMTP transformer model including magnetization curve can be replaced by two EMTP elements, Fig. 5: resistor representing primary winding resistance and inductor with constant value equal to the sum of leakage inductance and inductance of transformer with saturated magnetic core. Inductance of transformer with saturated magnetic core can be calculated using expression (3): L = μ0 · π · N 2 ·

2 Dav · k[H ]. 4·l

(3)

where: μ0 is magnetic permeability of vacuum, N—transformer primary winding number, Dav —average diameter of primary windings, l—primary winding height and k—Nagaoka factor, i.e. correction factor for the inductance of a long solenoid coil applied for a finite length coil [8]. ˇ Tests have been performed in KONCAR-Electrical Engineering Institute HighVoltage laboratory. Tests are done with test circuit shown in Fig. 6. Capacitor C1 , representing line capacitance, was loaded to the peak value of the rated phase to earth voltage. Charge generated on C1 is transferred to tested transformer by discharge gap. Transformer units VPU-170 and VAU-170 are tested with line capacitance 3 µF and transformer unit VPU-420 is tested with line capacitance 6 µF, according to Table 1. During the test, transformer primary voltage and current wave shapes were recorded with digital system for impulse voltage measurement and registration (HIAS).

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233

Fig. 6 Equivalent diagram of test circuit

Results of EMTP discharge simulations performed on saturated transformer model and those performed on simplified model are shown parallel with voltage and current wave shapes recorded during discharge tests. No significant differences in voltage and current amplitude and wave shapes between ten discharges performed on the same transformer unit were found. Therefore, the first recorded wave shape of each tested transformer unit have been chosen to be compared with simulation results. As, it can be seen in Figs. 7, 8, 9, 10, 11 and 12, oscillations of voltage are damped and voltage decay time is relatively short, Table 3. Decay time values of residual line voltage give insight into how fast trapped charge is discharged. Decay time to residual voltage of 50 and 20% of voltage initially trapped on the line is the shortest for VPU-170 unit, although the similar energy was discharged through VAU-170 unit. Decay time for VPU-420 is much longer due to the significantly higher discharge energy, see Table 4. Values of energy stored in primary winding confirm assumption that most of the energy trapped on the line is converted into thermal energy stored in transformer primary winding represented by copper losses. Values of temperature rises of primary windings are calculated for first line discharge for all units. There is no danger of overheating of VPU-170 and VAU-170 units even in case of ten consecutive discharges assuming no heat dissipation due to the short period between the first and the last discharge. The VPU-420 unit has significant temperature rise which can lead

150

U (full model simulation)

U (simplified model simulation)

U(test results)

Voltage [kV]

100 50 0

0.00

0.05

0.10

0.15

0.20

-50 -100 Time [s]

Fig. 7 Voltage curves obtained by VPU-170 discharge simulations and test

0.25

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I (simplified model simulation)

I (test results)

5 4

Current [A]

3 2 1 0 -1

0

0.05

0.1

0.15

-2

0.2

0.25

Time [s]

Fig. 8 Current curves obtained by VPU-170 discharge simulations and test U (full model simulation)

U (simplified model simulation)

U (test results)

400 350 Voltage [kV]

300 250 200 150 100 50 0 -500.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

-100 Time [s]

Fig. 9 Voltage curves obtained by VPU-420 discharge simulations and test I (full model simulation)

5

I (simplified model simulation)

I (test results)

Current [A]

4 3 2 1 0 0 -1

0.1

0.2

0.3

0.4

0.5

Time[s]

Fig. 10 Curent curves obtained by VPU-420 discharge simulations and test

0.6

0.7

Line Discharge Capability of Inductive Voltage … U (full model simulation)

235

U (simplified model simulation)

U (test results)

150

Voltage [kV]

100 50 0 0.00

0.05

0.10

0.15

0.20

0.25

-50 -100

Time [s]

Fig. 11 Voltage curves obtained by VAU-170 discharge simulations and test 4

I (full model simulation)

I (simplified model simulation)

I (test results)

3.5 3 Current [A]

2.5 2 1.5 1 0.5 0 -0.5 0

0.05

0.1

0.15

0.2

0.25

-1 Time [s]

Fig. 12 Current curves obtained by VAU-170 discharge simulations and test Table 3 Decay time value results Unit designation

VPU-170

VPU-420

VAU-170

Decay time to 50%U (simulation, full model) (s)

0.073

0.278

0.081

Decay time to 50%U (simulation, simplified model) (s)

0.066

0.272

0.072

Decay time to 50%U (test result) (s)

0.064

0.229

0.070

Decay time to 20%U (simulation, full model) (s)

0.100

0.568

0.125

Decay time to 20%U (simulation, simplified model) (s)

0.091

0.562

0.117

Decay time to 20%U (test result) (s)

0.089

0.450

0.119

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Table 4 Temperature rise results Unit designation

VPU-170

VPU-420

VAU-170

Discharged energy (kJ)

21.74

324.13

22.92

Energy stored in primary winding (kJ)

21.63

323.98

22.83

1.48

11.94

1.74

Temperature rise of primary winding (K)

Table 5 Current peak value results

Unit designation

VPU-170

VPU-420

VAU-170

Ipeak (A) − (EMTP simulation)

3.99

4.46

3.29

Ipeak (A) − (test result)

4.31

4.31

3.39

−7.42

+3.48

−2.95

7.12

5.39

4.86

I (%) Ipeak − theoretical maximum

to transformer thermal overload in case of many consecutive discharges. This is the reason why discharge sequence should be defined by technical specification. Furthermore, wave shapes in Figs. 7, 8, 9, 10, 11 and 12 show that the simplified (RL) model gives equal current peak value for all transformer types and therefore is omitted from the Table 5. Soon after discharge starts, within the first 10 ms of transient, increase of current simulated by simplified models is faster than recorded current increase during tests and current increase obtained by EMTP transformer model simulation. The reason for this is lack of non-linear magnetizing characteristic in simplified model representing saturated transformer. Also, in Table 5, theoretical current peak value is given for comparison with obtained results. Theoretical maximum of discharge current is calculated based on assumption of infinite high capacitance i.e. trapped voltage will not decrease at all. In this case discharge current is limited by resistance of the transformer primary winding. It can be calculated with expression (4): I M AX =

U [A] RP

(4)

where, U is maximum voltage trapped at line and RP is resistance of primary winding [1]. There is a time difference between current peak value time between simulations and test results. Generally, compared to results obtained by EMTP simulations test results show faster reaching of current peak and faster decreasing of voltage and current after peak value than results obtained by simulations. Differences between results obtained by simulations and those obtained by discharge tests are consequence of approximations made on EMTP transformer model; such as calculation of inductance of transformer with saturated core. Primary winding coils with different inner

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and outer diameters and number of turns were represented by one coil determined by average diameter of all coils and their total height and number of turns.

