Detection of Corona Discharge in Electric Networks (Studies in Systems, Decision and Control, 509) 3031440242, 9783031440243

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Studies in Systems, Decision and Control 509

Yevgen Sokol · Vitalii Babak · Artur Zaporozhets · Oleg Gryb · Ihor Karpaliuk   Editors

Detection of Corona Discharge in Electric Networks

Studies in Systems, Decision and Control Volume 509

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control–quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the fields of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output. Indexed by SCOPUS, DBLP, WTI Frankfurt eG, zbMATH, SCImago. All books published in the series are submitted for consideration in Web of Science.

Yevgen Sokol · Vitalii Babak · Artur Zaporozhets · Oleg Gryb · Ihor Karpaliuk Editors

Detection of Corona Discharge in Electric Networks

Editors Yevgen Sokol National Technical University “Kharkiv Polytechnic Institute” Kharkiv, Ukraine

Vitalii Babak General Energy Institute National Academy of Sciences of Ukraine Kyiv, Ukraine

Artur Zaporozhets General Energy Institute National Academy of Sciences of Ukraine Kyiv, Ukraine

Oleg Gryb National Technical University “Kharkiv Polytechnic Institute” Kharkiv, Ukraine

Ihor Karpaliuk National Technical University “Kharkiv Polytechnic Institute” Kharkiv, Ukraine

ISSN 2198-4182 ISSN 2198-4190 (electronic) Studies in Systems, Decision and Control ISBN 978-3-031-44024-3 ISBN 978-3-031-44025-0 (eBook) https://doi.org/10.1007/978-3-031-44025-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Paper in this product is recyclable.

Preface

Ukraine’s transition to European institutions opens up opportunities for our country to enter the European market. However, the requirements for goods at the European level are much higher than the current standards used in Ukraine. One of the most important goods for Ukraine is electric energy. Ukraine has a powerful power supply system and can supply a sufficient amount of electric energy to European countries. This can become the basis for the development and growth of Ukraine’s economy. However, the quality requirements for goods also apply to the quality of power supply. Hence, there are corresponding requirements for the energy sector to meet the quality criteria of the European market. Currently, there is a question of further improving the quality of electric energy to meet European standards. The regulated indicators in these standards not only address the parameters of electric energy itself but also the parameters of the network, network configuration, network operation, and consumers. Therefore, a proposal has been made to shift from purely qualitative parameters of electric energy to the parameters of power supply as a more comprehensive concept, where the quality of electric energy will be included as a component. The qualitative parameters of power supply and the quality of electric energy as an element of power supply have become the subject of research by renowned scientists. From the perspective of power supply quality indicators, one influential phenomenon is corona discharge. It occurs under normal operating conditions of the system and affects the operation of relay protection. It can become a source of conditions for arc discharge and is one of the factors affecting the continuity of supply, electrical energy losses, and the performance of network equipment. According to the Electric Power Research Institute (EPRI) in the USA, there has been an increase in the number of failures of polymer insulators on 115 kV and 138 kV transmission lines. EPRI’s research has shown that these failures are related to the continuous impact of corona discharges on the insulation. Based on the characteristics of corona discharge, it has largely been considered as a parasitic power consumer. However, this book focuses on the correlation between corona discharge and the deterioration of power quality indicators. The

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study proposes the detection of corona discharge and its coordinates to facilitate measures for its elimination. Remote methods for detecting the presence of corona discharge are relevant and these technologies are being developed. Methods for determining corona discharge based on ultraviolet radiation, infrared radiation, existing electromagnetic background, and the presence of chemical compounds are already known and used in practice. However, remote inspection methods for isolators have limitations that prevented them from replacing visual inspection of electrical equipment; instead, they complement it. At the same time, visual inspections may not always detect defects since corona discharges are often not visible. Thus, there is an important scientific problem associated with the insufficient effectiveness of existing methods for detecting the presence of corona discharge. Analysis has revealed the need for the development and research of new methods for detecting the presence of corona discharge and its coordinates. These methods should be remote, galvanically isolated, and have minimal influence from external factors such as weather conditions, time of day, and others. In this book, the presence of corona discharge and its coordinates are proposed to be determined based on its acoustic radiation. A solution to the mentioned problem is proposed based on methods of spectral analysis of the acoustic noise accompanying corona discharge. Kyiv-Kharkiv, Ukraine June 2023

Yevgen Sokol Vitalii Babak Artur Zaporozhets Oleg Gryb Ihor Karpaliuk

About This Book

The book is devoted to the solution of the problem of determining the presence of corona discharge on electrical equipment with acoustic radiation. It is shown that corona discharge leads not only to irreversible losses of electrical energy, but also interferes with the transmission of high-frequency signals, deteriorates insulating elements, can become a source of conditions for the occurrence of a destructive arc discharge and is one of the factors of changing the continuity of the electrical system as a whole. The book describes the processes in a corona discharge that lead to the occurrence of acoustic waves. The authors analyzed acoustic radiation from a corona discharge reproduced in laboratory conditions. The received acoustic signals were processed by Fourier transform. Thus, the features of the spectral function, which belong specifically to the corona discharge in electrical networks with industrial frequency current, were determined. Based on the inverse Fourier transform, a simplified model of the acoustic radiation of the corona discharge was constructed. The authors proposed a method for detecting the presence of a corona discharge based on the spectral characteristics of acoustic radiation. Techniques were developed to determine the presence of a corona discharge for the creation of stationary and mobile devices. The advantages of the method of detecting the presence of corona discharge by the acoustic spectrum are shown. The method makes it possible to determine the presence of a corona discharge remotely, even out of direct sight, regardless of the time of day and regardless of the season. The book states that determining the presence of a corona discharge is not enough, it is still necessary to determine its location. The method of finding the coordinates of the corona discharge as a source of sound was described. Methods of searching for corona discharge coordinates with a fixed scanning device and a moving scanning device are proposed. A UAV is proposed as a mobile platform for the scanning system. The influence of the Doppler effect on acoustic measurements when the UAV speed changes was taken into account. The authors have shown that the use of coronal discharge detection with UAVs will not only enable the prevention of coronal discharge, but also increase the frequency of surface inspections. This will allow timely measures to be taken to improve the

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About This Book

reliability of the power system operation. The book is intended for the researchers, postgraduate students and students specialized in theory and calculations of electrical systems.

Contents

Development of Approaches to the Quality of Electricity Supply . . . . . . . Yevgen Sokol, Vitalii Babak, Artur Zaporozhets, Oleg Gryb, Ihor Karpaliuk, and Roman Demianenko Influence of Corona Discharge on Electric Power Supply Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yevgen Sokol, Vitalii Babak, Artur Zaporozhets, Oleg Gryb, Ihor Karpaliuk, and Oleksiy Luka Detection of Corona Discharge in Power Supply System . . . . . . . . . . . . . . . Yevgen Sokol, Vitalii Babak, Artur Zaporozhets, Oleg Gryb, Ihor Karpaliuk, and Yevgen Kaurkin Theoretical Principles of Acoustic Radiation Created by Corona Discharge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yevgen Sokol, Vitalii Babak, Artur Zaporozhets, Oleg Gryb, Ihor Karpaliuk, and Oleksandr Svetelik Recognition of Corona Discharge Presence by Spectral Characteristics of Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Artur Zaporozhets, Vitalii Babak, Oleg Gryb, Ihor Karpaliuk, Viktor Starenkiy, and Andrii Solodovnyk

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Instruments for Identification of Corona Discharge Presence by Spectral Characteristics of Acoustic Radiation . . . . . . . . . . . . . . . . . . . . 113 Artur Zaporozhets, Vitalii Babak, Viktor Starenkiy, Oleg Gryb, Ihor Karpaliuk, and Oleksiy Luka Theoretical Basis of Determination of Corona Discharge Coordinates by Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Yevgen Sokol, Vitalii Babak, Artur Zaporozhets, Oleg Gryb, Ihor Karpaliuk, and Roman Demianenko

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Instruments for Corona Discharge Coordinate Search as a Source of Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Yevgen Sokol, Artur Zaporozhets, Vitalii Babak, Viktor Starenkiy, Oleg Gryb, and Ihor Karpaliuk Prospects for the Development of Corona Discharge Detection Method by Spectral Acoustic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Artur Zaporozhets, Vitalii Babak, Viktor Starenkiy, Oleg Gryb, Ihor Karpaliuk, and Roman Demianenko Economic Effect of the Use of the Method of Diagnosing the State of Power Lines at the Expense of UAVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Oleg Gryb, Ihor Karpaliuk, Vitalii Babak, Viktor Starenkiy, Artur Zaporozhets, and Yevgen Kaurkin

Editors and Contributors

About the Editors Prof. Yevgen Sokol is the Rector in the National Technical University “Kharkiv Polytechnic Institute”. He graduated from the Kharkiv Polytechnic Institute in 1975. He obtained his Ph.D. in 1979 and Dr. Sc. (Eng.) in 1994. The title of Professor he obtained in 1998. He is a laureate of the State Prize of Ukraine in the field of Science and Technology (2017), chosen as a Corresponding Member of the National Academy of Sciences of Ukraine (2012), winner of the all-Ukrainian competition “Leader of the fuel and energy complex” in the nomination “Scientific and technical development” (2005), winner of the competition “High Potential” scientific for the sake of complex problems of energy of the National Academy of Sciences of Ukraine (2004), laureate of the certificate of honor of the Cabinet of Ministers of Ukraine for significant personal contribution to the development of education and science (2002), laureate of the Lebedev Prize of the National Academy of Sciences of Ukraine (2001) and others. His main professional activity is associated with institutions of the NAS of Ukraine and institutions of higher education of the Ministry of Education and Science of Ukraine: Institute of Mechanical Engineering Problems named after A.M. Pidgorny; Institute of General Energy; National Technical University “Kharkiv Polytechnic Institute (1969—till now). For more than 35 years, he has led scientific projects funded by the National Academy of Sciences of Ukraine and the Ministry of Education and Science of Ukraine. Prof. Yevgen Sokol taught undergraduate courses in “Microprocessor technology” for students of the National Technical University “Kharkiv Polytechnic Institute”. He supervises the training of postgraduate and doctoral students at National Technical University “Kharkiv Polytechnic Institute”. Prof. Yevgen Sokol has published more than 400 scientific works, among them over 24 articles and 100 conference proceedings in international peerreviewed journals. His current research interests include: Microprocessor control of semiconductor electrical energy converters; Methods of analysis and synthesis of microprocessor control algorithms with mapping on the complex plane; Applied

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research in the field of development of medical devices and systems that are associated with the development of microprocessor control system; Development of new types of physiotherapeutic medical equipment. Prof. Vitalii Babak is the Director of the General Energy Institute of the National Academy of Sciences of Ukraine. He graduated from the Information-Measuring Equipment Department of the Kyiv Polytechnic Institute in 1977. He obtained his Ph.D. in 1981 and Dr. Sc. (Eng.) in 1995. From 1977 to 1995, he worked in various positions at the Kyiv Polytechnic Institute. From 1995 to 1998, he worked as Deputy Minister of Education and Head of the Main Accreditation Department of the Ministry of Education of Ukraine. From 1998 to 2008, he was the Rector of the National Aviation University (Kyiv, Ukraine). In 2003, Vitalii Babak was elected as a Corresponding Member of the National Academy of Sciences of Ukraine. From 2008 to 2021 he worked as the Deputy Director for Science, Head of the Department, and Chief Researcher of the Institute of Engineering Thermophysics of the National Academy of Sciences of Ukraine. From 2022 till now Vitalii Babak has been the Acting Director of the General Energy Institute of the National Academy of Sciences of Ukraine. Vitaly Babak is a well-known scientist in the field of energy and information-measuring technologies. He created scientific schools in the field of technical diagnostics and information-measuring technologies. Among his students are 19 doctors and 30 candidates of sciences. During his professional activity, Vitalii Babak was awarded the State Prize of Ukraine in the field of science and technology, the Honorary Diploma of the Verkhovna Rada of Ukraine, the Honorary Diploma of the Cabinet of Ministers of Ukraine, Orders of Merit (II degree, III degree). Vitali Babak is the author of more than 600 scientific works, including 20 monographs, 40 textbooks and dictionaries, and 120 patents. Dr. Artur Zaporozhets is working as Deputy Director at the General Energy Institute of the National Academy of Sciences of Ukraine. He graduated from the Applied Physics Department of the National Aviation University in 2013. He obtained his Ph.D. in 2017 and Dr. Sc. (Eng.) in 2022. The title of Senior Researcher in Metrology and Information-Measuring Technology he obtained in 2019. He is a laureate of the Medal “For work and achievement” (2022), Award of the NAS of Ukraine for young scientists (2022), Award of the Verkhovna Rada of Ukraine to young scientists (2021), Award of the President of Ukraine for young scientists (2019) and others. His main professional activity is associated with institutions of the NAS of Ukraine: G.V. Kurdyumov Institute of Metal Physics (2009–2011), Institute of Engineering Thermophysics (2013–2021), General Energy Institute (2022–till now). Since 2013 he has taken part in 20 research projects funded by NAS of Ukraine and Ukrainian Ministry of Education and Science. In 2014–2016 Dr. A. Zaporozhets taught undergraduate courses in Advances in Information Systems, Software Engineering and Programming Technologies, Information and Measuring Systems, Metrology, Biomedical Methods, and Laboratory workshops for students of the Applied Physics Department of the National Aviation University. Dr. A. Zaporozhets has published more than

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200 scientific works, among them 14 books in Springer, over 50 articles in international peer-reviewed journals, and 60 conference proceedings. His current research interests include Energy Informatics, Power Equipment Diagnostics, Environmental Monitoring, Algorithms and Data Structures, Big Data, and Data Processing. Prof. Oleg Gryb is working as a Full Professor in the National Technical University “Kharkiv Polytechnic Institute”. He graduated from the Ukrainian Correspondence Polytechnic Institute in 1973. He obtained his Ph.D. in 1979 and Dr. Sc. (Eng.) in 1992. The title of Professor he obtained in 1995. He is the laureate of the Certificate of Honor “For special services to the Ukrainian people” of Verkhovna Rada of Ukraine (2017), laureate of the State Prize of Ukraine in the field of Science and Technology (2013), Winner of the All-Ukrainian competition “Leader of the Fuel and Energy Complex” (2009) and others. His main professional activity is associated with institutions of higher education of the Ministry of Education and Science of Ukraine and institutions of the NAS of Ukraine: Ukrainian Correspondence Polytechnic Institute (1980–1992); Kharkiv National University of Municipal Economy (1992–2010); Northeast Scientific Center of the NAS of Ukraine (2010); National Technical University “Kharkiv Polytechnic Institute” (2010–till now). He took part in more than 30 research projects funded by NAS of Ukraine and Ukrainian Ministry of Education and Science. Prof. Oleg Gryb taught undergraduate courses in “Electricity supply”, “Basics of electricity supply and energy saving”, and “Systems of accounting and quality control of electric energy” for students of the National Technical University “Kharkiv Polytechnic Institute”. Dr. Oleg Gryb has published more than 380 scientific works, among them 49 books (monographs, textbooks), 26 articles in international peer-reviewed journals, and 102 conference proceedings. His current research interests include quality of electrical energy and diagnostics of power lines using UAV. Prof. Ihor Karpaliuk is working as a Full Professor in the National Technical University “Kharkiv Polytechnic Institute”. He graduated from the Faculty of Power Supply and Lighting of Cities of the Kharkiv Institute of Urban Engineers in 1993. He obtained his Ph.D. in 1998 and Dr. Sc. (Eng.) in 2021. The title of Professor he obtained in 2022. His main professional activity is associated with institutions of higher education of the Ministry of Education and Science of Ukraine: Kharkiv National University of Municipal Economy (2003–2018); National Technical University “Kharkiv Polytechnic Institute (2018–till now). Since 2004 he has taken part in 10 research projects funded by Ukrainian Ministry of Education and Science. In 2019–2022 Prof. Ihor Karpaliuk taught undergraduate courses in “Security of operating systems”, “Automated monitoring of energy facilities by unmanned aerial vehicles”, and “Digital energy” for students of the National Technical University “Kharkiv Polytechnic Institute”. Prof. Ihor Karpaliuk has published more than 150 scientific works, among them 18 books (monographs, textbooks), 11 articles in international peer-reviewed journals and 32 conference proceedings. His current research interests include Quality of electrical energy; Digital energy; and Diagnostics of power lines using UAV.

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Contributors Vitalii Babak General Energy Institute of NAS of Ukraine, Kyiv, Ukraine Roman Demianenko National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Oleg Gryb National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine; National Power Company “Ukrenergo”, Kyiv, Ukraine Ihor Karpaliuk National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine; National Power Company “Ukrenergo”, Kyiv, Ukraine Yevgen Kaurkin National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Oleksiy Luka National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Yevgen Sokol National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Andrii Solodovnyk National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine Viktor Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology of the National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine Oleksandr Svetelik National Power Company “Ukrenergo”, Kyiv, Ukraine Artur Zaporozhets General Energy Institute of NAS of Ukraine, Kyiv, Ukraine; Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan

Development of Approaches to the Quality of Electricity Supply Yevgen Sokol , Vitalii Babak , Artur Zaporozhets , Oleg Gryb , Ihor Karpaliuk , and Roman Demianenko

Abstract A brief history of approaches to the quality of electricity supply is given. The main parameters of electric power supply quality, which were grouped according to various factors, are shown. Attention was drawn to the fact that the quality of electrical energy can be considered as one of the elements of quality indicators of electricity supply. The results of the research of quality parameters of electric power in the Ukrainian energy system are presented. The presence of deviations in quality parameters of electric power is shown. Keywords Quality of electricity · Power quality · Parameters · Power supply systems · Energy equipment · Consumers

1 Introduction Electric energy, since its discovery in the form of an electric field, is used by mankind in various forms. And its most widespread use is associated primarily with the possibility of transmitting mechanical energy over long distances. There are already and continue to be developed a variety of electricity consumers who can do the work of converting electricity into other types of energy. The ability to generate large capacities in combination with the convenience of transmitting electricity over long distances has led to a large branching of wire networks. Power networks are becoming more complicated, and their control system is becoming more complicated [1–5]. And at the management of systems now conditions of reliability of power supply Y. Sokol · O. Gryb · I. Karpaliuk · R. Demianenko National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_1

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are by all means observed [6–8]. But not only has the reliability of the power supply system become an important additional condition. It should be noted that electricity now acts as a commodity. And as any product is subject to the conditions of the economic market, and this is primarily the quality of the product. Over time, the quality of this specific product began to be subject to more and more requirements. So, if at the beginning of the century the quality, requirements were determined by the voltage level in the power supply system. Consumer appliances mainly consisted of incandescent light bulbs, respectively; the product of these lamps is light, which directly depended on the voltage in the power supply system. And on an urban scale, electricity consumption was associated with electric trams, electric street lighting, and telephone [9]. Accordingly, requirements were set for the quality of the electricity supply [9]. With the development of devices, mechanisms, and machines of those who work on electricity, the requirements for the supplied electricity began to change. Standardization began to develop after December 22, 1920, when the plan of the State Electrification of Russia (SELRU) was adopted [4]. That is, the introduction of advanced technology of production and distribution of electricity required the entire economic complex to move to more advanced technological cycles. The International Electrotechnical Commission was formed in the world (IEC). The task of this organization was and still is the creation of international standards in the field of electrical, electronic, and combined technologies. Already in 1921 RSFSR became a member of the IEC [5]. The purpose of the international non-profit organization MEC is also to promote international cooperation in the solution of standardization issues in the field of electrical engineering. Thus, the first standards for the quality of electrical energy, which is supplied, were developed by the IEC. But since the IEC is a non-commercial organization, its recommendations are voluntary. That is why many countries have developed their standards for the quality of electrical energy. But in the world, the development of the electrical industry was innovative, and such that leads to technologies for other industries [6]. At the beginning of the nineteenth century, the attitude to electric power in the Soviet Union was not as a commodity or product but was evaluated as state technical requirements. Therefore, the development of quality standards was not anticipated. And actually, the first state standard for the quality of electrical energy was introduced only in the GOST 1310967 “Electrical Energy. Standards for the quality of electrical energy in their receivers connected to the electrical networks of general-purpose”. Then it was replaced by GOST 13109-87 “Electric energy. Requirements for the quality of electrical energy in the electrical networks of general-purpose” and as a result after the collapse of the USSR was adopted by GOST 13109-97 “standards of quality of electrical energy in the electrical power supply systems of general-purpose”. Now Ukraine has adopted international standards for the quality of electrical energy EN50160 (DSTU EN 50160:2014) “Electricity supply voltage characteristics in electric utilities of generalpurpose”. Since the quality of electrical energy (EE) at the outlets of its receivers depends on both the energy system and the consumers, The standard stipulates both responsibilities of the organizations, which provide energy supply, and the responsibility

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of the consumers for compliance with the indicators of electric power quality. The scope of responsibility of the energy system and consumers is specified in another document—“Rules for Use of Electric and Thermal Energy” [7]. The quality of electricity outside the country is given great attention in industrialized countries. Different countries at different times developed their standards defining the quality of electricity supply. The quality of the electricity supply of industrial enterprises was separately distinguished. Industrial enterprises are the largest consumers of electricity and its quality determines the financial structure [8]. In the power systems of different countries, the main indicators of electric power quality are voltage and frequency, which are maintained within the limits of nominal, and under conditions of normal operation, only small deviations are allowed [10–13]. Today there is no international standard for the quality of electricity, but standards or tolerances for the quality of certain parameters are already available in all countries. In most cases, the requirements for the quality of electricity supply are related to property ownership. Thus, in France, the energy systems are nationalized, but there is a single standard of the French State Electricity Directorate (EDF), which covers a large number of indicators of electric power quality [14, 15]. In Sweden, the Swedish Electrical Code regulates permissible voltage deviations [16, 17]. The U.S. does not have a standard or a nationwide standard for electrical power quality. There are rules adopted by individual power systems. Germany also does not have any general standards, but the European Union’s guidelines for the coordination of production and transmission of electrical energy (UCPTE) are followed in terms of permissible frequency deviations [18–20].

2 Voltage Control in Power Supply Systems As a rule, under normal operating conditions the voltage is maintained close to the nominal value. Allowed the following deviations in normal operating conditions: the greatest allowable deviation is (15%) in the direction of increase in the regulations of Turkey, the smallest deviation is (2%) in Sweden. For step-down in voltage, the highest permissible departure rate is (10%), the lowest (3%) in Canada. In eight countries ±5% deviation and six countries +10% deviation are tolerated. In Denmark and Poland deviations in voltage are only permitted in the direction of increasing. In extreme conditions large deviations are tolerated: drops of up to 15% in four of the countries and rises of up to 15% in Germany and Norway. In 10 countries deviations of ±10% are tolerated. In some regions a deviation towards ups and downs are different, e.g., in England—increase of 6%, 12% downgrade; Ireland—11.5% increase, 13.5% downgrade, Ukraine—10% increase, 15% downgrade. In France, when connecting a new subscriber (depending on his requirements, the connection point, and other conditions), a certain voltage is selected and fixed in the contract within the limits of the nominal value of ±5% [21].

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But at the same time, under unfavorable operating conditions of power supply systems, it is allowed to regulate the consumers’ power by means of voltage regulation. In 11 of the countries listed in [21], when the need arises in the power system to reduce the load instead of disconnecting some of the consumers or introducing restrictions, the voltage in the power supply systems is allowed to be reduced. Thus, in some areas of the U.S. with weak electricity supply systems to ensure the stability of the system when the load fluctuates, voltage regulation is used. In the USA this method of load reduction was repeatedly used in case of capacity deficit in some power systems which appeared due to low capacity of interconnections and nervous distribution of the generating capacities reserve. In the year of maximum load, the voltage in the power supply system was decreased to maintain the frequency, and thus the power system was disconnected. This way was used, in particular, in the power system of New York City under emergency conditions instead of automatic frequency switching off or before the beginning of its activity. At the time of the New York City event, with 6 GW of load, the dispatcher was recorded to have reduced the load by 8% and the system load reduced by 280 MW (close to 4.5%). A similar 8% power reduction during another accident in New York resulted in the reduction of the load by 250 MW [22]. This method of reducing the load was also used in Romania. In the countries of Western Europe which are members of UCPTE and whose power systems are electrically interconnected and operate synchronously, the voltage in the high and medium voltage grids is maintained at the same level as the nominal voltage that is recorded in the UCPTE monthly reports. In France, EDF also foresees all cases of forced prolonged voltage reduction. For example, due to the low-water season in the summer and the limited capacity of GES in the distribution networks, the voltage was reduced by 5% for up to three days. In Japan, in low-voltage networks during the period of switching the network voltage level is reduced: 127 V by 6% and 220 V by 10%.

