Electrical Systems 2 : From Diagnosis to Prognosis. 9781119720560, 1119720567

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Electrical Systems 2

Electrical Systems 2 From Diagnosis to Prognosis

Edited by

Abdenour Soualhi Hubert Razik

First published 2020 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd 27-37 St George’s Road London SW19 4EU UK

John Wiley & Sons, Inc. 111 River Street Hoboken, NJ 07030 USA

www.iste.co.uk

www.wiley.com

© ISTE Ltd 2020 The rights of Abdenour Soualhi and Hubert Razik to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2019956924 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-608-1

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1. Diagnosis of Electrical Machines by External Field Measurement . . . . . . . . . . . . . . . . . . . . . . . . Remus PUSCA, Eric LEFEVRE, David MERCIER, Raphael ROMARY and Miftah IRHOUMAH 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Extracting indicators from the external magnetic field . 1.2.1. External field classification . . . . . . . . . . . . . . . 1.2.2. Attenuation of the transverse field . . . . . . . . . . . 1.2.3. Measurement of the transverse field . . . . . . . . . . 1.2.4. Modeling a healthy machine . . . . . . . . . . . . . . . 1.2.5. Modeling a faulty machine . . . . . . . . . . . . . . . . 1.2.6. Effect of the load . . . . . . . . . . . . . . . . . . . . . . 1.3. Information fusion to detect the inter-turn short-circuit faults . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1. Belief function theory: basic concepts . . . . . . . . . 1.3.2. Fault detection with the fusion method . . . . . . . . 1.3.3. Calculation example . . . . . . . . . . . . . . . . . . . . 1.4. Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.1. Presentation of rotating electrical machines . . . . . 1.4.2. Presentation of experimental results . . . . . . . . . . 1.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 2. Signal Processing Techniques for Transient Fault Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . José Alfonso Antonino DAVIU and Roque Alfredo Osornio RIOS 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Fault detection via motor current analysis . . . . . . . . . . . 2.2.1. Classical tools (MCSA) . . . . . . . . . . . . . . . . . . . 2.2.2. New techniques based on transient analysis (ATCSA) 2.3. Signal processing tools for transient analysis . . . . . . . . . 2.3.1. Example of a discrete tool: the DWT . . . . . . . . . . . 2.3.2. Example of a continuous tool: the HHT . . . . . . . . . . 2.4. Application of transient-based tools for electric motor fault detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1. Application of the DWT for the detection of rotor damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2. Application of the HHT for the detection of rotor damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3. Accurate Stator Fault Detection in an Induction Motor Using the Symmetrical Current Components . . . . . . . Monia BOUZID and Gérard CHAMPENOIS

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3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Study of the SCCs behavior in an IM under different stator faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1. Simulation study . . . . . . . . . . . . . . . . . . . . . . 3.2.2. Analytical study of the SCCs in an IM under different stator faults . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Extracting stator fault indicators from an IM . . . . . . . 3.4. Automatic and accurate detection and diagnosis of stator faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1. Description of the monitoring system of the IM operating state . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2. Improving the accuracy of incipient stator fault detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3. Automatic incipient stator fault diagnosis in an IM 3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  

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Contents

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Chapter 4. Bearing Fault Diagnosis in Rotating Machines . . Claude DELPHA, Demba DIALLO, Jinane HARMOUCHE, Mohamed BENBOUZID, Yassine AMIRAT and Elhoussin ELBOUCHIKHI

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4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Bearing fault detection and diagnosis overview . . . . . . 4.1.2. Problem statement and proposal . . . . . . . . . . . . . . . 4.2. Method description . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1. The global spectral analysis description . . . . . . . . . . . 4.2.2. Discrimination of faults in the bearing balls using LDA 4.3. Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1. Experimental test bed description. . . . . . . . . . . . . . . 4.3.2. Time-domain detection . . . . . . . . . . . . . . . . . . . . . 4.4. Global spectra bearing diagnosis. . . . . . . . . . . . . . . . . . 4.4.1. Data preprocessing . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2. Global spectra results with PCA . . . . . . . . . . . . . . . 4.4.3. Global spectra results with LDA . . . . . . . . . . . . . . . 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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124 124 128 130 130 133 135 135 137 139 139 141 143 146 147

Chapter 5. Diagnosis and Prognosis of Proton Exchange Membrane Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhongliang LI, Zhixue ZHENG and Fei GAO

153

5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. PEMFC functioning principle and development status . 5.2.1. From a PEMFC to a PEMFC system . . . . . . . . . 5.2.2. Current status of the PEMFC technology . . . . . . . 5.3. Faults and degradation of PEMFCs . . . . . . . . . . . . . 5.3.1. Degradation related to the aging effects . . . . . . . . 5.3.2. Degradation related to system operations . . . . . . . 5.3.3. Variables used for PEMFC degradation evaluation 5.4. PEMFC diagnostic methods . . . . . . . . . . . . . . . . . 5.4.1. Model-based diagnostic methods . . . . . . . . . . . . 5.4.2. Data-driven diagnostic methods. . . . . . . . . . . . . 5.4.3. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Prognosis of PEMFCs . . . . . . . . . . . . . . . . . . . . . 5.5.1. Health index and EoL . . . . . . . . . . . . . . . . . . . 5.5.2. Model-based prognostic methods . . . . . . . . . . . . 5.5.3. Data-driven and hybrid prognostic methods . . . . . 5.5.4. Case study . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Remaining challenges . . . . . . . . . . . . . . . . . . . . . 5.7. References. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201

Summary of Volume 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Introduction

The diagnosis and prognosis of electrical systems is still a relevant field of research. The research that has been carried out over the years has made it possible to acquire enough knowledge, to build a base from which we can delve further into this field of research. This study is a new challenge that estimates the remaining lifetime of the analyzed process. Many studies have been carried out to establish a diagnosis of the state of health of an electric motor, for example. However, making a diagnosis is like giving binary information: the condition is either healthy or defective. Of course, this may seem simplistic, but detecting a failure requires the use of suitable sensors that provide signals. These will be processed to monitor health indicators (features) for defects. Then, we witnessed a multitude of research activities around classification. It was indeed appropriate to distinguish the operating states, to differentiate them from one another and to inform the operator of the level of severity of a failure or even of the type of failure among a predefined panel. A major effort has been made to estimate the remaining lifetime or even the lifetime consumed. This is a challenge that many researchers are still trying to meet. This book, which has been divided into two volumes, informs readers about the theoretical approaches and results obtained in different laboratories in France and also in other countries such as Spain, and so on. To this end, many researchers from the scientific community have contributed to this book by sharing their research results.

                                        Introduction written by Abdenour SOUALHI and Hubert RAZIK.

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Chapter 1, Volume 1, “Diagnostic Methods for the Health Monitoring of Gearboxes”, by A. Soualhi and H. Razik, presents state-of-the-art diagnostic methods used to analyze the defects present in gearboxes. First of all, there is a bibliographical presentation regarding different types of gears and their defects. We conclude that gear defects represent the predominant defect at this level, thus justifying the interest in detecting and diagnosing them. Then, we present various gear analyses and monitoring techniques proposed as part of the condition-based maintenance and propose a diagnostic method. Thus, we show the three main phases of diagnosis: First, the analysis presented as a set of technical processes ensuring control of the representative quantities of operation; then the monitoring that exploits the fault indicators for detection; finally, the diagnosis which is the identification of the detected defect. Chapter 2, Volume 1, “Techniques for Predicting Defects in Bearings and Gears”, by A. Soualhi and H. Razik, deals with strategies based on features characterizing the health status of the system to predict the appearance of possible failures. The prognosis of faults in a system means the prediction of the failure imminence and/or the estimation of its remaining life. It is in this context that we propose, in this chapter, the three methods of prognosis. In the first method, the degradation process of each system is modeled by a hidden Markov model (HMM). In a measured sequence of observations, the solution consists of identifying among the HMMs the one that best represents this sequence which allows predicting the imminence of the next degradation state and thus the defect of the studied system. In the second method (evolutionary Markov model), the computation of the probability that a sequence of observations arrives at a degradation state at the moment t+1, given the HMM modeled from the same sequence of observations, also allows us to predict the imminence of a defect. The third method predicts the imminence of a fault not by modeling the degradation process of the system, but by modeling each degradation state. Chapter 3, Volume 1, “Electrical Signatures Analysis for Condition Monitoring of Gears in Complex Electromechanical Systems,” written by S. Hedayati Kia and M. Hoseintabar Marzebali, deals with a review of their most remarkable research, which has been carried out in the last 10 years. A particular emphasis has been placed on the topic of noninvasive fault detection in gears using electrical signatures analysis. The main aim is to utilize the electrical machine as a sensor for the identification of gear defects. In this regard, a universal approach is developed for the first time by the authors which allows evaluating the efficacy of noninvasive techniques in the diagnosis of torsional vibration induced by the faulty gear located

Introduction

xi

within the drive train. This technique can be considered an upstream phase for studying the feasibility of gear fault detection using noninvasive measurement in any complex electromechanical system. Chapter 4, Volume 1, “Modal Decomposition for Bearing Fault Detection”, by Y. Amirat, Z. Elbouchikri, C. Delpha, M. Benbouzid and D. Diallo, deals with induction machine bearing faults detection based on modal decomposition approaches combined to a statistical tool. In particular, a comparative study of a notch filter based on modal decomposition, through an ensemble empirical mode decomposition and a variational mode decomposition, is proposed. The validation of these two approaches is based on simulations and experiments. The achieved simulation and experimental results clearly show that, in terms of fault detection criterion, the variational mode decomposition outperforms the ensemble empirical mode decomposition. Chapter 5, Volume 1, “Methods for Lifespan Modeling in Electrical Engineering”, by A. Picot, M. Chabert and P. Maussion, deals with the statistical methods for electrical device lifespan modeling from small-sized training sets. Reliability has become an important issue in electrical engineering because the most critical industries, such as urban transports, energy, aeronautics or space, are moving toward more electrical-based systems to replace mechanical- and pneumatic-based ones. In this framework, increasing constraints such as voltage and operating frequencies enhance the risk of degradation, particularly due to partial discharges (PDs) in the electrical machine insulation systems. This chapter focuses on different methods to model the lifespan of electrical devices under accelerated stresses. First, parametric methods such as design of experiments (DoE) and surface responses (SR) are suggested. Although these methods require different experiments to organize in a certain way, they reduce the experimental cost. In the case of nonorganized experiments, multilinear regression can help estimate the lifespan. In the second part, the nonparametric regression tree method is presented and discussed, resulting in the proposal of a new hybrid methodology that takes advantages of both parametric and nonparametric modeling. For illustration purpose, these different methods are evaluated on experimental data from insulation materials and organic light-emitting diodes. Chapter 1, Volume 2, “Diagnosis of Electrical Machines by External Field Measurement”, by R. Pusca, E. Lefevre, D. Mercier, R. Romary and M. Irhoumah, presents a diagnostic method that exploits the information

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delivered by external flux sensors placed in the vicinity of rotating electrical machines in order to detect a stator inter-turn short circuit. The external magnetic field measured by the flux sensors originates from the airgap flux density and from the end winding currents, attenuated by the magnetic parts of the machine. In the faulty case, an internal magnetic dissymmetry occurs, which can be found again in the external magnetic field. Sensitive harmonics are extracted from the signals delivered by a pair of flux sensors placed at 180° from each other around the machine, and the data obtained for several sensor positions are analyzed by fusion techniques using the belief function theory. The diagnosis method is applied on induction and synchronous machines with artificial stator faults. It is shown that the probability of detecting the fault using the proposed fusion technique on various series of measurements is high. Chapter 2, Volume 2, “Signal Processing Techniques for Transient Fault Diagnosis”, by J.A. Daviu and R.A.O. Rios, revises the most relevant signal processing tools employed for condition monitoring of electric motors. First, the importance of the predictive maintenance area of the electric motors due to the extensive use of these machines in many industrial applications is pointed out. In this context, the most important predictive maintenance techniques are revised, showing the advantages such as the simplicity, remote monitoring capability and broad fault coverage of motor current analysis methods. In this regard, two basic approaches based on current analysis are explained: the classical methods, relying on the Fourier transform of steady-state current (motor current signature analysis – MCSA), and novel methods based on the analysis of startup currents (advanced transient current signature analysis – ATCSA). In the chapter, the most significant signal processing tools employed for MCSA and ATCSA are explained and revised. For MCSA, the basic problems derived from the application of the Fourier transform as well as other constraints of the methodology are explained. For ATCSA, the most suitable signal processing techniques are described, classifying them into continuous and discrete transforms. One representative of each group is accurately described (the discrete wavelet transform for discrete tools and the Hilbert-Huang transform for continuous tools), accompanying the explanation with illustrative examples. Finally, we discussed several examples of the application of each tool to electric motor fault diagnosis. Chapter 3, Volume 2, “Accurate Stator Fault Detection in an Induction Motor Using the Symmetrical Current Components”, by M. Bouzid and G. Champenois, deals with the accurate detection of stator faults such as inter-turns short circuit, phase-to-phase and phase-to-ground faults of the

Introduction

xiii

induction motor, using the symmetrical current components. The detection method is based on the monitoring of the behavior of the negative and zero sequence stator currents of the machine. This chapter also develops analytical expressions of these components obtained using the coupled inductance model of the machine. However, despite its efficiency, the negative sequence current-based method has its own limitations to detect accurate incipient stator faults in an induction motor. This limit can be explained by the fact that the negative sequence current generated in a faulty motor does represent not only the asymmetry introduced by the fault, but also by other superposed asymmetries, such as the voltage imbalance, the inherent asymmetry in the machine and the inaccuracy of the sensors. This aspect can generate false alarm and make the achievement of accurate incipient stator fault detection very difficult. Thus, to increase the accuracy of the fault detection and the sensitivity of the negative sequence current under different disturbances, this chapter proposes an efficient method able to compensate the effect of the different considered disturbances using experimental techniques having the originality to isolate the negative sequence current of each disturbance. The efficiency of all these proposed methods is validated experimentally on a 1.1-kW motor under different stator faults. Moreover, an original monitoring system, based on neural networks, is also presented and described to automatically detect and diagnose incipient stator faults. Chapter 4, Volume 2, “Bearing Fault Diagnosis in Rotating Machines”, by C. Delpha, D. Diallo, J. Harmouche, M. Benbouzid, Y. Amirat and E. Elbouchikhi, is focused on detection, estimation and diagnosis of mechanical faults in electrical machines. Nowadays, it is necessary to rapidly assess the structural health of a system without disassembling its elements. For this in situ diagnosis purpose, the use of experimental data is very imperative. Moreover, the monitoring and maintenance costs must be reduced while ensuring satisfactory security performances. In this chapter, we focus on vibration-based signals combined with statistical techniques for bearing fault evaluation. Based on a four-step diagnosis process (modeling, preprocessing, feature extraction and feature analysis), the combination of several techniques such as principal components analysis and linear discriminant analysis in a global approach is explored to monitor the condition of vibration-based bearings. The main advantage of this approach is that prior knowledge on the bearing characteristics is not required. A particularly reduced frequency analysis has led to efficiently differentiate the bearing fault types and evaluate the bearing fault severities.

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Chapter 5, Volume 2, “Diagnosis and Prognosis of Proton Exchange Membrane Fuel Cells”, by Z. Li, Z. Zheng and F. Gao, deals with the diagnostic and prognostic issues of fuel cell systems, especially the proton exchange membrane (PEMFC) type. First, the basic functioning principle of PEMFCs and their current development and application status are presented. Their high cost, low reliability and durability make them unfit for commercialization. In the following sections, degradation mechanisms related to both the aging effect and the system operations are analyzed. In addition, typical variables and characterization tools, such as polarization curve, electrochemical impedance spectroscopy, linear sweep voltammetry and cyclic voltammetry, are introduced for the evaluation of PEMFC degradation. Various diagnostic and prognostic methods in the literature are further classified based on their input-to-output process model of the system, namely model-based, data-driven and hybrid methods. Finally, two case studies for diagnosis and prognosis are given at the end of each part to give the readers a general and clearer illustration of these two issues.

1 Diagnosis of Electrical Machines by External Field Measurement

1.1. Introduction Rotating electrical machines are found in all areas of modern domestic and industrial life [TAV 08]. They are the main electromechanical energy conversion devices in all industrial processes and have been widely used in different industrial applications for several decades. They account for approximately 70% of all electricity consumed on the grid and 80% of industrial engines involved in manufacturing processes. Regardless of the size of these units, from 1 kilowatt to several megawatts, the production losses due to a shutdown relating to an engine failure are greater than those induced by the actual engine efficiency. The failure of the machines, therefore, reduces the production rate and increases production and maintenance costs. It is then important to reduce maintenance costs and avoid unplanned downtime for these machines. Electrical machines must be monitored during the production process to improve their reliability and reduce their downtime [STO 04, ESE 17, NOR 93]. Monitoring of rotating electrical machines is still an essential part to increase reliability and operational safety of electrical systems and has been the subject of much research in recent decades [STO 04, HAN 10, PET 17]. Electric motors encounter a wide range of mechanical problems common to most machines, such as imbalance, misalignment, bearing faults and resonance [FOU 15, HAM 15, KAT 16]. But electric motors also encounter                                         Chapter written by Remus PUSCA, Eric LEFEVRE, David MERCIER, Raphael ROMARY and Miftah IRHOUMAH.