3 Mechanical Capability Analysis Besides thermal stress analysis for transformers VPU-170, VPU-420 and VAU-170, a mechanical impact of line discharge on transformers primary windings needs to be evaluated. Mechanical impact on transformer windings is a consequence of mechanical forces caused by discharge current through large number of primary windings (more than 105 primary turns for analysed units). The transformer geometry and circuit parameters were simulated in Infolytica MagNet software. Due to the nature of the discharge current, which has a single pronounced peak, transient analysis is not necessary, thus 3D time-harmonic solver was used [9]. The numerical simulation results are compared with discharge capability results obtained by testing on an inductive voltage transformer type VPU-72.5. To define the reference criteria for the mechanical impact, discharge tests on the inductive voltage transformer type VPU-72.5 have been previously performed. They were performed by gradually increasing multiple discharges [6], until reaching discharge current that causes physical deformation on the primary winding coils. The measured discharge current through the transformer, which caused the loss of mechanical integrity on one coil, was used in Infolytica MagNet software for numerical calculation of forces on the primary winding, in an attempt to form a criterion for mechanical withstand. Complete numerical model of the tests object VPU-72.5 and the electrical diagram with the corresponding discharge current on the primary winding are given in Fig. 13. As presented in Figs. 14 and 15, the critical mechanical force has been exhibited on the coil 7, is in the Y-axis direction, having value of 30 kN. Previous testing has shown that individual axial force on one coil can be more perilous than cumulative axial force, which is typically analysed in power transformers. Reference criteria based on presented test results and calculations is that the force exceeding 30 kN can impose damage to the primary windings coils. Same simulations were performed for all tested transformers VPU-170, VPU420 and VAU-170. For every transformer, forces caused by the corresponding first discharge current were simulated. Figure 16 shows calculated Y-axis forces for all coils of their primary windings, and it can be seen that all of them meet the criteria shown above. Furthermore, several improvements have been introduced in the mechanical design of the coils: additional fixing of coil conductors using Diamond Dotted Paper as interlayer insulation, and stronger coil formers. The anticipated mechanical withstand is increased for approximately 50% with these improvements, which enables transformers to withstand even higher mechanical stresses and obtain more conservative safety factor in design.

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Fig. 13 Infolytica MagNet 3D model of VPU-72.5

4 Conclusion For proper electrical and mechanical design of the transformer units intended for line or cable discharge, it is advisable to specify the following requirements: line capacitance, initially trapped voltage on the line, decay time of residual line voltage and time cycle of consecutive discharges. Specifying line discharge requirements boils down to two problems; thermal withstand and mechanical withstand. This paper presents tools, calculations and procedures on how to accurately estimate both in early stages of transformer design. All presented calculations correspond to measurements with satisfactory precision.

Line Discharge Capability of Inductive Voltage …

239

X-axis

0.012

Z-axis

0.010 0.008 0.006 F [kN]

0.004 0.002 0.000 -0.002 1

2

3

4

5

6

7

6

7

-0.004 -0.006 -0.008

Coil

Fig. 14 Radial forces on primary coils Y-axis

30 20

F [kN]

10 0 1

2

3

4

5

-10 -20 -30 -40

Coil

Fig. 15 Axial forces on primary coils VPU-170

50

VPU-420

VAU-170

Standard design

Improved design

40 30

Fy [kN]

20 10 0 -10

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

31

33

-20 -30 -40 -50

Coil

Fig. 16 Graphical representation of forces on primary coils compared to design criteria limits

35

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This also means that line discharge capability of units already installed in service can be calculated, which can be an essential piece of information for the end user. Furthermore, tests performed corroborate design principles and criteria presented in the paper. The three units, which this paper is based on, have successfully completed all tests including the repetition of routine tests after line discharge testing. Since requirements for line discharge are still not present in relevant standards, this paper provides useful insight in how to design, specify and test units with such requirements.

References 1. Csida S, Kromer LI (1978) An improvement method for determining line discharge through potential transformers. IEEE Trans Power Appar Syst PAS-97 (1) 2. IEC 61869-1:2009 (2009) Instrument transformers—part 1: general requirements 3. IEC 61869-3 (2011) Instrument transformers—part 3: additional requirements for voltage transformers 4. IEEE Standard Requirements for Instrument Transformers (2016) IEEE Std C57.13-2016 5. Kano K, Kawabuchi Y, Uchida K, Yashiro T, Shibata T (1992) Line trapped charge discharging characteristic of gas insulated magnetic voltage transformer. Trans Power Deliv 7(1) 6. Marks LW (1969) Line discharge by potential transformers. IEEE Trans Power Appar Syst PAS-88(4) 7. Krajtner D, Žiger I (2015) Influence of HV inductive voltage transformers core design to the ferroresonance occurrence probability. In: International conference on power systems transients in Cavtat, Croatia 8. Nagaoka H (1909) The inductance coefficients of Solenoids. J College Sci. Imperial University, Tokyo, Japan 9. Infolytica package for magnetic Analysis using finite elements, INFOLYTICA CO. Montreal, Canada

Influence of Conductor Transposition on Transformer Winding RLC Parameters Ana Drandi´c, Bojan Trkulja, and Željko Štih

Abstract In this paper the influence continuous transposition of the conductor has on winding RLC parameters and electric field distribution is analysed. Study is made on two types of windings, one winding with and one without conductor transposition. 3D finite element method (FEM) based software is used for electric field computation and the computation of RLC matrices of the windings. Keywords Transformer · Transformer windings · Numerical simulation · FEM · Continuously transposed conductor

1 Introduction Windings of power transformers are usually made of copper conductors. Research and improvement of copper conductors in terms of reducing energy losses resulted in the development of continuously transposed conductors (CTC) [1]. Transformers performance and efficiency depend on the losses in conductors. These losses have an effect on the costs of transformer maintenance during its life cycle. The need to reduce the eddy current losses in transformers have led to the widespread use of CTC in power transformer windings [2]. The use of CTC in transformers has lead to different modeling techniques for CTC windings and research on CTC and its influence on different transformer parameters [3–6]. Eddy currents can be reduced by replacing the conductors in windings with sets of several conductors of a smaller cross section. Transposition of the conductors in those sets disables possible circulating current loops [3]. Besides the reduction in eddy current losses, some of the advantages of continuously transposed cables in transformer design, compared to the paper insulated rectangular wires are [4]: faster winding of the turns during production of the transformer, increased space factor of the winding, better short circuit stability of the winding, and better mechanical strength of the winding. The greatest disadvantage is the cost of CTC which is more expensive than classical conductor material. A. Drandi´c (B) · B. Trkulja · Ž. Štih Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_19

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Power transformers are critical for normal functioning of the power system. Therefore, transformers have to be designed to withstand overvoltages that occur during their operation. This means that transient voltage distribution simulation is a necessity while designing the transformer. Impulse voltage distribution is influenced by the type of winding. Since RLC parameters can be used in equivalent lumped parameter model for simulation of transient voltage distribution, it is very important to analyse the changes in those parameters influenced by conductor transposition. This paper analyses of influence using CTC has on RLC parameters of the winding, while also analysing electric stresses during normal operation of the transformer. This is done on a small 3D transformer model using finite element method based software Ansys Electromagnetic suite 17.2.

2 Model Development Due to its challenging geometry, where each conductor is transposed in every turn, in order to properly calculate the wanted transformer parameters a 3D model of the windings must be done. This also requires significant computational effort so a small transformer example is modeled in this paper.

2.1 Description of CTC As previously mentioned, continuously transposed cables are used in transformer winding design to improve the eddy current losses. Continuously transposed cables consist of a group of enameled rectangular copper conductors, arranged in two parallel stacks as shown in Fig. 1. The number of conductors is an odd number that usually lies between 5 and 81. Each conductor is continuously transposed, always staying in parallel to other conductors without twists along its end. An example of transpositions of each conductor is given in Fig. 2. For an example of 5 conductors in a stack. A fixed distance between the transpositions is called transposition pitch. Fig. 1 CTC cross section

Influence of Conductor Transposition on Transformer Winding RLC …

243

Fig. 2 Transpositions of CTC with 5 conductors in a stack. Each conductor is assigned a number and color in order to better show the transpositions (conductor 1—green, conductor 2—yellow, conductor 3—orange, conductor 4—red, conductor 5—teal). The transpositions are made until each of the conductors has passed every position and in the next transposition it is set to arrive in its original position

After every transposition pitch, conductors on the top and bottom of the stacks change their stacks in the clockwise or counter-clockwise direction. The group of several transposed conductors is wrapped in several layers of insulation paper to make a complete continuously transposed cable.