3 Frequency Control in Power Supply Systems The frequency constant is maintained more strictly than the voltage level [21]. Under normal operating conditions the following frequency deviations are allowed: In the upward direction, the highest (1 Hz) in France and the lowest (0.04–0.06 Hz); in the downward direction, the highest value of deviation (1 Hz) in Denmark and France, the lowest value of deviation (0.05 Hz) in Canada, Poland, and Finland. In other countries, frequency deviations are allowed within ±(0.1–0.3 Hz). Under adverse conditions the tolerance is wider: from 1 Hz (upward) in Hungary to 0.1 Hz in Finland and the Czech Republic; from 2.5 Hz (downward) in Denmark and the Netherlands to 0.1 Hz in Finland. In general, in other countries, symmetrical deviations from ±0.5 to ±1 Hz are allowed. In the power systems of the countries belonging to UCPTE, at a deviation from the set frequency of 50 ± 0.5 Hz the system of automatic frequency regulation (AFR) begins to operate, using digital and analog devices [23–26]. UCPTE created

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a workgroup that systematically monitors the frequency and voltage stability and develops appropriate recommendations [21]. To maintain the frequency in adverse conditions in some countries use ARF. In Austria, England and Norway, the AFFs are not used. In France, the nominal frequency value is officially set at 50 ± 1 Hz (2%), but in operation, the actual frequency deviation is much lower, ±0.5 Hz (1%). In England, the frequency must be kept within 50 ± 0.5 Hz (1%) but in practice, CEGB reduced the tolerance to ±0.2 Hz (0.4%)—deviations from this value are rare and only in some areas. In Germany, the association of German power plants, according to the UCPTE recommendations, when the frequency is lowered to 49.5 Hz, the power system must be disconnected with the help of AFR [27–30]. The frequency (60 Hz) is very stable in the USA [31–33]. According to the survey conducted by the Institute of Electrical and Electronics Engineers, more than 100 large power systems and communities use the AFR, However, in most of them (72%), the first step of VSF is at frequency dropping down to 59.3 Hz, i.e. just at the moment when frequency dropping goes beyond the limit of 1%. Steadily maintain the frequency in the power systems of Japan. Thus, if the frequency of 60 Hz deviates by ±0.2 Hz, it is considered a poor indicator. The International Electrotechnical Commission [34–36], apart from general recommendations on nominal voltages, standard frequencies, etc., develops standards for certain types of electrical equipment, electronic apparatus, measuring devices, etc. These standards also specify the main requirements for the quality of generated and transmitted electric power to consumers. At present, the parameters that require control to ensure quality performance are much more than the nominal voltage and nominal current.

4 Main Parameters of Electric Power Supply Quality Current regulations regulate the quality of electrical energy. In Ukraine, the standards are EN50160 (DSTU EN 50160:2014), GOST 13109-97 [37, 38]. However, in the current environment, there is a whole low number of parameters that must be controlled and they go beyond the indicators that can be defined as indicators of electric power quality. Therefore, it was suggested to introduce such a notion as the quality of electricity supply. First of all, it is due to the impossibility to achieve quality indicators of electric power in the “average” scheme of electric power supply. When determining the quality indicators of electrical energy, it is necessary to take into account the parameters of the source, the parameters of the distribution network, the parameters of the consumer. Therefore, the proposed indicators of electric power supply quality should be taken into account: – electric power sources (it is necessary to define the sources, the main source, and the supplementary source; to distinguish between sources that can be classified as

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sources of non-metric capacity and those that meet these requirements; to identify the sources by the generation system; to identify the power sources which can be considered as external; other parameters of the sources); – electric network (to determine parameters of the electric network; to determine parameters of the transforming equipment and distribution system); – customer parameters (to determine customer parameters, for example, impulsivity of consumption, deformation responsibility). From above review of the literature, it is clear that the list of parameters of electric power supply quality depends on a number of events, which take place in a disconnected electric system, for example, related to the emergency modes, The following are some physical phenomena, such as induced electromagnetic fields on lines and equipment of electric systems, weather phenomena, and others. The current norms regulate the quality parameters of electrical energy. Regulatory documents do not cover responsible events in the electrical system. For example, the loss of electric energy associated with an accident and post-war conditions, losses from the failure to meet the requirements of continuity, parameters of electric energy saving, which are strictly dependent on the parameters of the network and circuit solutions, as well as the interconnection of the elements of the network for mutual influence. The quality of the electric power supply may be affected by the proposed parameters of electric power supply quality. There was a need to standardize quality indicators not only electric energy but also additional parameters. Therefore, the decision was made to introduce power supply quality indicators. According to the main criteria used by the Council of European Energy Regulators (CEEC), they can be presented in three main aspects [39]. – reliability, security of electricity supply; – electricity supply voltage quality; – commercial quality of electricity supply. According to the European Union Directive 2009/72/EC [40, 41] on common rules for the internal market in electricity, EU member states have the right to control the activities of electricity utilities to meet their obligations regarding the security and quality of electricity supply, as well as to participate in the price regulation. Regulatory bodies in the electricity sector of these countries have to make a report on monitoring the current level of electricity supply security at least once every two years. These reports often contain information on the state policy in the energy sector and compliance with national legal acts with the international regulatory framework, Volume, and structure of generating capacities, including renewable energy sources, as well as plans for the development of main and distribution networks, which make it possible to meet the requirements of consumers. Thus, this directive only regulates the aspect of reliability, continuity, and security of electricity supply. Indicators of security of electricity supply characterize the availability of electricity to the consumer, and indicators of the quality of electricity supply characterize those properties of electricity that allow consumers to use it properly [39].

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We consider the quality of electrical energy as one of the elements of quality indicators of electricity supply. Thus, the performed measurements of electrical energy quality parameters can be considered in a wider range.

5 Analysis of Power Quality Parameters in the Power Supply System In order to study the quality of electric power (EE) in different modes of operation of electric power supply systems and technological equipment, we measured the indicators of electric power quality (IEQ). The measurements were carried out at the real objects of the Ukrainian energy complex in the plants with different levels of nominal voltage. Thus, the IEQ measurements at the power lines of 0.4, 35, 110, 220 kV were performed at the enterprises: plant “Pivdenkabel” in Kharkiv, Ukraine; traction substation No. 43 AT “Ukrzaliznytsia”; 220 kV substation “Azovska”; 330 kV substation of the Nevnichnaya Power System; at the inputs of the Institute of scintillation materials of the National Academy of Sciences of Ukraine; – 35 kV substation of Zhytomyrsky region. – – – – –

The measurements were made using IEQ instrument “Resource UF2” №1480, certificate of inspection №09-0414 dated 05.08.2009 (these measurements were performed from 2010 to 2012). The meter performs statistical processing of the results of the IEQ measurement in accordance with the methodology described in RD 153-34.0-15.501-00 and identifies the interval at the same time of the measurement of the following characteristics: – time duration of normal tolerance values in the time interval of the highest (index-I) and lowest (index-II) stresses; – time of exceeding the permissible limit values in the time interval of the highest (index-I) and lowest (index-II) stresses; – became the deviation of current values of a voltage of phase (δUa , δUb , δUc ), inter-phase (δUab , δUbc , δUca ) and direct consequence (δU1 ) of Unom ; – the largest deviations of actual values of the steady-state voltage in the interval of time of the highest (index-I) and lowest (index-II) stresses; – the smallest deviations of actual values of steady-state voltage in the interval of time of highest (index-I) and lowest (index-II) stresses; – upper intervals of δUy range, where 95% of measured values are in the interval of time of highest (index-I) and lowest (index-II) stresses; – the lower interval of δUy range, where 95% of measured values are in the interval of time of highest (index-I) and lowest (index-II) stresses;

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– – – –

Af—frequency shift; Af(nb) —the highest value of frequency deviation; Af(nm) —the lowest value of frequency deviation; Af(n) —lower limit of the range, within which 95% of the measured values of Af are found; Af(c) —lower limit of the range in which 95% of the measured values of Af are found; K0U , K2U —values of coefficients of non-symmetry of zero and negative sequence voltage; K0(nb) —the highest value of the voltage non symmetry coefficient at zero sequences; K0(c) —value of the coefficient of power non-symmetry on zero sequences, which does not exceed 95% of measured values; K2(nb) —the highest value of the voltage unsymmetric coefficient by the bellwether sequence; K2(c) —value of the coefficient of unsymmetry of the voltage by negative sequence, which does not exceed 95% of the measured values; KU —coefficients of coincidence of sinusoidally of inter-phase and phase voltage (KUa , KUb , KUc , KUab , KUbc , KUca ); K(nb) —the highest value of the voltage sinusoidal coefficient; K(c) —the value of the coefficient of coincidence of sinusoidal voltage, which does not exceed 95% of the measured values of KU ; KU(n) —coefficients of voltage hormones Ua , Ub , Uc , Uab , Ubc , Uca ; KU(nb) —the highest value of the coefficient of n-harmonic component of the voltage; KU(c) —value of coefficient n-harmonic component of the voltage, which does not exceed 95% of measured values.

– – – – – – – – – – – –

5.1 Electricity Supply Quality Measurement Results Results of electric power quality measurements in 35–220 kV substations (Fig. 1) are showed in Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 and 22. Results of Measurements at the 220 kV Substation See Figs. 2, 3, 4 and 5. Results of Measurements at the 110 kV Substation See Figs. 6, 7, 8, 9 and 10. Results of Measurements at the 35 kV Traction Substation See Figs. 11, 12, 13 and 14.

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Fig. 1 Schematic diagram of the main step-down substation

Results of Measurements at the 6 kV Substation of the Enterprise Institute of Scintillation Materials of the National Academy of Sciences of Ukraine See Figs. 15, 16, 17 and 18. Results of Measurements on 0.4 kV Buses of “Pivdenkabel” Plant See Figs. 19, 20, 21 and 22.

5.2 Conclusions on the Measurement of Electricity Supply Quality As a result of the conducted investigations, the attention was focused on the presence of harmonic components in the results. Causes of the occurrence of such storms were analyzed and the structural scheme is shown in Fig. 23.

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Fig. 2 Coefficients of sinusoidality of phase voltages (220 kV)

Fig. 3 Coefficients of n-th harmonic components of voltage 220 kV U a

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Fig. 4 Coefficients of n-th harmonic components of voltage 220 kV Ub

Fig. 5 Coefficients of n-th harmonic components of voltage 220 kV Uc

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Fig. 6 Coefficients of sinusoidality of phase voltages (110 kV)

Fig. 7 Coefficients of coincidence of sinusoidal voltage between phases

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Fig. 8 Coefficients of n-th harmonic components of voltage 110 kV U a

Fig. 9 Coefficients of n-th harmonic components of voltage 110 kV U b

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Fig. 10 Coefficients of n-th harmonic components of voltage 110 kV U c

Fig. 11 Coefficients of sinusoidality of phase voltages (35 kV)

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Fig. 12 Coefficients of n-th harmonic components of voltage 35 kV U a

Fig. 13 Coefficients of n-th harmonic components of voltage 35 kV U b

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Fig. 14 Coefficients of n-th harmonic components of voltage 35 kV U c

Fig. 15 Coefficients of sinusoidality of phase voltages (6 kV)

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Fig. 16 Coefficients of n-th harmonic components of voltage 6 kV U a

Fig. 17 Coefficients of n-th harmonic components of voltage 6 kV U b

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Fig. 18 Coefficients of n-th harmonic components of voltage 6 kV U c

Fig. 19 Coefficients of sinusoidality of phase voltages (0.4 kV)

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Fig. 20 Coefficients of n-th harmonic components of voltage 0.4 kV U a

Fig. 21 Coefficients of n-th harmonic components of voltage 0.4 kV U b

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Fig. 22 Coefficients of n-th harmonic components of voltage 0.4 kV U c

Fig. 23 Stirring in the energy complex, which leads to the appearance of harmonic components in the stream

All occurrences of wildfires are divided into external and internal. Causes related to human activity (anthropogenic) and those resulting from the activity of natural factors (natural) are attributed to external ones. Examples of anthropogenic external impacts include demolition of elements of the electrical complex, aggressive economic activities, vandalism, military actions, and others. The consequence of such activities is a violation of operating conditions. Occurrence of overcurrent modes, emergency, and post-emergency are the source of harmonic components.

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Examples of natural influences include weather conditions such as precipitation, ice, fog, hurricanes, seismic activity, animal activity, and others. The consequence of such actions is, as in the previous case, disruption of operating modes and, accordingly, the emergence of modes that are the source of harmonic components. Intrinsic causes include all processes of electric nature. This is the creation of a stream as a result of stream transformations in electric consumers (consumers) and all transformations in the energy equipment itself (energy equipment). Everything related to the consumer’s actions is caused by the characteristics of the electric consumers and their modes of operation. Obtaining harmonic components is linked primarily to the construction of electrical devices themselves of their electrical parameters and characteristics. Examples of these activities are inverters, pulse converters, electric motors of various designs, and other equipment. Harmonic components occur during the operation of such devices, which are based on the conversion of electrical energy into mechanical and other, or conversion of electrical energy into other types of energy and back into electrical energy. In terms of nuclear power, all the above parameters that influence the presence of harmonic components cannot be coordinated by any particular low level of measures. In addition, energy companies that supply electrical energy must deliver the highest possible quality product to the consumer. Therefore, the primary task for the electric power supply company is to bring the supply chain into such a state, to minimize the sporadic generation of power at the stage of conversion and transportation. For companies engaged only in the distribution and supply of electric energy, the question of coherent energy supply is a topical issue, as confirmed by measurements at actual energy facilities. Elements of electric power supply systems have a significant length and also significant parameters of wear. In this chapter, we consider only such NPSEs which are connected with the presence of corona discharge. One of the effects of the corona discharge is harmonic components. In Fig. 23 the corona discharge is presented as a proximity factor. And it is shown that this variable factor can also be influenced by natural factors. For example, volatility in the heating medium changes the corona discharge jet, and accordingly the power of harmonic components changes. Let us briefly describe the influence of corona discharge on the parameters of the electric power supply in next chapters.

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26. Glavitsch, H., Stoffel, J.: Automatic generation control. Int. J. Electr. Power Energy Syst. 2(1), 21–28 (1980) 27. Bakken, B.H., Faanes, H.H.: Technical and economic aspects of using a long submarine HVDC connection for frequency control. IEEE Trans. Power Syst. 12(3), 1252–1258 (1997) 28. Brumshagen, H., Schwarz, J.: The European power systems on the threshold of a new East-West co-operation. IEEE Trans. Energy Convers. 11(2), 462–474 (1996) 29. Flassbeck, W., Liegl, K., Hofbauer, F., Ritcher, W.: Availability and Reliability of the 600 MW HVDC Back-to-Back Stations. Etzenricht/Germany and Vienna Southeast/Austria (1996) 30. Heijungs, R., Suh, S., Kleijn, R.: Numerical approaches to life cycle interpretation-the case of the Ecoinvent’96 database (10 pp). Int. J. Life Cycle Assess. 10, 103–112 (2005) 31. Owen, E.L.: The origins of 60-Hz as a power frequency. IEEE Ind. Appl. Mag. 3(6), 8–14 (1997) 32. Rosheuvel, F.: Changing Curacao’s Electric Supply from 50 Hz to 60 Hz. An Integral Economic Perspective (2019) 33. Johnson, D.O., Hassan, K.A.: Issues of power quality in electrical systems. Int. J. Energy Power Eng. 5(4), 148–154 (2016) 34. Buck, J.: International electrotechnical commission. In: Handbook of Transnational Economic Governance Regimes, pp. 573–584. Brill Nijhoff (2010) 35. Büthe, T.: Engineering uncontestedness? The origins and institutional development of the International Electrotechnical Commission (IEC). Bus. Polit. 12(3), 1–62 (2010) 36. Ramos, V., Ringwood, J.V.: Exploring the utility and effectiveness of the IEC (International Electrotechnical Commission) wave energy resource assessment and characterisation standard: a case study. Energy 107, 668–682 (2016) 37. Start, D.J.: A review of the new CENELEC standard EN 50160. In: IEE Colloquium on Issues in Power Quality, pp. 1–4. IET (1995) 38. Masetti, C.: Revision of European Standard EN 50160 on power quality: reasons and solutions. In: Proceedings of 14th International Conference on Harmonics and Quality of Power-ICHQP 2010, pp. 1–7. IEEE (2010) 39. Zharkin, A.F., Novsky, V.O., Palachov, S.O.: Technical regulation of voltage quality in electrical grids with sources of distributed generation. Tech. Electrodyn. 3, 55–57 (2016) 40. Grimm, N.S.: The Shift of Energy Regulatory Powers Under the Framework of Directive 2009/ 72/EC (2011) 41. Network, S.L., Roggenkamp, M., Winter, H., de Vries, F., Mauger, R.: Assessing the Independence and Effectiveness of National Regulatory Authorities in the Field of Energy (2019)

Influence of Corona Discharge on Electric Power Supply Parameters Yevgen Sokol , Vitalii Babak , Artur Zaporozhets , Oleg Gryb , Ihor Karpaliuk , and Oleksiy Luka

Abstract The chapter considers corona discharge as one of the factors of changes in electric power supply quality parameters. It is shown that corona discharge results not only in non-short losses of electric energy but it interferes with the transmission of high-frequency signals, disturbs isolation elements, can become a source of conditions for arcing diode occurrence, and is one of the factors of change in continuity. The analysis of the literature shows that the corona discharge exists under normal modes of operation of the system, and its intensity depends on the parameters of power supply systems, as well as on external factors, such as rain, snow, frost, fog, hoarfrost. Attention is paid to the correlation between the corona discharge and the deterioration of quality indicators of power supply. Keywords Corona discharge · Power supply systems · Protection · Power losses · Weather conditions · Rain · Snow

1 Introduction The influence of corona discharge on parameters of electric power supply can be in several manifestations (Fig. 1). Overhead power lines (OPLs) as a part of the power supply system are used as a channel for high-frequency connection. High-frequency connection (HFC) is a complex of technical devices, which use darts of high voltage lines of energy complexes for the transmission of information Y. Sokol · O. Gryb · I. Karpaliuk · O. Luka National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan, Taiwan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_2

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Fig. 1 Influence of corona discharge on electric power supply

[1–5]. HF receivers are installed at the ends of lines. The principle of operation of high-frequency connections is in the transmission of modulated electromagnetic waves on the wires and cables of high-voltage lines. HF connection is a strong source of interference to radio connection systems, but it is also sensitive to the influence of many strong electromagnetic fields, including the corona discharge of high-voltage lines. HF connection is also used for transmission of telephone and dispatching information, data control systems and telemechanics, organization of relay protection systems and automation (RPA), anti-damage automation (ADA). This important value is the correct (reliable) transfer commands acceleration and blocking protection, simulated current signal of high-frequency protection. Failure in the high-frequency connection in the lines of power systems through corona discharge leads to incorrect actions of the RPA, which leads to significant material losses and technical losses. High-Frequency (HF) Protection (HFP) is a fast-acting protection device for lines over 1 kV [6–9]. It is used for quick disconnection of the line in case of short circuit at any of its points to ensure the continuity of parallel operation of power plants and power systems in general, as well as due to increasing demands from customers to preserve the continuity of the technological process [10–13] (Fig. 2). HFP is composed of two sets placed at the ends of the lines to be protected [10– 13]. The peculiarity of HFP is that for its selective action it is necessary to have a connection between the protection sets, which are carried out HF currents, which are transmitted through the wires of the lines to be protected. By the principle of their action does not react to short circuit beyond the lines that are protected and thus, as well as differential relay, do not have a window of time. Three types of

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Fig. 2 Functional diagram of high-frequency protection: Q1, Q2—switches, CT—current transformer, BF—barrier filter, VT—voltage transformer, C—capacity, RF—receiver filter, MP— measuring part, LP—logical part, RT—receiver-transmitter

HFP are used: directed RPA with HF-blocking, based on the correlation of voltage signs of the power at the ends of the protected OPLs; phase-differential HFP, based on phase comparison of short-circuit currents at the line ends; combined conjugate and phase-differential HFP, which combine both of the above-mentioned principles. In connection with the mentioned features, the rewired RPA is composed of two parts—relay and high-frequency. Differential-phase protection matches the phases of the currents at the ends of the protected line. When a short circuit occurs in the protection zone, the currents at the ends of the line are matched in phase, but when a short circuit occurs behind the protection zone, they are tilted by 180°. During the positive momentum in the line, the transmitters work at both ends of the linework and send the alarm signals to the receivers of both their own and the opposite ends. The transmitters do not work during the negative forward flow period, therefore, there are no alarm signals and the protection can work. If the damage occurred outside the protection zone, the phases of the currents at the ends of the line are shifted by 180° and the positive intrinsic coils of these currents do not converge in time. So, during one penetrant will work the left transmitter in the second—the right, thus, the line will continuously be the high-frequency signal, which blocks (prevents action) protection at both ends of the line. When a short circuit is in the protection zone, for example, at point K1, the phases of the currents are the same, and their positive overhangs at the ends of the line in time to converge. Therefore, two transmitters will operate simultaneously during one penetration period and will not operate during the other one. The high-frequency signal in the line will be intermittent with pauses after each industrial frequency interval. During the pauses, the blocking signal will disappear and the protection at the ends of the line will turn on the corresponding taps. The TV disconnection system is used in cases where the protection zone of Q2 and Q3 is smaller than the distance between the ends of the line to be protected. If, for example, point k1 is near the left end of the line, on switch Q2 its protection will be switched off, but the protection on switch Q3 in this case will not work through

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a lack of sensitivity. The TV switch system corrects this defect. When protection is activated on one end of the line, a transmitter of this protection comes into effect and transmits a signal to the other end of the line which causes disconnection of the switch, protection of which has not worked. Such a system is used in the protection of the device of contact networks, and as a line of connection channels are used telemechanics. In this case, the receiver operates at a fixed frequency in the range of 2–3 kHz. Thus, the negative influence of corona discharge on high-frequency protection systems is shown.

2 Description of Corona Discharge and Its Peculiarities in Power Supply Systems 2.1 Forms of Corona Discharge and Loss of Energy Corona discharge is a type of spontaneous discharge which occurs in air (gas) medium at atmospheric pressure. A necessary condition for corona discharge occurrence is the significant inhomogeneity of electric field, which is characteristic for non-isolated stream-forming parts of high voltage electric equipment [14–18]. The zone of elevated gradients of potential is mainly located on a small distance in the narrow space near the surface of electrodes with a small radius of curvature. Due to this fact, when the discharge voltage at a certain level of potential difference is sufficient for initiation of the discharge is inherent and the discharge occurs [17, 18]. In the zones of discharge interruption, apart from the processes of ionization and excitation of neutral atoms and molecules, ion decay, recombination processes take place as well. Recombination is accompanied by the release of electromagnetic impromptu. And photons as a result of recombination can belong to both infraredwave, visible and short-wave parts of the spectrum. The light, which creates a halo near the surface of the corona electrodes, gave the name to this type of electric discharge. The external appearance and structure of the ionization zone light depend on the polarity and shape of the voltage applied to the corona electrode, as well as the size, shape, and state of the surface of this electrode. According to Kaptsov [19], the entry of negative ions from the interfacial coronation balloon into the outer region of the negative corona is in the form of single, relatively intense pulses. These pulses are concentrated at coronagraphs and are accompanied by the generation of less intense electric wind, which leads the gas near the ionization zone to turbulent flow. Thick wires (with a radius of about a centimeter), together with a homogeneous covering, may also have streamer channels [20–22], which lead to the occurrence of powerful current impulses and radio emission, the level of which significantly exceeds the level of radio interference from negative corona. The streamer form of

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the corona plays a significant role in the transition of the corona discharge to a spark discharge [23–25]. On the corona-covered sections of the wire surface, there are either continuous coronal coverings or streamer channels at different points in time. During the presence of a coronal covering on this section of the wire surface, the corona is continuous. Disruptions of this continuity, both in time and in space, are caused by the appearance of streamer channels. Here we are considering only the corona discharge at industrial frequency voltage. The processes in the outer zone in this case have a number of common features with both transient unipolar corona and bipolar corona of direct current [26–28]. Based on the known spatial distribution for different moments in time, the volumetric charge density and electric field strength can be determined for all these time distribution moments. From these, the distribution of active power losses caused by the movement of positive and negative ions can be determined: } p+ (r ) = p+ · k+ ·E 2 . p− (r ) = p− · k− · E 2

(1)

Integration of the received dependences on the volume in which the ions are located allows determining the total power loss for that moment: {r2 p(ti ) = 2π

[

] p+ (r ) + p− (r ) r · dr,

(2)

r1

where r 1 , r 2 are radii of the lower and upper intervals of the region filled with ions at a given moment. The curve p(t) for the third half a period after switching on the voltage is shown in the left-hand graph (Fig. 3). There the curve of energy loss for the corona as a function of time is also given, i.e.: {t E(t) =

p(t)dt.