Electrical Systems 2: From Diagnosis to Prognosis, First Edition. Edited by Abdenour Soualhi and Hubert Razik. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Electrical Systems 2

their specific problems, which are the result of electromagnetic phenomena. The methods conventionally used for the diagnosis of electrical machines are based on measurements of current, voltage, vibration and noise. Although their effectiveness has been demonstrated, the generalization of these methods in the industrial environment remains limited on account of their relatively important cost. Other methods based on magnetic field measurements outside the machine are interesting because they are inexpensive and easy to implement. Thus, monitoring devices based on the information provided by the magnetic flux produced by the imbalances in the magnetic or electrical circuit of the motors can be effectively used in addition to, or as an alternative to the current monitoring more conventionally used. Thus, many recent methods, used for the diagnosis of electrical machines, are based on the analysis of combining measurements of current and magnetic flux, where, on the basis of an evaluation of many tests, the stator current and the external leakage flux were selected as the most practical signals containing the information needed to detect broken bars and short circuit between turns of the stator winding [CEB 12a, YAZ 10]. The methods presented in this chapter propose solutions to improve the detection of stator inter-turn short-circuit fault by external field analysis [CEB 12b]. For this, it uses the processing of data obtained by several field sensors and fusion methods suitable for applications in signal processing. In this area, the information fusion must take into account the specificities of the data in considered process [DAS 01]. In our case, information fusion tools use the belief function theory [SHA 76, PUS 12, IRH 18]. This theory is a mathematical framework that offers modeling and fusion tools, and it also enables a relatively natural integration of the data imperfections in the analysis. For implementation of the proposed method, the measurements of the external magnetic field are exploited in order to construct two specific pieces of information: the difference of variation and the ratio of the amplitudes. In order to make a more relevant decision, a fusion process is applied to merge these two pieces of information by transforming them into belief functions. After their fusion, a decision can be made. The method proposed in this chapter is fully noninvasive and can be implemented for asynchronous (AM) and synchronous machines (SM). Its main advantage is that it does not require the knowledge of the healthy state of the machine. In the analysis, it exploits the load variation of sensitive spectral lines instead of their magnitude. The sensitive lines are chosen

Diagnosis of Electrical Machines by External Field Measurement

3

considering the AM or SM specificity as presented in the following section. 1.2. Extracting indicators from the external magnetic field One of the main issues for exploiting the external magnetic field is to define reliable indicators from it. This requires a good knowledge of the electromagnetic behavior of the machine in the faulty condition. Here, we present an analytical modeling of an electrical machine with a stator interturn short circuit fault, associated with a simplified decomposition of the external magnetic field. 1.2.1. External field classification From a physical point of view, an external magnetic field appears in the vicinity of an electrical machine because the internal magnetic field is not perfectly channeled by the ferromagnetic parts of the machine. This external magnetic field can be decomposed in transverse and axial components. The axial field is in a plane that contains the machine axis. It is generated by the winding overhang effects. The transverse field is located in a perpendicular plane to the machine axis. It is an image of the airgap flux density b which is attenuated by the stator magnetic circuit. Figure 1.1 shows a simplified representation of both fields.

(a)

(b)

Figure 1.1. (a) Axial field. (b) Radial field

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Electrical Systems 2

Using a simple wound sensor, it is possible to discriminate the transverse component from the axial component. Figure 1.2 shows different positions of a wound sensor around the machine. In position A, only the axial field is measured. Position E, although defined as being a position for measuring the transverse field, can also embrace a part of the axial field depending on whether the sensor is more or less distant from the end coils. Position D is described as “pure radial” since, in theory, no axial line field can cross the section of the sensor in this position. It should be pointed out that the amplitude of the signal delivered by the sensor in positions B and D are generally lower. Actually, in these positions, the sensor is further away from the motor compared to position E where the sensor is pressed against the external frame. It is, therefore, possible to define the ideal position of the sensor that it is placed against the motor, in the center to limit the end coil effect, and when possible at design, between the stator sheets and the external frame. In this position, the sensor mainly measures the transverse field. However, practically, the sensor setting depends on the construction of the machine, its environment and the accessibility places.

Figure 1.2. Different sensor positions

In the following sections, only the transverse field will be considered and particularly its normal component that requires us to define an attenuation coefficient that affects the airgap flux density.

Diagnosis of Electrical Machines by External Field Measurement

5

1.2.2. Attenuation of the transverse field Let us define the airgap flux density as the following double sum expression:

b

bK ,H ,

[1.1]

K ,H

where bK,H is an elementary flux density component defined as bK , H

bˆK , H cos( K t

H

s K ,H

[1.2]

)

with K being the frequency rank and H the pole pair number of the component. Figure 1.3 shows a simplified representation of an electrical machine, with smooth airgap, where the main dimensions are presented. The external transverse field can be itself decomposed in a normal component bn and a tangential component bt. An elementary component generated in the airgap of the machine is attenuated across the stator yoke and is found in the air outside the machine and can be measured by a coil flux sensor.

 M Bx  x B M bn bt sy Rint

s

s 0

0

sy Rext

Figure 1.3. Simplified geometry of the machine

ds

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Electrical Systems 2

An attenuation coefficient CH is defined as the ratio between the magnitude of the normal component of the transverse filed at the level of the external periphery of the stator and the magnitude of the component in the airgap. This attenuation coefficient depends on the inner and the outer radii s s and Rext , and the of the stator laminations, respectively, denoted by Rint magnetic permeability r [ROM 09]. It has been shown that CH can be expressed as CH

2 s int

s ext

r (( R / R )

H 1

s s ( Rint / Rext ) H 1)

.

s Figure 1.4 shows the evolution of CH versus H for Rint

[1.3]

82.5mm,

s ext

R 121mm and r = 1,000. We can observe that the more H increases, the more the components are attenuated.

CH 

Figure 1.4. CH versus H

1.2.3. Measurement of the transverse field We will assume that the measurement is performed with a wound flux sensor placed very closely to the stator core such that only the CH attenuation coefficient will be considered. Let bx denotes the normal transverse flux s density at radius x Rext . Here bx is defined by

CH bˆK , H cos( K t H

bx K ,H

s K ,H

).

[1.4]

Diagnosis of Electrical Machines by External Field Measurement

7

Let introduce bKx the harmonic of K rank of bx at the given point M (x

s Rext ,

s

s 0

), corresponding to the center of the wound flux sensor.

x K

b can be defined by bKx

bˆKx cos( K t

x K

),

[1.5]

where bˆKx can be computed by introducing complex quantities: bˆKx

CH bˆK , H e

j( H

s 0

K ,H

)

[1.6]

.

H

The measurements are performed with a coil flux sensor constituted of an nc turn coil (see Figure 1.3) of area S. The angular frequency flux K linked by the sensor results from integration of bKx on S: x K

bKx dS .

S

[1.7]

The integration depends on the sensor shape, the nc value, S, H and x. By introducing these parameters in the coefficient K Hx , Kx is given by C Kx , H K Hx Bˆ K , H cos( K t

x K

x K ,H

).

[1.8]

H

x Among the components which constitute K , only few of them, relative to low pole number (low H), have a significant contribution, whereas the other components will be absorbed by the ferromagnetic parts of the machine. The induced emf ex delivered by the sensor is given by

ex

eKx sin( K t K

 

x K

)

[1.9]

8

Electrical Systems 2

with eˆKx

K

K Hs K Hx bˆK , H e

j( H

s 0

K K bˆK , H e

j( H

s 0

K ,H

)

K ,H

)

,

H x K

[1.10] s H

arg

x H

.

H

1.2.4. Modeling a healthy machine The airgap flux density b results from the product between the airgap permeance and the magneto-motive force (mmf) . The following analytical developments consider a general case relating to a p pole pair AM. To determine the airgap flux density b, the following assumptions are formulated: – the magnetic permeability of the iron is high enough to neglect the ampere-turns consumed in the iron compared to those in the airgap, – the stator inter-turn short circuit only affects the stator flux density. Therefore, even for the healthy machine, we will focus only on the flux density components generated by the stator. – the p pole pair three-phase stator winding, made up by diametrical opening coils, is energized by a balanced three-phase system of sinusoidal s currents iq (q=1, 2 or 3) of rms value IS and angular frequency : iqs

I s 2 cos

t

q 1

2 . 3

Let us define as space references: – the d s axis which is confounded with the stator phase 1 axis, – the d r axis which corresponds to one tooth axis. Any point M in the airgap can be located by the variables s in relation to d and r in relation to d r . The axes d s and d r are distant of . s

Diagnosis of Electrical Machines by External Field Measurement

9

1.2.4.1. Airgap permeance The airgap permeance model is based on rectangular-shaped slots, assuming that the field lines which cross the airgap are radial. As the field lines never join the bottom of the slots, practically, in order to express , the airgap can be modeled considering a fictitious slot with a depth equal to the fifth of their opening and assuming the field lines are radial. In such conditions, can be expressed as kskr ks

cos (ksN s

krN r ) p

s

pkrN r

.

[1.11]

kr

Here, kskr is a permeance coefficient that depends on the slot geometry. N s and N r are, respectively, the number of stator and rotor slots per pole pair. ks and kr are positive, negative or null integers. s is the angular abscissa of any point in the airgap related to the stator referential d s . represents the angular position of the rotor tooth 1 axis relatively to d s. When the machine rotates R angular frequency, can be expressed as . For an SM, R is given by R (1 s) t / p, where s is the slip Rt 0 of the machine. 1.2.4.2. Healthy machine mmf s

The mmf s

generated by a healthy stator can be expressed as

Is h

s

Ahss cos( t

hs p

s

[1.12]

),

where hs is defined by hs=6k+1, where k varies between

s to + . Ahs is a

function that takes into account the winding coefficient tied to the rank hs. 1.2.4.3. Airgap flux density The calculus developments lead to define b= related to d s as follows: ∑

with bˆhs kskr

,

I 0s Ahss

,

kskr

cos 1

1

s

in the reference frame

[1.13]

10

Electrical Systems 2

After regrouping the components of same frequency and same polarity, we obtain b

[1.14]

bK , H K ,H

with bK , H

bˆK , H cos( K t

H

s K ,H

[1.15]

)

and

K 1 krN r (1 s ), H

p (hs

[1.16]

krN r ).

ksN s

1.2.5. Modeling a faulty machine For modeling the faulty machine, we will consider a three-phase stator winding. It is supposed that y turns from the n s turns of an elementary section belonging to the phase q are short-circuited. If y is small compared with pns, the total number of turns per phase, then it is possible to consider that the currents flowing in the three phases remain practically unchanged in faulty conditions. This hypothesis can, therefore, characterize the short circuit, thanks to a model that preserves the original structure of the machine. This model assumes that the stator winding in default is equivalent to the healthy winding, associated with y independent turns in which circulate the short-circuit current. It will be assumed that these two circuits are independent. The healthy part of the winding generates, therefore, the same flux density components without fault. s iqsc

s iqsc

iqs s q

i

s qsc

i

=

iqs s

n turns

Figure 1.5. Model of a faulty machine

+

y s.c.turns

Diagnosis of Electrical Machines by External Field Measurement

11

Figure 1.5 shows an elementary section with short-circuit turns. In this way, the resulting airgap flux density b* is equal to the initial airgap flux density b, to which is added the flux density bsc generated by the y turns s flowing through by the current iqsc : b b bsc . The short-circuit current is defined as s iqsc

I sc 2 cos( t

sc

),

[1.17]

where sc is the phase lag between the short-circuit current and the phase 1 current (see Figure 1.6). This phase actually depends on several parameters such as the impedance that limits the short-circuit current, the short-circuit winding, and the position of the fundamental airgap flux density relative to the phase current q (depending on the load).

i1 s sc

iqscs Figure 1.6. Diagram of current

The mmf generated by the y short-circuit turns, shifted of from ds, is shown in Figure 1.7 in the case of a four-pole machine. It is also shown the mmf generated by the healthy elementary winding. is an unidirectional mmf and can be decomposed in rotating fields can be which rotates in the opposite direction. In a stator referential, written as s qsc

I scs

Ahs cos( t h

s

h

),

[1.18]

h

where Ahs is a function obtained from the Fourier series of

s qsc

and h is a

not null relative integer, which can take consequently all the values of hs. s is defined as h h q sc .

h

12

Electrical Systems 2

n

n

y

3y

s qel

s s q

i

2

2 0

s s q

i

s

2

(a) s qsc

s iqsc

4 s iqsc

2

0

s

s q

4

(b)

Figure 1.7. mmf generated by the faulty turns

s qsc

As bsc

, the calculus developments lead us to define this quantity

in the reference frame related to ds. After regrouping the components of same frequency and same polarity, we obtain

bsc K sc , H sc

bˆscKsc , Hsc cos( K sc t

H sc

s sc, K sc , H sc

)

[1.19]

with

Ksc 1 kr N r (1 s), H sc

h

p(ks N s

kr N r ),

[1.20]

ks and kr are equivalent to ks and kr, respectively, where they vary from to + . The resultant flux density appears, after attenuation, at the level of the external transverse field. Considering the values that K can take as given by [1.16] and Ksc by [1.20], it results that Ksc does not bring new frequencies. This means that with the traditional method of diagnosis, the presence of failure will be appreciated through the variation of the amplitudes of already existing lines in the spectrum. This makes the diagnosis by analysis of the changes in the amplitudes of the measured components difficult.

Diagnosis of Electrical Machines by External Field Measurement

13

Concerning the polarities H and Hsc, we can observe that Hsc can take all positive and negative integers, whereas H is multiple of p. Hsc can particularly be equal to 1 corresponding to components that are weakly attenuated by the stator iron. In the following, the properties relating to the dissymmetry generated by such components will be exploited.

1.2.6. Effect of the load The analysis concerns the behavior, when the load varies, of the amplitude of the sensitive harmonic of rank Ksc measured using two sensors C1 and C2 shifted by 180° with respect to each other to a radius x from the axis of the machine (as shown in Figure 1.8). To simplify the analysis, we will consider the main effects generated by the components having the lowest polarities, namely of polarity p (H = 1) for the healthy machine and with polarity Hsc = 1 for the components generated by the fault. These low polarities lead to the lowest attenuation of the flux density components through the stator laminations.

Figure 1.8. Positioning of two coil sensors. For a color version of the figures in this book, see www.iste.co.uk/soualhi/electrical2.zip

For both positions: 0 (position 1 for sensor C1) and (position 2 for sensor C2), the flux density components • and • of rank K = Ksc can be expressed as the sum of a term relative to the healthy machine of amplitude and a term related to the faulty turns of amplitude , : Position 1: bKx1

bˆKx cos( K t

x K

x ) bˆsc, Ksc cos( K sc t

x sc, Ksc

),

[1.21]

Position 2: bKx 2

bˆKx cos( K t

x K

x ) bˆsc, Ksc cos( K sc t

x sc, Ksc

).

[1.22]

14

Electrical Systems 2

The only change between positions 1 and 2 is the change in the sign of the faulty term. This is due to the polarity Hsc=1 that changes the sign of the cosinus (cos( )= cos( )). The vector diagram for the rank K harmonic associated with a variation of the load is given in Figure 1.9 (in this diagram, 0). To make this diagram, it is considered that the current we take ∅ of the short-circuit part is modified in phase when the load varies, which leads to a change in the phase of the flux density bsc generated by the short circuit and consequently the sensitive harmonics of rank Ksc. The load variation also modifies the flux density coming from the healthy part of the machine because of the increase in the in-line current . We can observe several properties concerning the harmonic of rank K. First, we note that the amplitudes of the resulting complex quantities • and • are different in the presence of a fault (except in the case where ∅ , would be close to /2). For the healthy machine, as the faulty does not exist, then the amplitude of the harmonic should component , remain identical all around the machine. This property related to the difference in amplitude can be used for the detection of an inter-turn shortcircuit fault. However, the magnetic attenuation effects that are in theory independent of the position around the machine can disturb the analysis based on this property. Indeed, practically, structural asymmetries due to the presence of ferromagnetic parts in the environment close to the machine will possibly lead to a non-uniform attenuation of the flux density according to the angular position. It will thus be possible to obtain different amplitudes even in the case of a healthy machine. Nevertheless, in this case, the amplitudes • and • , even different, will at least evolve in the same direction as load variations. To overcome this problem, we can exploit the behavior of the sensitive harmonics in the case of load variation. We can see in Figure 1.9 that a load and ∅ (and consequently variation, which induces a change in , ∅ , ), will lead to a difference in the amplitude variation between • and • . This difference in amplitude variation is likely to change when the load varies. Actually, the positioning of the sensors regarding the axis of the faulty winding affects the results. Indeed, the best positioning is when the sensors are placed perfectly in the axis of the faulty winding. In this position, the difference in amplitude variation is maximum, and in this case, the

Diagnosis of Electrical Machines by External Field Measurement

15

amplitudes may vary in the opposite direction [PUS 10], which is a very reliable indicator of fault.

(a)

(b)

Figure 1.9. Phasor diagram variation: (a) load 1; (b) load 2

Figure 1.10 shows the variations with the load level of the Ksc rank harmonic of the emf delivered by the two sensors positioned at 180° from each other around an electrical machine. Two cases are presented: the healthy case and the case with a stator inter-turn short-circuit fault. The following observations are consistent with the theoretical analyses: – in the healthy case, the harmonics vary in the same direction and have in this case almost the same amplitudes; – in the faulty case, the harmonics vary differently, and sometimes in opposite directions. These types of curves obtained in different machines can be analyzed from two indicators: – the ratio of amplitudes (RA), which gives the ratio between the amplitudes of the harmonics measured on both sides of the machine, – the difference of variation (DV), which is a Boolean quantity: either the harmonics vary in the same direction, or they vary in opposite directions. As the detection performance depends on the position of the sensors regarding the localization of the fault in the winding, it is possible to improve the diagnosis using several sensor positions around the machine. The pair-forming sensors will be shifted by π as shown in Figure 1.11, where six sensors are used. However, it will not be possible to cover the entire periphery of the machine, for example, it is not possible to place a sensor under the base of the machine.

16

Electrical Systems 2

Figure 1.10. Variation of sensitive harmonic versus the load

Figure 1.11. Measurements with three pairs of sensors

1.3. Information fusion to detect the inter-turn short-circuit faults As shown previously, to improve the reliability of the approach, measurements at several positions will be performed. Each measurement constitutes a piece of information regarding the presence of a fault. Fusion technique [BLO 07, KHA 13] using the belief function theory [DEM 67, SHA 76, SME 94] is used here as a frame to represent and combine information to make a final decision. This theory is a powerful mathematical framework used to deal with partial and unreliable information [DUB 10] in many fields [DEN 16].