2.2 Finite Element Modeling As already mentioned, 3D modeling is used in order to obtain the results. Two ironcore transformers with 16 turns on the primary and 3 turns on the secondary side are modeled. One of the models has windings made of classical wire of rectangular cross section, while for the other model CTC is used for the production of windings. Spiral windings are assumed to be rings of the same radius. The number of rings corresponds to the number of turns of the winding. Models of the transformers are presented in Fig. 3. The CTC windings are made of several parallel conductors which are transposed in every turn meaning each of the conductors passes through every position. For the example in this paper, each turn is made of 5 conductors (strands) of the continuously

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Fig. 3 Transformer models used for simulation a windings made of flat wire b windings made of CTC

transposed cable. Their transpositions are made following the scheme in Fig. 2. A closer look of the CTC turn where the transpositions can be clearly seen is shown in Fig. 4. Paper is used as insulation of the rectangular conductors and the CTC, with the insulation dimensions constant in both models, as to have a better comparison of the models. The used FEM software performs capacitance matrix calculation using a set of electrostatic simulations. In every simulation, the voltage of one conductor is set to one, and the others are set to zero. When CTC winding is modeled, the voltage of a set of conductors that make the turn is set to one. The capacitance between conductors i and j Ci, j is calculated with [7]:

Fig. 4 A closer look of the modeled CTC turn

Influence of Conductor Transposition on Transformer Winding RLC …

Ci, j =

2W E i, j = υ

245

 Ω

Di E j dΩ,

(1)

where W E i, j is the electric field energy between conductors, Di is the electric flux density when voltage of 1 V is applied to conductor i, and E j is the electric field when voltage of 1 V is applied to conductor j. Calculation of both inductance and resistance matrix is done using eddy current field simulation. This simulation is performed in a way that in every step the current through one conductor circuit is 1A, and the other current excitations are set to zero. Inductance values L i, j are calculated using energy storage calculation: L i, j

2W Mi, j = = I2

 Bi H j dΩ,

(2)

Ω

where W Mi, j is the magnetic field energy determined by the magnetic flux density and field intensity in the solution space. The resistances are calculated using the power loss in the respective conductor due to a known conduction current passing through the conductor [7]: R=

P I R2 M S

=

P 2 I Peak

,

where the ohmic losses are calculated with:  1 P= J · Jd V , σ

(3)

(4)

V

where J is the current density and σ is the conductivity.

3 Simulation Results The simulation was done using Ansys Electromagnetic suite 17.2, Maxwell 3D. As assumed, the CTC model required higher computational effort due to its complicated geometry. Due to the computational effort of the eddy current simulation of the CTC winding, for resistance and inductance values only the values on three turns were analysed. A mesh of 187 518 tetrahedra for rectangular wire winding model and 1 415 838 tetrahedra for CTC winding model was used. The results of both models, where model 1 denotes the transformer model with windings made of classical wire of rectangular cross section and model 2 denotes the transformer model with windings made of CTC, are shown in Tables 1 and 2. Inductance and resistance values have changed less than 3.6% when CTC was used. This differences in inductance and resistance

246 Table 1 Inductance values on primary winding turns in nH

Table 2 Resistance values on primary winding turns in mΩ

A. Drandi´c et al. Turn number

P1

P2

P3

Model 1

4444.2

4440.7

4440.9

Model 2

4439.84

4437.92

4439.44

Turn number

P1

P2

P3

Model 1

0.3125

0.3126

0.3119

Model 2

0.3123

0.3241

0.3228

values can be attributed to mesh settings, but finer mesh would require even more computational effort which means that calculations could take days instead of hours, and to non-conducting areas in the CTC model. As expected, capacitance values have been influenced the most when the classical conductor of rectangular cross section has been replaced with a CTC. Capacitance matrix diagonal values for all turns of the primary winding are presented in Table 3 for both transformer models. The differences in capacitance values that can reach as far as 10.69% as presented in Fig. 5. This proves the importance of using 3D modeling when dealing with windings made of CTC conductors if very accurate results are needed. Electric field calculation was made with voltage decrease from one turn to another, from outer to inner turns. The results of electric field calculation show that lower maximum electric field intensities can be expected in CTC windings. Electric field distribution for both models is shown in Figs. 6 and 7. Both models are shown with the insulation around the turns. As already mentioned, the dimensions of the turns with the insulation are the same in both models, the difference is the use of the rectangular wire and CTC. The results of the electric field analysis confirm that CTC usage in transformer windings production can influence the maximum electric field intensity when insulation distance is constant.

4 Conclusion This paper presents the application of FEM based 3D software to analyse the influence the use of CTC windings instead of paper insulated rectangular wires has on transformer RLC parameters and electric field distribution. Two transformer models are solved, one model with CTC windings and one with rectangular wire windings. The difference in obtained results shows the need of using 3D modeling to achieve accurate results when using CTC in transformer windings. Further research may include the analysis of CTC influence on voltage distribution during lighting impulse tests and development of CTC modeling techniques.

34.1

31.68

P2

Model 2 25.07

P1

Model 1 26.4

Turn number

31.921

35.05

P3

25.33

28.2

P4

28.43

31.47

P5

Table 3 Capacitance on primary winding turns in p F

32.527

34.99

P6

32.187

34.66

P7

28.004

29.86

P8

24.458

26.46

P9

28.13

30.3

P10

28.258

30.39

P11

24.678

27.45

P12

18.189

20.36

P13

21.895

24.04

P14

21.83

24.02

P15

18.05

19.88

P16

Influence of Conductor Transposition on Transformer Winding RLC … 247

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A. Drandi´c et al.

Fig. 5 Percentage difference in capacitance results for the model with and without CTC. Pn denotes the n-th turn of the primary winding, while Sn denotes the n-th turn of the secondary winding

Fig. 6 Electric field distribution for the model with classical rectangular wire winding

Influence of Conductor Transposition on Transformer Winding RLC …

249

Fig. 7 Electric field distribution for the model with CTC winding

References 1. Welch Jr AU, Cederstrom CM. Rectangular cable and method of making the same. US Patent no. 2249509, 15 July 1941 2. Dubey JP (2017) Role of copper in continuously transposed conductors. Transformers Mag 4:108–116 3. Lopez-Fernandez XM, Alvarez-Gomez LA (2019) “ Calculation of stray losses in continuously transposed conductor cable transformer windings by multi-slice methodology. Int J Elect Power Energy Syst 111:25–33 4. Faridi M, Nabaei V, Mousavi SA Mohammadi M (2009) Modeling of continuously transposed cable in power transformer for fault analysis based on FEM. In: 2009 International conference on electrical machines and systems, Tokyo, pp 1–4 5. Geissler D, Geissler C, Leibfried T (2016) Simplified simulation model of continuously transposed cable for linear and nonlinear buckling analysis. Math Comput Simul 130:81–94 6. Preis K, Renhart W, Rabel A, Bíró O (2018) Transient behavior of large transformer windings taking capacitances and eddy currents into account. IEEE Trans Magn 54(3):1–4 7. Hosseini SMH, Enjavi Madar SM, Vakilian M (2015) Using the finite element method to calculate parameters for a detailed model of transformer winding for partial discharge research. Turk J Elec Eng Comp Sci 23:709–718