(3)

0

The curve in Fig. 3a, which characterizes the change in the time of energy loss by the corona E, shows that the “time” of 95% E loss is 6.6 ms or 2/3 of the half period. The time of 90% E loss appears to be 5.7 ms, which is only three times longer than the duration of the quarter and practically corresponds to the time of corona burning at the dart during this intra-period. Figure 3b shows radiuses of areas corresponding to different shares of power losses for the corona, the total mittens values of which are determined by curve p of the left graph of the same figure.

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Fig. 3 “Time” (a) and “radius” (b) losses

2.2 General Characteristics of the Power Loss on the Corona Losses of capacity on the corona are determined by the expression: 1 P= T

{T

1 q · du = T

0

{T qk · du,

(4)

0

where qk is the compensating charge. At sinusoidal frequency pressure ω: P=

ωQ k.max Umax k1 cosϕk1 , 2

(5)

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31

Fig. 4 Corona power loss characteristics in cylindrical condenser for mole drums of different diameters: 1–0.6 mm: 2–2.95 mm; 3–6 mm

1 where k1 = QQk.max ; ϕ k1 —angle of deviation of the first harmonic of the “compensated” stream to the voltage; Qk.max —the amplitude of the “compensated” charge; Q1 —the amplitude of the first harmonic of the “compensated” charge. In Eq. (5) the values Qk.max , k 1 , cosϕ k1 depend on the voltage. After the dependence between Qk.max and U max , P has been determined:

P = ωC 2

Umax (Umax − U0 ) k1 cosϕk1 · . 2 CE − C

(6)

Corona power loss characteristics for the area of the general corona are straight lines. These characteristics are shown in Fig. 4 based on experimental data of power loss measurements in a cylindrical condenser with an outer cylinder diameter of 2 m and corona discharge diameters of 0.6, 2.95, and 6 mm. The transcription of the matured characteristic with the voltage value determines, according to Eq. (6), the critical voltage of the total corona U 0 . In the case of smooth wires with ideal surface conditions, the ratio U o /U on can be considered as a characteristic of surface roughness (coefficient of smoothness). However, in the presence of surface contaminants and damage, it can also serve as a characteristic of surface roughness. Therefore, reducing the power loss characteristics of corona can be used to study the influence of various factors on a crucial parameter of corona discharge, such as the critical voltage of general corona [29, 30].

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3 AC Corona in Bad Weather Conditions of Various Types 3.1 Power and Energy Losses Per Corona During Rainfall Various atmospheric phenomena—rain, snow, fog, increased air humidity, rain, frost, and ice—significantly affect the corona discharge of power lines, resulting in an increased level of power loss to the corona (compared to this level for normal weather conditions). The influence of rain lines on the corona is the most studied [31–36]. An analysis of a large number of experimental characteristics of the corona power loss in rain has shown that the developed characteristics for different densities and intensities of rain and different values of the atmospheric relative permittivity are truly linear. As an example, Fig. 5 demonstrates some mature corona power loss characteristics of AC-150 mol by means of measurements. Characteristics for daylight conditions are really manifested by linear functions of voltage. They are deviated in the direction of less tension in comparison with the characteristic of smooth weather and to a greater extent, the greater the intensity of the light. The latter point to the dependence of the critical corona voltage in the rain on its intensity. Another noteworthy feature of the mature corona power loss characteristics at daytime, in comparison with the characteristic for the good Fig. 5 Corona power loss characteristics of AC-150 for different conditions: 1—warm weather (δ = 0.91); 2—rain with an intensity of 1 mm/year (δ = 0.895); 3—rain with an intensity of 3 mm/year (δ = 0.895); 4—rain with an intensity of 30 mm/year (δ = 0.875)

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Fig. 6 Dependence of weather coefficient on intensity of rain: 1—Cable AC-150 (δ = 0.875– 0.915); 2—Cable ACS-300 (δ = 0.811–0.834); 3—Cable ACS-710 (δ = 1.02); 4—Cable 2XACO2801 (δ = 0.97); 5—Cable 3xACO-230/300 (δ = 0.98); 6—Cable 3xACO-400/400 (δ = 1.0)

weather, is their significantly lower magnitude and, consequently, lower values of the coefficient bp . By extending the reduced characteristics to intersect with the voltage axis, the voltage at that intersection point is determined, which is called the critical corona voltage under rainy conditions (U 0r ). The ratio of these determined values to the initial corona voltage under fair weather conditions yields the weather coefficient for rain. The critical corona voltage for fair weather conditions is determined by the air density, wire geometry, and the coefficient of surface smoothness. The surface smoothness has less significance under rainy conditions, and its inclusion in determining the weather coefficient introduces some uncertainty. Therefore, the weather coefficient for rain is determined by relating the found values of U 0r from the reduced characteristics to the critical corona voltage, which is computed using the Peek’s formula for smooth wires with an ideal surface [37–39]. The results of determining the weather coefficient for rain for individual and stranded wires of various radii and for different values of relative air density are presented in Fig. 6. In Fig. 6, the intensity of rain is limited to 36 mm/year. The curve in Fig. 6 should be regarded as a generalized dependence of the weather index in rain on the intensity of rain for these ditches of practical sizes. Another element necessary for the calculation of power loss and energy loss to the corona is a generalized characteristic of the power loss to the corona. Cable characteristics shown in Fig. 7, as well as conditions under which these characteristics are obtained, are shown in Table 1. Figure 7 shows 12 characteristics of power loss on the corona in conditions of rain. For an area U/U 0r > 1, which can be nominally called the region of the general corona, the characteristics for the most different recalculated conditions coincide. This proves that the applied generalization correctly takes into account all the main factors determining the course of the corona power loss characteristic under conditions of rain, exactly as it was for the good weather.

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Fig. 7 General characteristic of power loss on the corona under daylight conditions

Table 1 Power and energy losses per corona at different intensities Cable (Fig. 6)

δ

AC-150 (1)

0.895

1.0

J, mm/year

Cable

δ

2HASO-280/700 (7)

0.970

J, mm/year 0.54

AC-150 (2)

0.875

36.0

3XACO-280/300 (8)

0.980

9.00

ASU-300 (5)

0.834

0.6

ZHASU-400/300 (9)

0.985

25.00

ASU-300 (4)

0.828

2.3

ZHASU-500/400 (10)

1.000

0.30

ASO-710 (5)

1.020

0.4

ZHASU-400/400 (11)

1.000

3.00

ASO-710 (6)

1.020

0.8

ZHASU-400 400 (12)

1.000

73.00

For the area of local corona U/U 0r < 1, there is a variability of some characteristics. Among other reasons, the structure of the rain (the size of the droplets) can be of importance. From it the measure of change of trajectory of their fall and corresponding power inputs which always at the expense of the electric field forces take place in the nearest periphery of the shot which is under pressure depend on it. The size of the droplets due to the uniqueness of their falling trajectories determines the coefficient of the capture of the rain droplets by the wind, and consequently, the intensiveness of the entry of water onto the wind-blast surface and, consequently, to some extent, the intensiveness of the corona. And, finally, the intensity of corona generation and its intensity on the droplets passing near the drone surface can depend on the size of the droplets. The above causes can manifest themselves to the greatest extent in the area of the local corona, for which the absolute value of the coronal

Influence of Corona Discharge on Electric Power Supply Parameters

35

power loss is low and due to this change in the above-mentioned components of the loss, which are, presumably, relatively small in value, can lead to an appreciable increase in the total characteristics. An important parameter of power transmission lines is the ratio between the operating voltage and the critical corona voltage on the winding for good weather conditions. The selection and adjustment of this correlation are actually one of the main tasks of corona control when designing the line. Therefore, it seemed reasonable to calculate the resultant characteristics of the average corona power losses at the wind power in the form of dependences on the ratio of the operating voltage to the critical corona power for the conditions of the good weather—the unreasonable overloading of the good weather [40]: n pc =

Up , U0x y

(7)

where U p is the operating line voltage; U 0xy is the critical corona voltage, which is determined by means of the Peek’s formula at the smoothness coefficient of the cable, equal to 1. For different values of npc , based on the generalized dependence of the weather coefficient of nr (Fig. 6), the actual overload at these operating voltage levels for any intensity can be found: n=

n pc Up = . nr U0 pc

(8)

Based on the values of n and the generalized characteristic of power loss to the corona for each fixed value, which is, in this case, a constant parameter, the dependence of power loss to the corona in definite units on the intensity of the rain was calculated: P ∗ = f (J ).

(9)

Similar dependencies for intensities of rainfall up to 5 mm/year for several values of npc are shown in Fig. 8. The peculiarity of these curves consists of the sharp increase of losses in the initial area (for J = 0 (5–1 mm/year)) and then in their gradual increase with the increase of intensity above the indicated values. A generalized distribution function for the intensities of rain for a given number of precipitation H, mm, and their total duration h, i.e. for a given average intensity of rain for a period of days: Jav =

H . h

(10)

It allows to determine the relative duration of daylight Ahi /h for intensities intervals from J i to J i+1 .

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Fig. 8 Dependence of corona power loss in relative units on the intensity of rain for different npc

3.2 Power and Energy Losses Per Corona Under Snow Conditions An analysis of a large number of meteorological observations of the intensities of rain and snow showed that the overall distribution functions of the intensities of these atmospheric phenomena practically coincide. Thus, the curve in Fig. 8 can be used to calculate the coronal energy loss during snowfall as one of the generalized initial characteristics. The comparison of characteristics for rain and snow of approximately equal intensities shows that the dependence of weather coefficients on the intensities of rain and snow can be assumed to be approximately the same. Another generalized characteristic, necessary for calculations, is the dependence of power loss on the corona on the full overloading. Such a generalized characteristic of power loss to the corona in snow, based on practical measurements, is shown in Fig. 9. Cables, characteristics of which are shown in the graph, as well as air pollution, at which these characteristics are obtained, are shown in Table 2. The analysis of the matured characteristics of the power loss to the corona under snow conditions shows that, as in the case of rain, to correspond to the calculated

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37

Fig. 9 General characteristics of power loss by the corona in snow conditions

Table 2 Air grades and wire grades (for Fig. 10) Cable (number in the figure)

δ

Wire

δ

AC-150 (1)

0.955

3xASU-300/400 (7)

1.050

AC-150 (2)

0.959

3xASU-300/400 (8)

1.067

AC-150 (3)

0.975

3xASU-300/400 (9)

1.090

ASU-300 (4)

0.848

3xASO-480/600 (10)

1.052

ASU-300 (5)

0.863

3xASO-480/600 (11)

1.070

ASU-300 (6)

0.872

3xASO-480/600 (12)

1.070

and studied values of bp coefficient it is necessary to decrease approximately 2 times (in correlation with the conditions of normal weather) the value of the volatility of charge carrier, that is to take its equal to 1–1.1 cm2 /(V-c). The calculated curves of the corona-free average power loss during snow cover for four values of average snow intensity (0.1; 0.15, 0.2; 0.25 mm/year) in Fig. 10 (also see Table 3). The values of average snow intensity calculated correspond to the range of snow intensity determined from meteorological data. It should be noted that the average intensity of snow is significantly lower than the average intensity of rain.

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Fig. 10 Dependence of average values of power loss to the corona in terms of units in terms of nxy for different average values of snow intensity. 1—J = 0.25 mm/year; 2—J = 0.2 mm/year; 3—J = 0.15 mm/year; 4—J = 0.1 mm/year; hyphen—snow; spaced hyphen—rain

Table 3 Crown losses during snowfall Cable

Ul.cf. kV

hc , hh

Hs , mm

JCP, mm/year

Energy consumption, kWh/km Experience Aop

Calculation Ar

Ar /Aop

3xASO-330/ 400

498

1035

153

0.148

21,047

17,600

0.835

3xASO-480/ 400

482

295

63.2

0.214

1483

1870

1.26

3.3 Energy Losses for Flicker Corona During Bad Weather of Other Species An increase in the level of power and energy loss to the corona on high voltage power line rods is caused not only by rain and snow but also by several other atmospheric phenomena: increased air humidity, fog, frost, frost, and ice. Long and systematic studies of the corona power losses on the derricks of operating 500 and 750 kV power transmission lines have shown, Corona power losses increased in comparison to fine weather are regularly observed under increased air humidity and fog, and, therefore, these atmospheric phenomena should not be classified as fine weather. Systematic registration of the increased losses under conditions of increased air humidity allows us to assume that the increase in losses is related not only to the deposition of moisture on darts but also to some other physical mechanism. Because of the absence of visible precipitations and normal operating load, the corona on the high-tension line derricks exists only in some points of the derricks

Influence of Corona Discharge on Electric Power Supply Parameters

39

where there are some irregularities on their surface (underpants, breaks, etc.). As shown by laboratory observations and photographs of corona lines, a streamer corona exists in these conditions on the heterogeneities in the positive voltage periods. The initial voltage of the general corona due to the presence on the dart surface of individual irregularities, on which the so-called local corona is formed, decreases due to the influence of the total charge (generated by the local corona) on the parts of the dart surface, located in the outskirts of irregularities. This action of the total charge established during the preceding intensification period leads, as is known, to the strengthening of the field on the dart surface during this intensification period, which can lead to corona formation on the parts of the dart surface adjacent to the irregularities as well. When the volumetric charge, which is generated by the local corona, is increased, the zone of its action near the dart surface expands. Since the increased volatility contributes to the intensification of the streamer corona on irregularities and increase of the corona volumetric charge, we should expect the zone of its action to expand and the corona to arise in the core areas adjacent to the irregularities of the dart surface. The very intensification of the streamer corona on inhomogeneities accompanied by an increase in mean jets will cause an increase in the corona power loss. The action of an increased volumetric charge on the neighboring areas of the inhomogeneous dart surface and the occurrence of a corona on them will further contribute to an increase in the corona power loss. Proceeding from the above, as well as taking into account the lack of necessary general characteristics for fog, as well as for the case of increased air humidity, it can be argued that the determination of the level of power loss and energy loss to the corona is still possible only experimentally. A similar statement can be found for several other atmospheric phenomena related to negative weather. For example, there are no data for wet snow required to derive the dependence of the weather coefficient on the intensity of the precipitation. This is since in wet snow there can be balls on the droplets, which are axed and differ significantly in structure, thickness, and time of occurrence from the covered balls in the case of rain and dry snow. The influence of the intensity of ground precipitation—frost, frost, and ice—on the coronation of the lines is also unidentified. There is no function of distribution of intensity of deposition of these types of precipitation and moreover the dependence of the weather coefficient on intensity. One characteristic that can now be determined from experimental data for the corona under the above types of ground deposition (primarily for frost) is a generalized characteristic of the power loss to the corona. The characteristics were also obtained for different darts, the types of which are shown in Table 4, the row numbers of which correspond to the curve numbers in Fig. 11. Characteristics 6–10 had no known values of air purity, therefore air purity was assumed to δ > 1, as a constant air purity for low elevation regions under frost conditions sometimes amounted to 1.07–1.14 [41]. Comparison of the graph in Fig. 11 with the analogous curve for rain (Fig. 7) shows that they are practically the same but differ from the characteristics for dry snow and fine weather.

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Table 4 Values of atmospheric permittivity under frost conditions for different types of drought (to Fig. 11) Curve in Fig. 11

Cable

δ

Curve in Fig. 11

Cable

δ

1

AC-150

0.990

7

2xASA-400/300

>1

2

AC-150

0.997

8

2xASO-330/400

>1

3

ASU-300

0.822

9

3xASU-400/400

>1

4

ASU-300

0.878

10

4xASO-700/600

>1

5

ASU-300

0.912

11

3xASO-700/1000

1.06

6

ACS-400

>1

Fig. 11 General characteristics of power losses per corona under frost conditions (to Table 4)

The characteristic features of different types of bad weather show that weather disturbances such as rain, snow, fog, and frost. Frost leads to the change of corona discharge modes and as a result—to the increase of the corona discharge current, i.e. to the increase of the energy which the current discharge consumes and to the increase of the energy of the green harmonic component.

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41

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Detection of Corona Discharge in Power Supply System Yevgen Sokol , Vitalii Babak , Artur Zaporozhets , Oleg Gryb , Ihor Karpaliuk , and Yevgen Kaurkin

Abstract Chapter deals with the issues related to the detection of corona discharge on the elements of the power supply system. The methods of corona discharge detection by different types of medium stirring are investigated: by ultraviolet radiation, by infra black sea radiation, by the present electromagnetic background, by the presence of a chemical compound, and by detection of corona discharge by the method of fixation acoustic radiation. The description of the processes in the corona discharge, which are the sources of acoustic radiation, is given as the origin of the ionic current and the stream of displacement in the outer corona discharge zone. The experiments on the acoustic radiation of the corona discharge were carried out. The results of acoustic measurements are presented. The results of acoustic signals processing of the corona discharge are presented. Keywords Corona discharge · Detection · Power supply system · Ultraviolet radiation · Infrared radiation · Chemical compounds · Noise · Electromagnetic field

1 Different Types of Environmental Disturbance by Corona Discharge Quality indicators of electric power at the presence of extinction factors in electric power supply systems as a result of the occurrence of corona discharge will change. As shown in the previous section, the corona discharge consumes energy, i.e. a Y. Sokol · O. Gryb · I. Karpaliuk · Y. Kaurkin National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_3

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corona discharge current appears, which includes a reactive component [1–3]. As a result, a current of reactive nature appears in the network, which changes the performance indicators of electricity. The frequency structure of the corona discharge includes different harmonics. Many investigators have documented that in the corona discharge on high-voltage lines there are the third and fifth harmonic currents [4–10]. Currents of these harmonic devices have a reactive composition. This indicates that the corona discharge is the source of the voltage and current coexistence. One of the components of low-quality electrical energy is the presence of faulty interference in the electricity supply system [11, 12]. The sources of high harmonics are traction power stations of mainline electric transport and other non-linear and nonuniform elements of structures of electric power supply system objects. In addition, high harmonics increase the likelihood of corona discharge occurrence in characteristic places of electric power supply systems. Corona discharge itself spots the voltage and flow curve in the electrical supply systems. The two mentioned factors are connected, the appearance of high harmonics leads to the corona discharge, and the corona discharge in its turn leads to the appearance of high harmonics [4, 5, 13–16]. Therefore, the determination of the location of corona discharge on high-voltage lines is an urgent issue in the development of diagnostic equipment [17–24]. Indirect detection of corona discharge occurrence by electric parameters: the form of stream and the form of voltage is problematic for making direct measurements on the lines because it is not a simple task to operate the equipment at high voltage values. Moreover, the value of corona discharge streams in the local place is insignificant and it is not always possible to perform measurements with high accuracy to detect only corona discharge streams, or to perform such measurements only when high-precision devices are used. The electric supply system always has a significant number of flow meters, which leads to obtaining unprecedented results. Such measurements and devices are very expensive. Therefore, the developers go by the way of determining the presence of the corona discharge by other (indirect) parameters. As it was shown in the previous chapter, the corona discharge consumes energy which is converted into other kinds of energy (or into chemical combustibles) and is left in the backspace (Fig. 1). Corona discharge has been investigated by various scientists for a long time [1, 7, 14, 16, 25–27]. Particular attention was paid to corona discharge in high-voltage lines [1, 2, 7, 20–22, 28–30]. The power loss occurs due to corona discharge when electric energy is transformed and transported. Therefore, electric parameters of corona discharge are well studied. For high-voltage and extra-high-voltage lines, direct measurements of corona discharge parameters have a significant disadvantage, namely due to the inadmissibility of high voltages. Therefore, several attempts were made to diagnose the presence of corona discharge by concomitant strokes, which accompany the corona discharge. Figure 1 shows the external stagnation from the corona discharge grouped by type of energy. Electromagnetic disturbances in the external environment are included: – optical radiation in the ultraviolet spectrum;

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Fig. 1 Energy of corona discharge in the medium

– optical radiation in the infrared-wave spectrum; – electromagnetic background. The devices for the detection of corona discharge occurrence control have been developed based on such radiation solutions.

2 Ultraviolet Radiation of Corona Discharge For carrying out optical detection of corona discharge by radiation in the ultraviolet range there have been developed a lot of devices [31–37]. They all share a common principle. It is necessary to register UV radiation on objects where its natural occurrence is not possible—on the elements of the energy complex. The spectrum of corona discharge radiation looks as follows Fig. 2.

Fig. 2 Spectra of corona discharge and Sonz Spectra

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Fig. 3 External view of UV-260 device for optical detection of corona discharge in UV range

As it can be seen in Fig. 2, the spectral intensity of the Sun’s radiation outshines the spectral intensity of the corona discharge radiation. Therefore, the best time for carrying out the recognition is the time of the week when the solar impulse is absent. Such a request greatly limits the use of this method. However, corona discharge has the range 240–280 nm where the corona discharge spectrum does not overlap. Therefore, modern devices for the detection of UV emission are set up for such a spectrum. For example, the equipment of the Polish company SONEL (https://sonel.ua/). Figure 3 shows the UV-260 corona discharge registrar (optical ultraviolet range). Table 1 shows the device parameters. When such a spectral range is used for recognition, recognition devices can be used during the day. But the power of corona discharge radiation in this range is insignificant. This leads to the use of expensive optical devices and signal amplifiers. Figure 4 shows the results of corona discharge fixation by UV-emission conducted by Chinese State Grid Corporation [http://www.ee.co.za/article/corona-dischargedetection-using-ultraviolet-imaging-camera.html]. Therefore, the shortcomings of corona discharge recognition by ultraviolet impregnation come out: – background illumination (in which it is impossible to distinguish optical splashes from corona, for example, solar radiation); – low energy corona discharge bursts (sensitive optical sensors); – presence of optical disturbances (most often corona discharges occur during rain, fog, or snowfall); – display can only be used at short distances (up to ten meters).

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Table 1 Parameters of the device SONEL UV-260 Parameter

Value

Image

Monochromatic

Discharge color

White, black, blue

Minimal sensitivity of ultraviolet light

3 × 10–18 W/cm2

Minimal value of detected discharge

1.5 pC at 8 m distance

Spectral range of ultraviolet imaging

240–280 nm

Field of view (W × S)

5.5° × 4.0°

Focusing

Automatic or manual

Focus range

More than 2 m

Detector durability

Not prone to wear

Power frequency

50/60 Hz

Visible image parameters Image

Full color

Accuracy of summation of UV/visible images

More than 1 milliradians

Minimum sensitivity

0.1 lx

Scale

26× optical and 12× digital

Display

5.7'' VGA TFT, touchscreen

Video standard

PAL/NTSC

Video modes

Mixed (UV + visible)/only UV/only visible

3 Infrared Radiation with the Presence of Corona Discharge When the corona discharge occurs, thermal phenomena also occur. For example, heating of electrodes on which the corona discharge is formed. Such heat can be detected by a thermal imager [38–42]. For example, the Fluke thermal imaging cameras (Fig. 5). The device parameters are shown in Table 2. Photographic images (Figs. 6 and 7) in the infrared range were taken at the substation of Kharkivoblenergo. These methods fixation of corona discharge appearance have shortcomings of corona discharge detection by infrared radiation: – background illumination (significant thermal background can illuminate the corona discharge zone); – presence of optical obstacles (presence of visual obstacles in the field of vision, weather conditions hindering infrared recognition); – display can only be used at short distances (up to ten meters).