Diagnosis of Electrical Machines by External Field Measurement

17

In our case, this theory enables us to model the uncertainty of the information and to make a decision concerning the question of the presence of a fault in the winding of a tested machine. In this section, the basic concepts of the belief functions are first exposed in section 1.3.1. Then, in section 1.3.2, the proposed approach is introduced. Finally, an illustrative example is presented in section 1.3.3. 1.3.1. Belief function theory: basic concepts

Basic useful concepts of the belief function theory are exposed in this section. Belief functions offer a rich and flexible mathematical frame to represent and manipulate imperfect information. 1.3.1.1. Representation of available information

Let us consider a variable of interest x taking its values in a finite set {x1 , x2 , x3 , , xK } called the frame of discernment. A piece of information regarding the true value taken by x can be represented by a mass function (MF) m defined as an application from the power set of denoted by A A to [0, 1] such that , x1 , x2 , x1 , x2 , [1.23]

m( A) 1. A

With A a subset of , a mass m(A) represents the degree of knowledge in favor of the fact that the true value of x belongs to A. The mass m( ) represents the degree of total ignorance regarding the value taken by x, especially m ( ) 1 represents a total uncertainty on the value taken by x does not bring any new piece of evidence concerning the (indicating x searched value taken by x). 1.3.1.2. Combining evidence

Two pieces of information represented, respectively, by MFs m1 and m2, and coming from two distinct sources, can be combined using the conjunctive rule of combination (CRC) [DEM 67, SME 07] defined by

m1

m2 ( A)

m1 ( B)m2 (C ) B C A

A

.

[1.24]

18

Electrical Systems 2

This rule being associative and commutative, the order in which the sources are combined does not affect the combination result. Let us consider as an example a very simple diagnosis problem with a frame composed of two elements y and n, where y means “yes, there is a fault in the inspected winding” and n means “no, there is no fault”. Let us suppose two independent and reliable experts E1 and E2 expressing their opinions regarding the presence of a fault with, respectively, the two following MFs m1 and m2 defined, respectively, by m1 ({y})=0.1, m1( ) = 0.9, m1 ({y})=0.2 and m2( ) = 0.8. Both experts think there is a little chance that there is a fault but are not sure at all of the presence of a fault. A large mass (90% for expert E1 and 80% for expert E2) is on the ignorance regarding the fact that there is a fault. The combination or fusion, denoted by m, of pieces of information m1 and m2 using CRC rule [1.24] is illustrated in Table 1.1 and is given by m({ y}) 0.02 0.08 0.18 0.28 and m( ) 0.72 . The mass supports the fact that there is a fault that has then been reinforced using the CRC rule. m1 m2

{y} 0.2

{y} 0.1

⋂ 0.1 0.2

0.9

Ω⋂ 0.9 0.2

0.8 0.02

⋂Ω 0.1 0.8

0.08

0.18

Ω⋂Ω 0.9 0.8

Ω 0.72

Table 1.1. Conjunctive combination of MFs m1 and m2

1.3.1.3. Decision making

A way to make a decision [DEN 97] once the available information concerning the true value taken by x is represented by a single MF m consists of transforming this MF into the following probability measure BetP defined by BetP ( x) x A, A

m( A) , x | A | (1 m( ))

.

[1.25]

Diagnosis of Electrical Machines by External Field Measurement

19

The chosen decision maximizes BetP. As an example, the BetP measure associated with MF m depicted in Table 1.1 is given by Ω /2

0.28

0.72 2

0.64

and Ω /2

0

0.72 2

0.36

The chosen decision maximizes BetP and is in favor of y, meaning “there is a fault”. 1.3.2. Fault detection with the fusion method

In this section, we detail how to use the measurements of two flux sensors obtained at different positions around the electrical machine to indicate the presence of a fault. More precisely, we propose a fusion process taking into account, for each position of the sensors: – the DV of the measurements output by each sensor while the load increases; – the RA computed with the sensor measures. Information DV and RA can be obtained for different positions of the two sensors. The number N of possible positions, which can be used, depends on the size of the machine and the possibility to place sensors on the housing of the machine. To model the fusion and how far each piece of information indicates a fault, we use the belief function framework presented in previous section. In the present application, the main question of interest is “Is there a fault?”. Let us then define a variable of interest x which takes as possible values y standing for “yes there is a fault” or n for “no, there is no fault”. Then, the frame of discernment is Ω = {y,n}.

20

Electrical Systems 2

For a given position i, i = 1,…,N, of the sensors, it remains to build the pieces of information mDV,i and mRA,i regarding the presence of a fault, which comes, respectively, from the pieces of evidence DV and RA. So, the MF mDV,i has been defined as follows: – If there is at least one difference of evolution between sensor measurements while the load increases, then mDV,i ({y}) = 0.95 and mDV,i (Ω) = 0.05. It represents the fact that there is surely a fault. – Otherwise (there is no opposite evolutions), we do not know if there is a fault, and there is a little chance that there is no fault, so we define mDV,i by mDV,i ({n}) = 0.05 and mDV,i (Ω) = 0.95. The second piece of evidence mRA,i regarding the presence of a fault is defined using the following ratio RAi between amplitudes measurements AC1,i and AC2,i obtained, respectively, from sensors C1 and C2 in position i (in the following equation ch corresponds to the load with ch = 0,…,chmax): min

: →

,

,

,

,

,

,

[1.26]

Values of ratio RAi belong to [0, 1]. When RAi is close to 1, it means that the two measurements are close and then the machine is in a healthy state. When it is close to 0, we are almost sure that there is a fault. Between 0 and 1, we suppose the existence of two thresholds S1 and S2 representing a transition. One example of the evolution of the MF according to the ratio RAi is given in Figure 1.12 with S1 = 0.45 and S2 = 0.55. The area between S1 and S2 represents a transition area between the two views. With N being the number of possible positions, we have 2N MFs (mDV,1,…,mDV,N and mRA,1,…,mRA,N) corresponding to 2N pieces of information regarding the presence of a fault on the machine. These pieces of information are then combined using CRC [1.24]. The resulting MF m is given by ⋂

,

⋂ ⋂

,



⋂

[1.27]

The chosen decision maximizes the probabilistic transformation BetP of m [1.25].

Diagnosis of Electrical Machines by External Field Measurement

21

Figure 1.12. Definition of MF mRA,i according to the ratio value with S1 = 0.45 and S2 = 0.55

1.3.3. Calculation example In this section, we expose a calculation example for the proposed approach. For that, we take measurements obtained from the induction machine presented in the following section. In this case, the four possible positions are considered and loads increase has been chosen equal to 0 (no load), 600 W, 1,000 W and 1,400 W (in this example, this last load corresponds to chmax). The measurements obtained by sensors C1 and C2 are summarized in Table 1.2. In this example, the machine has a short-circuit fault.

22

Electrical Systems 2

Load

Position 1

Position 2

Position 3

Position 4

(W)

C1 ( V)

C2 ( V)

C1 ( V)

C2 ( V)

C1 ( V)

C2 ( V)

C1 ( V)

C2 ( V)

0

46

126

98

206

101

122

84

146

600

24

235

160

337

175

192

147

217

1000

34

316

232

514

276

303

176

267

1400

163

387

368

625

389

401

248

356

Table 1.2. Measurements obtained by sensors C1 and C2 using the induction machine

Differences of variations, according to the load, for each sensor at position 1 are exposed in Table 1.3. Load (W)

Sensor C1 ( V)

0

46

600

24

22

1000

34

1400

163

Sensor C1 Variation

Sensor C2 ( V)

Sensor C2 Variation

Same direction?

235

109

No

10

316

81

Yes

129

387

71

Yes

126

Table 1.3. DV obtained from sensors C1 and C2 using the induction machine for position 1

It can be observed from Table 1.3 that in position 1, when the load increases from 0 to 600 W, measurements from sensor C1 decrease from 46 to 24 V, whereas those of sensor C2 increase from 126 to 235 V. Variations in opposite direction are obtained. Table 1.4 summarizes the number of different variations observed for all positions. Number of different variations

Position 1

Position 2

Position 3

Position 4

1

0

0

0

Table 1.4. Number of different variations detected for each position of the sensors

Diagnosis of Electrical Machines by External Field Measurement

Consequently, the obtained MFs mDV,i, for each position i, i 1, are given in Table 1.5. Position 1 , ,

Ω

Position 2

0.95 0.05

, ,

Ω

Position 3

0.05 0.95

, ,

Ω

23

, N,

Position 4

0.05 0.95

, ,

Ω

0.05 0.95

Table 1.5. MFs mDV,i obtained from the measurement exposed in Table 1.2

As a difference of evolution was detected in position 1, MF mDV,1 indicates the presence of a fault, whereas it is not the case for positions 2, 3 and 4. We can combine these four MFs using [1.27]. The result of this combination is the following:

Ω ∅

0.814 0.007 0.043 0.136

Now we consider the RA as a second piece of information regarding the presence of a fault. Ratios obtained in position 1 are presented in Table 1.6. Only the smallest is conserved for RA1. Load (W)

Sensor C1 ( V)

Sensor C2 ( V)

Ratio

0

46

126

0.365

600

24

235

0.102

1000

34

316

0.107

1400

163

387

0.421

RA1

0.102

Table 1.6. MFs mDV,i obtained from the measurement exposed in Table 1.2

Ratios RA2, RA3 and RA4 are similarly computed for all positions. Associated MFs are then computed using Figure 1.12. For instance, by plotting the value of RA1 in Figure 1.12, the MF obtained for position 1 is defined as follows:

24

Electrical Systems 2

0.95 0 0.05

, ,

Ω

,

The same method is used to compute mRA,2, mRA,3 and mRA,4. These MFs are presented in Table 1.7. Position 2 RA2 = 0.475 , , ,

Ω

0.71 0,02 0.27

Position 3 RA3 = 0.828 0.05 0 0.95

, , ,

Position 4 RA4 = 0.575

Ω

, , ,

Ω

0 0.05 0.95

Table 1.7. MFs mRA,i from the measurement exposed in Table 1.2

The combination of these MFs yields

Ω ∅

0.872 0.003 0.012 0.113

Combining mDV and mRA gives an MF m defined by

Ω ∅

0.757 0.001 0.001 0.241

Finally, the transformation of m into a probability [1.25] is given by 0.999 0.001

It follows a decision in favor of {y} (i.e. there is a fault in the winding of this machine).

Diagnosis of Electrical Machines by External Field Measurement

25

1.4. Application 1.4.1. Presentation of rotating electrical machines

The proposed method has been tested considering two specific electrical machines whose parameters are presented in Table 1.8. These two machines allow us to simulate a damaged coil (short-circuit coils) and to test the method. AM

SM

Machine type

Asynchronous

Synchronous

Power (kW)

11

10

Frequency (Hz)

50

50

Poles

4

4

Stator slots

48

54

Rotor slots

32

32

Balanced line voltage (V)

380/660

230/400

Synchronous speed (rpm)

1500

1400

Rated speed (rpm)

1450

1400

cos

0.83

0.7

Table 1.8. Characteristics of the tested machines

The AM shown in Figure 1.13, with 32 rotor slots (Nr=16) leads to sensitive spectral lines at 750 and 850 Hz. Actually, both harmonics have rather low magnitude, and for better robustness of the method, it is preferable to take the harmonic with higher magnitude. For the AM, the considered frequency depends on the slip, but it will be still denoted as “the line at 850 Hz”. In a practice, without any prior information about harmonic magnitudes, it can be advised to extract both harmonics from the signal, with an FFT. In the presented test bench, the flux sensors measuring the external magnetic field of the three-phase induction machine are placed around the machine. The machine can operate under no load or load conditions and the connecting box above the machine allows us to simulate a fault by shortcircuiting coils.

26

Electrical Systems 2

Figure 1.13. Test bench with an 11-kW AM used for the experiments

For this machine, the stator winding has been modified to offer the possibility to make different levels of short-circuit faults as it can be seen in the electrical winding scheme presented in Figure 1.14.

Figure 1.14. Electrical winding scheme of an 11-kW AM

This configuration allows us to short circuit any elementary coil (turns placed in one slot) in the stator windings that correspond to 12.5% of a full phase. A rheostat is used to limit the value of the short-circuit current during the tests.

Diagnosis of Electrical Machines by External Field Measurement

27

Figure 1.15. Test bench for a 10-kW SM

The SM illustrated in Figure 1.15 is a machine with a smooth rotor similar to the rotor of a turbo generator (contrary to a salient pole machine). The rotor is regularly slotted similar to the stator, and its winding is supplied with a DC current. It has also 32 rotor slots (Nr=16) but some slots are not filled by the winding. The analytical model also leads to sensitive spectral lines at 750 and 850 Hz, but for the SM, the 750-Hz spectral line has a higher magnitude than the 850-Hz spectral line, contrary to the AM. Therefore, the 750-Hz line will be chosen for the analysis. This choice is realized in correlation with experimental tests which take into consideration the solid iron frame of the SM which acts as a low-pass filter for magnetic fields that leads to a higher magnitude for the 750-Hz harmonic compared to the one at 850 Hz. In experimental tests on the SM operating as a motor, the elementary sections have been chosen such that it is possible to study a short circuit close to the input of the phase (phase A), in phase medium (phase B) or near the neutral (Phase C) as presented in Figure 1.16. The global number of turns in phase A is 126 and a short-circuit between 1 and 2 corresponds to one short-circuit turn (0.8% of a full phase), between 2 and 3 to three short-circuit turns (2.38%), and between 1 and 4 to five short-circuit turns (4%).

28

Electrical Systems 2

a) external access at different turns positions between the four poles of each phase

b) electrical winding schema

Figure 1.16. Stator configuration of an SM

As mentioned earlier, for this machine, the analyzed amplitude is realized for the harmonic at 750 Hz.

1.4.2. Presentation of experimental results The rewinding of the AM and SM allows us to simulate a damaged coil (short-circuit coils) and to test the proposed method considering a wide variety of fault positions. The detection of short-circuit faults depends on the severity of the fault and its position relative to the location of the sensors. For this reason, for the AM, eight sensors are used, that is to say four possible positions (P1, P2, P3 and P4) where the pairs of sensors are placed at 180° from each other. For this purpose, a number of experiments are carried out on the considered machines. Each one is assembled and designed

Diagnosis of Electrical Machines by External Field Measurement

29

to study the behavior of the motor in a faulty condition. The total number of measurements for the AM test is 260 corresponding to the healthy and faulty machine for 12 different connections in the stator windings (four per phase) as presented in Figure 1.14: – healthy machine, – with two faults in phase A (short circuit between the coils 1-2 and 1-3), – with two faults in phase B (short circuit between the coils 9-10 and 9-11), – with two faults in phase C (short circuit between the coils 17-18 and 17-19), – with two faults in phase A (short circuit between the coils 25-26 and 25-27), – with two faults in phase B (short circuit between the coils 33-34 and 33-35), – with two faults in phase C (short circuit between the coils 41-42 and 41-43). Position 1

Position 2

Position 3

Position 4

Fusion results

Results obtained with DV information

69.23 (4)

46.15 (7)

53.85 (6)

53.85 (6)

84.61 (2)

Results obtained with RA information

76.92 (3)

69.23 (4)

76.92 (3)

76.92 (3)

92.31 (1)

Results obtained by fusion of DV and RA

84.61 (2)

76.92 (3)

84.61 (2)

84.61 (2)

92.31 (1)

Table 1.9. Percent of correct decisions obtained, for the AM in the case of different short circuit positions in the stator windings, obtained by using direct information signals and fusion of signals. The numbers in parentheses indicate the numbers of errors

The percent results obtained by the information fusion tools using the belief function theory are illustrated in Table 1.9. We have 13 considered configurations. The first analysis is based only on information concerning the fusion of sense of variation indicators (DV), the second by the fusion of

30

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the ratio of the amplitude indicators (RA) and the last one by fusion of DV and RA. For each case, the fusion of information obtained by the four positions of the sensors is realized and the thresholds used to obtain the MFs are S1 = 0.45 and S2 = 0.55. For all the presented tests, the short-circuit current intensity Isc always remains equal to 12 A rms and four levels of load were imposed for each considered case: 0, 600, 1,000 and 1,400 W. From Table 1.9, we perform common analyses between the methods by analyzing the results of each position and the results obtained by measurement according to the sensor belt. It appears that when the measurements are limited to a single position, we are not able to detect all faulty cases. We remark for DV indicator that, the fusion process increases at 84.61% the good decision for detection of the faulty case (only two cases from 13 are not detected). The result obtained by fusion of DV and RA gives 92.31% good decisions, similar to results obtained from the RA. Another test realized with the AM is presented in Table 1.10. Here the information DV and RA are obtained from three positions of the sensors considering several levels of fault severity. The winding of the machine limits the short-circuit positions but allows us to create three levels of faults on the accessible elementary coils. The studied configurations are the following: – healthy machine (without short circuit) – with two faults in phase A, – with two faults in phase B, – with two faults in phase C, that corresponds to 19 analyzed cases (18 with faults and one healthy). The values of the short-circuit currents measured in each case are: – Isc = 5 A, – Isc = 10 A, – Isc = 15 A. In Table 1.10, the detection percent for each short-circuit severity level with fusion or without fusion of information is presented.