Appropriate Modelling of Transformer High Current Leads in 3D FEM Karlo Petrovi´c, Bruno Juriši´c, and Tomislav Župan

Abstract In generator step-up power transformer units (GSU), low voltage windings carry sufficiently high currents which generate high magnetic field levels. Therefore, when it comes to 3D finite element method (FEM) calculation of the stray losses of such transformer units, it is not enough to model low voltage windings just as two cylinders. Low voltage leads should also be modelled, and it is necessary to know how to accurately model and connect leads to the windings. Modelling windings and leads in 3D FEM is very demanding and calculation is time-consuming, so an appropriate model of leads can therefore reduce the mesh size and solver time. In this paper, multiple modelling approaches are tested and compared with the model without leads. Keywords Leads · High current windings · Stray losses · 3D FEM

1 Introduction Stray losses in the metallic parts of power transformers, caused by high current leads, account for approximately 30% of the total stray losses. Therefore, it is of great importance to take these losses into account in the design phase of the transformer [1, 2]. In the last few decades, 3D FEM simulation has become more applicable, and can now handle complex geometries such as helical windings and different connection leads within the acceptable calculation time frame. Appropriate modelling of the high current leads of a power transformer in 3D FEM gives more information about the stray losses, especially regarding the losses in the transformer tank and the clamping structure of transformer’s active part [3, 4]. These losses can cause local overheating and reduce the lifetime of the transformer [5]. In this paper, the scope has been put on the high current, low voltage windings and leads of the generator transformer units (GSU). In the second chapter of the paper standard model with cylindrical windings and the several advanced models of low K. Petrovi´c (B) · B. Juriši´c · T. Župan Konˇcar - Electrical Engineering Institute Inc., Fallerovo šetalište 22, 10002 Zagreb, Croatia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_20

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voltage windings and leads are presented. In the third chapter, 3D FEM simulations are described and results are compared and commented. Finally, lead modelling guidelines and recommendations are given.

2 FEM Modelling In this section, different advanced models of the windings and leads are presented. In the paper, the observed winding is a low voltage double-helical winding with both lead exits at the top of the winding. Except the leads and the windings, the lower and upper clampings, core, tie bars, tank and tank shields have also been modelled. A. Modelling of leads in 3D FEM Multiple models of leads and windings in CAD tool are constructed for a fictitious transformer unit. Then, the models are solved using the electromagnetic time harmonics solver in FEM tool Mentor Graphics MagNet v7.9. To build up a full FEM model with leads, first a real winding geometry has been taken into account, which makes it the most demanding model among the observed ones. In the simulations, the leads are connected directly to the top of the winding and pulled out at the top of the transformer tank. For modelling the helical winding geometry, the following parameters are necessary: the winding height, distance from winding to core yoke, number of turns, and height of radial cooling ducts spacers. Those parameters are defining the winding position in the transformer core window. Each continuously transposed conductor (CTC) bundle (i.e. turn) is modelled as a solid conductor without representing the inner strand insulation. In models, the distance between turns (copper without isolation) remained equal to the height of radial cooling ducts spacers. Note that the inner and outer low voltage windings are wounded in the opposite directions, because of the way the current flows in these windings. It is important that low voltage windings produce magnetomotive forces that act along the same direction in the magnetic circuit [1]. The coils in this model are defined as stranded because skin and proximity effects, which affect the losses in the conductors, are not of the interest in this work. To compare different advanced models with the reference model without leads, the changes are made only for these parts of geometry. Other parts including metallic structures remained the same. In addition to the reference case with the cylindrical low voltage winding without leads, the following models with leads are investigated: 1. The model with the real-case helical winding geometry. 2. The model with the low voltage winding modelled as two cylinders. From the inner side of the cylinders, a few turns of the helical winding are modelled and connected to the leads.

Appropriate Modelling of Transformer High Current Leads …

253

Fig. 1 a The model with the real winding geometry. b Model with a few turns from the inner side. c Model with a few turns from the outer side. d Model with straight leads connected at the bottom. e Model with straight leads connected at the top

3. The model with the same configuration as the previous one, with the difference that the mentioned few turns are placed on the outer side of the cylinders. 4. The model with straight leads connected at the bottom of the cylindrical winding. 5. The model with straight leads connected at the top of the cylindrical winding. In Fig. 1 all the advanced models listed above are shown. In the figures of the advanced models with cylinders (Fig. 1b–e), one half of the outer cylinder is hidden for a better overview. When defining the height of the representative cylinders, one must take into account the effective height of the winding, since the helical winding’s distance from the yoke changes angularly. The second and third models are modelled in such a way that the thicknesses of both cylinders are reduced in half and helixes with a few turns (five in this case) are drawn in that place. For the second model, thicknesses for both cylinders are reduced from the inner side, and for the third model from the outer side. For coils placed on the cylinders, five turns are subtracted from the total number of turns, so that the magnetomotive force remains the same. In this case, also the coils on the cylinders and the coil on the helix have to produce magnetomotive forces that act along the same direction. For the fourth and fifth models, cylinders are defined with the total number of turns from the transformer project. In these models, helix is not modelled, only straight leads are drawn and connected on the bottom or top of the low voltage windings respectively. B. Test case on single-phase transformer unit Once the models of a transformer high current winding were defined, they had to be applied to the realistic transformer geometry. For that purpose, the single-phase transformer unit is used. Nominal data of that fictitious transformer unit is given in Table 1. As it is shown, the core has been modelled as a 1/1 type, for the purpose of reducing the simulation time.

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Table 1 Nominal data of the fictitious transformer Nominal data Number of phases

1

Frequency (Hz)

50

Nominal power (kVA)

380,000

Core type

1/1

Number of turns (LV)

66 (33 per layer)

Phase current (LV)

6900 A

Materials and mesh size used in FEM simulations are shown in Table 2. Also, to reduce the mesh size and solving time, the parts of geometry made from magnetic steel are represented using the surface impedance boundary condition. This condition may be used when the thickness of the geometry is more than 10 times larger than the skin depth of the material [6]. The model of a single-phase transformer is shown in Fig. 2a. The leads exit the transformer tank through the holes at its cover to the end of the modelling domain. The tank shields are modelled as a single plate for the sake of simplicity. C. Test case on three-phase transformer unit The three-phase transformer model is modelled as the extended version of the onephase model. One limb of the core with the same limb distance and limb diameter is added. The distance from the core limb to the tank remained the same. In other words, Table 2 Material properties and mesh size of different parts of transformer Material

Material properties

Part of the transformer

Mesh size

Grain-oriented electrical steel

Isotropic, nonlinear permeability, with P-B curve, no conductivity

Core Tank shields

Automatic

Magnetic steel

Isotropic, nonlinear permeability, with P-B curve, linear conductivity

Tank, clamping plates and tie bars

Tank bottom and wall = 100 mm Tank cover = 50 mm Clamping plates = 75 mm Tie bars = 40 mm

Copper

Isotropic, relative permeability = 1, conductivity = 57.7 MS/m

Windings and leads

Curvature refinement angle: LV winding and leads = 5° HV winding = 10°

Air

Isotropic, relative permeability = 1, conductivity = 0 MS/m

Air box

150 mm

Appropriate Modelling of Transformer High Current Leads …

255

Fig. 2 View of the a single-phase and b three-phase model of the transformer

the transformer tank length increased proportionally. Windings are added on each limb of the core which is now 3/0. Clamping plates are extended, tie bars are added on the third limb and tank shields are placed parallel to the two added windings. The front view of the three-phase transformer model is shown in Fig. 2b. In the figure, one half of the HV cylinder and low voltage tank shield are hidden, and tank wall is set as transparent. Materials, mesh size, boundary conditions, number of turns and the phase current of each winding (with a shift of 120° and 240° depending on the phase) remained the same as in the single-phase model.