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Fig. 4 Corona discharge photos made with UVSee TD90 device for corona discharge fixation in UV range

Fig. 5 Fluke TiX580 thermal imager

4 Electromagnetic Field Created by Corona Discharge At the appearance of corona discharge conversion of electric energy into energy of electromagnetic radiation occurs. Corona discharge can be identified by created spectra of electromagnetic radiation [3, 13, 43–49]. But it is not possible to record the exact spectrograph of corona discharge. Radiation in the indicated frequency range strongly depends on external factors, for example, the presence of insects. And it

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Table 2 Fluke TiX580 parameters Name

Value

Measured temperature range (NOT calibrated below −10 °C)

−20 to +1000 °C (−4 to +1832 °F)

Accuracy

±2 °C or 2% (at a nominal temperature of 25 °C, select a higher value)

Thermal sensitivity (thermal equivalent of noise NETD)

≤0.05 °C at 30 °C (50 mK)

Coefficient of impression on the screen

Yes (according to the set values)

Temperature compensation of the background display on the screen

Yes

Adjusting the transmission ratio on the screen

Yes

Line marker in real time scale

Yes

Fig. 6 Outlets in a 110 kV substation

is not possible to predict such a state. At the same time, it is possible to create a comparable radiation electromagnetic noise from the overhead power lines (OPLs) in the ideal state and to compare it during the occurrence of disturbances, which include corona discharge. For RD-50-723-93 type frequency spectrum is given. Figure 8 shows the radio shield profiles that create corona discharge on OPLs of some types (measuring frequency 0.5 MHz). Based on the provided profiles of radio interference, the disadvantages of the method can be formulated as follows:

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Fig. 7 Stream transformers in a 110 kV substation

Fig. 8 Typical frequency spectrum of radio interference fields created by OPL (left) and the profiles of radio interference for OPLs (110–220–330 kV) (right): 1—during heavy rain; 2—average values during good weather

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– The method has low accuracy in identifying corona discharges on OPLs. – The method is not designed to recognize corona discharges on elements of the power system other than the lines. – The method does not allow determining the coordinates of corona discharges.

5 Chemical Compounds Created by Corona Discharge Corona discharge is not only a harmful phenomenon; it can be utilized in various applications. There are several directions for the use of corona discharge. For example, one of the first industrial applications of corona discharge was the development of an apparatus by F. G. Cottrell for air filtration from sulfuric acid vapor [50, 51]. In another study [52], corona discharge was employed to detect integrity violations of a metal wire rope. Corona discharge is widely used in electrophotography and electrostatic printing [53–58], as well as in drying various materials [59–63]. A promising direction for the application of corona discharge in high-voltage switches is presented in [64]. At the same time, one of the main areas of corona discharge application is its high efficiency in ozone generation. Industrial-scale synthesis of ozone in plasmachemical reactors using corona discharge is carried out [65–70]. Ozone generated in plasma-chemical reactors is widely used for water disinfection and treatment of various materials. This particular characteristic of corona discharge allows to its detect. In other words, the presence of corona discharge can be indirectly identified based on ozone sensor readings [26, 58, 71–73]. Additionally, corona discharge is a source of air ions, which can also be measured. Figure 9 shows the ozone concentration as a function of distance from the ionizer. Figure 9 depicts the relationship between the concentration of air ions and the distance from the ionizer, as well as the duration of its operation. Based on the provided graphs of ozone and air ion concentrations resulting from the action of corona discharge, the disadvantages of the method can be formulated as follows: – The method has limited accuracy in identifying corona discharges. – The method cannot be used to detect corona outside of indoor environments. – The method operates effectively within small distances of 1–5 m and can only serve as a warning of potential danger to individuals present in an ozone-rich environment. – The method does not allow for determining the coordinates of the corona discharge.

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Fig. 9 Dependence of ozone concentration in the room on the distance from the ionizer (left): 1—1 m; 2—2 m; 3—5 m; and the dependence of the concentration of air ions on the distance to the ionizer and the time of its operation (right): 1—0.1 m; 2—1 m; 3—4 m

6 Detection of the Presence of Corona Discharge Using the Method of Mechanical Work Detection Mechanical work performed by corona discharge includes vibration and noise. The source of noise is the local expansion of atmospheric air caused by the discharge. This local expansion creates sound vibrations. Attempts to diagnose electrical equipment based on its acoustic noise have been made by many authors [74–79]. However, such diagnostics are mostly associated with the detection of mechanical damage or related to the mechanical parameters of the electrical device itself. For example, in the case of an electric motor, deterioration of its bearing parameters leads to additional noise. The noise characteristics will vary for different types of defects and different types of motors. Additionally, even on electric machines without mechanical mechanisms (such as power transformers), the occurrence of additional noise is possible, which can be a result of several factors associated with emergency and pre-emergency conditions [78, 79]. This study focuses specifically on the sound vibrations created by the corona discharge. The detection and localization of the corona discharge will be performed based on the noise parameters associated with it.

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Theoretical Principles of Acoustic Radiation Created by Corona Discharge Yevgen Sokol , Vitalii Babak , Artur Zaporozhets , Oleg Gryb , Ihor Karpaliuk , and Oleksandr Svetelik

Abstract It is suggested to use the method of acoustic noise generation by corona discharge to search for the presence of corona discharge. It is shown the physical processes of acoustic noise occurrence from the corona discharge—ionic current and the current displacement in the outer zone of the corona discharge. The experimental study of corona discharge and acoustic impromptu interconnection was carried out. The investigation confirmed the existence of the link between acoustics and corona discharge. During conducting the measurement experiment, the elements of the informational theory of measurements were used. The data were processed by methods of mathematical statistics. The analysis showed that the results of theoretical prediction and experimental measurements were not consistent, so there was a need for generalization and mathematical modeling. Therefore, it is necessary to carry out mathematical modeling in order to describe the acoustic and energy dependence of the corona discharge. Keywords Corona discharge · Electric field · Volumetric charge · Acoustic radiation · Acoustic field · Spectral distribution

Y. Sokol National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan O. Gryb · I. Karpaliuk · O. Svetelik National Power Company “Ukrenergo”, Kyiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_4

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1 Explanation of Mechanism of Acoustic Radiation by Corona Discharge 1.1 Electric Field and Volumetric Charge Distribution in the External Corona Discharge Zone of the Alternating Current The electric field of the outer corona zone of the alternating current, as well as the distribution and regularity of the volumetric charge flow in the outer zone have a number of characteristic features [1–3]. Order of the volumetric charge in the corona external zone, was obtained on a cylindrical capacitor with diameters of the inner and outer electrodes of 3 mm and 3 m accordingly and at an amplitude of the alternating voltage applied to the electrodes, exceeds the initial corona voltage by 2.1 times (discharge overload n = U m /U 0 = 2.1). The calculations on charge distribution and its flow were carried out according to for the transient unipolar corona discharge [3–5]. Distribution in space of the volumetric charge and the electric field strength [6– 11] for several moments of time of the first impulse after switching on the voltage is shown in Fig. 1. The state of the outer zone, which corresponds to the moment of coronal recession (moment of time 1), for which in the outer zone the total charges are still absent, and the field strength in the entire interval is divided by the hyperbolic law [12]: E (r ) =

E 0 · r0 , r

(1)

where E 0 —voltage at the crushed rock surface, kV/cm, r 0 —radius of dart surface, cm, r—radius at which the electric field strength is determined, cm. Such law of distribution is retained at all subsequent moments of the time with the only difference that after the corona extinction the power in the dart surface does not appear equal to E0 , at first decreasing and remaining positive, but then changing its sign and reaching the value −E before the new corona extinction0 . In Fig. 1 the resilience distribution curves are given for r > 3 cm. These curves are also restricted on the side of large radii with value r = 25 cm because the hyperbolic law of distribution also takes place for radii that exceed the radius of the charge volume front: E (r ) =

E fr · r fr , r

(2)

where E fr —strength of the electric field front, kV/cm, r fr —radius of the electric field front, cm, r—radius at which the electric field strength is determined, cm.

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Fig. 1 Distribution of the volumetric charge and electric field strength in the outer zone of the transient unipolar corona (for the first half-period after switching on the voltage)

At 2-moment of time, the corona outer zone is already filled up to r = 5 cm with a volumetric charge whose power is nervously distributed in space and reaches 6– 10–11 C/cm at the dart surface. The electric field strength in all points of the outside zone (except for the area adjacent to the surface of the dart) is higher than at the moment of time 1.

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At 3-moment of time, the front of the volumetric charge wave moves further into the discharging interval, and the distribution of the volumetric charge intensity remains intrinsically nerve-wracking. In the electric field strength curve at the point, which corresponds to the front of the volumetric charge wave, there is a flaw, which is more manifested at the 4-moment. Here for a significant part of the area, filled by the total charge, the electric field strength appears more or less constant. For 4-moment of time, the position of the maximum value of the volumetric charge did not coincide with the dart surface, but moved into the deep gap. On the whole, the distribution of the total charge volumetricity appears to be more even in comparison with the distribution in the previous and previous moments of time. At 5-moment of time the corona on the winding is extinguished. It should be noted that the magnitude of the voltage in this case slightly differs from the amplitude value. The torsion of the volumetric charge is completely formed, and its head is detached from the dart surface, and in the next moments of time, it is displaced into the trough. The field strength here already practically for all parts of the outside zone, filled with the total charge, is approximately constant. As a consequence of this all the circle of the total charge, except for a small part of its tail, is moved to the trough at approximately the same speed. After the corona disappears, the charge of the dart and the electric field strength at its surface begin to decrease, which is accompanied by a decrease in the strength in the entire external zone—6-point of time. At the same time, the sharpest decrease occurs for the areas of space closer to the surface of the shot. The velocity of the volumetric charge also decreases considerably, more for the charge’s tail balls and less for the front ones. Due to the latter, the length of the volumetric charge curve increases. At moments 7, 8, 9 this tendency is more noticeable, which is caused by more and more nervousness in the distribution of field strength in a part of the external zone, filled with the total charge. At 9-moment of time the field strength at the point which corresponds to the radius of the tail of the volumetric charge reaches zero value, and at all points the left-hand axis becomes negative. As a consequence, the divergence of the divergence curve is terminated, while the front continues to move away from the dart. At moment 9 the head of the range and a part of the whole range (up to r = 12 cm) are moving not from the cable but to the cable. The other part of the whirl continues its movement from the shot. Characteristic for the curves of the distribution of the volumetric charge in moments 6, 7, 8, and 9 is more and more extent of the correlation of this distribution. For the end of the half-period, it appears already practically equal. It is important to note another peculiarity of the field of the outside zone. The electric field strength at the dart surface and in the area adjacent to it changes the sign earlier than the dart potential changes the sign, which is conditioned by the presence in the outer zone of the volumetric charge created in the process of the dart corona discharging. This displacement in time of the electric field in the dart surface with respect to its potential leads to earlier coronal ignition in the second penetration period than in the first one, and in accordance with the decrease in the coronal relaxation mitt rate in

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the second half-period as compared to the first one, when the coronal relaxation mitt rate was equal to the initial coronal relaxation rate. In this case (n = 2.1) the new corona decay in the second half-period period occurs immediately after the voltage goes through zero, i.e., even at a zero value of the voltage. The state of the continuum for this and a number of subsequent moments of the second half-period is characterized by the graphs in Fig. 2. Fig. 2 Distribution of volumetric charge and electric field strength in the outer corona zone of the alternating current for the second half-period after switching on the voltage

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At time 1 (the new corona decay) the head of the positive charge, created in the previous half-period, is at some distance from the dart surface, although it is already moving to it under the influence of the inertia of the reversed polarity field. At this time the front of the corona and a part of the corona (approximately half) are still distant from the dart, and the process of expansion of the corona of the volumetric charge continues. It is important to note that at a new coronal recession the ions of the previous half-period do not enter the zone of ionization, i.e. The recombination takes place in the space inherent to the total charge and regardless of polarity will occur when the gradient of the dart reaches the initial, rather than critical value characteristic of the evolved corona. At the moment of time 2, when the front of a new negative total charge will reach a significant distance from the crushing surface, the tail of the charge torque of the preceding intensification period will not reach the crushing surface yet. At this time the front of this wave is swinging away from the dart because the electric field strength for r > 20 cm has not changed its intensity. Thus, starting from the 2-moment of time, the negative charge front of the negative charge of this half-period and the positive charge front of the preceding half-period move in the same direction—from the jerk, due to the peculiarities of the corona field. Earlier at the 2-moment negative-valued charges of opposite signs come into contact, and at the moment 2 they already partially overlap one another. This is accompanied by the occurrence of the process of recombination of ions, which does not cease at the next moments of time and is one of the main reasons for the reduction of volumetric charges of both signs, which occupy the outer corona zone. For the 3-moment of time the positive total charge of the dart surface is reached by the tail of the tail and in connection with this the beginning of the return of ions, created in the previous period, to the drains, and their neutralization on it. Thus, an ionic current return generated and another reason for the decrease of the outer corona space charge comes into play. The recombination process and the recirculation current are the main features of the bipolar corona variable mode, which distinguish this mode from the unipolar mode of the first superposition. At the 3-moment of time in the whole discharging interval, the electric field strength has the same voltage. As a consequence, in the outer zone, only the counter polarity of the total charge twirling occurs. On the field resistivity distribution curve, there is a characteristic plane (for g = 11 cm), which for a number of subsequent moments of time is transformed into a horizontal curve plot, which is widening, corresponding to the field area with practically constant resistivity values. At the moments 4, 5, 6 there is a formation of the negative volumetric charge wave and its penetration into the outside zone, which is accompanied by the expansion of the area, in which the process of recombination of ions takes place. At the same moments of time due to movement of positive charge to the dart and subsequent withdrawal of a part of charges to the drone the length of the positive charge and the value of its total charge are increasing. After the corona is extinguished, the time that occurs between moments 6 and 7, the fully formed negative volume charge tails detach from the surface of the dart and

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all move away from the dart. The twist of positive volume charge continues to flow to the dart, and its separate spheres go to the dart. After the extinction of the corona, as there is little space for the first impulsive period, the charge of the dart decreases, and consequently the electric field intensity in all points of the outside zone decreases. Finally, at a certain moment of time, interspersed between the moments 9 and 10, the field strength on the crushing surface changes its intensity, and this process (change of sign) begins to extend into the gap. Because of this the tail spheres of the positive volume charge of the previous intensification period, which remained, are moving away from the surface of the dart. The head of a new, negative volumetric charge wave, the distribution of which is already approaching equal, begins to move to the dart. At this time the front of this wave continues its course from the dart. The specified condition is preserved in the general and for the 11-moment of time, with the only difference that here already all part of the positive volumetric charge wave, which has remained, moves away from the dart, as the point of zero electric field tension has moved outside of its front. 11-moment of time precedes a new, third, coronal recombination in the third halfperiod. If we deny the presence of a bipolar charge in some part of the outer zone, this state is otherwise analogous to the existing one at the beginning of the second halfperiod before another coronal recurrence. This refers to the similarity in distribution of both the electric field strength and the volumetric charge. The part of the outside zone adjacent to the dart surface appears to be isolated from the total charge, i.e. the new, third, coronal recombination takes place, as well as the two previous ones, in the non-polar conditions. In the next half-periods of the corona existence, the outer coronal zone of the alternating current is complicated by the fact that in the interval there are leftovers of the previous half-periods. However, it is not marked by the principle peculiarities of the volumetric charge flow and on the electric field and the processes proceed analogously to those described above.

1.2 Ion Current and Flux in the Outer Zone of the Corona Discharge In the outer corona zone of the variable current, the total current is divided into two components: transmittance current (ionic current), associated with the movement of the volumetric charge, and the displacement current, conditioned by the change in the time of the electric field strength. The volumetric charge strength and the electric field strength of the corona extrinsic zone of the time and space vary. Therefore, the ratio between the ionic and displacement currents as well as their values at different points of the outer zone will be different. Figure 3 shows the dependencies of the width of the volumetric charge of different interruptions of the outer corona zone of the alternating current.

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Fig. 3 Frequency dependence of the volumetric charge in different breaks of the outer corona zone of the alternating current (solid curves—positive ions; dotted curves—negative ions)

Fig. 4 Time dependence of electric field strength in different breaks of the outer corona zone of the alternating current

Dependences on the hour of the electric field in its form are characteristically different from the sinusoidal one, and this difference is the greater, the smaller radius of the break is. At the same time for different crossings there is a time shift of both amplitudes of curves and moments of their passing through zero value. The resulting ionic particle intensity curves are shown in Fig. 4. Here the solid curves correspond to the flow of positive ions, dotted curves—to negative ions, and the dash-dotted curves give the resulting particle intensity of the current.

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The intensity curve of positive ions in the third half-period (t > 0.02 s), which is the closest to the stationary curves and so, which corresponds to the positive ions flow in the direction from the dart (direct flow ion travel), has the form of spontaneous pulses. For the breaks with radiuses r = 10, 15, 20 cm the current sharply increases at some moments of time after t = 0.02 s (the later, the greater r). These moments of time correspond to the arrival to these points of the front of positive ions, which are created in the ionization process in the third half-period. For more distant points of space (r = 25 cm) a peak in the current power curve coincides with the arrival to this point of the front of the positive volumetric charge of the first superposition. On the ionic current curves, there are plots with a sharp increase in the steepness of the front of the volumetric charge (Fig. 5). Thus, it can be concluded that the shifting of the volumetric charge in the space, followed by the ionic current, leads to the shifting of a certain amount of gas in the air, thereby encouraging the appearance of the acoustic wave.

2 Experimental Measurements of Corona Discharge Acoustic Signals in Electric Power Supply Systems In this work, the analysis of acoustic vibrations is carried out, the source of which is not the equipment, but the electrical phenomenon. There are many types of equipment and it is a very extensive task to create reference models of sound fields of the appropriate type of equipment. If we consider models of sound waves from electrical phenomena, for example, corona discharge, the parameters in such models will be much less, and as a result, the creation of reference models is more improbable. The goal of this work is to create models of acoustic noise with corona discharge as a source. According to the works of researchers on the phenomenon of corona discharge [11, 13–16], it can be concluded that the source of acoustic vibrations in corona discharge can be the front of ion shifting, expansion of the air due to streamer breakdowns, expansion-sounding of the air due to chemical reactions that take place in the corona discharge. The discharge can be in several spatial manifestations: in the form of a point discharge and in the form of a group discharge (cover). Registration of sound vibrations from the corona discharge is carried out at a distance of several meters to tens of meters. Areas of acoustic radiation by the corona discharge are much smaller than the indicated distances, so, for distances greater than the main radius of loss of the corona discharge (20 cm for the corona on the 500 kV line) the discharge itself in space can be considered as a point source, and in the case of a discharge in the form of a choke, it can be regarded as a line discharge.

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Fig. 5 Time dependence of ionic current intensity in different crossings of the outer corona zone of the alternating current (solid curves—intensity of positive ions current; dotted curves—intensity of negative ions current; spaced dotted curves—intensity of total current)

In this way, we will consider the acoustic sources in two variants: a point source and a line source. Accordingly, the modeling of acoustic wave propagation from the indicated forms of the sound source is performed. A series of experiments on diagnostics of the corona discharge occurrence was carried out on the basis of sound vibrations [17]. The method itself was called spectral-acoustic. The measurements are made on acoustic vibrations of atmospheric air with the following distribution of the acoustic signal into spectrum components.

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2.1 Laboratory Equipment for Acoustic Measurements of the Acoustic Corona Discharge Signal Acoustic impromptu measurements from corona discharge were carried out in a small high-voltage hall of National Technical University “NTU KhPI”. The corona discharge was obtained at the facility for overcurrent of the highvoltage insulator of P-3 type (with 35 kV breakdown interval) (Fig. 6). High-voltage voltage was taken from the step-up transformer (150,000/100 V), which was connected to the 220 V network via laboratory autotransformer (Fig. 7). The voltage on the high-voltage transformer was measured with a voltmeter mounted on the low-voltage winding. The readings of the voltmeter were converted into the voltage on the high-voltage side. Calibration of the voltage ratio on the high-voltage coil to the low-voltage coil was carried out according to the discharge on the volumetric arrester. The electric diagram of the laboratory bench for investigation of acoustic parameters of the corona is shown in the Fig. 8. The PH is a laboratory transformer used to regulate the voltage. Voltage level control is performed according to PV voltmeter readings. Voltage level increase is provided by an HV step-up transformer (outward view is shown in Fig. 7). Corona discharge interruptions were performed on high voltage isolator El. Acoustic measurements were carried out by a group of devices for acoustic fluctuations. The main device was a microphone UMIK-1 with linear frequency response (Fig. 9), additional were small-sized voice recorders by Sony Walkman NWZ-B173F, and Transcend and others (Figs. 10, 11, and 12). UMIK-1 microphone parameters are shown in Table 1. Small-sized recorders were used as additional audio fixation systems, as shown in Table 2 and Figs. 11, and 12. These recorders have small dimensions and a built-in power supply system, which is suitable for measurements on high-voltage electrical installations. Thus, there is a

Fig. 6 Insulator of P-3 type (left—standard dimensions; right—photo of the insulator in installation)

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Fig. 7 Drive transformer (150,000/100 V)

Fig. 8 Electrical diagram of the laboratory bench Fig. 9 Photo of the UMIK-1 calibrating microphone used in the experiment

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Fig. 10 Typical amplitude-frequency response of the UMIK-1 microphone Fig. 11 Sony Walkman NWZ-B173F small voice recorder

Fig. 12 Transcend T.sonic 330 8 GB compact voice recorder

galvanic coupling, which reduces the probability of induction of potential from highvoltage equipment. Therefore, these recorders could be located at short distances to the place of occurrence of the corona discharge. Thus, the influence of incidental noise was reduced.

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Table 2 Transcend T.sonic 330 microphone parameters

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Parameter

Value

1

Capsule type

Electrically controlled

2

Frequency response

20 Hz—20 kHz

3

Frequency response deviation

±1 dB

4

Frequency and sampling rate

24 bit, 44.1 or 48 kHz

5

Output noise level

−74 dBFS

6

Strengthening

133 dB

7

Weight

120 g

8

Supply

USB

№

Parameter

Value

1

Capsule type

Electrically controlled

2

Frequency response

20 Hz–20 kHz

3

Frequency and sampling rate

32; 48; 64 kHz

4

Output noise level

≥90 dB

5

Weight

25 g

6

Supply

Battery in the house

2.2 Performing Acoustic Measurements and Their Results The experiment was carried out as follows: the voltage on the isolator was increased until the corona discharge occurred. The first voltage limit for the beginning of the experiment was controlled by the perception of the operator. The operator distinguished the characteristic noise of the corona discharge and gave a command about the possibility to carry out acoustic recording. This mode was taken as an initial one for recording acoustic noise from the corona discharge. The mode was kept for about 10 s to obtain the record without dips and changes in amplitude. Then the operator changed the voltage to a higher one and the next mode was activated. In general, the record of the whole experiment was carried out by one phase. Acoustic fixation equipment was placed in the high voltage zone. During the entire experiment, human access to the equipment was restricted. The result of the experiment recording fragment is shown in the figure (Fig. 13). The figure shows the moment of switching on the equipment switch, the gradual increase of voltage to visual detection of corona discharge. At the moment when the characteristic noise of corona discharge appears, the operator announces by a command that the mode has been established and stops increasing the voltage. Acoustic parameters of the corona discharge mode are recorded by the recording equipment. After a period of time for recording the mode, the operator announces in the voice about the transition to the next mode and performs the increase in voltage. When the desired voltage is reached, the operator will announce to the voice that the

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Fig. 13 Amplitude values of acoustic corona noise depending on the corona voltage

mode has been reached. Such operator’s actions were repeated until the experiment was completed. Figure 13 shows the resulting acoustic file of the experiment. During the processing of acoustic files in the conducted experiments, the following was done. Only the intervals with equal amplitudes, which corresponded to the modes (corona discharge voltages) were extracted from the general file. Such detached fragments are shown in Fig. 14. For the convenience of processing the fragments with operating modes were cut at the level of hourly intervals. Each of these fragments of the audio file was rotated to a period of 50 Hz. Recorders are equipped with a system of automatic regulation of the recording level. Therefore, the distance from the microphone to the corona discharge can not be calculated with respect to the strength of the recorded signal. Therefore, each of the received signals was amplified to a specified value. The signals were amplified according to the maximum amplitude value. The shape of the indicative curve of the audio signal is different from that of the corona discharge voltage (Fig. 15).