Diagnosis of Electrical Machines by External Field Measurement

Healthy machine

Fault with Isc= 5 A

Fault with Isc = 10 A

Fault with Isc = 15 A

Fusion results

Results obtained with DV information

100 (0)

100 (0)

83.33 (1)

16.66 (5)

68.42 (6)

Results obtained with RA information

100 (0)

100 (0)

100 (0)

100 (0)

100 (0)

Results obtained by fusion of DV and RA

100 (0)

100 (0)

100 (0)

100 (0)

100 (0)

31

Table 1.10. Percent of correct decisions obtained for the AM in the case of different levels of short-circuit severity using direct information signals and fusion of signals. The numbers in parentheses indicate the numbers of errors

The global results show that the fusion of information concerning only the DV information can detect 68.42% of faulty cases (13 from 19 analyzed). For this approach, high fault levels give low percent detection value (16.66% corresponding to five cases not detected from six). With information concerning only the RA parameter, the presented method detects 100% of the faulty cases; by fusion of the DV and RA, also 100% of the faulty cases are detected. We can remark that for this test, the use of fusion (DV + RA) allows us to obtain the best results. For SM, the measurements were carried out in the generator mode using a resistive load and with only one sensor position. For this machine, it is possible to access to 1, 3 and 5 turns on certain elementary coils distributed on the three phases. The studied configurations are the following: – without short circuit; – three faults (short circuit between coils 1-2, 2-3 and 1-4; see Figure 1.4(a)) for the three phases (A, B and C). The value of the current measured in each case of short circuit depends on the number of short turns: – one coil (short circuit between the output connection 1-2, Isc = 3 A);

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– three coils (short circuit between the output connection 2-3, Isc = 6 A); – five coils (short circuit between the output connection 1-4, Isc = 15 A). Here, the healthy configuration has been considered three times which diagnose 12 different configurations (three healthy cases and nine with faults). The results are presented in Table 1.11. Healthy machine

Fault with 1 coil Isc= 3 A

Fault with three coils Isc= 6 A

Fault with five coils Isc= 15 A

Results obtained with DV information

100 (0)

66.67 (1)

100 (0)

66.67 (1)

83.33 (2)

Results obtained with RA information

100 (0)

66.67 (1)

33.33 (2)

33.33 (2)

58.33 (5)

Results obtained by fusion of DV and RA

100 (0)

100 (0)

100 (0)

66.67 (1)

91.67 (1)

Fusion results

Table 1.11. Percent of correct decisions obtained for the SM in the case of different levels of short-circuit severity using direct information signals and fusion of signals. The numbers in parentheses indicate the numbers of errors

The comparative analysis measures the influence of the short-circuit current magnitude Isc for detecting the faults. In the case of the faulty machine, it appears that the best results are obtained with the small defects of one and three turns. The proposed methods allow us to detect 91.67% of the faulty cases (a single fault not detected) by using all the information obtained by the fusion of DV and RA. The three studies presented here show that the fusion of the indicators DV and RA always improves the results obtained compared to the cases where these indicators are taken separately.

Diagnosis of Electrical Machines by External Field Measurement

33

1.5. Conclusion

The external magnetic field is an interesting variable to be exploited for the diagnosis of electrical machines. Indeed, this variable can be measured with simple, fully noninvasive and low-cost coil flux sensors. The exploitation of the external magnetic field has also other advantages. First of all, this variable is more sensitive than the line current, especially in the case of a stator inter-turn short circuit because the short-circuit current creates its own magnetic effect which contributes to modify the external magnetic field. On the other hand, any fault that causes a dissymmetry will also affect the dissymmetry of the external field. In this case, the use of several external flux sensors around an electrical machine can be an interesting way to exploit this dissymmetry and to detect the fault. In this chapter, we have presented a methodology that exploits amplitudes and amplitude variations of a sensitive harmonic measured in the voltage delivered by several sensors. Two indicators are extracted from a pair of sensors positioned at 180° from each other: the RA of the harmonic measured on both sides and the DV of these harmonic amplitudes when the charge varies. The analysis is based on the theory of belief functions, which allows both to represent in a quite natural way the different types of imperfections in the information used (imprecision, uncertainty, incompleteness, etc.), to merge the information and to decide. The results on two different machines show that the fusion at several positions makes it possible to obtain better results than those obtained from each sensor taken separately. Similarly, the best results are obtained by the fusion of RA and DV with probability of fault detection around 92%. 1.6. References [BLO 07] BLOCH I. (ed.), Information fusion in signal and image processing: major probabilistic and non-probabilistic numerical approaches, ISTE Ltd, London and Wiley, Hoboken, New Jersey, 2007. [CEB 12a] CEBAN A., PUSCA R., ROMARY R., “Study of rotor faults in induction motors using external magnetic field analysis” IEEE Transactions on Industrial Electronics, vol. 59, no. 5, pp. 2082–2093, 2012. [CEB 12b] CEBAN A., Méthode globale de diagnostic des machines électriques, PhD thesis, Université d’Artois, 2012. [DAS 01] DASARATHY B.V., “Information fusion – what, where, why, when, and how?”, Information Fusion, vol. 2, no. 2, pp. 75–76, 2001. [DEM 67] DEMPSTER A.P., “Upper and lower probabilities induced by a multivalued mapping”, Annals of Mathematical Statistics, vol. 28, pp. 325–339, 1967.

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[DEN 97] DENOEUX T., “Analysis of evidence – theoretic decision rules for pattern classification”, Pattern Recognition, vol. 30, no. 7, pp. 1095–1107, 1997. [DEN 16] DENOEUX T., “40 years of Demspter–Shafer theory”, International Journal of Approximate Reasoning, vol. 79, pp. 1–6, 2016. [DUB 10] DUBOIS D., PRADE H., “Formal representations of uncertainty”, in BOUYSSOU D., DUBOIS D., PIRLOT M., PRADE H., (eds), Decision-making Process, ISTE Ltd, London and Wiley, Hoboken, New Jersey, pp. 85–186, 2010. [ESE 17] ESENAND G.K., ÖZDEMIR E., “A new field test method for determining energy efficiency of induction motor”, IEEE Transactions on Instrumentation and Measurement, vol. 66, pp. 3170–3179, 2017. [FOU 15] FOURNIER E., PICOT A., RÉGNIER J., YAMDEU M.T., ANDRÉJAK J.-M., MAUSSION P., “Current-based detection of mechanical unbalance in an induction machine using spectral kurtosis with reference”, IEEE Transactions on Industrial Electronics, vol. 62, no. 3, pp. 1879–1887, 2015. [HAM 15] HAMADACHE M., LEE D., VELUVOLU K.C., “Rotor speed-based bearing fault diagnosis (rsb-bfd) under variable speed and constant load”, IEEE Transactions on Industrial Electronics, vol. 62, no. 10, pp. 6486–6495, 2015. [HAN 10] HANXIN C., YANG H., CHUA P, HIAN L.G., “Fault diagnosis of water hydraulic motor by Hilbert transform and adaptive spectrogram” in IEEE in Prognostics and Health Management Conference, PHM’10, pp. 1–6, 2010. [IRH 18] IRHOUMAH M., PUSCA R., LEFÈVRE E., MERCIER D., ROMARY R., DEMIAN C., “Information fusion with belief functions for detection of interturn shortcircuit faults in electrical machines using external flux sensors”, IEEE Transactions on Industrial Electronics, vol. 65, pp. 2642–2652, 2018. [KAT 16] KATO M., HIRATA K., “Proposal of electro mechanical resonance for linear oscillatory actuator”, in XXII International Conference in Electrical Machines (ICEM), pp. 871–876, 2016. [KHA 13] KHALEGHI B., KHAMIS A., KARRAY F.O., RAZAVI S.N., “Multisensor data fusion: A review of the state-of-the art”, Information Fusion, vol. 14, no. 1, pp. 28–44, 2013. [NOR 93] NORRIS J.A., “Vector control of ac motors”, in IEEE Proceedings of Annual Textile, Fiber and Film Industry Technical Conference, pp. 3/1–3/8, 1993. [PET 17] PETROV A., PLOKHOV I., RASSÕLKIN A., VAIMANN T., KALLASTE A., BELAHCEN A., “Adjusted electrical equivalent circuit model of induction motor with broken rotor bars and eccentricity faults”, in IEEE 11th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), pp. 58–64, 2017.

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[PUS 10] PUSCA R., ROMARY R., CEBAN A., BRUDNY J.F., “An online universal diagnosis procedure using two external flux sensors applied to the AC electrical rotating machines”, Revue Sensors, vol. 10, pp. 7874–7895, Nov. 2010. ISSN 1424-8220. [PUS 12] PUSCA R., DEMIAN C., MERCIER D., LEFÈVRE E., ROMARY R., “An improvement of a diagnosis procedure for ac machines using two external flux sensors based on a fusion process with belief functions”, in IECON 2012-38th Annual Conference on IEEE Industrial Electronics Society, pp. 5096–5101, 2012. [ROM 09] ROMARY R., ROGER D., BRUDNY J.F., “Analytical computation of an AC machine external magnetic field”, European Physical Journal-Applied Physics EPJ-AP, EDP Sciences, Paris, vol. 47, no. 3, Article 31102, Sept. 2009. [SHA 76] SHAFER G., A mathematical theory of evidence, Princeton University Press, Princeton, NJ, 1976. [SME 07] SMETS P., “Analyzing the combination of conflicting belief functions”, Information Fusion, vol. 8, no. 4, pp. 387–412, 2007. [SME 94] SMETS P., KENNES R., “The transferable belief model”, Artificial Intelligence, vol. 66, pp. 191–243, 1994. [STO 04] STONE G.C., BOULTER E.A., CULBERT I., DHIRANI H., Electrical insulation for rotating machines: design, evaluation, aging, testing and repair, IEEE Press Series on Power Engineering, Wiley, USA, 2004. [TAV 08] TAVNER P., RAN L., PENMAN J., SEDDING H., Condition monitoring of rotating electrical machines, IET, Stevenge, UK, 2008. [YAZ 10] YAZIDI A., HENAO H., CAPOLINO G.-A., BETIN F., CAPOCCHI L., “Experimental interturn short circuit fault characterization of wound rotor induction machines” in IEEE International Symposium on Electronics (ISIE), pp. 2615–2620, 2010.

 

2 Signal Processing Techniques for Transient Fault Diagnosis

2.1. Introduction Nowadays, electric motors are extensively used in a number of processes in different sectors such as cement, petrochemical, steel, food, textile industries and so on. According to recent surveys, there are more than 300 million motors worldwide [DEL 12] which, altogether, consume more than 40% of the total power generated. This gives an idea of the importance of these machines, which are considered by some authors as the “workhorses” of industry [THO 01]. Their importance is rapidly increasing due to their prominent role in applications such as electric vehicles or clean energy generation, which are crucial for the sustainable development of human life. Owing to the extensive use of these machines, their maintenance also plays a crucial role. It is true that electric motors (and, especially, induction motors that are the most widespread in industry) are more reliable than other types of machines. However, it does not mean that these machines are excluded from unexpected faults which, in some cases, can lead to catastrophic effects for the process or factory in which the machine operates. Due to this, during recent decades, there has been an increasing interest in the investigation on new and reliable techniques that can detect anomalies or defects in these motors when they are in their early stages of development. If these incipient anomalies are detected, proper maintenance actions can be adopted, preventing the catastrophic consequences that the aggravation of these faults may have. In this context, the development and optimization of                                         Chapter written by José Alfonso Antonino DAVIU and Roque Alfredo Osornio RIOS.

Electrical Systems 2: From Diagnosis to Prognosis, First Edition. Edited by Abdenour Soualhi and Hubert Razik. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Electrical Systems 2

techniques to detect the possible failures in an earlier stage is the motivation of many research studies over recent years [RIE 15]. Statistical studies [THO 01] on the occurrence of electromechanical faults in induction motors have revealed that the most frequent failures are related to degradation of the stator insulation (caused by thermal, electrical, mechanical and environmental effects) as well as bearing damages (which can be due to a wide variety of causes including incorrect assembly, deficient or excessive lubrication, overload or circulation of bearing currents, among many others). Damages in the rotor, especially in applications involving heavy startups or aggressive duty cycles, can also amount for a significant percentage. This type of faults is more likely in large cage motors having fabricated copper bars [LEE 13]. In small motors, the probability of rotor fault is lower, which may be caused either by porosity problems or by rotor overheating due to an inadequate utilization of the motor [LEE 13]. Other possible failures in induction motors are related to deterioration of the insulation between magnetic sheets of the stator core, missing stator wedges or to eventual cooling problems in the machine, among others. Most of the aforementioned failures affect different electromechanical quantities of the machine such as currents, vibrations, fluxes, noise, torque and so on. A proper analysis of these quantities may help diagnose the presence of the corresponding failure. In this regard, the different techniques that have been developed during recent decades rely on the analysis of specific quantities of the machine. Each technique has certain advantages in the detection of specific faults in the motor: – Mechanical monitoring, often based on the installation of accelerometers or proximeters to measure the vibratory data at different points of the machine, has shown good results for the detection of faults with mechanical origin (e.g., bearing defects, misalignments, unbalances, etc.) [FIN 00]. However, in certain conditions, the technique cannot be applied (e.g., submersible motors, traction applications, etc.) [ANT 16] or the diagnosis may be not conclusive (difficulties to discern between faults with mechanical and electrical origins). – Electrical monitoring (currents, voltages) has shown good results to detect failures with an electrical nature (rotor asymmetries, eccentricities) and also give interesting information for other types of failures (bearing faults, coupling system problems) [THO 17].

Signal Processing Techniques for Transient Fault Diagnosis

39

– Thermal monitoring, based on the installation of thermocouples to measure the temperature in internal points of the machine or on the use of infrared (IR) thermography to monitor the superficial temperature, has also given interesting results for the diagnosis of specific faults such as coupling system problems, defective bearing lubrication, cooling system problems or even stator asymmetries [LOP 17], but is not adequate for the diagnosis of other failures (e.g., rotor problems) [PIC 15]. – Flux monitoring has recently emerged again, revealing itself as a very interesting informational source to diagnose several types of faults [RAM 18, CEB 12]. However, the influence of the flux sensor position on the results and the lack of reliable fault severity indicators are some of the pending issues of the technique. – Partial discharge monitoring, which relies on the use of coupling capacitors (or other technologies) to monitor the particle discharge activity in the motor, is the preferred technique to determine the condition of the motor insulation [STO 16]. – Other technologies (ultrasound, acoustic, chemical monitoring) have also proved their potential for the detection of specific faults or anomalies [GIE 13]. In spite of all these possibilities to determine the induction motor condition, it has been proved that there is no single technique that detects all possible failures that can happen in a machine. Each technique is valid for diagnosing a certain number of faults but not all of them. Therefore, the recent trend in the condition monitoring of electric motors is to combine the information obtained from techniques relying on different quantities in order to reach a more reliable conclusion about the condition of the machine [PIC 15]. In this context, the analysis of the currents demanded by the motor has been proved to be an excellent informational source for the diagnosis, with following advantages [LEE 13]: – Possibility of remote monitoring of the motor condition: the measurement can be carried out in the motor control center (MCC) or inverter, that is, without accessing the machine. – Noninvasive nature: the measurement of the necessary current signals can be carried out without disturbing the operation of the machine.

40

Electrical Systems 2

– Simplicity of the required equipment: a simple current clamp and an oscilloscope are required to acquire the necessary signals. – Reduced cost: minimum investments are required to purchase the necessary equipment for the acquisition of the signals. – Broad fault coverage: the technique is able to diagnose the presence of certain faults with high reliability, such as rotor damages or eccentricities [THO 17]. It also gives interesting information for the diagnosis of bearing faults, transmission system problems or even load faults [BLO 10, BON 12]. Basically, the fault diagnosis technique based on the analysis of motor currents relies on: (1) capturing the waveform of the current demanded by the motor, (2) analyzing it with suitable signal processing tools and (3) identifying potential indicators of the presence of the fault in the results of these transforms. The signal processing tools that are employed as bases of the technique depend on the approach that is used within the current analysis technique: – The classical current analysis approach is based on analyzing the waveform of the current demanded by the motor in a steady state [THO 17]. This approach, commonly known as motor current signature analysis (MCSA), makes use of the fast Fourier transform (FFT) for the analysis of the stationary current signals. The objective is to identify, in the resulting FFT spectrum, fault components linked with the fault and evaluate their amplitude in order to determine the fault severity [THO 17, BEL 02]. – Modern current analysis techniques are based on capturing the waveform of the current demanded by the motor under transient operation. More specifically, the startup current is commonly used as a basis for this approach; the idea is to capture the current waveform during the startup and analyze it afterward with suitable signal processing tools. The objective here is to track the time–frequency (t–f) evolutions of the fault-related components under starting, which are very reliable evidences of the presence of the fault [ANT 06]. In order to do so, special signal processing tools, known as t–f transforms, must be employed. These tools extract the t–f content of the analyzed signal, yielding a t–f map where the evolutions of the fault components can be identified [ANT 06]. This approach has been recently named as advanced transient current signature analysis (ATCSA) and provides important advantages versus the conventional methods relying on steady-state analysis [ANT 06].