3 Result Discussion For all the models, electromagnetic time harmonics solver in FEM tool Mentor Graphics MagNet v7.9 was used with the same solver and mesh settings. The maximum number of computational cores used for solving is set to 4, Newton tolerance is set to 0.5%, and CG tolerance to 0.001%. Ohmic losses and iron losses (P-B curves) were summed up for the transformer tank and clamping structure. The total loss table for every model and the comparison of the models with leads with the reference model for a single- and a three-phase transformer units are shown in Tables 3 and 4. To validate the mesh settings and hence the results, one additional simulation has been conducted for the model with real winding geometry with the finer mesh settings as a benchmark model. The percentage deviation of total losses was smaller than 2%, which is a confirmation of adequate mesh settings in the models. A number of tetrahedra in solver mesh was largest in the model with the real winding geometry both for the one-phase and the three-phase transformer model. Other models used around 3% fewer tetrahedra in the one-phase simulations, and around 7% more tetrahedra in three-phase simulations, than the simulations of the

256

K. Petrovi´c et al.

Table 3 Comparison of the losses and mesh complexity for the presented single-phase transformer models Losses (W)

Clamping plates Tie bars Core Tank wall

Without leads

The real winding geometry

Few turns from the inner side

Few turns from the outer side

Connected at the bottom

Connected at the top

3,856

4,165

3,757

4,827

4,750

3,853

905

1,144

1,054

1,356

1,296

908

988

979

936

1,059

989

988

3,509

6,108

3,558

3,979

3,811

3,506

Tank bottom

181

45

133

151

191

182

Tank cover

150

604

249

261

212

202

Tank HV shields

253

236

244

251

253

253

Tank LV shields

325

304

333

345

324

324

Total Number of tetrahedra

10,167

13,585

10,264

12,228

11,824

10,217

1,784,797

1,941,852

1,749,558

1,735,363

1,722,703

1,719,602

Table 4 Percentage deviation of the losses and mesh complexity from the reference model for the presented single-phase transformer models Losses (%)

The real winding geometry (%)

Few turns from Few turns from Connected at the inner side the outer side the bottom (%) (%) (%)

Connected at the top (%)

+8.0

-2.6

+25.2

+23.2

−0.1

+26.4

+16.5

+49.8

+43.2

+0.3

Core

−0.9

−5.3

+7.1

+0.0

0.0

Tank wall

+74.0

+1.4

+13.4

+8.6

−0.1

Tank bottom

−74.9

−26.4

−16.6

+5.7

+1.0

Tank cover

+303.0

+66.5

+74.1

+41.3

+34.7

Tank HV shields

−7.0

−3.7

−1.0

−0.2

0.0

Tank LV shields

−6.3

+2.5

+6.2

−0.3

−0.3

Total

+33.6

+1.0

+20.3

+16.3

+0.5

+8.8

−2.0

−2.8

−3.5

−3.7

Clamping plates Tie bars

Number of tetrahedra

Appropriate Modelling of Transformer High Current Leads …

257

reference model. This parameter is showing which model is the most complex one from the point of time and memory the solver is using. Because of the nonlinearity of the materials and usage of the Newton-Raphson method in FEM software simulations, the comparison of solver times of each model is not relevant. From the results of simulations that are shown in the Tables 3, 4, 5 and 6, it can be seen that high current leads impact stray losses, and standard modelling of windings using two cylinders is not enough in such cases. Advanced models had a similar trend of loss deviation from the reference model for the one-phase and the three-phase transformer model. If we assume that the model with the real winding geometry is the most appropriate to model the transformer leads, then the largest difference compared to other advanced models are the losses in the tank wall. This modelling approach indicates that the helical winding model can increase losses in the tank wall for about 80%. In clamping plates, tie bars and shields the differences are much smaller, and loss results are comparable. As the losses induced in the tank wall and clamping plates make up the majority of the total stray losses, these big differences in tank wall losses are affecting the total stray losses. Also, the model with the real winding geometry has a larger difference in the losses in the tank bottom and the tank cover. These observations are leading to a conclusion that modelling of real winding geometry is necessary if tank losses are part of the interest. Otherwise, some other investigated models, except for the model with the leads connected at the top, can be used to calculate losses on the clamping system and tank shields. Table 5 Comparison of the losses and mesh complexity for the presented three-phase transformer models Losses (W)

Clamping plates Tie bars

Without leads

The real winding geometry

Few turns from the inner side

Few turns from the outer side

Connected at the bottom

Connected at the top

12,127

12,458

12,529

13,090

12,960

12,576

3,258

5,021

3,989

4,269

4,144

3,407

Core

2,852

2,862

2,696

3,050

2,852

2,852

Tank wall

7,614

14,090

8,135

8,372

8,005

7,927

Tank bottom

445

86

366

379

455

454

Tank cover

345

1,138

613

627

541

536

Tank HV shields

611

673

592

610

611

611

Tank LV shields

806

882

833

864

807

807

Total Number of tetrahedra

28,058

37,210

29,753

31,260

30,376

29,169

2,413,354

3,077,244

2,640,227

2,587,723

2,589,878

2,577,781

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K. Petrovi´c et al.

Table 6 Percentage deviation of the losses and mesh complexity from the reference model for the presented three-phase transformer models Losses (%)

Clamping plates Tie bars

The real winding geometry (%)

Few turns from Few turns from Connected at the inner side the outer side the bottom (%) (%) (%)

Connected at the top (%)

+2.7

+3.3

+7.9

+6.9

+3.7

+54.1

+22.4

+31.1

+27.2

+4.6

+0.3

−5.5

+6.9

0.0

0.0

Tank wall

+85.1

+6.8

+10.0

+5.1

+4.1

Tank bottom

−80.7

−17.8

−15.0

+2.3

+1.9

Tank cover

+230.4

+77.9

+81.9

+57.2

+55.7

Tank HV shields

+10.1

−3.1

−0.2

0.0

0.0

Tank LV shields

+9.3

+3.3

+7.1

+0.1

0.0

Total

+32.6

+6.0

+11.4

+8.3

+4.0

Number of tetrahedra

+27.5

+9.4

+7.2

+7.3

+6.8

Core

In Fig. 3, time average total losses on the low voltage side of the tank wall are shown. In all figures, the same scales are used for valid visual comparison of plots. Figures are showing the reference model and the two investigated models. It can be noticed that the model with helical winding has more losses distributed on the tank wall. In Fig. 4, magnetic flux density distribution on the low voltage tank shields is shown. This figure correlates with Fig. 3. Around the edges of the shields with larger magnetic flux density, more flux is impinging in the surrounding tank wall and so induces more losses in it. The loss distribution in the three-phase transformer model is shown in Fig. 5. In this case, the largest difference is located on the tank wall between the shields. The real winding geometry is inducing much more losses in this part of the model. In Figs. 6 and 7, the magnetic flux density distribution on the low voltage side tank shields of the three-phase transformer model is shown. The model with the leads connected at the bottom is not shown because the magnetic flux density distribution is similar to that of the reference model. The same conclusions that are given for the single-phase model apply here as well. Figures 3, 4, 5, 6 and 7 are showing that appropriate FEM calculation of tank losses in the transformers with high current leads demands usage of the real winding geometry. In this case it is helical winding, which is most commonly used for the low voltage windings of the GSU transformers.