2.3 Spectral Distribution of Corona Discharge Audio Signal According to the rules of mathematical statistics and applied analysis [18, 19], the results of the experiments were processed. Each audio fragment was analyzed for harmonic components. For this purpose, we used Fourier’s row decomposition. We used fast Fourier transformation to get the analysis on the whole range of frequencies. For the possibility to carry out Fourier transformations we introduce a list of restrictions on the initial function: the function must satisfy the Dirichlet criterion (it is defined on the entire number axis, has a finite number of breakpoints at each +∞ { | f (x)|d x < ∞). endpoint, and is absolutely integrated −∞

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Fig. 14 Cut equal intervals of the audio file for each voltage: a—31 kV; b—47 kV; c—59 kV; d—71 kV

If the above limitations are fulfilled, the acoustic signal f(x) can be transformed by the Fourier transform. The Fourier series of function f (x) on the interval (−π; π) is a trigonometric series of the form: f (x) =

∞ E

k fˆk ei2π τ x ,

k=−∞

where fˆ—k-complex amplitude, τ—the range where the function is defined (signal length). The Fourier transformation allows to represent the continuous function f (x) (signal) defined on the space {0, T } in the form of the sum of unbounded

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Fig. 15 Fragments of audio signals ignited to one period, amplitudes increased to a conditional unit: a—31 kV; b—47 kV; c—59 kV; d—71 kV

number (unbounded series) of trigonometric functions (sine and cosine) with definite amplitudes and phases, which are also viewed on the frame {0, T }. Spectral tests were performed using the MatLab software. The data analysis module listing of the program created in MatLab is shown below. The first analysis was performed in 1024 fragments. The obtained results are presented in Figs. 16, 17, 18, and 19, showing the spectral distribution of corona discharge audio signal for the voltages of 31, 47, 59, and 71 kV.

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Fig. 16 Spectral distribution of audio fragments according to corona discharge voltage (31 kV)

Fig. 17 Spectral distribution of audio fragments according to corona discharge voltage (47 kV)

Fig. 18 Spectral distribution of audio fragments according to corona discharge voltage (59 kV)

It is well seen that for frequencies higher than 4000 Hz the shape of the spectral curve of audio fragments is more or less the same for different corona discharge voltages. During summing up these curves on one graph, they completely coincide for different voltages (Fig. 20).

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Fig. 19 Spectral distribution of audio fragments according to corona discharge voltage (71 kV)

Fig. 20 Spectral curves for different corona discharge voltages for the frequency range of 4–20 kHz

At the same time, in the range of spectrum from 0 to 4000 Hz the comparison of curves of spectra for different corona discharge voltages gives discrepancies as shown in Fig. 21. The Frequency range from 0 to 4000 Hz has more differences depending on the corona discharge voltage. It is possible to identify the regularity where for higher levels of energy in the corona discharge the spectral intensity curve accordingly occupies a higher position. But this behavior of the spectral intensity curve cannot be used as a marker for detection of presence of the corona discharge. As for the determination of the corona discharge intensity by the spectral curve level, the level of amplitude values will greatly depend on the distance to the corona discharge source according to the intensity decay of the acoustic signal. Difficulties may arise for the determination of the corona discharge capacity within the specified range. First of all, to determine the amplitude data it is necessary to have a reference signal. And

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Fig. 21 Spectral curves for different corona discharge voltages for frequency range of 0–4000 Hz

when it is impossible to identify the direct distance to the signal, so such a method is considered very difficult. And in the framework of this study, such work was not carried out. The other is to identify the corona discharge dependence of the signal by the spectrum data, which also causes significant difficulties. That is why the more precise analysis on the Fourier distribution was carried out. We used the distribution with the sampling frequency of 65,536 Hz. Thus, in this application Time_Resolution = 1024/65.536 = 15.6 ms, and the distribution capacity of the frequency is 65536/2/512 = 64 Hz. The range from 0 to 500 Hz was selected for the analysis. The comparison of spectral curves from the corona discharge with different capacities (voltages on the corona discharge) resulted in the following graph shown in Fig. 22. In such a detailed analysis, splashes, which correspond to the harmonic components of the industrial frequency, are well visible. The spectrogram shows the paired and unpaired harmonic components, which create the corona discharge in the audio range.

Fig. 22 Spectral analysis at 0–500 Hz

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Fig. 23 100 Hz frequency for different corona discharge voltages

Fig. 24 150 Hz frequency for different corona discharge voltages

Frequency bursts have a narrow range (sharp), that is why in the simplified analysis the discreteness overstepped the bursts and could not fictionalize them. These frequency splashes are attributed to the corona discharge itself. Let’s consider these harmonic components separately. 50 Hz (first harmonic) is the industrial frequency of the electrical network. The equipment connected to the network operates at this frequency. Acoustic splashes at this frequency can be created not only by corona discharge. Although the amplitude of this harmonic is the most important, we will not be focused on it. 100 Hz (the other harmonic). For the frequency of 100 ± 1 Hz, there is an increase of intensity values by 12 dB in comparison with the background values (Fig. 23). And it can reach −64 dB (according to the results of measurements on the conducted experiment), that is such an overshoot is sufficient for recognition. 150 Hz (third harmonic). At the frequency of 150 ± 1 Hz, there is an increase of intensity values by 40 dB in comparison with the background (Fig. 24). And it can reach −29 dB. Such gradient of intensity values is significant when using this frequency for detection of the presence of corona discharge.

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Fig. 25 200 Hz frequency for different corona discharge voltages

Fig. 26 250 Hz frequency for different corona discharge voltages

200 Hz (fourth harmonic). At a frequency of 200 ± 1 Hz, there is an increase of intensity values by 24 dB compared to the background (Fig. 25). And it can reach by 51 dB. 250 Hz (one-harmonic). At a frequency of 250 ± 1 Hz, there is a 20 dB increase in intensity values compared to the background (Fig. 26). And it can reach by 58 dB. 300 Hz (one-hundredth harmonic). At a frequency of 300 ± 1 Hz, there is a 12 dB increase in the intensity values compared to the background. And it can reach by 58 dB (Fig. 27). 350 Hz (symphony harmonic). At the frequency of 350 ± 1 Hz, there is an increase of intensity values by 20 dB compared to the background (Fig. 28). And it can reach by 58 dB.

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Fig. 27 300 Hz frequency for different corona discharge voltages

Fig. 28 350 Hz frequency for different corona discharge voltages

Table 3 Intensity of corona sound depending on voltage by harmonics Frequency

31 kV

47 kV

59 kV

71 kV

1, (50 Hz), dB

−1.07

−2.86

−2.25

−3.08

2, (100 Hz), dB

−38.52

−44.77

−45.56

−44.17

3, (150 Hz), dB

−20.73

−21.08

−19.34

−19.82

4, (200 Hz), dB

−34.91

−40.37

−40.57

−45.86

5, (250 Hz), dB

−38.25

−44.40

−44.38

−44.62

6, (300 Hz), dB

−41.88

−48.23

−46.09

−51.10

7, (350 Hz), dB

−51.94

−62.36

−61.43

−54.33

Let’s summarize all values by hormones in Table 3.

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Fig. 29 Spectral analysis of acoustic file fragment (31 kV)

During performing separate processing of acoustic files received at the laboratory bench we get the results, which are shown in the figures (Figs. 29, 30, 31, and 32). Here is the following: the upper left graph is the acoustic signal picture, which was obtained after the analog–digital conversion. Left bottom—the file is stretched to one period (50 Hz). Upper right-hand side—the result of decomposition by Fourier transform. Lower right arm—spectral lines are increased (50 Hz line is excluded). It is well seen that the corona discharge presence is represented by spectral lines of 100, 150, 200, 250, 300, 350 Hz (other lines have small order values which can be neglected). Based on the narrowness of the spectral lines of the corona discharge at multiple harmonic values, to increase clarity, you can exclude background frequencies and build graphs in the form of stem histograms (Fig. 33).

Theoretical Principles of Acoustic Radiation Created by Corona Discharge

Fig. 30 Spectral analysis of acoustic file fragment (47 kV)

Fig. 31 Spectral analysis of acoustic file fragment (59 kV)

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Fig. 32 Spectral analysis of acoustic file fragment (71 kV)

Fig. 33 Diagram of corona discharge frequency spectrum at voltage: a—31 kV; b—47 kV; c— 59 kV; d—71 kV

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The corona discharge on the string-conductor parts is imposed by the industrial frequency of 50 Hz and causes acoustic turbulence that mandatorily contains harmonic frequencies of 50, 150, 250, 350 Hz, and additionally 100, 200, 300 Hz (Fig. 33). The processing was carried out according to the algorithm of the program code presented below. Algorithm of the Program Code %Test program for building the frequency spectrum of the function clear % clearing the workspace %% Data retrieval from the file FileName = 'Singl_50Gh.wav'; % load an audio file [y, fs] = audioread(FileName); % load an audio file y = y(:, 1); % get the first channel N = length(y); % signal length t = (0:N-1)'/fs; % time vector fc = 512; %% Spectral analysis fc_min = min(fc); %Determine the minimum frequency Z = abs(fft(y)); Z_max = max(Z); xx = (0:N-1)'/N*fs; %% Spectrum maxima nmax = 50,000; nummax = find((Z(2:nmax-1)>Z(1:nmax-2))&(Z(2:nmax-1)>Z(3:nmax))&... (abs(Z(2:nmax-1)-Z(1:nmax-2))>100)); xxmax = xx(nummax+1); Zmax = Z(nummax+1);%+Ynoise(nummax+1); F_max = [xxmax Zmax] Freq_xx = [100 150 200 250 300]; %Setting the frequencies for control %% Block of graphs figure('Position',[500 100 1000 800])% Create new window + start point of window and its dimensions Ttitle = ['Spectrum of signal Y, signal ', 'Fwav']; title(Title);% Title of the graph

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% Graph The signal amplitude subplot(2,2,1);% Select the window area to be built plot(t,y)% Generation of the first graph xlim([0 1/fc_min*200]); % Determine the display area along the ОХ axis title('Signal Y');% Chart caption xlabel('Time, s');% Axis caption x graph ylabel('Amplitude, Ed ');% Axis caption in the graph % Graph The signal amplitude Increased subplot(2,2,3);% Select the window area to be built plot(t,y, 'b', 'LineWidth', 2)% Create another graph FirstX = 0.1; % Start of enlarged graph xlim([FirstX 1/fc_min*15+FirstX]); %The display area along the ОХ axis title('Signal Y (increased)');% Caption of the graph xlabel('Time, s');% Axis caption x graph ylabel('Amplitude, Units');% Axis caption in the graph box on grid on % Graph of the signal spectrum subplot(2,2,2);% Select the window area to be built plot(xx,Z,'r', 'LineWidth', 2)% Build the third graph set(gca, 'XTick',50:50:400,'YTick',0:5000:50000); axis([20 400 0 Z_max]); % Viewing of individual fragment of graph x1 x2 y1 y2 title('Spectrum of signal Y');% Title of the graph xlabel('Frequency, Hz');% Axis caption x graph ylabel('Amplitude, Units');% Axis caption in the graph % Graph The signal spectrum Increased subplot(2,2,4);% Select the window area to be built plot(xx,Z,'r', 'LineWidth', 4); axis([90 310 0 8000]); % Viewing of a separate fragment of graph x1 x2 y1 y2 title('Spectrum of signal Y (increased)');% Graph title xlabel('Frequency, Hz');% Axis caption x graph

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References 1. Bradley, D., Gupta, M.L.: Direct and alternating current coronas in flame gases. Combust. Flame 40, 47–63 (1981) 2. Fridman, A., Chirokov, A., Gutsol, A.: Non-thermal atmospheric pressure discharges. J. Phys. D Appl. Phys. 38(2), R1 (2005) 3. Loeb, L.B.: Electrical Coronas: Their Basic Physical Mechanisms. University of California Press (2022) 4. Scholtz, V., Julák, J., Kríha, V., Mosinger, J.: Decontamination effects of low-temperature plasma generated by corona discharge. Part I: an overview. Prague Med. Rep. 108(2), 115–127 (2007) 5. Satyanand, U.S.: An Experimental Investigation of Ionization of Supersonic Air by a Corona Discharge. The University of Texas at Arlington (2005) 6. Rezinkina, M.M., Sokol, Y.I., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V.: Mathematical modeling of the electromagnetic processes of the corona’s formation during the operation of electric power facilities. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 99–118. Springer International Publishing, Cham (2021) 7. Rezinkina, M.M., Sokol, Y.I., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V.: Physical modeling of the electrophysical processes of the formation of the corona during the operation of electric power facilities. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 119–126. Springer International Publishing, Cham (2021) 8. Javandel, V., Akbari, A., Ardebili, M., Werle, P.: Simulation of negative and positive corona discharges in air for investigation of electromagnetic waves propagation. IEEE Trans. Plasma Sci. 50(9), 3169–3177 (2022) 9. Van Veldhuizen, E.M., Rutgers, W.R.: Corona discharges: fundamentals and diagnostics. Invited paper, Proc. Frontiers in Low Temp. Plasma Diagn. IV, Rolduc, Netherlands, pp. 40–49 (2001)

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10. Teramoto, Y., Fukumoto, Y., Ono, R., Oda, T.: Streamer propagation of positive and negative pulsed corona discharges in air. IEEE Trans. Plasma Sci. 39(11), 2218–2219 (2011) 11. Gryb, O.G., Karpaliuk, I.T., Zaporozhets, A.O., Shvets, S.V., Rudevich, N.V.: Acoustic diagnostics for determining the appearance of corona discharge. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 127–157 (2021) 12. Babak, V., Eremenko, V., Zaporozhets, A.: Research of diagnostic parameters of composite materials using Johnson distribution. Int. J. Comput. 18(4), 483–494 (2019) ˇ 13. Bálek, R., Cervenka, M., Pekárek, S.: Acoustic field effects on a negative corona discharge. Plasma Sources Sci. Technol. 23(3), 035005 (2014) 14. Béquin, P., Joly, V., Herzog, P.: Modeling of a corona discharge microphone. J. Phys. D Appl. Phys. 46(17), 175204 (2013) 15. Dong, M., Ma, A., Ren, M., Zhang, C., Xie, J., Albarracín, R.: Positioning and imaging detection of corona discharge in air with double helix acoustic sensors array. Energies 10(12), 2105 (2017) 16. Xinlei, Z.H.U., Zhang, L., Huang, Y., Jin, W.A.N.G., Zhen, L.I.U., Keping, Y.A.N.: The effect of the configuration of a single electrode corona discharge on its acoustic characteristics. Plasma Sci. Technol 19(7), 075403 (2017) 17. Gryb, O., Karpaliuk, I., Shvets, S., Zaporozhets, A.: Recognition of corona discharge presence by acoustic system installed on unmanned aerial vehicle. Proc. Natl. Aviat. Univ. 4(85), 46–53 (2020) 18. Gupta, S.C., Kapoor, V.K.: Fundamentals of Mathematical Statistics. Sultan Chand & Sons (2020) 19. Shao, J.: Mathematical Statistics. Springer Science & Business Media (2003)

Recognition of Corona Discharge Presence by Spectral Characteristics of Acoustic Radiation Artur Zaporozhets , Vitalii Babak , Oleg Gryb , Ihor Karpaliuk , Viktor Starenkiy , and Andrii Solodovnyk

Abstract In the chapter the mathematical model of spectroacoustic dependence of the corona discharge was described. To solve the task of creating the model, the acoustic spectrum was decomposed by Fourier transform. The results of the decomposition are described, the regularities in the spectrum of acoustic radiation by corona discharge are found and spectral lines which are attributed to the corona discharge are shown. The model of acoustic radiation corona discharge was created according to the Fourier transformations applied to the results of experiments processing. Application of the model of mathematical dependence of the acoustic spectrum allowed to create of a method of recognition of the presence of corona discharge by the spectral characteristics of acoustic radiation. The developed method was used to develop a method of corona discharge detection in the presence of external acoustic noises. For the possibility of using the method in the development of corona discharge detection devices, the methods for non-rusting and overloading devices were developed. The method of acoustic detection of corona discharge occurrence is shown to be advantageous—it is possible to detect corona discharge occurrence without contact with jet-active parts, remotely, even behind the direct visibility, with minimal influence of external factors, such as weather conditions, years of work and others. Keywords Corona discharge · Acoustic radiation · Spectral acoustic bursts · Harmonics · Noise classification · Noise spectra

A. Zaporozhets (B) · V. Babak General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan O. Gryb · I. Karpaliuk · A. Solodovnyk National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology of the National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_5

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1 Analysis of Acoustic Corona Discharge Radiation with Mathematical Model There is no direct dependence on the intensity of spectral “lines” and the power of corona discharge. And it is well explained by the transition to other types of gas breakdown at increasing voltage with the increase of power of corona discharge. Accordingly, there is the presence of spectral change of acoustic impregnation. Although the integral estimation of the spectrum bandwidth for the frequency range of 0–4000 Hz gives a regularity between the power of the acoustic spectrum and the power of the corona discharge [1, 2]. But, as it was stated earlier, it is not possible to determine the presence of the corona discharge by such an integral indicator and the integral indicator can show the value which is not related to the corona discharge. At the same time, one should pay attention to the gradient of spectral bursts [3–5]. Only certain spectral lines are assigned to the corona discharge and for them, it is possible to determine the overshoot of the bursts amplitude over the background. Let’s calculate by the formula: ( n ) n E A f +i 1 E A f −i + AA f = − Af, 2 i=1 n − 1 i=1 n − 1 where Af is the amplitude at the frequency f ; Af−i , Af +i —amplitude step value by left-hand and right-hand from frequency f ; n—number of steps from the maximum. The results of the calculation are recorded in Table 1. Data from Table 1 can be presented in a more detailed graphical form (Fig. 1). This enables us to formulate the criterion of corona discharge presence by the acoustic spectral lines multiple to the industrial frequency harmonics [1, 2]. Therefore, the model of the acoustic corona discharge signal can be presented in the following way: f (t) = A0 +

n E

Ami sin(2πi f (t) + ϕi ),

i=1

Table 1 Intensity of corona sound over background depending on voltage, by harmonics Frequency

31 kV

47 kV

59 kV

71 kV

1, (50 Hz), dB

42.7

44.8

45.0

43.2

2, (100 Hz), dB

14.8

16.4

14.2

13.8

3, (150 Hz), dB

34.3

40.9

40.1

36.7

4, (200 Hz), dB

27.9

27.6

28.0

19.7

5, (250 Hz), dB

28.9

28.3

26.1

23.3

6, (300 Hz), dB

25.0

20.9

22.3

13.6

7, (350 Hz), dB

18.6

11.3

11.5

14.8

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Fig. 1 Corona sound intensity over background depending on voltage, by harmonics

where A0 —acoustic background noise; Ami —amplitude of the i-th harmonic component; i—number of the harmonic unit; f (t)—frequency of the electric network 50 Hz; ϕi —phase for the i-th harmoniconic component; n—given number of harmonic components (we assume that it is equal to 7). We are considering that sharp bursts in the acoustic range occur on the harmonic. These bursts have a significant steepness and have a width of −2 Hz…+2 Hz, as can be seen in the Fig. 2, where all the bursts are summarized by their maximum value. The curves are obtained as the average value of different strengths of the corona discharge. Burst at a frequency of 50 Hz was not considered, because not only corona discharge but also other processes and equipment take part in its formation. In Fig. 2 it is well seen that the bursts have a narrow range, which does not go beyond the range [−2 Hz; +2 Hz] of the maximum value. The total width of the spectral line range is 4 Hz. During defining the bandwidth of 10 Hz, the increase of the acoustic signal intensity within the range limits can be detected. Let’s use the formula:

Fig. 2 Spectral acoustic bursts for different hormones are aligned by maximum value

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Fig. 3 Intensity increasing of acoustic signal from corona discharge at window width (−5 Hz; + 5 Hz)

AAk =

n E Ak−i − Akmax , n i=1

where Akmax —maximum amplitude within the spectral bandwidth of the k-th harmonic line; Ak−i —value of amplitude by crops in the limits of spectral line band; n—number of steps within the spectral line band (we use the value 10). Therefore, it is possible to present the acoustic signal intensity increase for the average value of different corona discharge intensities on harmonics 2, 3, 4, 5, 6, 7 (Fig. 3). Therefore, the model of the acoustic corona discharge signal can be presented in the following way: f (t) = A0 +

7 E

( ) Ami sin 2π · i· f i · t + ϕi ;

i=2

f (t) = A0 + Am2 sin(2π 100t + ϕ2 ) + Am3 sin(2π 150t + ϕ3 ) + Am4 sin(2π 200t + ϕ4 ) + Am5 sin(2π 250t + ϕ5 ) + Am6 sin(2π 300t + ϕ6 ) + Am7 sin(2π 350t + ϕ7 ), where A0 —acoustic background noise; f i —frequency of the corresponding i-th harmonic; Am2 … Am7 —amplitudes from 2 to 7 harmonic component; ϕ2 …ϕ7 — phases from 2 to 7 of the harmonic component. If we calculate the amplitude value of the harmonic amplitude to the background value, then we have: Am2 = 25; Am3 = 500; Am4 = 50; Am5 = 150; Am6 = 50; Am7 = 20. These values are taken as minimal amplitude value of harmonic components, the approximation to which corresponds to the corona discharge.

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Fig. 4 Harmonic component 2 with an amplitude of 25 relative units

Fig. 5 Harmonic component 3 with an amplitude of 500 relative units

Fig. 6 Harmonic component 4 with an amplitude of 50 relative units

And if we assume that ϕ2 …ϕ7 = 0, then the model will have the following form in graphical view (Figs. 4, 5, 6, 7, 8 and 9). The general view of the acoustic corona signal curve is shown in Figs. 10 and 11.

2 Recognition of Corona Discharge by the Presence of Spectral Components We take the system in a general view as such, as shown in the Fig. 12. This is the simplest model of registration of acoustic fluctuations. At this stage, we accept the model in which the source and receiver are taken into account as ideal.