Signal Processing Techniques for Transient Fault Diagnosis

41

The previous considerations show that the underlying signal processing tools (which are used as bases of the fault diagnosis techniques) play a crucial role. In conventional approaches such as MCSA, it is enough to extract the frequency content of the analyzed signal (steady-state current), since the only objective is to evaluate the amplitudes of frequency components associated with each fault. However, in recent transient-based methodologies, the objective is to identify specific “patterns” caused by the evolutions of the fault harmonics in the t–f map. Therefore, the characteristics and performance of the t–f transforms that are used for the analysis are of paramount importance for the proper identification of such patterns; this may not be an easy task, since these patterns may coexist with others created by other faults. This chapter reviews the basic signal processing tools that are employed in the current-based fault diagnosis, with a special emphasis on the t–f transforms that are employed for transient analysis. In the chapter, these t–f transforms are reviewed and divided into two main groups: discrete and continuous. The advantages of each particular group of transforms are emphasized, and the operation of some of their most important representatives is explained. The chapter is intended to be a guideline for researchers or engineers that may be interested in selecting the most suitable option for analyzing motor currents with fault diagnosis purposes. 2.2. Fault detection via motor current analysis As mentioned above, the analysis of motor currents can be carried out with different signal processing tools depending on the fault diagnosis approach that is considered. While conventional methods often rely on the use the FFT for the analysis of the steady-state current signals such as MCSA, new methodologies are based on analyzing startup currents with suitable t–f transforms (ATCSA). Both types of signal processing tools are explained in the following sections. 2.2.1. Classical tools (MCSA) The conventional method for electric motor condition monitoring based on the analysis of currents is the well-known MCSA [THO 17]. In synthesis, this method relies on three steps:

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Electrical Systems 2

1) Register the waveform of the steady-state current demanded by the motor. 2) Analyze the current signal by means of the FFT. 3) Evaluation of the amplitude of characteristic frequency components in the FFT spectrum. It is well known that the Fourier transform extracts the frequency content of the analyzed signal. Intuitively, it yields a frequency–amplitude representation that quantifies how each frequency component is present in the analyzed signal. When there is a fault, the amplitudes of certain frequency components are amplified in the FFT spectrum. Therefore, the evaluation of these amplitudes enables us to determine the severity of that fault in the machine. This is the basic principle of the MCSA approach. For instance, in the case of broken rotor bars, the most significant frequency components related to the fault are the sideband harmonics (SHs), with frequencies given by

fSH

f (1 2 s ),

[2.1]

where s is the slip and f is the supply frequency. The evaluation of the amplitudes of the two harmonics given by [2.1] – lower sideband harmonic (LSH, negative sign) and upper sideband harmonic (USH, positive sign) – enables us to determine the level of rotor damage in the machine. This is illustrated in Figure 2.1 which compares the FFT for a healthy motor (Figure 2.1(a)) and for a motor with one broken bar in the rotor cage (Figure 2.1(b)). Note the clear differences between both figures. The prominent amplitudes of the SHs in Figure 2.1(b) (the amplitude of the LSH is above the alarm threshold that is defined for this specific fault, i.e., between 55 and 45 dB) indicate the faulty condition of the rotor for that motor. On the other hand, in Figure 2.1(a), the SHs have low amplitudes, a fact that confirms the healthy condition of the rotor. The same idea is also applied to the detection of other faults based on MCSA, such as eccentricities or bearing faults. In the event that these faults are present in the motor, some specific frequency harmonics are amplified in the FFT spectrum. The frequencies of the fault components amplified in the FFT spectrum by eccentricities/misalignments were demonstrated in previous works [BEN 00, THO 17]. The same happens with the frequencies

Signal Processing Techniques for Transient Fault Diagnosis

43

linked with bearing faults [BLO 10]. In recent years, MCSA has also been extrapolated to detect faults in transmission systems or even problems in the driven loads [BON 12], a fact that confirms the great potential of this technique. In spite of the good results provided by MCSA over recent decades [THO 17], the technique also has some important constraints. Some of them were discovered and theoretically proved in the last decade: 0

Amplitude (dB) Amplitud (dB)

-20

(a)

-40 -60 -80 -100 -120

44

46

48

50 Frecuencia (Hz)

52

54

56

Frequency (Hz) 0

Amplitude (dB) Amplitud (dB)

-20

(b)

LSH

USH

-40 -60 -80 -100 -120

44

46

48

50 Frecuencia (Hz)

52

54

56

Frequency (Hz)

Figure 2.1. FFT of the steady-state current for a (a) healthy motor and (b) motor with a faulty rotor. For a color version of the figures in this book, see www.iste.co.uk/soualhi/electrical2.zip

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1) The application of MCSA is not suitable (or it may be difficult) under variable speed conditions: in the event that the motor speed is changing during the capture of the current signal that is necessary to apply the MCSA method, the frequencies of the fault-related components (that are slipdependent, as shown in [2.1]) will also change. This implies that, instead of being represented by a single “peak” in the FFT spectrum, the fault component will spread over different frequencies. In this situation, the determination of the actual amplitude of the fault harmonic may become difficult or even erroneous. This may lead to false indications or unclear diagnosis of the fault [ANT 18]. 2) The application of MCSA may lead to occasional false diagnosis: it has been proved that there are some situations, either related to the operation conditions of the motor or to the constructive characteristics of the machine, which may lead to false indications when MCSA is applied. In this regard, the presence of pulsating load torque, the existence of cooling rotor ducts or significant levels of rotor magnetic anisotropy have been identified as some of the potential causes of false-positive indications [ANT 06, YAN 14], since these phenomena can introduce harmonics that can be very close or even identical with those caused by rotor problems. In contrast, the motor operation under reduced slip conditions, the occurrence of nonadjacent bar breakages or the diagnosis of outer cage breakages in double cage motors are typical sources of false-negative indications when MCSA is used, as pointed out in several studies [ANT 06, ANT 12, RIE 10]. Figure 2.2 shows an example of false-negative indication when using MCSA: the case of a motor with broken bars operating under no load conditions. As reported in previous studies [ANT 06], due to the reduced value of the slip, the frequencies of the SHs given by (1) overlap the supply frequency, making their identification very difficult. 0

Amplitude (dB)

-20 -40 -60 -80 -100 -120

44

46

48

50 Frequency (Hz)

52

54

56

Figure 2.2. FFT of the steady-state current for a faulty motor under no load conditions

Signal Processing Techniques for Transient Fault Diagnosis

45

Due to the problems of the MCSA approach, alternative technologies based on current analysis have been proposed in the last decade. In this regard, techniques based on the Park’s vector approach [GYF 17] or on the zero sequence current [GYF 16], among others, have been developed. Despite their advantages, their complexity and other issues made them difficult to apply in industry. In this context, another interesting alternative emerged in the early 2000s. This approach, known as advanced transient current signature analysis (ATCSA) [ANT 06], proposes analysis of currents demanded by the motor under transient operation and, more specifically, during the startup transient. To this end, advanced signal processing tools (t–f transforms) must be used, as explained in the following section. 2.2.2. New techniques based on transient analysis (ATCSA) As pointed out in the previous section, the ATCSA approach was proposed in order to overcome the drawbacks of the traditional MCSA method. In its most common modality, ATCSA relies on the following steps: 1) capturing the signal of the current demanded by the motor during the startup; 2) analyze the startup current signal by means of suitable t–f transforms; 3) identifying characteristic patterns caused by the fault components in the resulting t–f maps. 4) evaluating fault severity indicators based on the outputs of the transform. Therefore, the basic idea of the ATCSA approach relies on analyzing the transient signal (e.g., the startup current signal) with a suitable t–f tool and identifying the characteristic evolutions followed by the fault components in the resulting t–f map. Let us consider, for example, the LSH associated with rotor damages. The frequency of this fault harmonic is given by [2.1], considering the negative sign in the expression. At steady states, suppose that the speed remains stable during the capture of the current (and assuming that f is also fixed), then the frequency of this harmonic will be constant (given by expression [2.1]). Nonetheless, the situation is different during a startup. In a direct-on-line startup, the slip s will vary between 1 (when the machine is connected) and near 0 (when the steady-state regime is reached).

46

Electrical Systems 2

Hence, the frequency of the LSH (fLSH, which depends on the slip according to [2.1]) will change accordingly. Considering that the supply frequency f=50 Hz, the following evolution yields: • When s=1

fLSH=50 Hz

• When s=0.5

fLSH=0 Hz

• When s 0

fLSH=50 Hz

Therefore, the frequency of the LSH will vary in a very characteristic way during a direct-on-line startup, as the slip s changes: first, fLSH will drop from f to 0 Hz and it will later increase again until reaching its steady-state value near f. A graphical representation of the t–f evolution of the LSH associated with rotor damages during a simulated direct-on-line startup of a laboratory motor is shown in Figure 2.3. This evolution of the LSH in the t–f map is very characteristic and follows a V-shaped pattern. Therefore, the identification of a component with such characteristic evolution during the startup would enable us to confirm the existence of the rotor damage in the machine (since it clearly indicates that the LSH is present). The same idea can be extrapolated to other harmonics amplified by the fault (such as the USH) which are also slip-dependent and which will follow characteristic evolution during the startup as the slip changes. 50

Frequency (Hz) Frecuencia (Hz)

40

30

20

10

0 0

0.2

0.4

0.6 Tiempo (s)

0.8

1

Time (s)

Figure 2.3. t–f evolution of the LSH during a simulated direct-on-line startup of a laboratory induction motor

1.2

Signal Processing Techniques for Transient Fault Diagnosis

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One important advantage of this approach is that the detection of the fault patterns (such as the V pattern linked with the LSH) is a much more reliable evidence of the presence of the fault, since they cannot be caused by other fault of phenomena, avoiding the appearance of false indications (unlike what happens with the MCSA approach). However, the disadvantage of ATCSA is that, for the detection of such patterns, special signal processing tools capable of providing a t–f representation of the analyzed signal (startup current) are needed: these tools are known as t–f transforms. The following section provides a synthesis of the most important t–f tools used for electric motor condition monitoring based on current analysis. 2.3. Signal processing tools for transient analysis The ATCSA fault diagnosis approach has been optimized in the last decade. One of the objectives has been to find the most suitable t–f transform to be used as a basis of the methodology. In this regard, many different options have been explored by different research groups: wavelet transforms [ANT 06, PON 15], Hilbert–Huang transforms (HHT) [ANT 09], the short-time Fourier transform (STFT) [ANT2 16], Wigner–Ville and Choi Williams distributions [CLI 14] and so on. The most important conclusion is that there is no single transform showing superiority over the others, since each of them has their own advantages and disadvantages. This implies that, for each specific fault detection of certain harmonics, some transforms may be preferable over the others, but these later may be preferable under other conditions. Considering the experience of authors with these transforms over many years, in rough terms, we can classify the t–f transforms that have been employed in the electric motors fault diagnosis field into two main groups [PON 15]: (1) discrete transforms and (2) continuous transforms. Each group has specific advantages and disadvantages. Table 2.1 shows the synthesis of the most important characteristics, as well as some example tools of each group [PON 15]. The following sections are dedicated to explain two basic transforms, each one belonging to one of the groups presented in Table 2.1: the discrete wavelet transform (DWT) and the HHT. These sections also describe the basic operation of both tools, with some illustrative examples, and explain how these tools can be applied in the fault diagnosis of electric motors. These explanations have been written taking into consideration [ANT 13, ANT2 13].

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Advantages

Drawbacks

Examples

Discrete transforms

– Simple – Low computational burden – Easy definition of fault severity indicators

– Less clear representation of the evolutions of the fault harmonics – Limited resolution in certain cases

DWT

Continuous transforms

– Provide clearer representations of the fault harmonics – More reliable

– More complex – Higher computational burden – More difficult introduction of fault severity indicators

Continuous wavelet transform (CWT), STFT, HHT

Table 2.1. Groups of t–f tools

2.3.1. Example of a discrete tool: the DWT When the DWT is applied to a certain sampled signal i(t), this signal is decomposed as the addition of a set of signals, known as wavelet signals: an approximation signal at a certain decomposition level n (an) plus n detail signals (dj with j varying from 1 to n). The mathematical expression characterizing this process is given by [2.2], where in and i j are the scaling and wavelet coefficients, φn(t) and ψj(t) are the scaling function at level n and wavelet function at level j, respectively, and n is the decomposition level [BUR 97, MAL 08, CHU 97]: n i

s (t ) i

n i

n

j

(t)

i j 1

ψ ij (t)

an

dn

... d1

[2.2]

i

Each one of the wavelet signals (approximation and detail) has an associated frequency band, the limits of which are well established, once the sampling rate (fs) of the original analyzed signal s(t) is selected, in accordance with an algorithm enunciated by Mallat (Subband Coding Algorithm) [MAL 08]. The expressions that are employed to calculate the limits of the frequency bands associated with each wavelet signal, according to the Mallat algorithm, are specified in Figure 2.4 [ANT 06]. It is observed that the limits of the frequency band for each wavelet signal depend on the sampling rate (fs) as well as on the level of the corresponding wavelet signal

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(j). As an example, if the sampling rate used for capturing s(t) is fs=5,000 samples/second, and we perform the DWT decomposition in n=8 levels, the frequency bands associated with each wavelet signal are those specified in Table 2.2.

s (t)

DWT

an

[0 , 2‐(n+1) fs] Hz

dn

[2‐(n+1) fs , 2‐n fs] Hz

… dj

[2‐(j+1) fs , 2‐j fs] Hz

… d1

[2‐2 fs , 2‐1 fs] Hz

Figure 2.4. DWT decomposition in wavelet signals and associated frequency bands

Wavelet signal

Frequency band (Hz)

a8

0–9.78

d8

9.78–19.5

d7

19.5–39.06

d6

39.06–78.12

d5

78.12–156.25

d4

156.25–312.5

d3

312.5–625

d2

625–1250

d1

1250–2500

Table 2.2. Frequency bands associated with wavelet signals for fs=5 kHz and n=8

The intuitive idea underlying the application of DWT relies on the following fact: each one of the wavelet signal acts as a filter, extracting the temporal evolution of the components of the original signal contained within the frequency band associated with that wavelet signal. For instance, in the previous example, the wavelet signal d6 (detail signal 6) will reflect the time evolution of every harmonic component of the original signal when its

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Electrical Systems 2

frequency falls in the band 39.06–78.12 Hz. For instance, if the signal is a pure 50 Hz sinusoidal waveform, the whole signal evolution would be reflected in that signal d6. In conclusion, the DWT performs a dyadic band-pass filtering process in frequency bands whose limits depend on fs and on n. This filtering is illustrated in Figure 2.5. Depending on the mother wavelet that is selected for the DWT decomposition, the filtering between bands is more or less ideal, as it was proved in the previous studies [ANT2 06].

Figure 2.5. Dyadic filtering process carried out by the DWT

2.3.1.1. Examples of application of the DWT In this section, several illustrative examples of the operation of the DWT are explained [ANT 13]. They are useful for an easy comprehension of how the transform works. In all the examples, the DWT decomposition is carried out in n=9 levels, and Daubechies-44 is used as the mother wavelet for the analyses. The corresponding frequency bands associated with each wavelet signal are specified beside each figure. 2.3.1.1.1. Example 1: DWT analysis of a pure sinusoidal signal Figure 2.6 shows the DWT decomposition for the case of a 50-Hz pure sinusoidal signal (signal s, plotted at the top of the figure). It is observed how, in accordance with the filtering process carried out by the transform, the whole signal is filtered into the detail signal d7. This is due to the fact that this signal reflects the evolution of every component evolving within the range 39–78.1 Hz. Since there is a single 50-Hz component in the original signal, d7 exactly reflects the evolution of the whole component and, hence, of the signal. The rest of the wavelet signals are approximately zero, since no other frequency components exist in the original signal.

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50 Hz

1 0 -1 1 a9 0 -1 1 d9 0 -1 1 d8 0 -11

s

0-9.7 Hz 9.7-19.5 Hz 19.5-39 Hz

d7 0

39-78.1 Hz

d6

78.1-156.2 Hz

d5 d4 d3 d2 d1

-1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1

156.2-312.5 Hz 312.5-625 Hz 625-1250 Hz 1250-2500 Hz 2500-5000 Hz 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Figure 2.6. DWT analysis of a 50-Hz pure sinusoidal signal

2.3.1.1.2. Example 2: Superposition of sinusoidal signals 5 Hz + 15 Hz + 30 Hz + 50 Hz

s a9 d9 d8 d7 d6 d5 d4 d3 d2

4 0 -4 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1

0-9.7 Hz 9.7-19.5 Hz 19.5-39 Hz 39-78.1 Hz 78.1-156.2 Hz 156.2-312.5 Hz 312.5-625 Hz 625-1250 Hz 1250-2500 Hz

1

d1 0 -1

2500-5000 Hz 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (s)

Figure 2.7. DWT analysis of a signal based on the superposition of four sinusoidal signals with frequencies 5, 15, 30 and 50 Hz

Figure 2.7 shows the DWT analysis of a signal s (plotted at the top of that figure) which has been built by adding four sinusoidal signals with respective frequencies 5, 15, 30 and 50 Hz. The result is a stationary signal in which all four frequencies are present at every time. The filtering nature of the DWT

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enables us to extract each frequency component in a separate wavelet signal, in agreement with the values of their respective band limits. As is observed, the 5-Hz component is filtered in a9, the 15-Hz component in d9, the 30-Hz component in d8 and the 50-Hz component in d7, remaining almost zero the rest of signals, since no other components exist within their bands. This example illustrates the filtering process carried out by the transform and its ability to separate the different components of the signals, provided that they fall in different frequency bands covered by the wavelet signals. 2.3.1.1.3. Example 3: Concatenation of sinusoidal signals s a9 d9 d8 d7 d6 d5 d4 d3 d2 d1

1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1 1 0 -1

5 Hz

30 Hz

15 Hz

50 Hz

0-9.7 Hz 9.7-19.5 Hz 19.5-39 Hz 39-78.1 Hz 78.1-156.2 Hz 156.2-312.5 Hz 312.5-625 Hz 625-1250 Hz 1250-2500 Hz 2500-5000 Hz 0.25

0.5

0.75

1

Time (s)

Figure 2.8. DWT analysis of a signal based on the concatenation of four sinusoidal signals with frequencies 5, 15, 30 and 50 Hz

Figure 2.8 represents the DWT analysis of a signal s (plotted at the top of the figure) which has been built by concatenating four sinusoidal signals with respective frequencies 5, 15, 30 and 50 Hz. The result is a nonstationary signal, in which each frequency component is present only during its corresponding time interval. The DWT filters each component in the wavelet signal covering the frequency band in which it is included. Hence, the 5-Hz component is filtered in a9, the 15-Hz component in d9, the 30-Hz component in d8 and the 50-Hz component in d7, remaining almost zero the rest of signals since no components exist within their bands. Moreover, the transform indicates

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when each component starts and ends in the analyzed signal; for instance, a9 shows how the 5-Hz component is present during the initial 0.25 seconds, d9 shows that the 15-Hz component is present between 0.25 and 0.5 seconds, d8 reveals that the 30-Hz component occurs between 0.5 and 0.75 seconds and, finally, d7 shows that the 50-Hz component is present between 0.75 seconds and 1 second.