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Fig. 3 Time average total losses (W/m3 ) on the low voltage side of the transformer tank wall on the single-phase transformer unit: a the reference model. b Model with straight leads connected at the bottom. c Model with real winding geometry

4 Conclusion In this paper, a simple reference model with cylindrical winding geometry without leads, and advanced models with leads are modelled in the FEM tool Mentor Graphics MagNet v7.9. A test case is carried out on the fictitious one- and three-phase transformer units. The models consist of the tank, tank shields, clamping plates, tie bars and active part. Simulations showed that for the transformers with high current leads the standard FEM modelling of windings as two cylinders is not enough for accurate calculations. Modelling of real high current winding geometry, in this case the helical winding, is

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Fig. 4 Magnetic flux density, RMS B [T] on low voltage side tank shields on the single-phase transformer unit: a the reference model. b Model with straight leads connected at the bottom. c Model with real winding geometry

Fig. 5 Time average total losses (W/m3 ) on the low voltage side of the transformer tank wall on the three-phase transformer unit: a the reference model. b Model with straight leads connected at the bottom. c Model with real winding geometry

necessary if tank losses are part of the interest. If a user only wants to calculate losses in the clamping system or tank shields, some different advanced models mentioned in the paper can be used. This is recommended only if calculation time is a critical parameter.

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Fig. 6 Magnetic flux density, RMS B [T] of low voltage side tank shields on the three-phase transformer unit for the reference model

Fig. 7 Magnetic flux density, RMS B [T] of low voltage side tank shields on the three-phase transformer unit for the model with real winding geometry

In future work, the low voltage bus bars (i.e. delta connections), winding inclination and detailed model of the magnetic shields will be considered to check the influence on the losses. The aim of this research is to cover all the cases and to make sure that the used approach in modelling of windings and leads gives us accurate results.

References 1. Kulkarni SV, Khaparde SA (2013) Transformer engineering : design, technology, and diagnostics. CRC Press, Taylor & Francis Group 2. Kulkarni SV, Khaparde SA (2000) Stray loss evaluation in power transformers—a review. In: 2000 IEEE power engineering society, conference proceedings, 2000, vol 3, pp 2269–2274

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3. Koppikar DA, Kulkarni SV, Khaparde SA, Jha SK (1997) Evaluation of eddy losses due to high current leads in transformers. In: IEE proceedings—science, measurement and technology, vol 144, no 1, pp 34–38 4. Calculation of eddy current losses caused by leads and other current sources in high current power transformers. In: IEEE Conference Publication. https://ieeexplore.ieee.org/document/4813095. Accessed 27 Aug 2019 5. Magdaleno-Adame S, Olivares-Galvan JC, Escarela R, Raichenko O, Kladas AG (2014) Hot spots mitigation on tank wall of a power transformer using electromagnetic shields. In: Proceedings—2014 international conference on electrical machines, ICEM 2014, pp 2235–2238 6. Mentor graphics. MagNet (2017)

Calculation of Eddy Current Losses in Iron Core of Transformer Stjepan Frlji´c, Bojan Trkulja, and Željko Štih

Abstract Due to the large number of thin laminations in the transformer core, homogenization of the core is necessary. Thus, new material of anisotropic characteristics is calculated. Anisotropic electrical conductivity tensor then allows large eddy current loops to be taken into account directly. In the case of low-frequency time-harmonic generator current, the influence of narrow eddy current loops on the distribution of the magnetic flux density within a domain can be taken into account by using additional manually calculated anisotropic magnetic reluctivity tensor. Therefore, no modification of the standard weak formulation of the magnetodynamics problem is required. The only code implementation is required in postprocessing to account for losses due to narrow eddy current loops. A real-size model is used as a numerical example. Keywords Transformer · Eddy currents · Losses

1 Introduction Transformers are an essential component of the power system. Eddy currents are generated in the transformer core as a side effect. Losses due to eddy currents represent a significant loss of energy on a large time scale. Laminating the transformer core is a standard approach in minimizing eddy current losses. FEM is the most suitable numerical method for the analysis of eddy currents on a computer, in the design phase. Due to the large ratio of transformer core dimensions to the lamination thickness, the laminated core requires an impermissibly large number of finite elements in finite element mesh. Hence, the transformation of the laminated core to the bulk model is a common approach for enabling eddy currents to be calculated [1]. Eddy currents are usually viewed as a superposition of two separate types of eddy currents [2]. The first type consists of eddy currents that close in large loops in the plane of the lamination and are induced by a component of a time-varying S. Frlji´c (B) · B. Trkulja · Ž. Štih Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2020 B. Trkulja et al. (eds.), 5th International Colloquium on Transformer Research and Asset Management, Lecture Notes in Electrical Engineering 671, https://doi.org/10.1007/978-981-15-5600-5_21

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magnetic field perpendicular to the plane of the lamination. The second type consists of eddy currents that are induced by the tangential component of a time-varying magnetic field, and these eddy currents close in narrow loops within the lamination. The use of an anisotropic conductivity tensor for a bulk core model has proven to be the best option for the direct computation of eddy currents that close in large loops within the lamination plane [3]. There are also much more precise approaches that couple 3D and 2D model of lamination, but they are more complicated to implement [4]. In the case of calculating eddy currents that close in narrow loops within the lamination, various approaches have been proposed. Since they are highly oscillatory, non-monotonous spatial functions, very dense finite element mesh is required to consider them properly inside the laminated core. Therefore, the homogenization of the problem variable is the standard approach. Homogenization by employing an ansatz for problem variable in the 2D model is proposed in [5, 6]. Although narrow eddy current loops are highly oscillatory, their effect on magnetic flux is monotonic [7]. Homogenization in 3D using a monotonous variable of locally averaged magnetic flux proved to be a good option [8, 9]. It also proved to be an applicable method for the nonlinear case as well [10]. To properly take the non-symmetric distribution of the magnetic flux along the lamination thickness, different homogenization method is proposed in [11]. In this paper, the homogenization method is also employed. Additional anisotropic  ϕ − A reluctivity tensor is calculated in preprocessing, and no modification of the A, weak formulation is necessary [12, 13].

2 Problem Definition Problem domain  is defined as a union of iron core region C and nonconductive outside region 0 . Maxwell’s equations are written in complex representation, with imaginary unit j and angular frequency ω. In the iron core region C follows [14] ∇ × E = − jω B

(1)

∇ × H = J

(2)

∇ · B = 0

(3)

where E represents the electric field and B represents magnetic flux density. Magnetic field intensity is denoted by H , and eddy currents with J. As already stated in the introduction, eddy currents are considered as superposition of the large eddy current loops Jyz induced by time-varying magnetic flux perpendicular to the lamination plane and narrow current loops Jxt induced by the time-varying magnetic flux

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Fig. 1 Eddy currents in laminated iron core

component parallel to the lamination plane, that is J = Jxt + Jyz

(4)

where index t denotes tangential direction with respect to the lamination sheet. Orientation of the transformer core is assumed to be as in Fig. 1. Hence, tangential direction denoted with index t is some combination of directions of the y-axis and z-axis, i.e. for unit vector at holds at = sin ψ a y + cos ψ az , with ψ as some arbitrary angle. There is also the other tangential direction τ with respect to the lamination sheet that is perpendicular to the direction t, i.e. aτ = at × ax , as can be seen in Fig. 1. Material relations in C are following H = ν B

(5)

J = σ E

(6)

where ν represents magnetic reluctivity and σ represents local electric conductivity of transformer core lamination. Magnetic reluctivity is defined as a reciprocal value of magnetic permeability ν = μ−1 . In the space outside of the transformer core 0 , the following equations apply ∇ × H = J0

(7)

∇ · B = 0

(8)

where J0 represents generator current. Material relations in 0 are following B = μ0 H

(9)

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σ =0

(10)

where μ0 represent magnetic permeability of vacuum. Since region 0 is assumed to be nonconductive, eddy currents are not induced in 0 , hence equation of Faraday’s law is omitted in 0 .