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Fig. 7 Harmonic component 5 with an amplitude of 150 relative units

Fig. 8 Harmonic component 6 with an amplitude of 50 relative units

Fig. 9 Harmonic component 7 with an amplitude of 20 relative units

Fig. 10 Acoustic signal amplitude curve for the corona discharge model

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Fig. 11 Acoustic signal amplitude curve for the corona discharge model (for one period)

Fig. 12 Model of the acoustic oscillations recording system

At the output of the receiver, we obtain the function of the random signal depending on the time ξ (t) [6–8]. A random process ξ (t), which depends only on one real parameter t (time), is considered to be defined on the interval of time (0, T ), if at a constant number n for all moments of time t 1 , t 2 , …, t n on that interval, we know a n-dimensional probability density distribution pn (ξ1 , ξ2 …, ξn ; t 1 , t 2 , …, t n ) or n-dimensional characteristic function: { n } n On ( jv1 , jv2 , . . . , j vn ; t1 , t2 , . . . , tn ) = M exp( j vi ξi ) , i−1

where ξ1 = ξ(t 1 ), ξ2 = ξ(t 2 ), …, ξ n = ξ(t n ). Since the acoustic signal source is powered by industrial frequency, we can assume that the acoustic signal, which it will be create, also includes harmonic component. Determination of the presence of corona discharge signal in the acoustic signal can be carried out as a choice of one of the hypotheses: H 0 —no corona discharge signal in the acoustic signal; H 1 —corona discharge signal present in the acoustic

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Fig. 13 Decreasing of corona discharge acoustic signal intensity depending on frequency

signal. The hypothesis can be expressed by the dispersion ratio with the intermediate maximum value [9, 10]: | | D = minM |(F(x) − Fkr (x))2 |, where F(x)—incidental acoustic signal, which is processed by Fourier transform, F kr (x) —model of corona discharge after Fourier transform. The calculation can be accelerated by limiting the frequency range, in which the comparison of acoustic signals will be carried out. According to the results of the experiments, it was determined that the main harmonic bursts from the corona discharge fall on the first seven harmonics: 50; 100; 150; 200; 250; 300; 350 [1, 2]. All others have values that are sharply decreasing and they can be not accepted for calculation (Fig. 13). In our case, it is possible not only to limit mode’s calculation to a certain frequency range (from 0 to 400 Hz), but also to conduct a comparison of the acoustic signal with the model only on the specific harmonic frequencies. Taking into account that the frequency of 50 Hz can be excluded from the algorithm of the comparison because most of the acoustic signals from the electrical installations are radiate at this frequency and they have no relation to the corona discharges. This can lead to abnormal detection. It is possible to consider the accelerated identification of the corona discharge presence not for all harmonics, but for example only for unpaired harmonics. Because unpaired harmonics have the highest intensities and are attributed to the corona discharge. The algorithm for recognizing corona discharge by acoustic oscillations was developed. The algorithm is based on the detection of certain spectral lines of acoustic radiation, which are related to the spectral lines of the corona discharge model. In the algorithm, we took into account the preparation and conservation of the results of

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recognition. The algorithm was developed for the possibility of its implementation in hardware form. The principle of the algorithm shown in the block diagram (Fig. 14). After the process is started, the microphone catches the acoustic signals and transmits them to the block of analog signals in the form of electrical impulses. Analog signal is processed for the presence of excess values of amplitudes and sent to the analog– digital processing unit. In the ADC unit, the signal is digitized and transmitted to the memory unit for recording. Recording of the acoustic signal is performed continuously during the entire time of the analyzing device. From the memory block the signal is selected to the file cutting unit into short fragments (e.g., 10 s in length). In the next block, the short file is decomposed using Fourier transform. Spectral frequency components of the acoustic signal are selected. The result of the Fourier transform is cleared from noise, compared to the corona discharge spectrum model and analyzed for the presence of the primary (150–150–350 Hz) and the secondary (100–200–300 Hz) frequency spectrum. If the value exceeds with the selected signal frequencies above the background, the corresponding marker is generated synchronized with the timer. The flow of corona discharge availability data is formed, which is sent to the external database. Thus, the information flow is formed, fixation of the corona discharge occurrence. Verification of the validity of the method of detection of the corona discharge presence by the acoustic spectrum was carried out on the data obtained independently. Thus, for the analysis of the corona discharge occurrence, two video clips were taken from the YouTube channel [11, 12]. Both videos show corona discharge, which is identified by visual method, with the recording of the soundtrack and recording of the acoustic composition of the corona discharge. Spectral analysis of soundtracks was carried out for two films.

2.1 Analysis of the Soundtrack of Documentary Film #1 As a verification of the method of corona discharge detection by acoustic impingement, the documentary film from YouTube was selected [11]. And an analysis of the soundtrack of the documentary film was carried out (Figs. 15 and 16). The track was divided into two fragments, which corresponded to two modes of corona discharge (Figs. 17, 18, 19, 20 and 21). The correlation of splices according to the recommended methodology confirms the presence of the corona discharge in the audio track of the documentary (Fig. 22).

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Fig. 14 Block diagram of corona discharge detection

2.2 Analysis of the Soundtrack of the Documentary Film #2 As a verification of the method of corona discharge detection by acoustic impregnation, the documentary film from YouTube was selected [12] (Figs. 23, 24, 25, 26, 27, 28 and 29). Burst coincidence according to the recommended methodology confirms the presence of corona discharge in the audio track of the documentary (Fig. 30).

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Fig. 15 Frames from film 1 about corona discharge

Fig. 16 Sound track from film 1 about corona discharge

Fig. 17 Two fragments of audio file from the film 1 about corona discharge: a mode 1; b mode 2

Although the equipment for sound recording was not focused on the spectrum and character of acoustic radiation corona discharge. Two conducted analyses confirmed the presence of spectral signatures of the corona discharge. The method has shown its usefulness.

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Fig. 18 Spectral analysis of fragment 1 (film #1)

Fig. 19 Spectral analysis of fragment 2 (film #1)

3 Recognition of Corona Discharge Presence in Terms of Acoustic Noise The presence of acoustic noise is an insignificant part of the real acoustic situation of the operating space. Therefore, taking into account the noise and its influence on the process of corona discharge detection by acoustic radiation is the next step in algorithm improvement and its approximation to the real conditions. To solve the task of noise control it is necessary to describe the nature of noise fluctuations and, as a result, to determine the acoustic parameters of the environment,

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Fig. 20 Comparison of the spectral analysis curves of fragments 1 and 2 of the documentary film 1 and the experiment data (at frequencies 4500–20,000 Hz)

Fig. 21 Comparison of the spectral analysis curves of fragments 1 and 2 of the documentary film 1 and the experiment data (at frequencies 0–4500 Hz)

noise characteristics of natural and industrial processes that may be related to human activity, functioning of technical objects, industrial objects [13–17].

3.1 Noise Classification by Time Characteristics All noises can be divided by their time characteristics into permanent and nonpermanent ones. Classification of noise by time characteristics is given in GOST 12.1.003-83. According to GOST 12.1.003-83 (GOST 12.1.003-83), the permanent noise is noise,

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Fig. 22 Comparison of the spectral analysis curves of fragments 1 and 2 of the documentary film 1 and the experiment data (at frequencies 0–500 Hz)

Fig. 23 Frames from film 2 about corona discharge

Fig. 24 Sound track from film 2 about corona discharge

which level of sound during 8 h of working day varies in the hour by at least 5 dBA if measured on the hourly characteristic “as usual” noise meter in accordance with GOST 17187-2010. Impermanent noise is the noise that changes by more than 5 dBA during 8 h of working day when measured at the “normal” sound level in accordance with GOST 17187-2010.

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Fig. 25 Two fragments of audio file from film 2 about corona discharge: a mode 1; b mode 2

Fig. 26 Spectral analysis of fragment 1 (film #2)

Impermanent noise in its turn according to GOST 12.1.003-83 is divided into those, which wobble, intermittent and impulse. Wobble noise is one that continuously varies in sound level over time. Intermittent noise is noise whose sound level varies by stepwise (by 5 dBA or more). The duration of intervals during which the level remains constant is 1 s or more. Impulse noise is composed of one or more sound signals with duration of less than 1 s, thus the level of sound, measured in dB and dBA according to the time characteristics “impulse” and “consistently” according to GOST 1718-2010, differ by at least 7 dBA. Impulse noise can be periodical and non-periodical (random) actions in time. Types of these noises are given in Table 2. As well as permanent noise, impermanent noise negatively influences the conditions of corona discharge recognition by acoustic oscillations. Impulse noises [18,

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Fig. 27 Spectral analysis of fragment 2 (film #2)

Fig. 28 Comparison of the spectral analysis curves of fragments 1 and 2 of the documentary 2 and the experiment data (at frequencies 4500–20,000 Hz)

19] are the most unreliable in relation to them by two reasons: first, significant shortterm overshoot of the amplitude sensitivity of microphones. This noise “clogs” the sensation system for some time. Otherwise, the decomposition of high-level bursts into the spectral composition may lead to erroneous in the recognition. As we know, the spectral characteristic of a single rectangular pulse (Fig. 31), which is described by the expression: / / ( ) { t D at − τ 2/≤ t ≤ τ /2 = x(t) = D · r ect , 0 at t < −τ 2i t < τ 2 τ

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Fig. 29 Comparison of the spectral analysis curves of fragments 1 and 2 of documentary film 2 and the experiment data (at frequencies 0–4500 Hz)

Fig. 30 Comparison of the spectral analysis curves of the fragment 1 of the documentary film 2 and the experiment data (at frequencies 0–500 Hz)

has the following view of Fourier transform: τ/ 2

X ( j ω) = D ∫ e −τ / 2

− jωt

( / ) ) sin ω τ 2 j ωt D ( − j ωt 2 2 / e = Dτ dt = −e . − jω ωτ 2

The spectral characteristic is a real function (Fig. 32). When the pulse duration τ increases, the distance between the zeros of the function X( jω) decreases, i.e. the spectrum become narrower. Thus, X(0) value increases. When the pulse duration decreases τ, on the other hand, the distance between the zeros of the function X( jω) increases, which indicates that the spectrum become more widely, and the value X(0) decreases. Thus, the overlapping of the corona discharge spectrum appears, which does not allow to perform recognition.

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Table 2 Types of noises by activity in time Nature of sound radiation energy by a noise source

Type of noise Permanent

Impermanent

Wobble

Intermittent

Impulse (periodical)

Impulse (non-periodical)

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Fig. 31 Direct single pulse

Fig. 32 Spectral characteristic of a rectangular single pulse

3.2 Noise Classification by Origin Thus, the main noise generators of machinery and equipment are various structural elements, engines, and moving parts [20–25]. Let’s give some examples: for an airplane, the noise is caused in its propellers or engines (depending on the airplane’s main frame design). Gas turbine engines of aircrafts [26, 27] generate noise with discrete and uninterrupted frequency spectra. In terms of intensiveness it dominates radiation with a discrete spectrum on the harmonics of rotary frequency of blades of working wheels (frequency range of 1000…4000 Hz) and the rotor frequency range (supersonic ventilators with frequency range of 500…2000 Hz). Reactive jet generates uninterrupted over frequency radiation noise with maximum spectral power density in the low-frequency range. Such noises are also present for helicopters [28, 29]. The main sources of noise in wheeled and tracked ground vehicles are the

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power plant, elements of the transmission, running gear (for tracked vehicles), and the elements of the exhaust system [30–32]. Different components of the acoustic field of the ground machinery are characterized by different straightness diagrams. Noise spreading of the power unit, as a rule, is connected with the direction of the exhaust system output. Noise from the running gear and transmission systems has a circumferential straightness diagram. External noise level can reach to 90 dB. The main energy of the acoustic signal is located in the smoothness of rotation frequencies of the crankshaft of the power plant. During modeling the propagation of such a signal in the atmosphere, energy losses must be taken into account. Since the coefficient of sound inhibition depends on its frequency, the amplitude of each of the components of the broadband harmonic signal will change over its own law. Thus, when a broadband acoustic pulse propagates in the atmosphere, in addition to a general decrease in amplitude, its shape will also change. Broadband acoustic impulse can be viewed as an aperiodic function of the sound pressure in the time, which turns to zero at infinity. To simplify calculations, assume that sound propagates in a single-order volume of air in which normal conditions prevail: temperature—293.15 K, pressure—1013 mbar, humidity—80%. In this case, the vertical gradient of the sound absorption coefficient is a linear dependence on distance. The dependence of the spectrum and the shape of the acoustic impulse on the distance is presented. Assuming that the atmosphere is homogeneous and there is no side wind, the acoustic impulse front will be a segment of a sphere. Burst acoustic functions in extreme forms can be represented as a consequence of an explosion, such acoustic waves have been investigated for a long time [33, 34]. As a result of these studies, it was found that the atmospheric waves at distances of 1…10 km are acoustic, because at this distance the waves save their phase characteristics, and their amplitudes decreased inversely to the distance. The spreading speed of the waves matched the speed of the sound, and the main energy of the sound waves is in the infrasound zone at a frequency of up to 1 Hz. The maximum spectral sound components in thunder strikes are in the frequency range of 50…500 Hz. The noise level of thunder strikes is up to 100 dB. Rain noise is up to 70 dB. Human voice power density at 1 m distance in a 0.1…10 kHz range to the sensitivity threshold (2 × 10–5 Pa) is: quiet speech—20 dB, loud speech—40 dB, cry—60 dB [35, 36]. The amplitude structure of the noise radiation can lead to an increase in the sensitivity of the perceptual acoustic system. Thus, the determining factor in the detection of acoustic sources of corona discharge is the background, which is caused by the presence of other sources of noise, so the range of detection of the acoustic source that creates the corona discharge can vary from a few meters to hundreds of meters. This is the reason for the necessity of proximity of recognition systems to electrotechnical objects.

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Table 3 Typical values of noise levels Noise source

Sound pressure level (dB)

Sound power density (W/m2 )

Bandwidth (Hz)

Complete silence

0

10–12

Rustle of leaves

10

10–11

Whisper

20

10–10

Rain

50…70

Normal conversation

60

Human steps

60…65

10–6 …3 × 10–6

Wind

65–77

3×

Non-moving crawler tractor

65–72

10–5

30–2000

Stationary truck

60–65

10–5

30–2000

Moving crawler tractor

80–89

10–4 …10 −4

15–1000

Flying plane

72–74

10–4 …10 −4

100–2000

Flying helicopter

82–89

10–4 …10 −4

100–2000

25–1000

10–6 …5

×

500–10,000 10−5

20–1000

3.3 Levels of Acoustic Noise Noise levels are evaluated at a sensitivity threshold level—10–12 W/m2 . Typical values of noise levels of some sources according to literature sources [35, 36] are given in Table 3. The distribution of signal strength over frequencies effect influenced on the strength of the acoustic noise signal, as well as the height of location of the noise source in relation to the surface of the Earth. For example, if the noise source is motor vehicles or tractors (land machines), they are characterized by two sound sources—combustion engine exhaust system and mechanics (equipment). In this case, the height of a noise source location is 0.8…1.2 m for the engine, and 0…3.0 m for mechanics. The height of receiving microphones can be from 1.5 to 2 m. Dependence of linear attenuation for different frequencies is shown in Figs. 33 and 34. It can be seen that linear attenuation decreases with the increase of temperature and humidity.

3.4 Acoustic Noise Spectra To estimate the influence of acoustic noise spectrum depending on the distance to the corona discharge source, it is necessary to know spectra of noise and accordingly dispersed properties of the environment. We will consider only anthropogenic noises

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Fig. 33 Dependence of linear attenuation with the propagation of acoustic signal in the atmosphere on the relative humidity η at temperature t = 15 °C

Fig. 34 Dependence of linear attenuation with the propagation of acoustic signal in the atmosphere on the temperature t, °C at humidity η = 70%

because it is impossible to influence natural noises; only protection can be provided against them. But the noises created by people can be taken into account and in some cases they can be controlled, for example, they can be anticipated (aircraft approaching, tractor crossing, etc.). Ground and air objects generate sound in a very wide range, but in the spectra, there are characteristic spectral components related to blades of the rotor or turbines and compressors (Fig. 35a, b), and to engine operation (frequencies multiple of rotation frequencies of the engine shaft—Fig. 35c). The character of the signal is quasi-stationary. During carrying out calculations of the influence of noise on the range of the noise source, it is proposed to use a model of spectrum approximation with a certain effective parameter that characterizes its effective width. Figure 36 presents the spectra of radiation measurements for different distances at ambient temperature 15 °C and humidity 20%. The effect of the separation surface

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Fig. 35 Acoustic signal spectra: a helicopter MI-2; b aircraft FALCON; c diesel engine with 800 rpm

was not taken into account, i.e. V ( f, R, h r , h T ) ≈ 1. The calculations were based on the data on sound attenuation in the atmosphere. It can be seen that the spectra of more broadband noise sources are transformed more strongly. As the range increases, the highest-frequency components of the spectrum fade most strongly. The radiation spectra for all thus sources become

Fig. 36 Spectra of acoustic signals at different distances from the sources when expanding in the atmosphere: a near the source; b range 0.5 km; c range 2 km; d range 8 km; 1—diesel engine with 800 rpm; 2—diesel engine with 2000 rpm; 3—Mi-24 helicopter; 4—post-fire sound; 5—T-34 tank; 6—jet aircraft

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narrower (Fig. 36a–d), and at large distances from the noise source they become similar (Fig. 36d). At the same time, in the vicinity of the radiation source, the differences between them are significantly greater (Fig. 36a). Thus, the influence on the frequencies of the corona discharge model for 100– 500 Hz can be such values that lead to overlapping the signal from the corona discharge or to wrong detection of the presence of the corona discharge.

References 1. Gryb, O.G., Karpaliuk, I.T., Zaporozhets, A.O., Shvets, S.V., Rudevich, N.V.: Acoustic diagnostics for determining the appearance of corona discharge. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 127–157 (2021) 2. Gryb, O., Karpaliuk, I., Shvets, S., Zaporozhets, A.: Recognition of corona discharge presence by acoustic system installed on unmanned aerial vehicle. Proc. Natl. Aviat. Univ. 4(85), 46–53 (2020) 3. Bartnikas, R.: Partial discharges. Their mechanism, detection and measurement. IEEE Trans. Dielectr. Electr. Insul. 9(5), 763–808 (2002) 4. Trinh, G.N.: Corona and Noise. Electric Power Generation, Transmission, and Distribution: The Electric Power Engineering Handbook, pp. 1–16 (2018) 5. Chen, S., Van Den Berg, R.G.W., Nijdam, S.: The effect of DC voltage polarity on ionic wind in ambient air for cooling purposes. Plasma Sources Sci. Technol. 27(5), 055021 (2018) 6. Babak, V., Zaporozhets, A., Zvaritch, V., Scherbak, L., Myslovych, M., Kuts, Y.: Models and measures in theory and practice of manufacturing processes. IFAC-PapersOnLine 55(10), 1956–1961 (2022) 7. Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O., et al.: Models of measuring signals and fields. In: Models and Measures in Measurements and Monitoring, pp. 33–59 (2021) 8. Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O., et al.: Models and measures for the diagnosis of electric power equipment. In: Models and Measures in Measurements and Monitoring, pp. 99–126 (2021) 9. Shao, J.: Mathematical Statistics. Springer Science & Business Media (2003) 10. Wackerly, D., Mendenhall, W., Scheaffer, R.L.: Mathematical statistics with applications. Cengage Learn. (2014) 11. FizmatFilm. Corona Discharge. https://youtu.be/oYRlxcpvBXs 12. Corona Discharge. https://youtu.be/ddobPfJj11k 13. Vaseghi, S.V.: Advanced Digital Signal Processing and Noise Reduction. Wiley (2008) 14. Fahy, F.J., Gardonio, P.: Sound and Structural Vibration: Radiation, Transmission and Response. Elsevier (2007) 15. Lukas, J., Fridrich, J., Goljan, M.: Digital camera identification from sensor pattern noise. IEEE Trans. Inf. Forensics Secur. 1(2), 205–214 (2006) 16. Ilkhechi, H.D., Samimi, M.H.: Applications of the acoustic method in partial discharge measurement: a review. IEEE Trans. Dielectr. Electr. Insul. 28(1), 42–51 (2021) 17. Gupta, N., Ramu, T.S.: Estimation of partial discharge parameters in GIS using acoustic emission techniques. J. Sound Vib. 247(2), 243–260 (2001) 18. Srinivasan, K.S., Ebenezer, D.: A new fast and efficient decision-based algorithm for removal of high-density impulse noises. IEEE Signal Process. Lett. 14(3), 189–192 (2007) 19. Garnett, R., Huegerich, T., Chui, C., He, W.: A universal noise removal algorithm with an impulse detector. IEEE Trans. Image Process. 14(11), 1747–1754 (2005) 20. Han, Y., Song, Y.H.: Condition monitoring techniques for electrical equipment-a literature survey. IEEE Trans. Power Deliv. 18(1), 4–13 (2003)

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21. Smith, J.D.: Gear Noise and Vibration. CRC Press (2003) 22. Babak, V.P., Babak, S.V., Eremenko, V.S., Kuts, Y.V., Myslovych, M.V., Scherbak, L.M., Zaporozhets, A.O., et al.: Problems and Features of Measurements. Models and Measures in Measurements and Monitoring, pp. 1–31 (2021) 23. Stone, G.C.: Partial discharge diagnostics and electrical equipment insulation condition assessment. IEEE Trans. Dielectr. Electr. Insul. 12(5), 891–904 (2005) 24. Chen, J., Pan, J., Li, Z., Zi, Y., Chen, X.: Generator bearing fault diagnosis for wind turbine via empirical wavelet transform using measured vibration signals. Renew. Energy 89, 80–92 (2016) 25. Babak, V., Zaporozhets, A., Kuts, Y., Myslovych, M., Fryz, M., Scherbak, L.: Models and characteristics of identification of noise stochastic signals of research objects. In: CEUR Workshop Proceedings, vol. 3309, pp. 349–362 (2022) 26. Filippone, A.: Aircraft noise prediction. Prog. Aerosp. Sci. 68, 27–63 (2014) 27. Ntantis, E.L., Li, Y.G.: The impact of measurement noise in GPA diagnostic analysis of a gas turbine engine. Int. J. Turbo Jet-Engines 30(4), 401–408 (2013) 28. Zhou, L., Duan, F., Corsar, M., Elasha, F., Mba, D.: A study on helicopter main gearbox planetary bearing fault diagnosis. Appl. Acoust. 147, 4–14 (2019) 29. Randall, R.B.: Detection and diagnosis of incipient bearing failure in helicopter gearboxes. Eng. Fail. Anal. 11(2), 177–190 (2004) 30. Xiang, Z., Zhang, X., Zhang, W., Xia, X.: Fault diagnosis of rolling bearing under fluctuating speed and variable load based on TCO spectrum and stacking auto-encoder. Measurement 138, 162–174 (2019) 31. Bosso, N., Gugliotta, A., Zampieri, N.: Wheel flat detection algorithm for onboard diagnostic. Measurement 123, 193–202 (2018) 32. Qatu, M.S.: Recent research on vehicle noise and vibration. Int. J. Veh. Noise Vib. 8(4), 289–301 (2012) 33. Huang, W., Li, Y., Wu, X., Shen, J.: The wear detection of mill-grinding tool based on acoustic emission sensor. Int. J. Adv. Manuf. Technol. 124(11–12), 4121–4130 (2023) 34. Ren, F., Zhu, C., He, M.: Moment tensor analysis of acoustic emissions for cracking mechanisms during schist strain burst. Rock Mech. Rock Eng. 53, 153–170 (2020) 35. Tokozume, Y., Ushiku, Y., Harada, T.: Learning from Between-Class Examples for Deep Sound Recognition (2017). arXiv:1711.10282 36. Thomson, D.: The sound book. Am. J. Phys. 82(12), 1201–1202 (2014)

Instruments for Identification of Corona Discharge Presence by Spectral Characteristics of Acoustic Radiation Artur Zaporozhets , Vitalii Babak , Viktor Starenkiy , Oleg Gryb , Ihor Karpaliuk , and Oleksiy Luka

Abstract The chapter discusses the mathematical model of the spectrum-acoustic dependencies of corona discharge. The model was created using the inverse Fourier transform applied to the results of experimental data processing. The application of this mathematical model allowed the development of a method for detecting the presence of corona discharge based on the spectral characteristics of acoustic radiation. Using the developed method, a technique for recognizing corona discharge in the presence of external acoustic noise was devised. To enable the use of the method in the development of devices for detecting corona discharge, methodologies for stationary and mobile devices were developed. The effectiveness of the method for detecting the presence of corona discharge based on the spectral characteristics of acoustic radiation was verified using two DJI Mavic Pro quadcopters. Keywords Corona discharge · Detection · Acoustic radiation · Bursts · Control system · Device · Microphone · UAV · Noise analysis

A. Zaporozhets (B) · V. Babak General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan V. Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology of the National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine O. Gryb · I. Karpaliuk · O. Luka National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_6

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1 Corona Discharge Detection by Uncontrolled Device Let’s consider the detection of corona discharge presence by means of equipment with the simplest technical support. This equipment includes a microphone and a recording device [1, 2]. This is in the case where the audio file will be processed on a computer separately after recording. Also, there is another variant, when the microphone is equipped with an analog–digital converter (ADC) and can be connected directly to the mobile computer (e.g. netbook). In this case, you can not only record the sound, but also carry out an online analysis of the sound series on the signs of the presence of spectrum from the corona discharge. Schematically a set of such equipment is shown in Fig. 1. The order of work with such equipment is as follows: – the direction to the acoustic source, where the corona discharge is likely to be located, is determined. This action is performing by directing the microphone, which held in the hand of the operator, during this moment, when the maximum signal is received by the microphone. – the direction fixes for 10 s. For this time hardware will process the signal and display the result with the probability of corona discharge detection. The distance of operation of such set of devices will depend on the power of the acoustic source and the power of noise. Therefore, the detection probability depends on the distance to the corona discharge, but this parameter is controlled by the operator himself getting closer to the source. If the probability of corona discharge detection increases, then the direction to the corona discharge is found. The range of operation of the above set of devices can be increased by increasing the coefficient of amplification the microphone amplifier, or by sounding of the