Figure 2.9. Signal considered in Example 2 and its FFT analysis (top). Signal considered in Example 3 and its FFT analysis (bottom)

This example clearly illustrates the advantage of the DWT versus the classical FFT approach. With the FFT, the time information is lost and two rather different signals can be represented by similar FFT spectra (see in Figure 2.9 the similarity between the FFT analyses of the signals employed in Examples 2 and 3), however the DWT preserves the time information, enabling us to identify not only which frequencies are present, but also when they occur. Therefore, the DWT leads to a three-dimensional representation

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of the analyzed signal: frequency (because each wavelet signal covers a frequency band), time (since each wavelet signal is represented versus time) and amplitude (the amplitude of the wavelet signal informs on the corresponding amplitude of its filtered components in the analyzed signal). This is why the DWT is known as a t–f decomposition tool. 2.3.2. Example of a continuous tool: the HHT The HHT was first developed by Norden E. Huang and his colleagues [HUA 05, HUA 98]. Their motivation relied on the fact that most traditional data analysis methods are based on linear and stationary assumptions of the analyzed signals. Some approaches deal well with linear and nonstationary data, whereas others are designed for nonlinear but stationary and deterministic systems. Nonetheless, in many real-world applications, the data are both nonlinear and nonstationary. As Huang himself stated [HUA 05], “… new approaches are urgently needed, for nonlinear processes need special treatment.” The HHT was conceived to produce physically meaningful representations of data from nonstationary and nonlinear processes [HUA 05]. The result is an empirical approach, rather than a theoretical tool, which has been successfully used for the analysis of such data. The HHT has two different parts: (1) the empirical mode decomposition (EMD) and (2) the Hilbert spectral analysis (HSA). The EMD method is the main part of the HHT and it enables us to decompose a signal into a set of components called intrinsic mode functions (IMFs). These IMFs are individual, nearly monocomponent signals. Their nature guarantees a good behavior of their Hilbert transform. The EMD algorithm operates in the time domain and it is adaptive and highly efficient. Moreover, it is valid for nonlinear and nonstationary processes. In contrast, the HSA enables us to obtain the time evolution of the instantaneous frequency of each IMF. This t–f representation of the IMFs is crucial to comprehend the inherent structure of the analyzed data set. The main result of the HSA is an energy–frequency–time representation, known as the Hilbert spectrum. 2.3.2.1. Mathematical bases of the HHT As pointed out by Charlton-Pérez et al. [CHA 11] in their excellent work reviewing the operation of the HHT, Huang introduced a new signal

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analysis technique based on the decomposition of a signal in terms of empirical modes and on their representation within the framework of the complex trace method, introduced by Gabor several decades ago [GAB 46]. The formulation of the proposed methodology is as follows: let X(q) be a signal (with q representing either time or an spatial coordinate) that is the real part of a complex trace, Z(q) (given by [2.3]), where the imaginary part, Y(q), is the Hilbert transform of X(q) (given by [2.4], where PV is the principal value):

Z (q)

Y (q)

X (q) iY (q ),

1

PV

X (q ) dq . q q

[2.3] [2.4]

The complex conjugate pair (X(q); Y(q)) defines the amplitude, a(q), and phase θ(q), as an analytical function of the q-variable [CHA 11] (see [2.5]), with the instantaneous frequency defined by [2.6].

Z (q)

a (q ) ei

(q)

d (q) . dq

(q)

.

[2.5] [2.6]

The complex trace method enables us to define the concepts of instantaneous amplitude, phase and frequency, in such a way that the original signal can be expressed in terms of a Fourier-like expansion based on these concepts [HUA 05, CHA 11]. This process, along with the instantaneous frequency definition, work well for monocomponent signals. Nevertheless, in many real applications, the signals are multicomponents (and often noise-polluted). In these situations, the complex trace method fails due to the fact that the Hilbert transform processing of those noisy waves generates spurious amplitudes at negative frequencies [CHA 11]. The approach developed by Huang [HUA 05, HUA 98] enabled the signal analysis to avoid generating unphysical results. To this end, the Hilbert transform is not directly applied to the signal itself but to each of the members of an empirical decomposition of the signal into IMFs [CHA 11]. As Perez stated [CHA 11], these IMFs are “individual, nearly monocomponent signals with ‘Hilbert-friendly’ waveforms, to

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which the instantaneous frequency defined by equation [2.6] can be applied.” 2.3.2.2. Operation of the HHT 2.3.2.2.1. EMD Algorithm The EMD method is the basis of the HHT. By means of the EMD, the analyzed data set is decomposed into a set of almost orthogonal components called IMFs. The algorithm to create the IMFs is rather simple as well as smart, as explained in [CHA 11]: first, the local extrema of the data are identified; they are used to create upper and lower envelopes which enclose the signal completely. A running mean is created from this envelope. When subtracting this mean from the data, a new function is obtained; this function must have the same number of zero crossings and extrema (i.e., it must exhibit symmetry across the q-axis). Otherwise, if the function so constructed does not satisfy this criterion, the process continues until an acceptable tolerance is reached [CHA 11]. The process results in the first IMF, i1(q), which contains the highest frequency oscillations found in the data (the shortest time scales). The IMF1 is then subtracted from the original data and this difference R1 is taken as if it were the original signal and then the sifting process is applied to the new signal. The process of finding modes, ij(q), is carried out until the last mode, the residue Rn, is found. It contains the trend (i.e., the “time-varying” mean). Hence, the signal X(q) can be characterized as indicated by [2.7]. The scheme of the whole EMD algorithm is plotted in Figure 2.10.

X (q )

n

[2.7]

i j ( q ) Rn.

j 1

2.3.2.2.2. Hilbert spectral analysis When the IMFs have been obtained, the Hilbert transform can be applied to each IMF, computing the instantaneous frequency and amplitude. After applying the Hilbert transform to each IMF, the signal can be expressed according to (aj(q) and wj(q) are, respectively, the instantaneous amplitude and frequency corresponding to each IMF ij(q)):

X (q) Re

n j 1

a j (q)e

i

j ( q )dq

.

[2.8]

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The above equation allows us to represent the instantaneous amplitude and frequency as functions of q in a 3D plot or map. The t–f representation of the amplitude is called Hilbert spectrum, H(w,q) [PEN 05]. Another important concept is the marginal spectrum. Its mathematical definition is given by [2.9], where Q is the total data length [YU 05]. While the Hilbert spectrum provides a measure of the amplitude contribution for each frequency and time, the marginal spectrum offers a measure of the total amplitude (or energy) contribution from each frequency [PEN 05, YU 05]. The frequency in the marginal spectrum indicates only the likelihood that an oscillation with such a frequency exists; the exact occurrence time of that oscillation is given in the full Hilbert spectrum [HUA 98]: Q

h( w)

0

H ( w, q ) dq.

[2.9]

Empirical Mode Decomposition (EMD): Analysed signal: f (t) The local extrema of the data are identified and used to create upper and lower envelopes which enclose the signal completely.

A running mean is created

Substract the IMF i from the original signal f (t)

The “mean” is substracted from the data and a new function hi is obtained

¿ hi has the same number of zero crossings and extrema (or tolerance is reached) ?

YES IMF i = hi

NO ¿ Is i the last mode (Rn)?

YES

n

f (t)

IMFi

Rn

i 1

Figure 2.10. Scheme of the EMD algorithm

NO

s(t)

5

5

Time (s)

Analyzed signal

0

0

5

)0

5

0

IMF 2

Time (s)

Time (s)

IMF 1

Intrinsic Mode Functions (IMFs)

40

50

60

30

50

60

0 0

10

20

0 0

10

20

30

40

0.1

0.1

Hilbert Transform

) y( q

Figure 2.11. Schematic representation of the HHT results

EMD

Frequency (Hz) Frequency (Hz) F re q u e n c y (H z )

0.2

0.2

0.3

0.3

0.4

0.4

0.6

0.6

Time (s)

0.5

Time (s)

0.5

g

p

0.7

0.7

0.8

0.8

0.9

0.9

Hilbert Spectrum

1

1

58 Electrical Systems 2

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Figure 2.11 summarizes the results from applying the HHT to a certain signal s(t), considering two IMFs. Each IMF is a waveform which extracts the components of the original signal within a certain frequency range. In order to know the frequencies covered by each IMF, its Hilbert spectrum is computed; it provides a t–f amplitude representation of the corresponding IMF. 2.3.2.3. Examples of the HHT application In this section, several didactic examples of the operation of the HHT are presented [ANT2 13]. They are useful to understand how the transform works in a very simple way. In all the examples, the HHT is carried out and the next results are shown for each IMF: IMF waveform, IMF Hilbert spectrum and IMF marginal spectrum. 2.3.2.3.1 Example 1: HHT of the addition of two sinusoidal signals Figure 2.12 represents the waveform of a signal based on the addition of two sinusoidal signals with respective frequencies 50 and 15 Hz and respective amplitudes 5 and 1. Figure 2.13 shows the results of the application of the HHT to the previous signal, considering two IMFs in the decomposition. Figure 2.13(a) corresponds to IMF1, depicting the IMF1 waveform (Figure 2.13(a), top), the IMF1 Hilbert spectrum (Figure 2.13(a), middle) and the IMF1 marginal spectrum (Figure 2.13(a), bottom). Figure 2.13(b) is analogous, but for IMF2. 6 4

Amplitude

2 0 -2 -4 -6 0

0.1

0.2

0.3

0.4

0.5

Time (s)

0.6

0.7

0.8

0.9

Figure 2.12. Signal based on the addition of two sinusoidal signals

1

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Electrical Systems 2

The figure illustrates the way in which the HHT works: IMF1 extracts the largest component present in the signal (namely, the 50-Hz sinusoidal component with amplitude 5). This can be perfectly noticed in the IMF1 waveform (Figure 2.13(a), top). The Hilbert spectrum of this IMF1 (Figure 2.13(a), middle), as expected, reveals a single line at 50 Hz for every time instant (recall that the Hilbert spectrum is just a t–f amplitude representation of the IMF). Finally, the IMF1 marginal spectrum shows a single peak at 50 Hz. In contrast, IMF2 extracts the evolution of the rest of components in the analyzed signal (in this case, the 15-Hz sinusoidal component with amplitude 1).

Figure 2.13. HHT of the previous signal: (a) IMF1: waveform (top), Hilbert spectrum (middle) and marginal spectrum (bottom)

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Figure 2.13 (continued). HHT of the previous signal: (b) IMF2: waveform (top), Hilbert spectrum (middle) and marginal spectrum (bottom)

This can be observed in Figure 2.13(b, top) that depicts the IMF2 waveform revealing a sinusoidal component with a lower frequency (and amplitude) than that in Figure 2.13(a, top). This is confirmed by the Hilbert spectrum of IMF2 (Figure 2.13(b, middle)) which shows a single line at 15 Hz for every time instant. Accordingly, the marginal spectrum of IMF2 reveals a single frequency peak at 15 Hz. This example shows the adaptive filtering nature of the HHT, extracting the components present in the signal in the different IMFs.

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2.3.2.3.2. Example 2: HHT of the concatenation of sinusoidal signals The second example consists of the HHT analysis of the signal plotted in Figure 2.14, which is based on the concatenation of two sinusoidal signals with respective frequencies 50 and 15 Hz and respective amplitudes 5 and 1. As a consequence of the operation of the EMD algorithm, the HHT analysis leads to a single IMF (IMF1) which reflects the evolution of both components. Figure 2.15 represents the HHT results: IMF1 waveform (top), Hilbert spectrum of the IMF1 (middle) and marginal spectrum of IMF1 (bottom). 6

Amplitude

4 2 0 -2 -4 -6 0

0.1

0.2

0.3

0.4

0.5

Time (s)

0.6

0.7

0.8

0.9

1

Figure 2.14. Signal based on the concatenation of two sinusoidal signals

The waveform of the IMF1 (Figure 2.15, top) corresponds to that of the original signal, based on the concatenation of the two aforementioned components (initially, that of 50 Hz, which is present during the initial 0.5 second and, then, the 15-Hz component, present between 0.5 and 1 second. The Hilbert spectrum of IMF1 (Figure 2.15, middle) is especially interesting; a single line at 50 Hz reveals the presence of the first frequency component during the initial 0.5 second. A second trace at 15 Hz shows the occurrence of the second component during the last 0.5 second. The lower color intensity of this second trace is due to the lower amplitude of the 15-Hz frequency component. This Hilbert spectrum illustrates rather well the t–f nature of the tool, since it informs not only on which frequency components are present in the analyzed signal, but also when they occur. Finally, the marginal spectrum of IMF1 (Figure 2.15, bottom) shows two peaks at the corresponding frequencies present in the signal (15 and 50 Hz), the

Signal Processing Techniques for Transient Fault Diagnosis

63

Amplitude

amplitudes of which reflect the amplitude of the associated sinusoidal signals. IMF1

5 0 -5

0.1

0.2

0.3

0.4

0.5 Time (s)

0.6

0.7

0.8

0.9

1

0.8

0.9

1

4

4.5

160

180

Contour Plot of Hilbert-Huang Amplitudes

200 180

Frequency (Hz)

160 140 120 100 80 60 40 20 0 0

0.1

0.2

1

0.3

1.5

0.4

2

0.5

0.6

Time (s) 2.5

3

0.7

3.5

Mean Amplitude

Marginal spectrum IMF1 0.2 0.1 0 0

20

40

60

80

100 120 Frequency (Hz)

140

20

Figure 2.15. HHT of the previous signal: waveform of IMF1 (top), Hilbert spectrum of IMF1 (middle) and marginal spectrum of IMF1 (bottom)

2.3.2.3.3. Example 3: addition of a sinusoidal signal and two chirp signals The third example is based on the HHT analysis of the signal plotted in Figure 2.16(a). This signal is based on two waveforms: a 50-Hz sinusoidal signal with amplitude equal to 10 (Figure 2.16(b)) and a signal based on the concatenation of two chirp functions (Figure 2.16(c), the first chirp with

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Electrical Systems 2

linearly decreasing frequency (from 50 to 0 Hz) and the second chirp with frequency increasing linearly from 0 to 50 Hz). The frequency evolution of the resulting signal resembles the evolution under starting of the frequency of the LSH associated with rotor damages.

=

(a)

+

(b)

(c) Figure 2.16. Signal (a) based on the addition of a sinusoidal signal (b) and two chirp signals (c)

Signal Processing Techniques for Transient Fault Diagnosis

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Figure 2.17 represents results of the HHT analysis considering two IMFs. Figure 2.17(a) plots the IMF1 waveform (top), the Hilbert spectrum of IMF1 (middle) and the IMF1 marginal spectrum (bottom). Figure 2.17(b) is analogous but for IMF2.

(a) Figure 2.17. HHT of the previous signal: (a) IMF1: waveform (top), Hilbert spectrum (middle) and marginal spectrum (bottom)

The results plotted in Figure 2.17 are rather logical. IMF1 extracts the largest component present in the analyzed signal, that is, the 50-Hz

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sinusoidal component with amplitude equal to 10. Figure 2.17(a, top) confirms this fact, since IMF1 waveform corresponds to sinusoidal function with the aforementioned amplitude and frequency. Accordingly, the IMF1 Hilbert spectrum shows a single line at 50 Hz for every time instant. Of course, the IMF1 marginal spectrum is also coherent with these facts, revealing a single peak at 50 Hz.

(b) Figure 2.17(continued). HHT of the previous signal: (b) IMF2: waveform (top), Hilbert spectrum (middle) and marginal spectrum (bottom)

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On the other hand, IMF2 extracts the rest of the components present in the signal. This is the component based on the concatenation of the two chirp functions. IMF2 waveform confirms this idea (see similarity between Figure 2.17(b, top) and Figure 2.17(c); the slight deviations are due to inherent border effects of the analysis). Figure 2.17(b, middle) shows how the Hilbert spectrum of IMF2 is coherent with the time evolution of the frequency of such component based on the two chirps: first, its frequency decreases from near 50 to 0 Hz and later increases from 0 to near 50 Hz, leading to a Vshaped pattern that characterizes the t–f evolution of such component. Finally, Figure 2.17(b, bottom) shows a blurred marginal spectrum due to the varying nature of the frequency of the IMF2 (between 0 and 50 Hz). This example illustrates rather well the adaptive filtering nature of the HHT (since it separates the components present in the signal in different IMFs corresponding to different frequency bands). Moreover, it illustrates the t–f decomposition process carried out by the transform (since it indicates the frequencies present and when they occur). As a conclusion of the ideas exposed in the previous examples, we can summarize some of the advantages of the HHT in the following points: – Adaptive nature; it avoids fixed limits of the bans covered by each IMF. – Possible higher flexibility in comparison with other TFD tools. – Easy interpretation of the results. With regard to its drawbacks, we can remark, among others, the following: – Number of necessary IMFs is not known a priori. – Possible constraints when distinguishing different components with near frequencies. – Possible masking problems when high-energy components are present in the signal. 2.4. Application of transient-based tools for electric motor fault detection The previous t–f tools are only some examples of the possible transforms that can be applied for electric motor condition monitoring purposes. In the

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last decade, these and other alternatives have been used for the detection of the t–f patterns created by different types of faults. This section shows some of the results of the application of the tools presented in the previous section (DWT and HHT) for the detection of rotor damages in electric motors. Note that, despite only these tools being shown here, other alternatives are also perfectly viable for the detection of this failure: STFT, WVD, CWD and so on. 2.4.1. Application of the DWT for the detection of rotor damage Considering that, as commented in previous sections, the DWT performs a band-pass filtering of the signal being analyzed, it may be used for the detection of the evolution of the components linked with rotor damages during the startup. More specifically, if the DWT is applied to the startup current signal of a motor with a rotor fault, the resulting wavelet signals track the evolution during the startup of the LSH [ANT 06]. Let us consider, for example, an eight-level DWT decomposition of the startup current signal of a motor with broken bars. If the sampling rate of that signal is fs=5,000 samples/second, the frequency bands associated with each wavelet signal are those specified in Table 2.2 that was shown before. The fundamental component (FC) of that signal, whose frequency remains fixed at 50 Hz, will be totally included in signal d6, which covers the frequency band 39.06–78.12 Hz. On the other hand, the LSH will be initially contained in signal d6 and it will progressively penetrate, during the startup, in the signals d7, d8, a8 (as its frequency drops from 50 to 0 Hz) and it will later evolve again through d8, d7 and d6 (as its frequency increases from 0 to near 50 Hz). The result is that some oscillations will progressively appear in signals d7–d8–a8–d8–d7 due to the trip of the LSH under starting (these oscillations are not observable in signal d6 since the LSH will coexist there with the FC, which has much larger amplitude). These oscillations, which will not appear in the case of a healthy motor, are clear evidence of the presence of the fault in the machine and they are arranged in the same way as the frequency of the LSH evolves under starting. Figure 2.18(b) shows the DWT analysis of a motor with one broken bar (out of 28 rotor bars), whereas Figure 2.18(a) corresponds to a healthy motor. Note how the mentioned pattern clearly appears for the faulty case, whereas it is absent for healthy condition since, in this last case, the LSH is not present. Figure 2.18(c) is equivalent except for the motor with two broken bars; it reveals that the oscillations in the wavelet signals are higher in correlation with higher rotor fault levels.