3 Homogenization Since the ratio of the global core dimensions to the thickness of the lamination is large and the number of lamination sheets is significant, homogenization of the laminated core is the only valid option for the 3D analysis of eddy currents in the transformer core using FEM. Homogenization of the magnetic reluctivity of the laminated transformer core is performed by the principle of circuits averaging [1]. Index h in tensors [νh ] and [σh ] denotes homogenized tensors. The surrogate material obtained has anisotropic magnetic properties described by magnetic reluctivity tensor ⎡

⎤ νx x 0 0 [νh ] = ⎣ 0 ν yy 0 ⎦ 0 0 νzz

(11)

where νx x represents magnetic reluctivity component perpendicular to the lamination, whereas ν yy and νzz represent components tangential to the lamination, and following expressions usually hold, ντ τ = ν yy = νzz , νx x >> ντ τ . Calculations of νx x , ν yy and νzz are done as follows νx x = ν yy ≈ νzz =

ks (1 − ks ) + μlam μ0 ks μlam

1 + (1 − ks )μ0

(12) (13)

where ks is the stacking factor of the laminated core, and μlam is magnetic permeability of lamination. Analogously, electric conductivity tensor of the homogenized iron core is ⎡

⎤ σx x 0 0 [σh ] = ⎣ 0 σ yy 0 ⎦ 0 0 σzz

(14)

where σx x is a component of electric conductivity perpendicular to the lamination, whereas σ yy and σzz represent components tangential to the lamination and they

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generally have equal value, hence σ yy = σzz = σtt . The calculation of σtt is done as follows σtt = ks σ

(15)

where σ is electric conductivity of the core lamination, and ks is the stacking factor. Since there is an insulator between the lamination sheets, the electrical conductivity component σx x equals zero, i.e. σx x = 0. Consequently, only eddy currents lying in the planes parallel to the lamination can be induced, and those correspond to the large eddy current loops Jyz . Since eddy currents Jyz are monotone in nature across large enough parts of the region C , they can be properly considered on a course mesh. On the other hand, narrow eddy currents loops Jxt cannot be considered directly due to very oscillating nature in the direction perpendicular to the lamination, as already stated.

4 Low-Frequency Approximation of Eddy Currents Jx t Since only a coarse mesh is applicable, only a sufficiently monotone problem variable can be used. Although the eddy current Jxt is highly oscillating, the magnetic flux density that induces it is monotone function in large enough parts of the C . It is possible to link the amount of magnetic flux density in the finite element to the amplitude of eddy current Jxt , and thus indirectly take Jxt into consideration. Due to the large ratio of the height and length of a lamination to the thickness of a lamination, it is a good approximation to assume that eddy currents Jxt have only tangential component within a lamination. Hence, from now on, narrow eddy current loops Jxt = Jx + Jt will be considered only as a tangential current Jt , since Jx = 0 in a lamination is assumed. From (1) and (6) then follows ∂ 1  Jt = ax × jω Bτ ∂x σ

(16)

where ax is a unit vector in the direction of x-axis. Bτ represents the tangential component of magnetic flux density Bτ = B y + Bz in a finite element. As already stated, indices t and τ denotes tangential directions that are perpendicular to each other within the local coordinate system of a finite element, i.e. aτ = at × ax . It is a good approximation to assume that Bτ is constant along the thickness of a lamination, therefore after integration from (16) follows well-known low-frequency approximation of narrow eddy current loops [8] Jt = jωσ x ax × Bτ

(17)

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 ϕ − A weak In [8], Jt is then considered as a source current when deriving A, formulation. Hence, the term associated with Jt in a weak formulation follows    (18) Jt A d V = ( jωσ Bτ x)(− Bτ x)d V = − jωσ Bτ Bτ x 2 d V  where, the test function A is also linked with magnetic flux density Bτ , since generally J = − jωσ A holds. Averaging integrand in (18) over thickness of one lamination d, yields well-known expression [7]

1 d

d/2

− jωσ Bτ Bτ x 2 d x = − jωσ Bτ Bτ

−d/2

d2 12

(19)

Combining (18) and (19), weak formulation of eddy currents Jt is homogenized  ΩC

2

d Jt A d V = − jωσ 12



Bτ Bτ d V

(20)

Ω¯ C

Since the tangential component of magnetic flux density Bτ is defined as Bτ = B y + Bz inside one finite element of a lamination, the following equation holds ⎤⎡ ⎤ 0 0 0 Bx d 2 ⎥ ⎢ − jωσ Bτ = − j ⎣ 0 ωσ d12 0 ⎦⎣ B y ⎦ = − j[ν J ] B 12 2 Bz 0 0 ωσ d12 ⎡

2

(21)

With respect to (21), expression (20) is transformed to 

Jt A d V = − j[ν J ]



B B  d V = − j[ν J ]



 (∇ × A)(∇ × A )d V

(22)

 ϕ − A formulation then follows as The first equation of the weak A, 



 νh (∇ × A)(∇ × A )d V +

Ω

 Ω



+ Ω



jω σh A A d V

σh ∇ϕ A d V =

 Ω0



J0 A d V − j ν J



 (∇ × A)(∇ × A )d V

(23)

Ω¯C

where the last term in (23) represents approximative contribution of narrow eddy  and currents loops Jxt to the final distribution of the magnetic vector potential A, consequently magnetic flux density B within the problem domain  in the lowfrequency range. Since the variables within the integrand of the last term in (23) are

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equal to the variables within the integrand of the first term in (23), it is possible to  ϕ − A weak formulation sum them up, thus obtaining the final form of the A, 

  μ−1 0 (∇ × A)(∇ × A )d V +

Ω0



 × A )d V [νΣ ](∇ × A)(∇

Ω¯ C



+

jω[σh ] A A d V +

Ω¯ C



[σh ]∇ϕ A d V =

Ω¯ C

 d V + [σh ] jω A∇v

Ω¯ C







J0 A d V

Ω0

(24) [σh ]∇ϕ∇ϕ  d V = 0

(25)

Ω¯ C

where Ω¯ C represents homogenized core and [νΣ ] = [ν H ] + j[ν J ] represents total magnetic reluctivity of the homogenized core. Equation (25) represents a well-known  ϕ − A weak formulation [2]. second equation in the A, Hence, contrary to the large eddy current loops Jyz , narrow eddy currents loops  Jxt are taken into account indirectly, through the magnetic flux they generate, which is then manifested in the form of an increase in magnetic reluctivity of the transformer core. It is important to note that the tensor [ν J ] is easy to calculate, so no  ϕ − A formulation implementation of the new code is required, i.e. the standard A, can be used [13].