Fig. 1 Corona discharge detection by the handheld device

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microphone sensitivity curve, or by both parameters [3, 4] that can be achieved by using directional microphones (Figs. 2 and 3). Increasing the range of the specified set of devices can be increased by either increasing the gain of the microphone amplifier, or by narrowing the microphone

Fig. 2 Corona discharge detection by the handheld device with acoustic impulse concentrator

Fig. 3 Directional microphone

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sensitivity curve, or by both parameters that can be achieved using directional microphones (Figs. 2 and 3). Technical characteristics of the microphone on Fig. 3 are shown in Table 1. The algorithm of software for detecting the presence of a corona discharge works as follows. Step 1—mechanical filter cuts off the influence of wind on the microphone. Wind protection designed to eliminate extraneous noise that occurs when sound is transmitted through the air masses acting on the microphone [5, 6]. The airflow on the microphone creates vortices. Wind protection minimizes this effect, reducing noise by a dozen or more decibels (Fig. 4). Frequency characteristics of wind depending on the speed of the air are given in [7], presented in Figs. 5 and 6. Step 2—microphone detects acoustic fluctuations and converts them into a digital data stream for further processing. Table 1 Technical characteristics of the directional microphone №

Parameter

Value

1

Amplification level

Up to 107 dB

2

Distance to the captured sounds

Up to 100 m (depends on the volume of background extraneous noise)

3

Microphone directional angle

10°

4

Diameter of the plate

20 cm

5

Voice recorder

Up to 12 s

6

Audio jack

Mini Jack 3.5 mm

7

Power supply

9 V “Krona” battery

8

Range of captured frequencies

100–14,000 Hz

9

Weight

1.2 kg

10

Dimensions

17.5 × 28 × 5.5 cm

11

Temperature range

0 to +55 °C

Fig. 4 Variances of the microphone’s windproof equipment

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Fig. 5 Frequency characteristics of wind depending on the air speed

Fig. 6 Levels of noise generated by wind at certain frequencies depending on air speed

At the output of the microphone, we have the function x(t). Step 3—the first line of filters (digital) will pick up white noise, irregular bursts, and other noise: x(t) = f (t) + ξ(t),

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where f (t)—useful signal; ξ (t)—white noise. Step 4—timer splits the audio data stream into fragments of 10 s: f (t) =

N E

f (ti − ti−1 ) =

i=1

N E

f iAt (t),

i=1

where At—hourly interval for audio fragments (At = const); f iΔt —value of the function for the time interval At. Step 5—it will be performed Fourier transform [8, 9] for the fragment: {∞ F( jω) =

f iAt (t)dt. 0

Step 6—result of the Fourier transform is filtered by a set of narrow-band line filters [10, 11]: ⎧ ⎪ ∀ω; F 2 ( j ω2 ) ∈ R at 90 · 2π ≤ ω2 ≤ 110 · 2π ⎪ ⎪ ⎪ ⎪ ∀ω; F 3 ( j ω3 ) ∈ R at 140 · 2π ≤ ω3 ≤ 260 · 2π ⎪ ⎪ ⎨ ∀ω; F 4 ( j ω4 ) ∈ R at 190 · 2π ≤ ω4 ≤ 210 · 2π . M(ω) = ⎪ ∀ω; F 5 ( j ω5 ) ∈ R at 240 · 2π ≤ ω5 ≤ 260 · 2π ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ∀ω; F 6 ( j ω6 ) ∈ R at 290 · 2π ≤ ω6 ≤ 310 · 2π ⎩ ∀ω; F 7 ( j ω7 ) ∈ R at 340 · 2π ≤ ω7 ≤ 360 · 2π Only results that exist on the specified frequency ranges are considered. The width of each band is 20 Hz. Step 7—result after the filter is checked for compliance with the maximum value of the specified frequencies. The ratio of the maximum to the average value:  Fk_max (jωk ) n , Ak = k=2 Fk (jωk ) where Ak —value of the Fourier transform function and its ratio of maximum to average on the k-th interval Sk = Ak at

 n Ak ≥ Mk , then Sk = 0. k=2

Next operation is the checking for condition of the presence of maximum value Ak in the k-th range, which exceeds the given M k model value. If the assumption is fulfilled for all k, the corona discharge spectrum is probably present in the spectrum (we can define this probability at 60–80%). If the condition is fulfilled for all k (3, 5, 7), the probability of the presence of the corona discharge spectrum can be defined at

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50–70%. If the condition is fulfilled for all k (2, 4, 6), the probability of the presence of the corona discharge spectrum can be defined at 40–60%. This requirement can be defined as a necessary condition. Step 8—maximum values are checked for compliance the amplitude ratio mask to frequencies. Checking the relationship of Ak among themselves will answer the questions of corona discharge propagation. If this condition is true A3 A5 ≈ ≈ 2, A5 A7 or this condition is true A2 A4 ≈ ≈ 1, A4 A6 probability of the presence of the corona discharge spectrum can be estimated at 90%.

2 Corona Discharge Detection by the Device on the Moving Platform Automation of the power supply quality control process requires the use of systems for automatic detection of corona discharge presence and its coordinates [12–18]. The length of power lines of high and ultrahigh voltage (750, 330, 220, 110 kV) reaches thousands of kilometers. Corona discharge control requires the use of a significant number of diagnostic systems or the placing of such systems on moving platforms. The most promising platform is unmanned aerial vehicles (UAVs), because in most cases power lines are in private territories or pass through the areas that do not have roads for relocating road transport. UAVs can move quickly in the area and come closely to the energy objects at distances sufficient for conducting diagnostic operations [19–26]. Therefore, the UAV is accepted as the moving platform for the location of the diagnostic system. Currently, there are two main UAV designs: aircraft type and helicopter type (quadcopters). Each design has its disadvantages and advantages (Fig. 7). So, UAVs-quadcopters are designed to observed electrotechnical elements near the operator. The range can reach up to 5 km. This type of UAV can also be used for the inspection of structures and conductive elements. UAVs of aircraft type have longer range and higher speed of flight, so they are planned to use for operational inspection and location of damage of electrical equipment or lines.

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Fig. 7 Comparison of aircraft and quadcopter designs of UAVs

Let’s look at UAVs-quadcopters as the possibility of using for the placement of acoustic control equipment. Engines and rotors of the UAV produce acoustic vibrations during operation, which may interfere for acoustic measurements.

2.1 Noise Analysis of DJI Mavic Pro Quadcopter The quadcopter DJI Mavic Pro (Fig. 8) (Da-Jiang Innovations Science and Technology Co., China) was analyzed [27–29]. Time of working is 30 min, range of flight is up to 7000 m. The UAV uses electric motors that are powered by 4 rotors and provide for vertical takeoff and landing. Its flying speed is up to 65 km/h. Dimensions: 198 × 82 × 83 mm. Weight is 0.74 kg. Height of flight is up to 5 km (programmatically limited to 120 m from the starting point). The UAV is designed for a maximum weight of 1 kg, with a maximum load of 0.4 kg. Among the features of the device should be noted the low price and automatic return system (and landing). It is equipped by video camera.

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Sound files with different operation modes were recorded for this quadcopter (takeoff, hovering, and flying). These main modes of the quadcopter are necessary during performing diagnostics of electric power supply systems. Fragments of the acoustic files [2] of the quadcopter operation modes are shown in Figs. 9, 10 and 11.

Fig. 8 DJI Mavic Pro quadcopter

Fig. 9 Fragment of the acoustic file of DJI Mavic Pro quadcopter (takeoff mode)

Fig. 10 Fragment of the acoustic file of DJI Mavic Pro quadcopter (hovering mode)

Fig. 11 Fragment of the acoustic file of DJI Mavic Pro quadcopter (flying mode)

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Each of the indicated audio files was analyzed for the components of the acoustic spectrum (Figs. 12, 13 and 14). Let’s plot the spectral curves on one graph and compare it with the spectrum of the corona discharge (Fig. 15). By the enlarged spectral analysis (Fig. 15) it can be seen that spectral lines of the quadcopter engines operation modes [30, 31] overlap the spectral lines of the corona discharge. But if we consider the spectral functions in the range where the spectral feature of the corona discharge is better shown and which was included into the model for

Fig. 12 Spectrum of the acoustic file (takeoff mode)

Fig. 13 Spectrum of the acoustic file (hovering mode)

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Fig. 14 Spectrum of the acoustic file (flying mode)

Fig. 15 Comparison of spectra of quadcopter operation modes and different corona discharge powers (DJI Mavic Pro quadcopter)

recognizing the corona discharge (this is the range from 0 to 500 Hz), then in this range it can be seen the following (Fig. 16). It can be seen that at ranges from 0 to 150 Hz the corona discharge amplitudes can exceed the amplitudes of the quadrocopter engines. The increased detailing of the spectral analysis results is shown in Fig. 17. It can be seen that for some flying modes of the quadcopter there can be a situation when the acoustic noise of the engines does not overlap spectral corona discharge peaks. Let’s consider the situation in more details (Figs. 18, 19, 20, 21, 22 and 23). Obviously, during the flight of a quadrocopter, the corona discharge can be determined only by some peaks, which are shown in Fig. 24.

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Fig. 16 Comparison of spectra of quadrocopter and corona discharge at 0–500 Hz range (fast Fourier transform (FFT) discreteness 1024)

Fig. 17 Comparison of spectra of quadrocopter and corona discharge at 0–500 Hz range (FFT discreteness 65536)

But when piloting mode changing from flying to hovering, the spectrum of the quadrocopter changes, and in this case it is possible to determine a greater number of spectral peaks of the corona discharge (Fig. 25). This confirms the possibility of installing an acoustic system on a quadrocopter. But the procedure for determining the presence of a corona discharge will take some changes. Thus, during flight, the corona discharge can be determined only by two spectral components –150 Hz and 250 Hz. This determination of the presence has little accuracy, therefore, when such marker signals appear at certain frequencies, the quadcopter must go into hovering mode and check the presence for peaks at 100, 150, 200, 250, 300 Hz and, for example, 450 Hz. If there are peaks at these frequencies with a width of no more than 2 Hz, the presence of a corona discharge can be recognized.

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Fig. 18 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 100 Hz

Fig. 19 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 150 Hz

Fig. 20 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 200 Hz

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Fig. 21 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 250 Hz

Fig. 22 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 300 Hz

Fig. 23 Comparison of spectra of quadrocopter and corona discharge in the vicinity of 350 Hz

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Fig. 24 Spectral corona discharge peaks and spectrum of the quadcopter during flight

Fig. 25 Corona discharge spectral peaks and spectrum of the quadcopter during hovering

2.2 Sound Noise Analysis of Quadcopter of Unknown Manufacturer To test the possibility of using models of quadcopters from other manufacturers, a random video from YouTube with a quadcopter flight was selected. As a test of the possibility of using a UAV as a moving platform for acoustic diagnostic complex, a random file with a flight of a quadrocopter of an unknown manufacturer was selected (Figs. 26 and 27). The track was divided into two fragments corresponding to different quadrocopter piloting modes (Figs. 28, 29 and 30). Each of the audio files was analyzed on the components of the acoustic spectrum (Figs. 31, 32 and 33).

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Fig. 26 Frames from video clip with the quadrocopter flight

Fig. 27 Audio track from video clip with the quadcopter flight

Fig. 28 Fragment of the sound file of quadrocopter piloting (takeoff mode)

Fig. 29 Fragment of the sound file of quadrocopter piloting (hovering mode)

Spectral curves were reduced to one graph to compare it with the corona discharge spectrum (Figs. 34, 35, 36, 37, 38, 39, 40, 41 and 42). Obviously, during the quadrocopter flight it is possible to determine the corona discharge only by some peaks, which are shown in Fig. 43.

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Fig. 30 Fragment of the sound file of quadrocopter piloting (flying mode)

Fig. 31 Spectrum of acoustic file (takeoff mode)

Fig. 32 Spectrum of acoustic file (hovering mode)

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Fig. 33 Spectrum of acoustic file (flying mode)

Fig. 34 Comparison of spectra of quadcopter operation modes and different corona discharge powers (quadcopter of unknown manufacturer)

Fig. 35 Comparison of quadrocopter spectra and corona discharge at 0–500 Hz range (FFT discreteness 1024)

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Fig. 36 Comparison of quadrocopter spectra and corona discharge at 0–500 Hz range (FFT discreteness 65536)

Fig. 37 Comparison of quadrocopter spectra and corona discharge in the vicinity of 100 Hz

Fig. 38 Comparison of quadrocopter spectra and corona discharge in the vicinity of 150 Hz

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Fig. 39 Comparison of quadrocopter spectra and corona discharge in the vicinity of 200 Hz

Fig. 40 Comparison of quadrocopter spectra and corona discharge in the vicinity of 250 Hz

Fig. 41 Comparison of quadrocopter spectra and corona discharge in the vicinity of 300 Hz

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Fig. 42 Comparison of quadrocopter spectra and corona discharge in the vicinity of 350 Hz

Fig. 43 Corona discharge spectral picks and spectrum of the quadcopter during flight

When piloting mode changing into hovering, the spectrum of the quadrocopter changes and the spectral peaks of the corona discharge can be more determined (Fig. 44). Thus, the possibility of installing the acoustic system on the quadcopter and other manufacturers is confirmed. The results of the spectral analysis confirmed the possibility of using the UAV as a platform for deploying the acoustic diagnostics system.

3 Work Distance of Scanning System The range and resolution of the acoustic system depend on the level of the acoustic signal and its spectrum, as well as on the properties of the propagation medium and the underlying surface.

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Fig. 44 Spectral corona discharge peaks and spectrum of the quadcopter during hovering

The equivalent downwind sound pressure level P1 (R) at the receiver on a logarithmic scale can be calculated for each point source. Taking into account the radar equation, it can be written as: P1 (R) = P0 + G + L ,

(1)

where P0 —sound power level of the point noise source equal to 1 pW in [dB] unit; G—correction that takes into account the directionality of the point noise source and indicates how much the equivalent sound pressure level of the point source noise in a given direction deviates from the sound pressure level of the unidirectional point source noise with the same sound power level P0 , [dB]; L—attenuation at the extension of sound from the point noise source to the receiver taking into account the influence of all factors, [dB]. L(R) value in (1) calculates by the formula: L(R) = L div (R) + L atm (R) + Vgr (R, h r , h T ) + L bar + L misc ,

(2)

where L div (R)—attenuation through geometric divergence (attenuation in free space due to the difference in sound energy); L atm (R)—attenuation caused by the sound absorption of the atmosphere; V gr (R, hr , hT )—attenuation caused by the influence of the earth; L bar —attenuation caused by shielding; L misc —attenuation due to other reasons. Geometrical divergence attenuation (free space attenuation due to difference in sound energy) L div (R) [dB] resulting from the spherical sound propagation of a point noise source in a free sound field is calculated by the formula:  L div (R) = 20 · lg d d 0 , where d—distance from the noise source to the receiver in [m]; d 0 —reference distance (usually d 0 = 1 m is used).

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During calculating, it is necessary to use data on the level of noise from different sources and the calculated values of the integral factors of attenuation of the atmosphere of the detection range of objects of acoustic radiation under different weather conditions and external interference. It should be noted that during making estimates, the noise must be taken as stationary Gaussian processes with a given average intensity [32–34]. Motion sounds of people and animals are a highly non-stationary process and this can lead to additional losses in the signal-to-noise ratio when a corona discharge is detected.

References 1. Gryb, O.G., Karpaliuk, I.T., Zaporozhets, A.O., Shvets, S.V., Rudevich, N.V.: Acoustic diagnostics for determining the appearance of corona discharge. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 127–157 (2021) 2. Gryb, O., Karpaliuk, I., Shvets, S., Zaporozhets, A.: Recognition of corona discharge presence by acoustic system installed on unmanned aerial vehicle. Proc. Natl. Aviat. Univ. 4(85), 46–53 (2020) 3. Bahl, I.: Fundamentals of RF and Microwave Transistor Amplifiers. Wiley (2009) 4. Reichenbach, T., Hudspeth, A.J.: Unidirectional mechanical amplification as a design principle for an active microphone. Phys. Rev. Lett. 106(15), 158701 (2011) 5. Hurst, A.M., Goodman, S., Hilton, J.P., VanDeWeert, J.: Miniature low-pass mechanical filter for improved frequency response with MEMS microphones & low-pressure transducers. Sens. Actuators A 210, 51–58 (2014) 6. Rämö, J., Välimäki, V.: Digital augmented reality audio headset. J. Electr. Comput. Eng. 2012 (2012) 7. Murugan, S.S., Natarajan, V., Kumar, R.R.: Noise model analysis and estimation of effect due to wind driven ambient noise in shallow water. Int. J. Oceanogr. 2011 (2011) 8. Zaporozhets, A., Redko, O., Babak, V., Eremenko, V., Mokiychuk, V.: Method of indirect measurement of oxygen concentration in the air. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu 5, 105–114 (2018) 9. Zaporozhets, A., Eremenko, V., Babak, V., Isaienko, V., Babikova, K.: Using Hilbert transform in diagnostic of composite materials by impedance method. Periodica Polytech. Electr. Eng. Comput. Sci. 64(4), 334–342 (2020) 10. Seiler, R., Paul, T., Andrist, M., Merkt, F.: Generation of programmable near-Fourier-transformlimited pulses of narrow-band laser radiation from the near infrared to the vacuum ultraviolet. Rev. Sci. Instrum. 76(10), 103103 (2005) 11. Grotevent, M.J., Yakunin, S., Bachmann, D., Romero, C., Vázquez de Aldana, J.R., Madi, M., Shorubalko, I.: Integrated photodetectors for compact Fourier-transform waveguide spectrometers. Nat. Photonics 17(1), 59–64 (2023) 12. Senderovich, G.A., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V., Rudevich, N.V.: Improving methods for one-sided determination of the location of damage of overhead power lines in networks with effectively grounded neutral based on UAVs. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 9–34. Springer International Publishing, Cham (2021) 13. Senderovich, G.A., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V., Samoilenko, I.A.: Automation of determining the location of damage of overhead power lines. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 35–53 (2021) 14. Senderovich, G.A., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V., Samoilenko, I.A.: Experimental studies of the method for determining location of damage of overhead

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Theoretical Basis of Determination of Corona Discharge Coordinates by Acoustic Radiation Yevgen Sokol , Vitalii Babak , Artur Zaporozhets , Oleg Gryb , Ihor Karpaliuk , and Roman Demianenko

Abstract The issues of developing a method for determining the coordinates of a corona discharge from its acoustic radiation are considered. Theoretical foundations for constructing a three-dimensional acoustic wave pressure field are presented. For constructing a three-dimensional acoustic field, the parameters of a corona discharge as a sound source are described, namely, the acoustic intensity curves for the “source—corona discharge” were taken, which made it possible to calculate the pressure fields of the acoustic field for an insulator (point source) and for a wire (linear source). The isolines of the acoustic field of equivalent corona discharge sources are calculated. The acoustic field is constructed for different harmonic components (50; 150; 250 Hz). The location of the source of the acoustic field is determined from the isolines of the pressure field of the acoustic wave. This allows to create a method for finding the coordinates of the corona discharge source and adapt it for diagnostic devices. Keywords Corona discharge · Acoustic radiation · Acoustic field · Noise analysis · Energy characteristics · Pressure of acoustic wave

Y. Sokol · O. Gryb · I. Karpaliuk · R. Demianenko National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_7

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1 Three-Dimensional Pressure Field of the Acoustic Wave of Corona Discharge 1.1 Theoretical Information About the Acoustic Field of Corona Discharge For formation of the acoustic field, it was considered the equation for pressure wave [1–3]. Let’s write the wave equation for three dimensions. An air particle at the point (x, y, z) can move in any direction, so we will write the three components of its displacement from the equilibrium position. This displacement d is a vector of the ξ, η and ε components in the x, y and z directions. The corresponding particle velocity is u = ∂d and has components u, y and z. All these quantities together with the pressure ∂t p are functions of x, y, z and t. The elementary volume dxdydz, shifting during the passage of a acoustic wave, transforms into a parallelepiped of volume J, where   1 + ∂ξ  ∂x  J =  ∂∂ηx  ∂ς  ∂x

∂ξ ∂y ∂η ∂y ∂ς ∂y

∂ξ ∂z ∂η ∂z

1+

∂ς ∂z

   ∼  = 1 + di v(d).  

is called the particle displacement divergence. The quantity di v(d) = ∂∂ξx + ∂∂ηx + ∂ς ∂x According to the continuity equation δ = − ∂∂ξx , it can be written 1+δ =

1 ∼ ; δ = −di v(d). J

Also, we know, that p = γC P0 δ, where γC —the ratio of specific heat capacities at constant pressure and constant volume (for air of normal conditions it takes a value 1.4). For adiabatic gas compression, the following equation can be written: 1+

P 1 = (1 + δ)γC = γ ; p ∼ = −γC P0 di v(d), P0 J C

where γC = CCPv —the ratio of specific heat capacities at constant pressure and constant volume. It follows from Newton’s second law that p

∂u = −grad( p), ∂t

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where grad( p)—pressure gradient vector. Its components are: equations can be combined as follows:

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+ ∂∂ py + ∂∂zp . These

  γC P0 ∂2 p ∂u = = −γC P0 di v di v(grad( p)) = c2 ∇ 2 p, 2 ∂t ∂t ρ where c2 =

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(1)

of pressure, defined by the equation

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which called Laplacian. Formula (1) is a three-dimensional wave equation (for pressure). The particle velocity for a simple harmonic wave can be obtained from the pressure through the relation u=

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The potential energy of gas volume in some instantaneous state can be expressed using absolute temperature: ρC0 T =

P0 C0 P0 (1 + δ)γC P0 = . · (1 + δ)γC = R (1 + δ) (γC − 1) (γC − 1)J γC −1

0 is the internal energy of the gas at The equilibrium value of this quantity (γCP−1) equilibrium and is not included in the equation for the acoustic wave energy. If we expand the expression J γC1 −1 into a series in small quantities ∂∂ξx , etc., then the terms containing these quantities of the first order, as well as their multiplication of the , ∂η etc. can be ignored, since the average value of these terms is equal to form ∂ς ∂ y ∂z

zero. The average value of only those terms that contain the squares of the values etc., was not converted to zero, so   1 P0 P0 ∼ , − 1 = (γC − 1) J γC −1 (γC − 1)

∂η , ∂y

C di v 2 d—neglected components. because (γC −1)γ 2 The average acoustic wave energy is [4, 5]:

1 W ∼ = ρ 2

˚ 

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2

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 1 2 1 2 d xd ydz. ρu + p 2 2ρc2

By setting the initial data for a point acoustic emitter of a corona discharge, a further calculation can be made.