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(a)

(b)

(c) Figure 2.18. DWT of the startup current signal for: (a) healthy motor; (b) motor with one broken rotor bar and (c) motor with two broken bars

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The fact that the oscillations in the DWT are larger when the fault level increases has introduced some fault indicators that rely on the energy of those wavelet signals, as in those proposed in [ANT 06, ANT2 16]. 2.4.2. Application of the HHT for the detection of rotor damage The application of the HHT to the startup current has also provided good results for rotor fault diagnosis purposes. On the one hand, if the HHT is applied to the startup current signal of a motor with faulty rotor and a proper number of IMF is selected, certain IMF can reflect the evolution of the LSH under starting. This is the case of the example shown in Figure 2.19(b) that shows the IMF2 for a 1.1-kW motor with broken bars [ANT 11]. The IMF was obtained after applying the HHT to the startup current signal of that motor considering two IMFs for the decomposition. Compare it with the IMF2 obtained for the same motor but in a healthy condition (Figure 2.19(a)). The IMF2 represented in Figure 2.19(b) is a very precise representation of the waveform of the LSH under starting.

a)

IMF 2 Time (s)

b)

IMF 2 Time (s)

Figure 2.19. IMF2 resulting from the HHT of the startup current signal for: (a) a healthy motor and (b) a motor with two broken bars

Figure 2.20 shows the Hilbert spectrum of the IMF2 obtained from the HHT for the same cases represented in Figure 2.19. Note the presence of the V-shaped pattern in the Hilbert spectrum of the IMF2 for the motor with a faulty rotor. This is due to the fact that, since the IMF2 contains the LSH evolution during the startup, its Hilbert spectrum will reflect the t–f evolution of such harmonic, yielding the characteristic V-shaped pattern described before. Hence, this spectrum is a good way to determine whether the fault is present in the machine or not.

Signal Processing Techniques for Transient Fault Diagnosis

Frequency (Hz)

71

a)

Time (s) Frequency (Hz)

b)

Time (s)

Figure 2.20. Hilbert spectrum of the IMF2 resulting from the HHT of the startup current signal for (a) a healthy motor and (b) a motor with two broken bars.

2.5. Conclusions In this chapter, the most important techniques for condition monitoring electric motors based on current analysis have been reviewed. The chapter has put special emphasis on the novel methodologies for fault diagnosis that rely on the analysis of the current demanded by the motor while it operates under transient operation. More specifically, modern approaches based on the analysis of the startup current have been presented. In this context, it has been emphasized the importance of using suitable signal processing tools for the analysis of the startup current signal. The most important groups of t–f transforms that are employed to this end (discrete and continuous) have been described. Moreover, two important representatives of each group (DWT and HHT) have been commented, showing illustrative examples of their respective application. The most important conclusion drawn from this chapter relies on the fact that modern signal processing tools, which have been applied with success in other scientific fields, are proliferating in the condition monitoring of electric motors, having proved important advantages for the diagnosis that are crucial for many industrial applications. The research in this topic is one of the most important open issues and it will be even more crucial in the future due to the strong proliferation of electric motors in new applications in modern life.

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2.6. References [ANT 13] ANTONINO DAVIU J.A., Operation of the discrete wavelet transform: basic overview with examples, 2013, available at: http://hdl.handle.net/ 10251/30739 [ANT2 13] ANTONINO DAVIU J.A., Operation of the Hilbert–Huang transform: basic overview with examples, 2013, available at: http://hdl.handle.net/ 10251/30740 [ANT 06] ANTONINO-DAVIU J.A., RIERA-GUASP M., ROGER-FOLCH J., MOLINA M.P., “Validation of a new method for the diagnosis of rotor bar failures via wavelet transformation in industrial induction machines”, IEEE Transactions on Industry Applications, vol. 42, no. 4, pp. 990–996, Jul./Aug. 2006. [ANT2 06] ANTONINO-DAVIU J.A., RIERA-GUASP M., ROGER-FOLCH J., MARTINEZGIMENEZ F., PERIS A., “Application and optimization of the discrete wavelet transform for the detection of broken rotor bars in induction machines”, Applied and Computational Harmonic Analysis, vol. 21, pp. 268–279, Sept. 2006. [ANT 09] ANTONINO-DAVIU J.A., RIERA-GUASP M., PINEDA-SANCHEZ M., PEREZ R.B., “A critical comparison between DWT and Hilbert–Huang-based methods for the diagnosis of rotor bar failures in induction machines”, IEEE Transactions on Industry Applications, vol. 45, no. 5, pp. 1794–1803, Sept./Oct. 2009. [ANT 11] ANTONINO-DAVIU J.A., RIERA-GUASP M., PINEDA-SANCHEZ M., PUCHE R., PEREZ R.B., JOVER-RODRIGUEZ P., ARKKIO A., “Fault diagnosis in induction motors using the Hilbert–Huang transform”, Nuclear Technology, vol. 173, pp. 26–34, Jan. 2011. [ANT 12] ANTONINO-DAVIU J.A., RIERA-GUASP M., PONS-LLINARES J., PARK J., LEE S.B., YOO J., KRAL C., “Detection of broken outer cage bars for double cage induction motors under the startup transient”, IEEE Transactions on Industry Applications, vol. 48, no. 5, pp. 1539–1548, Sept.–Oct. 2012. [ANT 16] ANTONINO-DAVIU J., CLIMENTE-ALARCON V., QUIJANO-LOPEZ A., FUSTER-ROIG V., “Multi-regime current analysis for the rotor health assessment in cage pump motors: case stories”, in XXIIth International Conference on Electrical Machines, ICEM 2016, Lausanne, Sept. 2016. [ANT2 16] ANTONINO-DAVIU J.A., PONS-LLINARES J., LEE S.B., “Advanced rotor fault diagnosis for medium-voltage induction motors via continuous transforms”, IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 4503–4509, Sept./Oct. 2016. [ANT 18] ANTONINO-DAVIU J.A., QUIJANO-LOPEZ A., RUBBIOLO M., CLIMENTEALARCON V., “Advanced analysis of motor currents for the diagnosis of the rotor condition in electric motors operating in mining facilities”, IEEE Transactions on Industry Applications, vol. 54, no. 4, pp. 3934–3942, Jul.–Aug. 2018.

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[BEL 02] BELLINI A., FRANCESCHINI G., ROSSI A., TASSONI, C., GIOVANNINI M., FILIPPETTI F., PASAGLIA R., “On-field experience with on-line diagnosis of large induction motors cage failures using MCSA”, IEEE Transactions on Industry Applications, vol. 38, no. 4, pp. 1045–1053, Jul./Aug. 2002. [BEN 00] BENBOUZID M.H., “A review of induction motors signature analysis as a medium for faults detection”, IEEE Transactions on Industrial Electronics, vol. 47, no. 5, pp. 984–993, Oct, 2000. [BLO 10] BLODT M., GRANJON P., RAISON B., REGNIER J., Mechanical Fault Detection in Induction Motor Drives Through Stator Current Monitoring – Theory and Application Examples, Intech, Wei Zhang (ed.), 2010. [BON 12] BONALDI E.L., LACERDA DE OLIVEIRA L.E.., BORGES DA SILVA J.G., LAMBERT-TORRES G., BORGES DA SILVA L.E., Predictive Maintenance by Electrical Signature Analysis to Induction Motors, Intech Open, pp. 487–520, 2012. [BUR 97] BURRUS C.S., GOPINATH R.A., GUO H., Introduction to Wavelets and Wavelets Transforms. A Primer, Prentice Hall, New Jersey, 1997. [CEB 12] CEBAN A., PUSCA R., ROMARY R., “Study of rotor faults in induction motors using external magnetic field analysis”, IEEE Transactions on Industrial Electronics, vol. 59, no. 5, pp. 2082–2093, 2012. [CHA 11] CHARLTON-PEREZ C., PEREZ R.B., PROTOPOPESCU V., WORLEY B.A., “Detection of unusual events and trends in complex non-stationary data streams”, Annals of Nuclear Energy, vol. 38, nos 2–3, pp. 489–510, Feb./Mar. 2011. [CHU 97] CHUI C.K., Wavelets: A Mathematical Tool for Signal Analysis, SIAM, Philadelphia, 1997. [CLI 14] CLIMENTE-ALARCON V., ANTONINO-DAVIU J.A., RIERA-GUASP M., VLECK M., “Induction motor diagnosis by advanced notch FIR filters and the Wigner– Ville distribution”, IEEE Transactions on Industrial Electronics, vol. 61, no. 8, pp. 4217, 4227, Aug. 2014. [DEL 12] DE LA MORENA CANCELA J., “Eficiencia energética en motores eléctricos. Normativa IEC 60034”, in II Congreso de Eficiencia Energética, Madrid, Oct. 2012. [FIN 00] FINLEY W.R., HODOWANEC M.M., HOLTER W.G., “Diagnosing motor vibration problems”, in Conference Record of 2000 Annual Pulp and Paper Industry Technical Conference, pp. 165–180, 2000. [GAB 46] GABOR D., “Theory of communication”, Journal of Institute of Electrical Engineers, vol. 93, no. 26, pp. 429–457, Nov. 1946. [GIE 13] GIERLACH J.D., “Using ultrasound to identify electrical faults”, Maintenance Technology, vol. 1, pp. 37–40, 3 Jan. 2013.

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[GYF 16] GYFTAKIS K.N., ANTONINO-DAVIU J.A., GARCIA-HERNANDEZ R., MCCULLOCH M., HOWEY D.A., MARQUES-CARDOSO A.J., “Advanced rotor fault diagnosis for medium-voltage induction motors via continuous transforms”, IEEE Transactions on Industry Applications, vol. 52, no. 2, pp. 4503–4509, Mar./Apr. 2016. [GYF 17] GYFTAKIS K.N., MARQUES-CARDOSO A.J., ANTONINO-DAVIU J.A., “Introducing the filtered Park’s and filtered extended Park’s vector approach to detect broken rotor bars in induction motors independently from the rotor slots number”, Mechanical Systems and Signal Processing, vol. 93, pp. 30–50, Sept. 2017. [HUA 05] HUANG N.E., SHEN S.S.P., Hilbert–Huang Transform and Its Applications, World Scientific Publishing, Singapore, 2005. [HUA 98] HUANG N.E., SHEN Z., LONG S.R., WU M.C., SHIH H.H., ZHENG Q., YEN N.C., TUNG C.C., LIU H.H., “The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis”, Proceedings of the Royal Society of London A, vol. 454, pp. 903–995, 1998. [LEE 13] LEE S.B., WIEDENBRUG E., YOUNSI K., “ECCE 2013 tutorial: Testing and diagnostics of induction machines in an industrial environment”, in IEEE Energy Conversion Congress and Exposition, Denver, Sept. 2013. [LOP 17] LOPEZ-PEREZ D., ANTONINO-DAVIU J.A., “Application of infrared thermography to failure detection in industrial induction motors: case stories”, IEEE Transactions on Industry Applications, vol. 53, no. 3, pp. 1901–1908, May–Jun. 2017. [MAL 08] MALLAT S., A Wavelet Tour of Signal Processing, 3rd ed., Academic Press, Burlington, 2008. [PEN 05] PENG Z.K., TSE P.W., CHU F.L., “A comparison study of improved Hilbert–Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing”, Mechanical Systems and Signal Processing, vol. 19, pp. 974–988, 2005. [PIC 15] PICAZO-RODENAS M.J., ANTONINO-DAVIU J.A., CLIMENTE-ALARCON V., ROYO-PASTOR R., MOTA-VILLAR A., “Combination of noninvasive approaches for general assessment of induction motors”, IEEE Transactions on Industry Applications, vol. 51, no. 3, pp. 2172–2180, May/Jun. 2015. [PON 15] PONS-LLINARES J., ANTONINO-DAVIU J.A., RIERA-GUASP M., LEE S.B., KANG T-J., YANG C., “Advanced induction motor rotor fault diagnosis via continuous and discrete time–frequency tools”, IEEE Transactions on Industrial Electronics, vol. 62, no. 3, pp. 1791–1802, Mar. 2015.

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[RAM 18] RAMIREZ-NUÑEZ J.A., ANTONINO-DAVIU J.A., CLIMENTE-ALARCON V., QUIJANO-LOPEZ A., RAZIK H., OSORNIO-RIOS R.A., ROMERO-TRONCOSO R., “Evaluation of the detectability of electromechanical faults in induction motors via transient analysis of the stray flux”, IEEE Transactions on Industry Applications, vol. 54, no. 5, pp. 4324–4332, Sept.–Oct. 2018. [RIE 10] RIERA-GUASP M., FERNANDEZ-CABANAS M., ANTONINO-DAVIU J.A., PINEDA-SANCHEZ M., ROJAS C.H., “Influence of not-consecutive bar breakages in motor current signature analysis for the diagnosis of rotor faults in induction motors”, IEEE Transactions on Energy Conversion, vol. 25, no. 1, pp. 80–89, Mar. 2010. [RIE 15] RIERA-GUASP M., ANTONINO-DAVIU J.A., CAPOLINO G.A., “Advances in electrical machine, power electronic, and drive condition monitoring and fault detection: State of the art”, IEEE Transactions on Industrial Electronics, vol. 62, no. 3, pp. 1746–1759, Mar. 2015. [STO 16] STONE G.C., SEDDING H.G., CHAN C., “Experience with on-line partial discharge measurement in high voltage inverter fed motors”, in 2016 Petroleum and Chemical Industry Technical Conference (PCIC), Philadelphia, PA, pp. 1–7, 2016. [THO 17] THOMSON W.T., CULBERT I., Current Signature Analysis for Condition Monitoring of Cage Induction Motors, IEEE Press, Wiley, New Jersey, 2017. [THO 01] THOMSON W.T., FENGER M., “Current signature analysis to detect induction motor faults”, in IEEE Industry Applications Magazine, pp. 26–34, Jul./Aug. 2001. [YAN 14] YANG C., KANG T., HYUN D., LEE S.B., ANTONINO-DAVIU J.A., PONS-LLINARES J., “Reliable detection of induction motor rotor faults under the rotor axial air duct influence”, IEEE Transactions on Industry Applications, vol. 50, no. 4, pp. 2493–2502, Jul./Aug. 2014. [YU 05] YU D., CHENG J., YANG Y., “Application of EMD method and Hilbert spectrum to the fault diagnosis of roller bearings”, Mechanical Systems and Signal Processing, vol. 19, pp. 258–270, 2005.

 

 

3 Accurate Stator Fault Detection in an Induction Motor Using the Symmetrical Current Components 1

3.1. Introduction The induction motor (IM) is widely used in the major industrial processes. Although it is robust, it can be affected by many types of faults. The most common faults occurring in IMs are short-circuit faults in the stator windings. These account for up to 25% of the overall electrical faults [CHO 16, CAP 15] and include inter-turn short-circuit (ITSC), phase-tophase and phase-to-ground faults. Therefore, the reliability of IMs is a major concern for manufacturers to ensure the continuity and optimization of production. As a result, sophisticated monitoring systems are implemented. The aim of these systems is to accurately detect and diagnose incipient faults to prevent the complete destruction of these machines and to minimize the production losses. Many methods have been developed and proposed to detect and diagnose stator faults [RIE 15, GAO 15]. These methods are essentially based on the monitoring of one or more pertinent fault indicators [SID 15]. Hence, the first step of an efficient fault diagnostic procedure is to choose robust and reliable fault indicators. These indicators should properly and meaningfully represent the fault behavior even under different disturbances.                                         Chapter written by Monia BOUZID and Gérard CHAMPENOIS.

Electrical Systems 2: From Diagnosis to Prognosis, First Edition. Edited by Abdenour Soualhi and Hubert Razik. © ISTE Ltd 2020. Published by ISTE Ltd and John Wiley & Sons, Inc.

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Although the symmetrical components are powerful tools for detecting imbalance in a three-phase system, they have not been explored thoroughly in the context of stator fault detection in an IM. Hence, this chapter is focused on the use of the symmetrical current components (SCCs) of an IM to ensure accurate incipient stator faults. The first part of this chapter is dedicated to a new deep and thorough simulation study of the behavior of the SCCs under ITSC, phase-to-phase and phase-to-ground faults, based on an original model developed and published in [BOU 11a, BOU 13a]. This study consists of the evaluation of the behavior of the magnitudes and phase angles of the negative-sequence current (NSC) and the zero-sequence current (ZSC) under the three types of stator faults in an IM. This study will show that both the NSC and the ZSC display good features to represent the behavior of the different stator faults well. Afterwards, the simulation study will be followed by an analytical study of the SCCs where new and original expressions of the SCCs will be developed and validated experimentally. From these two studies, four new fault indicators will, therefore, be extracted to monitor the operating state of an IM. However, although it is efficient, the NSC-based method is limited when detecting incipient stator faults in an IM. The limit is that the NSC generated in a faulty motor represents not only the asymmetry introduced by the fault, but also by other superposed asymmetries, which are the voltage imbalance, the inherent asymmetry in the machine and the inaccuracy of the sensors. This aspect can generate a false alarm making accurate incipient stator fault detection very difficult. Thus, to increase the accuracy of the fault detection and the sensitivity of the NSC under different disturbances, the second part of this chapter proposes an efficient method that is able to compensate for the effect of the different considered disturbances using experimental techniques that have the originality of isolating the NSC of each disturbance. The efficiency of the proposed method is validated experimentally on a 1.1-kW motor under different stator faults. In addition, an original monitoring system, based on neural networks, will also be presented and described to automatically detect and diagnose incipient stator faults.