5 Calculation of Losses Due to Narrow Eddy Current Loops Assuming again that narrow eddy current loops have a predominantly tangential component in a lamination, that is Jxt = Jt , specific losses due to narrow eddy current loops are calculated as follows [7] Pxt =

1   ∗ Re E t · Jt 2

(26)

where the asterisk denotes complex conjugate. Using (6) and (17) with (26) yields Pxt =

1  Re ( jωx ax × Bτ ) · ( jωσ x ax × Bτ )∗ 2

(27)

where Bτ is also complex valued vector, i.e. Bτ = Bτr e + j Bτim , hence Pxt =

1  Re ( jωx ax × ( Bτr e + j Bτim )) · (− jωσ x ax × ( Bτr e − j Bτim )) 2

(28)

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Since the vectors in the scalar product in (28) are collinear, follows Pxt =

2 1 2 2 re 2 1

σ ω x (( Bτ ) + ( Bτim )2 ) = σ ω2 x 2 Bτ 2 2

(29)



where Bτ is a module of complex-valued vector Bτ . Since Bτ is assumed to be constant over lamination thickness, by integrating expression (29) along the thickness d of a lamination, average specific losses over lamination thickness P¯xt are obtained 1 P¯xt = d

d/2 −d/2

2 d 2 1 2 2



2

σ ω x Bτ d x = σ ω2 Bτ 2 24

(30)



Equation (30) is implemented in the postprocessing code, with Bτ calculated 



2 2





from the magnetic flux density solution vector as Bτ = B y + Bz , assuming core orientation as in Fig. 1.

6 Numerical Example For the purpose of applying the homogenization method, a real-size open core transformer model is used [15]. The model consists of a winding and a core. The winding is made as a hollow cylinder, 650 mm high, 130 mm outer radius, and 74 mm inner radius. The transformer core is a prism 850 mm high with a 100 mm wide square cross-section. The transformer core consists of 240 laminations, with a thickness of d = 0.4 mm each, hence the stacking factor equals ks = 0.96. The electrical conductivity σ of the lamination is σ = 2.4 · 106 S/m, and the relative magnetic permeability μr of the lamination is μr = 1000. The winding is given as electrically non-conductive, with a relative magnetic permeability equal to the relative magnetic permeability of the vacuum. Generator current with current density of J0 = 0.5 A/mm2 is imposed in the winding. The model with the homogenized core is shown in Fig. 2. Finite element mesh consists of around 200,000 finite elements.  ϕ − A formulation (24)–(25) was The problem described by the standard A, simulated in the open-source Elmer – CSC software. The values of [σh ] conductivity tensor and the values of [νΣ ] = [ν H ] + j[ν J ] reluctivity tensor, i.e. the anisotropic reluctivity tensor [νh ] and the reluctance tensor [ν J ], which compensates for the influence of narrow eddy current loops, were calculated in preprocessing by employing (11)–(15). Therefore, tensors have the following values

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Fig. 2 Homogenized open core transformer model ⎤ ⎡ ⎤ ⎡ ⎤ 0 0 0 32595 0 0 0 0 0 ⎥ ⎢ ⎢ ⎥ ⎢ ⎥ [σh ] = ⎣ 0 2.3 · 106 0 ⎦ S/m, [νh ] = ⎣ 0 829 0 ⎦ m/H, [ν J ] = ⎣ 0 10.05 0 ⎦ m/H 0 0 2.3 · 106 0 0 829 0 0 10.05 ⎡

6.1 Results The simulation lasted 10 h. The solution was obtained by using an iterative solver, and the convergence tolerance for linear system solution was set to 10−7 . The algorithm used by the iterative solver is the BiCGstab2 algorithm. The obtained results are visualized in visualization software ParaView. Figure 3 shows the distribution of the magnetic flux density magnitude over the core slices. In Fig. 3a, a slice of the core is located in the center of the core with the normal vector parallel to the x-axis. In the Fig. 3b, slice of the core is again located in the center of the core, but with the normal vector parallel to the y-direction. By comparing the results, the effect of anisotropy and eddy currents on the distribution of magnetic flux density can be seen. Losses due to large eddy current loops were calculated in postprocessing from the eddy current vector Jyz which is first calculated from the problem variables A and ϕ as Jyz = − jωσtt A − σtt ∇ϕ. Losses due to narrow eddy current loops are calculated by employing (30). Values for both types of losses are shown in Table 1. From Table 1 it can be seen that losses due to large eddy current loops are drastically higher than losses due to narrow eddy current loops. The reason for this lies in the large size of the surface of the lamination sheet within which the eddy currents Jyz close, resulting in a large current density Jyz , hence large specific losses Pyz . In contrast, according to (30), specific losses averaged along lamination thickness P¯xt depend only on the tangential component of the magnitude flux density which can be seen in Fig. 3.

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Fig. 3 Magnetic flux density distribution. a Left. b Right

Table 1 Eddy current losses

Eddy current type

Eddy current losses

Narrow eddy current loops

W = 5.3 J

Large eddy current loops

W = 706.8 J

7 Conclusion In the low-frequency range, with a time-harmonic current source, using only precalculated anisotropic magnetic reluctivity tensor and electrical conductivity tensor  ϕ − A weak formulation, it is possible to simulate a magnetodyin a standard A, namic problem on a real-size model of a transformer. The simulation example shown demonstrates the simplicity of the method. Since the simulation is made on the real size model, it is not possible to use a realistic laminated FEM model as a reference to verify the accuracy of the solution. In future works, a comparison with the measurements will be made.

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References 1. Kaimori H, Kameari A, Fujiwara K (2007) FEM computation of magnetic field and iron loss in laminated iron core using homogenization method. IEEE Trans Magn 43(4):1405–1408 2. Bíró O, Preis K, Ticar I (2005) A FEM method for eddy current analysis in laminated media. COMPEL—Int J Comput Math Electr Electron Eng 24(1):241–248 3. Silva VC, Meunier G, Foggia A (1995) A 3-D finite-element computation of eddy currents and losses in laminated iron cores allowing for electric and magnetic anisotropy. IEEE Trans Magn 31(3):2139–2141 4. De Gersem H, Vanaverbeke S, Samaey G (2012) Three-dimensional-two-dimensional coupled model for eddy currents in laminated iron cores. IEEE Trans Magn 48(2):815–818 5. Hollaus K, Schöberl J, Homogenization of the eddy current problem in 2D 6. Hollaus K, Hannukainen A, Schoberl J (2014) Two-scale homogenization of the nonlinear eddy current problem with FEM. IEEE Trans Magn 50(2):413–416 7. Gyselinck J, Vandevelde L, Melkebeek J, Dular P, Henrotte F, Legros W (1999) Calculation of eddy currents and associated losses in electrical steel laminations. IEEE Trans Magn 35(3):1191–1194 8. Dular P, Gyselinck J, Geuzaine C, Sadowski N, Bastos JPA (2003) A 3-D magnetic vector potential formulation taking eddy currents in lamination stacks into account. IEEE Trans Magn 39(3):1424–1427 9. Dular P (2008) A time-domain homogenization technique for lamination stacks in dual finite element formulations. J Comput Appl Math 215(2):390–399 10. Gyselinck J, Sabariego RV, Dular P (2006) A nonlinear time-domain homogenization technique for laminated iron cores in three-dimensional finite-element models. IEEE Trans Magn 42(4):763–766 11. Krahenbuhl L, Dular P, Zeidan T, Buret F (2004) Homogenization of lamination stacks in linear magnetodynamics. IEEE Trans Magn 40(2):912–915 12. Bíró O (1999) Edge element formulations of eddy current problems. Comput Methods Appl Mech Eng 169(3–4):391–405 13. Ren Z, Bouillault F (2008) 3. Magnetodynamic formulations. In: The finite element method for electromagnetic modeling, vol. The Finite, pp 117–137 14. Haznadar Z, Štih Ž (1997) Elektromagnetizam 1. Školska knjiga, Zagreb 15. Ziger I, Bojanic B, Krajtner D (2014) Open-core power voltage transformer: concept, properties, application. IEEE Int Energy Conf 246–253