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3.2. Study of the SCCs behavior in an IM under different stator faults 3.2.1. Simulation study 3.2.1.1. Behavior of the SCCs under ITSC faults in an IM On the basis of the symmetrical component method, any unbalanced three-phase system can be classified into three balanced systems: positive, negative and zero. For a three-phase direct current system (iA, iB, iC), the expressions of the NSC and ZSC are given by [3.1] and [3.2], respectively: i2

1 ( iA 3

a 2 iB aiC ),

[3.1]

i0

1 ( iA 3

iB

[3.2]

with a

e j2

/3

iC )

and a

2

e j4

/3

To analyze and understand the behavior of the SCCs under ITSC faults as well as the magnitudes and the phase angles of the NSC and ZSC in an IM, different ITSC faults in stator phases A, B and C are simulated using a specific algorithm given in Figure 3.1 [BOU 13b].

Figure 3.1. Block scheme of the algorithm used to extract the magnitudes and phase angles of the SCCs in an IM. For a color version of the figures in this book, see www.iste.co.uk/soualhi/electrical2.zip

The characteristics of the simulated IM are given in Table 3.1. The different values of the NSC and ZSC, with a maximum fault current equal to Ifmax = 4.24 A (If = 3 ARMS), are given in Table 3.2 [BOU 11b, BOU 13a]. Accordingly, it can be noted that: – The ZSC is null for any fault in phases A, B and C.

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– The magnitude I2 of the NSC is identical for a fault in phase A, B or C and it varies proportionally with the variation in the number of shorted turns in one phase. Therefore, I2 informs us about the severity of the fault but it cannot locate the faulty phase. Besides, I2 varies with the variation of the fault current If, as is shown in Figure 3.2, which depicts the behavior of I2 as a function of the shorted turns, under different fault currents. Note that for an important fault, the variation in I2 is more important with the increase in the fault current. Rated voltage (V)

230/400

Rated current (A)

4.5/2.6

Rated power (kW)

1.1

Rated speed (rpm)

1425

Power factor cos(φn) (°)

0.82

Frequency (Hz)

50

Rated slip s

0.043

Pair pole number p

2

Stator slot number

48

Turn number per phase

464

Type of windings

Concentric

Rotor bar number

28

Table 3.1. Characteristics of the simulated 1.1-kW IM

NA=NB=NC

Fault on phase A

Fault on phase B

Fault on phase C

I2max (A)

φ2 (°)

I0max (A)

I2max (A)

φ2 (°)

I0max (A)

I2max (A)

φ2 (°)

I0max (A)

8 (1.5%)

0.0244

0.0005

0

0.0244

120

0

0.0244

120

0

15 (3.2%)

0.0457

0.008

0

0.0457

120

0

0.0457

120

0

80 (17.2%)

0.244

0.08

0

0.244

119.9

0

0.244

120.1

0

120 (25%)

0.366

0.125

0

0.366

119.9

0

0.366

120.1

0

330 (71.1%) 1.006

0.358

0

1.006

119.6

0

1.006

120.4

0

Table 3.2. Magnitudes and phase angles of the NSC and ZSC for different ITSC faults in phases A, B and C with a fault current Ifmax=4.24 A (If =3 A)

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Figure 3.2. Variation of I2 as a function of the number of shorted turns on one of the three phases for different cases of fault current If

Figure 3.3. Behavior of φ2 for different ITSC faults in each phase of an IM

Regarding the phase angle φ2, note the following: – The phase angle φ2 has the same value for any fault in one phase, but its value changes with the change in the location of the fault. Therefore, φ2 is sensitive only to the location of the fault. Besides, it is insensitive to the variation in the fault current If. It can be seen from Table 3.2 that φ2 takes the value, in inverse rotating sense, of the phase angle of the faulty phase. Its behavior is as follows: φ2 = 0° for a fault in phase A. φ2 = 120° for a fault in phase B. φ2 = 120° for a fault in phase C.

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– The different values of φ2 are illustrated in Figure 3.3. It can be seen that they are very distinct for each case of ITSC faults, and this enables the location of the faulty phases without ambiguity and permits the discrimination between the three cases of ITSC faults. 3.2.1.2. Behavior of the SCCs under phase-to-phase faults To analyze the behavior of the SCCs under phase-to-phase faults in an IM, the magnitudes and the phase angles of the NSC and ZSC are simulated for different faults between phases (A and B), (B and C) and (C and A) [BOU 11b, BOU 13a]. The obtained results show that: – As in the case of ITSC faults, the ZSC is null for any fault between two stator phase windings. – The magnitude I2 has the same behavior in the case of faults between the phases (A and B), or (B and C) or (C and A). Hence, it is impossible to locate the two faulty phases. However, since their values change proportionally with the importance of the fault as it is shown in Table 3.3 for different faults between A and B (with If=3 A), I2 can inform us about the severity of the fault. According to Table 3.3, it can be noted that I2 cannot also inform us about the phase where the fault is more important. This can be explained by the fact that the values of I2 present a symmetry respect to the values corresponding to equal faults in the two faulty phases (represented in the diagonal of the table). As an example, for short-circuit fault of 15 turns on phase A and 80 turns on phase B, the value of I2 is equal to 0.27 A. This value is the same for a fault of 80 turns on phase A and 15 turns on phase B. Therefore, in the case of phase-to-phase faults, the amplitude I2 of the NSC can inform only about the severity of the fault without indicating neither the two faulty phases nor the phase the more affected by the fault. Furthermore, it has been shown that, as in the case of ITSC faults, I2 varies proportionally with the variation in the fault current If. NB 7 15 80 120 330

7 0.037 0.059 0.255 0.377 1.017

15 0.059 0.079 0.27 0.39 1.03

NA 80 0.255 0.27 0.422 0.531 1.15

120 0.377 0.39 0.531 0.633 1.23

Table 3.3. Magnitudes in (A) of the NSC for different faults between phases A and B with a fault current If = 3 A

330 1.017 1.03 1.15 1.23 1.74

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83

– The phase angles φ2 of the NSC for different faults between phases (A and B), (B and C) and (C and A) with If = 3 A are represented in Tables 3.4– 3.6, respectively. Note that φ2 is only sensitive to the location of the fault (the two phases where the fault occurs). In fact, for the three cases of phase-tophase faults, φ2 takes values situated in a sector bounded by the two angles, in reverse rotating sense, of the two considered faulty windings. In addition, φ2 is situated in the middle of the phase angle separating the two faulty stator windings in the case of equal faults in two phases. Moreover, φ2 can inform us about the phase that is most affected by the fault since it takes a value closer to the angle of the phase which has the important fault. Thus, the behavior of the phase angle φ2 for different phase-to-phase faults can be resumed as follows: –

2

0 ,120

for faults between phases A and B and φ2 = 60° for equal

faults on the two phases (see Table 3.4). –

2

120 , 120 for faults between phases B and C and φ2 = 180° for

equal faults on the two phases (see Table 3.5). –

2

120 , 0 for faults between phases C and A and φ2 = 60° for

equal faults on the two phases (see Table 3.6). NB 7 15 80 120 330

7 60.01 83.72 111.6 114.3 117.6

15 36.29 60.01 103.1 108.3 115.3

NA 80 8.24 16.84 60.01 73.2 98.6

120 5.51 11.55 46.8 60.01 90.05

330 1.74 4.09 21.04 29.73 60.01

Table 3.4. Phase angles φ2 in (°) of the NSC for different faults between phases A and B with a fault current If = 3 A

NC 7 15 80 120 330

7 180 156.3 128.5 125.8 122.5

15 156.2 180 137 131.8 124.8

NB 80 128.2 136.8 180 166.9 141.4

120 125.4 131.5 166.7 180 150

Table 3.5. Phase angles φ2 in (°) of the NSC for different faults between phases B and C with a fault current If = 3 A

330 121.7 124 141 149.7 180

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NA 7 15 80 120 330

7 60.01 36.32 8.45 5.812 2.47

15 83.77 60.01 17.20 11.8 4.75

NC 80 111.6 103.2 60.01 46.91 21.44

120 114.6 108.5 73.26 60.01 30

330 118.3 116 99.04 90.34 60.01

Table 3.6. Phase angles φ2 in (°) of the NSC for different faults between phases C and A with a fault current If = 3 A

Figure 3.4. Values of φ2 for different phase-to-phase faults in an IM

The values of φ2 for different cases of phase-to-phase faults are illustrated in Figure 3.4. Note that the values of φ2 are very distinct for each case of faults, and this allows the location of the faulty phases without ambiguity and permits the discrimination between the three cases of phase-to-phase faults. 3.2.1.3. Behavior of the SCCs under phase-to-ground faults in an IM The values of the magnitudes and phase angles of the NSC and ZSC in an IM, simulated with a fault current If =1.1 ARMS (Ifmax =1.5 A), are given in Table 3.7. The analysis of these values shows that, contrary to the ITSC and phase-to-phase faults, in the case of phase-to-ground faults, a significant ZSC appears in addition to the NSC having the same behavior as in the case

Accurate Stator Fault Detection in an Induction Motor Using the SCC

85

of ITSC faults [BOU 11b, BOU 13a]. Consequently, it is clear that the existence of a ZSC permits the discrimination between an ITSC fault and a phase-to-ground fault. Therefore, for a phase-to-ground fault, the behavior of the ZSC is as follows: – The magnitude I0 is not null. In addition, for any case of phase-toground faults, I0 is equal to one third of the faulty current I0 =1/3If. – The phase angle φ0 of the ZSC is affected only by the location of the faulty phase winding. As is shown in Table 3.7, φ0 takes the value, in direct rotating sense, of the phase angle of the faulty phase winding. The values that φ0 can take are: φ0 = 0° for faults between phase A and the ground. φ0 = 120° for faults between phase B and the ground. φ0 = 120° for faults between phase C and the ground. NA=NB=NC

7 (1.5%)

15 (3.2%)

80 (17.2%) 120 (25.8%) 330 (71.1%)

Faults between phase A and ground I2max (A)

0.007

0.016

0.0862

0.131

0.361

φ2 (°)

9.954

4.504

0.751

0.459

0.043

I0max (A)

0.511

0.499

0.498

0.506

0.507

φ0 (°)

11.39

5.002

0.703

0.390

0.023

Faults between phase B and ground I2max (A)

0.007

0.016

0.0862

0.131

0.361

φ2 (°)

110.8

116

119.3

119.6

120

I0max (A)

0.511

0.499

0.498

0.506

0.507

φ0 (°)

130.39

124.5

120.5

120.3

120

Faults between phase C and ground I2max (A)

0.007

0.016

0.0862

0.131

0.361

130

124.5

120.8

120.5

120

I0max (A)

0.511

0.499

0.498

0.506

0.507

φ0 (°)

108.6

115

119.3

119.6

120

φ2 (°)

Table 3.7. Magnitudes and phase angles of the NSC and ZSC for different phase-to-ground faults with a fault current Ifmax = 1.5 A

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Electrical Systems 2

The different values of the phase angles of the ZSC and NSC are depicted in Figure 3.5. It is clear that the ZSC is a pertinent indicator that is useful for discriminating between an ITSC and phase-to-ground faults.

2

0

Figure 3.5. Values of φ0 and φ2 for different phase-to-ground faults in an IM

3.2.2. Analytical study of the SCCs in an IM under different stator faults The objective of the analytical study of the SCCs under different types of stator faults is to verify the simulation study and look for all the variables that affect the behavior of the SCCs. To achieve this, for each type of stator faults, original expressions of these components are developed and published in [BOU 13b], since such expressions are not available in scientific literature. Therefore, to determine the expressions of the SCCs, it is first necessary to determine the expressions of the line currents ( iA , iB , iC ) of the IM in the presence of stator faults as it is shown by the following equation: i1

1 ( iA 3

aiB a 2 iC ),

i2

1 ( iA 3

a 2 iB aiC ),

i0

1 ( iA 3

iB

[3.3]

iC ).

For a linear system, the IM line currents in the presence of faults are obtained based on the superposition theorem, where each current is the result

Accurate Stator Fault Detection in an Induction Motor Using the SCC

87

of the superposition of the healthy current ih and the faulty current if generated by the fault. The three currents ( iA , iB , iC ) can, therefore, be written as

iA

ihA

ifA ,

iB

ihB ifB ,

iC

ihC

[3.4]

ifC .

The problem here is, how to determine the expressions of the three faulty currents ( ifA , ifB , ifC ). In this work, the expressions of ( ifA , ifB , ifC ) in each type of stator faults are obtained based on the electrical circuit of the IM taking into account only the effect of the fault. This can be achieved by considering three shorted stator windings with three null electromotive forces. The fault current If in the short circuit is generated by an ideal current source. In the aim to detect incipient stator faults, the value of If should be very low. Therefore, the expressions of the SCCs in the case of each type of faults are given in the following sections. Note that a short-circuit fault in the three phases A, B or C is quantified by a “relative quantity” xA, xB or xC relatively. These “relative quantities” are defined as the ratio between the shorted turns Ni (i = A, B or C) in the considered phase and the total turn N of the phase winding as it is expressed by xA

NA , N

xB

NB , N

xC

NC . N

[3.5]

3.2.2.1. Analytical study of the SCCs under ITSC faults The expressions of ( ifA , ifB , ifC ) under ITSC faults are deduced using the electrical circuit of the IM presented in Figure 3.6, with a short circuit of NA turns in phase A. As shown in the figure, the IM is modeled as three

88

Electrical Systems 2

short-circuited stator windings with three null electromotive forces. The fault current If is generated by an ideal current source [BOU 13b]. The expressions of the resistances, inductances and mutual inductances are given by [3.6]–[3.8], respectively, with R, L and l are the stator resistance, inductance and leakage inductance, respectively. R1

(1 xA ) R,

R0

RxA ,

R2

R3

L1

(1 xA ) 2 L (1 xA )l1 ,

L0

xA2 L xA l1 ,

L2

L3

[3.6] R,

[3.7]

L l1 ,

M 01

M 10

xA (1 x A ) L,

M 02

M 03

M 20

M 12

M 13

M 23

M 32

M 21

M 30

xA L , 2

M 31

(1 xA ) L , 2

L . 2

Figure 3.6. Electrical circuit used for the determination of the faulty currents (ifA, ifB, ifC) generated by the ITSC fault in phase A

[3.8]

Accurate Stator Fault Detection in an Induction Motor Using the SCC

89

By applying Kirchhoff’s law to the electrical circuit of Figure 3.6, differential equations are obtained (see [BOU 13b]). The resolution of these equations leads to the expressions of ( ifA , ifB , ifC ): ifA ifB

2 xA I f , 3 1 ifC xA I f . 3

[3.9]

Referring to Figure 3.7, representing the three stator windings with a short circuit in phase A with a faulty resistance Rf, the expression of the faulty current If is If

Vf . Rf

[3.10]

Based on the assumption that each stator winding behaves as an autotransformer’s winding and the neutral potential remains unchanged in the case of fault, it can be written as Vf VA

NA N

If

xA VA . Rf

xA

and Vf

xAVA ,

Figure 3.7. Configuration of the three stator windings in the case of ITSC faults in phase A with a faulty resistance Rf

[3.11]

[3.12]

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Electrical Systems 2

The developed expressions of the SCCs under ITSC faults based on [3.3] and [3.4] are given in Table 3.8, with V being the magnitude of the supply voltage (RMS) of the IM. Here, the IM is supposed to be supplied by a balanced voltage VA=VB=VC=V. It can be noticed that the ZSC is null and the NSC has the following characteristics [BOU 13b, CHA 11]: – The magnitude I2 varies proportionally with the importance of the fault, the fault current If and the supply voltage, which makes it sensitive to the unbalanced supply voltage. – The phase angle φ2 is sensitive only to the location of the fault. As is shown by simulation, φ2 takes the value of the angle, in reverse rotating sense, of the faulty phase winding. Fault on phase A I2 (A)

I2

1 xA2 V 3 Rf

1 xA I f 3

Fault on phase B

I2

1 xB2 V 3 Rf

1 xB I f 3

Fault on phase C

I2

1 xC2 V 3 Rf

φ2 (°)

0

120

120

I0 (A)

0

0

0

φ0 (°)

0

0

0

1 xC I f 3

Table 3.8. Analytical expressions of the magnitudes and phase angles of the NSC and ZSC for different ITSC faults

3.2.2.2. Analytical study of the SCCs under phase-to-phase faults Similar to the case of ITSC faults, the currents ( ifA , ifB , ifC ) are determined using the electrical circuit of Figure 3.8. The developed expressions of the NSC and ZSC under different cases of phase-to-phase faults are given in Table 3.9. The analysis of these expressions shows that as in simulation, the ZSC is null and the NSC has the following behavior [BOU 13b]: – The magnitude I2 of the NSC is sensitive to the importance of the fault, the fault current If and the supply voltage. – The phase angle φ2 of the NSC is only sensitive to the location of the fault as it is demonstrated in the simulation study.

Accurate Stator Fault Detection in an Induction Motor Using the SCC

Short-circuit faults between phases A and B

1 3 xA2 I2 (A)

If 2 C

x

xA xB

V 3 Rf

( xA2

( xA2 0.5 xB2 0.5 xB2

xA xB ) 2 (0.866( xB2 2 xA xB )) 2

xA xB ) 2

(0.866( xB2

xA=xB=x; I 2 Argument of ( x A2 φ2 (°)

1 3

0 .5 x B2

xA xB )

V x 2 / Rf

j(0 .8 6 6 ( x B2

2 x A x B ))

xA > xB xA = xB xA > xB 0