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1.2 Calculation of Equivalent Acoustic Pressure Levels During calculating equivalent acoustic pressure levels L req and maximum acoustic levels L Amax SP51.13330.2011 [6], it recommends to use equivalent acoustic power levels L weq and maximum acoustic power levels L Wmax in octave frequency band of technological and engineering equipment that creates noise that is not constant in time [7–9]. The main noise characteristic for non-constant noise is the equivalent acoustic pressure levels in octave frequency bands and the energy-equivalent acoustic level in dBA. Such a simplification is mainly due to the complexity and laboriousness of assessing the energy characteristics of non-constant noise fields in octave frequency bands during measurements and the lack of reliable methods for calculating their characteristics at the stage of designing noise protection facilities [10, 11]. Basically, such calculation methods are developed for constant noise fields. In this case, at calculating noise and designing noise protection means, acoustic pressure levels in octave bands are determined before and after the use of noise protection means, such as acoustic-absorbing linings [12–14], and then their acoustic efficiency is evaluated. At the same time, for non-constant noise, during assessing the noise level, at calculating the acoustic efficiency of measures to reduce non-constant noise, in addition to the equivalent level of non-constant noise, it is necessary to have information about its other energy characteristics: maximum and minimum levels, their relationship to each other, background noise level, ratios between non-constant noise levels and background noise levels [15–17]. In particular, under the action of periodic noise sources, it is necessary to have information about the rise and fall times of noise energy at the calculated points. As for constant noise, the main quantity that determines the energy parameters of non-constant noise is the acoustic pressure level [18, 19]. Level calculations perform for values averaged over octave frequency bands. If necessary, they can also be performed in one-third octave bands. It is assumed that the incoherence condition is observed for the waves arising in space, and, accordingly, the arithmetic summation of their energies is allowed. Noise sources are broadband and their power level does not depend on the environment parameters [20, 21]. The acoustic pressure level is defined as  2 p (3) L i (t) = 10 lg 2 , p0 where p—root mean square of acoustic pressure, p0 = 2 × 10–5 Pa—acoustic pressure at the hearing threshold. The distribution of acoustic energy can also be characterized by the intensity of the sound, which is related to the sound pressure ratio I =

p2 , ρc

(4)

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where ρ—medium density, c—sound velocity. In calculations, it is more convenient to use the scalar energy characteristic of the noise field, namely, the acoustic energy density related to the acoustic intensity and acoustic pressure by the equations ε=

p2 I = . c ρc

(5)

Then the level of acoustic pressure can be defined as L = 10 lg

p2 I cε ρc2 ε = 10 lg = 10 lg = 10 lg , I0 I0 p02 p02

(6)

where I 0 = 10–12 W/m2 —acoustic intensity at the hearing threshold. In practice, calculations performs with a scalar energy characteristic of the noise field—acoustic energy density S. The density of acoustic energy [22, 23] at the calculation points of the room with non-constant noise is determined by the density of the direct energy coming to the calculation point directly from the source of variable acoustic power, and the density of the reflected component of the acoustic energy that occurs when direct sound is reflected from fencing. I and other energy components create time-varying acoustic pressure levels L t , which in total at each i-th calculated point at any calculated time t can be determined as ⎤ ⎡  ref dir c εt,i + εt,i ⎦, (7) L t,i = 10 lg⎣ I0 ref

dir where εt,i , εt,i —acoustic energy density of the direct sound and the reflected noise component at time t at the i-th calculated point. Knowing the variable acoustic power of the noise source, it is possible to determine ref dir and εt,i , construct a spatio-temporal exposure of the levels of nonthe values of εt,i constant noise and, accordingly, determine all the above characteristics necessary for the analysis and evaluation of non-constant noise. As can be seen from formula (5), in order to evaluate non-constant noise, it is necessary to have methods for calculating the acoustic energy density of direct and reflected sound. To determine the density of direct sound, it is necessary to know the variable acoustic power of the source and the conditions for the emission of acoustic energy into objects surround the space source, namely, the form of the source in shape (point, linear, volumetric, complex), its geometric parameters, the heterogeneity of surfaces radiation, the factor directivity, the nature of the emitted noise, etc. [24–27].

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2 Acoustic Intensity Curves of Acoustic Source of Corona Discharge According to the measurements carried out in [28–31], the power losses for a corona discharge are average from 129.5 to 83.3 kW/km (for lines with a voltage of 500 kV). Let’s take the average value of power losses—100 kW/km or 100 W/m. The acoustic emitter is a sphere with a radius of 0.2 m. The source of acoustic waves from the corona discharge will be considered as a point source [32–37]. In accordance with the theory of acoustics, a “point” emitter is such an emitter, the dimensions of which, compared with the length of the emitted acoustic wave, can be neglected. The direction of radiation of a acoustic swave in the theory of acoustics is called the directivity pattern. Let’s expand this term and accept that the directivity pattern is a combination of the ends of the power vectors (acoustic pressure force) in space. For a flat representation, sections of a volumetric body by planes are used—a vertical plane and a horizontal plane. Then we can talk about the acoustic intensity curve (AIC) (Figs. 1 and 2). The occurrence of a corona discharge at one point does not lead to significant losses on the line and, accordingly, does not lead to significant acoustic emissions. But corona discharge occurs simultaneously in several places of conductive equipment. Therefore, the source of the acoustic signal from corona discharges can be considered as simultaneous in space [38–42]. At the same time, for a corona discharge on a wire, the AIC has the form shown in Fig. 3. Fig. 1 AIC of corona discharge on insulator

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Fig. 2 AIC of corona discharge on insulator in space

Fig. 3 AIC from a corona discharge on a wire

Let us construct the AIC as a simultaneous one from a corona discharge on insulators (Figs. 4 and 5) and on a wire (Fig. 6). For a corona discharge on an insulator in space, the AIC has the form shown in Fig. 2.

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Fig. 4 String of insulators for AIC calculating

3 Calculating Results of the Pressure Levels of the Acoustic Field from the Corona Discharge Calculating the pressure levels of the acoustic field from a string of insulators with a corona discharge To calculate the pressure levels of the acoustic field, we take a rectangular space, in the center of which it was placed a string of insulators (Fig. 7). Figure 7 denotes x—length, y—width, z—height of the space (x = 10 m, y = 10 m, z = 5 m), hd —height of the location of the research instruments (1.5 m), h—height from the string of insulators to registration devices (3.5 m). The picture of the isolines of the acoustic field is built in the XY plane. We accept the number of insulators in the string N = 5 pcs. We assume that a corona discharge will appear on each of them. We take the acoustic power of each of the acoustic sources W s = 1 W. The first calculation was made for a frequency of 50 Hz. The calculations were performed for the energy and interference fronts of the acoustic field (Fig. 8). The pattern of pressure isolines of the acoustic field for a frequency of 50 Hz shows that the detection of a corona discharge at this frequency is very problematic.

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The average gradient is very small. The acoustic field strength is less than 54 dB. But it turned out that for the interference pattern of the acoustic field, it is even possible to find the source of the location of the corona discharge, which creates an acoustic peak in the projection of the insulator onto the modeling plane. The gradient of the acoustic field in the interference calculation can be more than 2 dB, which is already noticeable for measuring instruments for finding the coordinates of the acoustic source. The pattern of pressure isolines of the acoustic field for the third harmonic frequency of 150 Hz (Fig. 9) shows that the detection of a corona discharge at this frequency can be performed by energy calculation. The acoustic field strength is 82–84 dB, which is sufficient. The average gradient is 6 dB. But the interference pattern of the acoustic field has interference radii of a powerful front of 86 dB greater than 5 m. The acoustic field gradient in the interference calculation is almost 0 dB, which is problematic for detecting a acoustic source at such a distance.

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Fig. 6 AIC from simultaneous corona discharge at several locations on a wire

Fig. 7 Space for calculating the acoustic field from a source with a corona discharge (string of insulators)

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Fig. 8 Calculating result of the pressure isolines of the acoustic field for a string with 5 insulators at a frequency of 50 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

Fig. 9 Calculating result of the pressure isolines of the acoustic field for a string with 5 insulators at a frequency of 150 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

The pattern of pressure isolines of the acoustic field for the fifth harmonic frequency of 250 Hz (Fig. 10) shows that the detection of a corona discharge at this frequency can be performed by energy calculation. The acoustic field strength is 78–80 dB, which is sufficient. The average gradient is 6 dB. But the interference pattern of the acoustic field has interference radii with a peak in the acoustic source projection of 70 dB, and a significant acoustic field gradient of almost 10 dB, sufficient to find the acoustic source.

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Fig. 10 Calculating result of the pressure isolines of the acoustic field for a string with 5 insulators at a frequency of 250 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

Calculating the pressure levels of the acoustic field from a wire with a corona discharge To calculate the acoustic field, we take a rectangular space, in the center of which we place a wire with an acoustic signal source, which should simulate the acoustic source of a corona discharge (Fig. 11). Figure 11 denotes x—length, y—width, z—height of the space (x = 20 m, y = 20 m, z = 10 m), hd —height of the location of the research instruments (1.5 m), h—height from a wire to registration devices (8.5 m). The picture of the isolines of the acoustic field is built in the XY plane. We accept the number of corona discharge sources on the wire N = 10 pcs. Let us take the acoustic power of each of the acoustic sources W s = 1 W. The first calculation will be made for a frequency of 50 Hz. The calculations were performed for the energy and interference fronts of the acoustic field (Fig. 12). The pattern of pressure isolines of the acoustic field for a frequency of 50 Hz shows that the detection of a corona discharge at this frequency is very problematic. The average gradient is very small. The acoustic field strength is less than 54 dB. However, for the interference pattern of the acoustic field, it is likely to find the source of the corona discharge location, which creates an acoustic peak not only in the projection of the wire on the modeling plane, but also the gradient maximum extends to a distance of 5 m. The intensity of the acoustic field at the epicenter of the interference pattern is 62–64 dB. The gradient of the acoustic field in the interference calculation can be more than 10 dB, which is noticeable for measuring instruments for finding the coordinates of the acoustic source. The pattern of pressure isolines of the acoustic field for the third harmonic frequency of 150 Hz (Fig. 13) shows that the detection of a corona discharge at this frequency by energy calculation can be performed. The acoustic field strength is 82–84 dB, which is a sufficient indicator. The average gradient is 6 dB. But the

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Fig. 11 Space for calculating the pressure of the acoustic field from a source with a corona discharge (cable-wire)

Fig. 12 Calculating result of the pressure isolines of the acoustic field for a wire with 10 sources at a frequency of 50 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

interference pattern of the acoustic field has interference radii of more than 5 m with a powerful front of 94–96 dB. The acoustic field gradient in the interference calculation is almost 20 dB, in the direction perpendicular to the wire and at distances of more than 10 m. This is enough to find the acoustic source.

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Fig. 13 Calculating result of the pressure isolines of the acoustic field for a wire with 10 sources at a frequency of 150 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

The pattern of pressure isolines of the acoustic field for the fifth harmonic frequency of 250 Hz (Fig. 14) shows that the detection of a corona discharge at this frequency can be performed by energy calculation. The intensity of the acoustic field is sufficient values of 78–80 dB. The average gradient is 8 dB over the calculated distance. In addition, the interference pattern of the acoustic field has a pronounced peak directed perpendicular to the acoustic source and with an acoustic intensity at the epicenter of 84–86 dB, and a significant acoustic field gradient of more than 20 dB, which allows to find the acoustic source. From pattern of pressure isolines for different acoustic frequencies (50; 150; 250 Hz) and different types of sources, it is clearly seen that there are zones where

Fig. 14 Calculating result of the pressure isolines of the acoustic field for a wire with 10 sources at a frequency of 250 Hz (energy fronts of the acoustic field—on the left, interference fronts—on the right)

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the detection of source coordinates is most probable. Such zones should be used for devices with a significant intrinsic speed, which will allow to determine the coordinates of the acoustic source, that is, the coordinates of the corona discharge.

References 1. Ziomek, L.: Fundamentals of Acoustic Field Theory and Space-Time Signal Processing. CRC Press (2020) 2. Kozuka, T., Yasui, K., Tuziuti, T., Towata, A., Iida, Y.: Noncontact acoustic manipulation in air. Jpn. J. Appl. Phys. 46(7S), 4948 (2007). https://doi.org/10.1143/JJAP.46.4948 3. Ghorbaniasl, G., Huang, Z., Siozos-Rousoulis, L., Lacor, C.: Analytical acoustic pressure gradient prediction for moving medium problems. Proc. R. Soc. A: Math. Phys. Eng. Sci. 471(2184), 20150342 (2015). https://doi.org/10.1098/rspa.2015.0342 4. Berkhout, A.J.: Seismic Migration: Imaging of Acoustic Energy by Wave Field Extrapolation: Imaging of Acoustic Energy by Wave Field Extrapolation. Elsevier (2012) 5. Shilton, R.J., Travagliati, M., Beltram, F., Cecchini, M.: Nanoliter-droplet acoustic streaming via ultra high frequency surface acoustic waves. Adv. Mater. 26(29), 4941–4946 (2014) 6. SNiP 03-23-2003: Noise Protection. DEAN (2004) 7. Rosowski, J.J., Chien, W., Ravicz, M.E., Merchant, S.N.: Testing a method for quantifying the output of implantable middle ear hearing devices. Audiol. Neurotol. 12(4), 265–276 (2007) 8. Pedersen, E., Waye, K.P.: Wind turbine noise, annoyance and self-reported health and wellbeing in different living environments. Occup. Environ. Med. 64(7), 480–486 (2007) 9. Elliott, S.J., Cheer, J., Murfet, H., Holland, K.R.: Minimally radiating sources for personal audio. J. Acoust. Soc. Am. 128(4), 1721–1728 (2010) 10. Martins, D.P., Alencar, M.S.: A new approach to noise measurement and analysis in an industrial facility. In: 2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC) Proceedings, pp. 964–967. IEEE (2014) 11. Sauro, R.: Improvements to the standards for the testing of noise protection equipment. J. Acoust. Soc. Am. 150(4), A117–A117 (2021) 12. Kang, C.W., Kim, M.K., Jang, E.S.: An experimental study on the performance of corrugated cardboard as a sustainable sound-absorbing and insulating material. Sustainability 13(10), 5546 (2021) 13. Kosała, K.: Experimental tests of the acoustic properties of sound-absorbing linings and cores of layered baffles. Vib. Phys. Syst. 32(1) (2021) 14. Groby, J.P., Huang, W., Lardeau, A., Aurégan, Y.: The use of slow waves to design simple sound absorbing materials. J. Appl. Phys. 117(12), 124903 (2015) 15. Wu, Z., Huang, N.E.: A study of the characteristics of white noise using the empirical mode decomposition method. Proc. R. Soc. Lond. Ser. A: Math. Phys. Eng. Sci. 460(2046), 1597– 1611 (2004) 16. Norton, M.P., Karczub, D.G.: Fundamentals of Noise and Vibration Analysis for Engineers. Cambridge University Press (2003) 17. Babak, V., Zaporozhets, A., Kuts, Y., Myslovych, M., Fryz, M., Scherbak, L.: Models and characteristics of identification of noise stochastic signals of research objects. In: CEUR Workshop Proceedings, vol. 3309, pp. 349–362 (2022) 18. Švec, J.G., Granqvist, S.: Tutorial and guidelines on measurement of sound pressure level in voice and speech. J. Speech Lang. Hear. Res. 61(3), 441–461 (2018) 19. Borucki, S., Boczar, T., Cichon, A.: Technical possibilities of reducing the sound pressure level emitted into the environment by a power transformer. Arch. Acoust. 36(1), 49–56 (2011) 20. Li, J., Deng, L., Gong, Y., Haeb-Umbach, R.: An overview of noise-robust automatic speech recognition. IEEE/ACM Trans. Audio Speech Lang. Process. 22(4), 745–777 (2014)

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21. World Health Organization: Environmental Noise Guidelines for the European Region. World Health Organization, Regional Office for Europe (2018) 22. Cui, N., Gu, L., Liu, J., Bai, S., Qiu, J., Fu, J., Wang, Z.L., et al.: High performance sound driven triboelectric nanogenerator for harvesting noise energy. Nano Energy 15, 321–328 (2015) 23. Meissner, M.: Acoustic energy density distribution and sound intensity vector field inside coupled spaces. J. Acoust. Soc. Am. 132(1), 228–238 (2012) 24. Ing, R.K., Quieffin, N., Catheline, S., Fink, M.: In solid localization of finger impacts using acoustic time-reversal process. Appl. Phys. Lett. 87(20), 204104 (2005) 25. Cummer, S.A., Christensen, J., Alù, A.: Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1(3), 1–13 (2016) 26. Choi, J., Jung, I., Kang, C.Y.: A brief review of sound energy harvesting. Nano Energy 56, 169–183 (2019) 27. Gurbuz, C., Schmid, J.D., Luegmair, M., Marburg, S.: Energy density-based non-negative surface contributions in interior acoustics. J. Sound Vib. 527, 116824 (2022) 28. Gryb, O., Karpalyuk, I., Gapon, D., Rudevich, N., Demianenko, R.: Relations between the coronal discharge and the electricity quality. Bull. Natl. Tech. Univ. “KhPI”. Ser.: Hydraul. Mach. Hydraul. Units 2, 74–79 (2021). https://doi.org/10.20998/2411-3441.2021.2.11 29. Mujˇci´c, A., Suljanovi´c, N., Zajc, M., Tasiˇc, J.F.: Corona noise on a 400 kV overhead power line: measurements and computer modeling. Electr. Eng. 86, 61–67 (2004) 30. Gunasekaran, B., Yellaiah, A.: Corona loss measurements in corona cage on UHV bundle conductors. In: 16th National Power Systems Conference, Hyderabad, pp. 558–561 (2010) 31. Lings, R.: Overview of transmission lines above 700 kV. In: 2005 IEEE Power Engineering Society Inaugural Conference and Exposition in Africa, pp. 33–43. IEEE (2005) 32. Gryb, O.G., Karpaliuk, I.T., Zaporozhets, A.O., Shvets, S.V., Rudevich, N.V.: Acoustic diagnostics for determining the appearance of corona discharge. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 127–157 (2021) 33. Lima, S.E., Frazão, O., Farias, R.G., Araujo, F.M., Ferreira, L.A., Santos, J.L., Miranda, V.: Mandrel-based fiber-optic sensors for acoustic detection of partial discharges—a proof of concept. IEEE Trans. Power Deliv. 25(4), 2526–2534 (2010) 34. Ghosh, R., Chatterjee, B., Dalai, S.: A method for the localization of partial discharge sources using partial discharge pulse information from acoustic emissions. IEEE Trans. Dielectr. Electr. Insul. 24(1), 237–245 (2017) 35. Yaacob, M.M., Alsaedi, M.A., Rashed, J.R., Dakhil, A.M., Atyah, S.F.: Review on partial discharge detection techniques related to high voltage power equipment using different sensors. Photonic Sens. 4, 325–337 (2014) 36. Castro, B., Clerice, G., Ramos, C., Andreoli, A., Baptista, F., Campos, F., Ulson, J.: Partial discharge monitoring in power transformers using low-cost piezoelectric sensors. Sensors 16(8), 1266 (2016) 37. Markalous, S.M., Tenbohlen, S., Feser, K.: Detection and location of partial discharges in power transformers using acoustic and electromagnetic signals. IEEE Trans. Dielectr. Electr. Insul. 15(6), 1576–1583 (2008) 38. Rezinkina, M.M., Sokol, Y.I., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V.: Physical modeling of the electrophysical processes of the formation of the corona during the operation of electric power facilities. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 119–126. Springer International Publishing, Cham (2021) 39. Rezinkina, M.M., Sokol, Y.I., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V.: Mathematical modeling of the electromagnetic processes of the corona’s formation during the operation of electric power facilities. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 99–118. Springer International Publishing, Cham (2021) 40. Rezinkina, M.M., Sokol, Y.I., Zaporozhets, A.O., Gryb, O.G., Karpaliuk, I.T., Shvets, S.V.: Physical modeling of discharges in long air gaps with the presence of the corona at the tops of grounded objects. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 85–98 (2021)

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Instruments for Corona Discharge Coordinate Search as a Source of Acoustic Radiation Yevgen Sokol , Artur Zaporozhets , Vitalii Babak , Viktor Starenkiy , Oleg Gryb , and Ihor Karpaliuk

Abstract To create diagnostic devices for finding the coordinates of the corona discharge, methods for searching for the coordinates of the corona discharge with a stationary scanning device and a mobile scanning device are proposed. A UAV has been proposed as a mobile platform for the scanning system. The effect of noise is taken into account in developed methods that shield acoustic radiation. The possible influence of the Doppler effect on acoustic measurements was taken into account at created technique for mobile scanning instruments. The developed method for searching for the coordinates of a corona discharge by acoustic radiation is fully consistent with the tasks set in the chapter. Keywords Corona discharge · Coordinate search · Acoustic radiation · Scanning device · Microphone · UAV · Acoustic shielding

1 Introduction Let’s consider the requirements to determine not only the presence of a corona discharge spectrum in acoustic radiation, but also the requirements to determine the direction to the source (corona discharge). Such devices can already be used to scan space and determine the presence of a corona discharge and direction in automatic Y. Sokol · O. Gryb · I. Karpaliuk National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine A. Zaporozhets (B) · V. Babak General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan City, Taiwan V. Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology, National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_8

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mode, which makes it possible to create systems with continuous monitoring of the state of power equipment and the state of overhead power lines (OPL) [1–10]. The algorithm for searching for the direction of the maximum amplitude value or the direction to the source of the acoustic signal will be performed by a scanning device with a circular orientation, in which the microphone bypasses 360° of the surrounding space (Fig. 1). In this case, we obtain a signal at the microphone output, the maximum value of which will depend on the rotation angle β. With a random signal amplitude, the maximum value may not coincide with the direction to the source. In this case, the mathematical expectation for the obtained function on the microphone is searched. Real microphones have irregular sensitivity in space (Fig. 2). The formula for determining the direction to the acoustic signal source, taking into account the microphone sensitivity diagram, will look like this:

Fig. 1 Scanning device with circular scan diagram

Fig. 2 Microphone sensitivity curves

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{2π MMβ =

β · f M (β) · f (tβ )dβ, 0

where f M (β)—microphone sensitivity function depending on the angle of rotation of the microphone in space by the angle β; f (t β )—function of the source radiation intensity depending on the time during which the microphone is rotated in space by an angle β; β—microphone rotation angle.

2 Searching for Corona Discharge Coordinates with a Mobile Scanning Device With a significant length of power lines in Ukraine and their significant wear, it becomes necessary to monitor the quality component (the presence of a corona discharge) in different, much remote areas. In addition, there is a need to conduct such control as often as possible. The problem can be solved in several ways. Limitations caused by limited financial resources should be taken into account. Therefore, the option to equip all spans of electrical networks with sensors cannot be implemented due to the impressive cost of such a solution. The option of installing the scanning system on a mobile platform is acceptable. The UAV is adopted as a mobile platform. Modern UAVs are already quite inexpensive and have negligible operating costs (Fig. 3) [11–20]. For fast movement along electric lines, this type of transport is the most suitable. It does not need roads, which in most cases do not exist. Also, there is no need to resolve

Fig. 3 Visualization of the monitoring of the OPL’s technical condition with UAV

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Fig. 4 UAV’s route during OPL scanning

issues with the land owner. Floor inspection can be done from the air. With scanning tools, you can not only inspect, but also measure various parameters, for example, perform an analysis for the presence of a corona discharge on current-carrying parts and even determine the exact location of a corona discharge, which will significantly reduce the cost of repair work. To solve the problem of determining the coordinates of a corona discharge from acoustic radiation, it is necessary to find out the possibility of performing a search for coordinates from the UAV. The movement of the UAV along OPL will not be carried out only in a parallel course. The presence of wind, physical obstacles, constant correction of the course of the UAV will lead to the fact that the course will look like a broken line near OPL. UAV’s route during OPL scanning on 2D map is shown in Fig. 4. We assume that the scanning acoustic sensor will be fixed to the UAV without the possibility of rotation, that is, it will be placed in only one direction relative to the UAV. Let this direction be normal to the axis of the UAV body, then the sensitivity curve will be directed as shown in Fig. 5. There are also cases when the source of acoustic radiation from the corona discharge will be more than one on the line. If we assume that the curve of the sound intensity from the corona discharge will have a circular direction (shown in Figs. 2 and 3 of chapter “Theoretical Basis of Determination of Corona Discharge Coordinates by Acoustic Radiation”), then the sound intensity captured by the acoustic receiver will be described by the equation: sm (t) = f (α) · s(t),

(1)

where f (α)—sensitivity function of the acoustic receiver according to the angle α; s(t)—source sound intensity function. If we accept the inverse square law for sound in gases, we can write s(t) =

P(t) , 4πr 2

(2)

where s(t)—sound intensity function; P(t)—sound power function of the sound source; r—distance to the sound source.

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Fig. 5 Location of the acoustic receiver on the UAV

Substituting (2) into (1), we obtain sm (t) = f M (α) ·

P(t) . 4πr 2

(3)

With taking into account Cartesian coordinates: ( ( )) xi , f M (α) = M0 · fm ar ctg yi where M 0 —microphone sensitivity in the direction α = 0; x i , yi —coordinates of the sound source relative to the receiver, then, taking into account the distance to the source, Eq. (3) will have the following form ( ( )) xi P(t) / · sm (t) = M0 · fm ar ctg . yi 4π xi2 + yi2

(4)

The coordinates of the UAV are known at every moment of time from the data transmitted by the GPS (Fig. 6). The OPL’s coordinates are known from the geographic information system (marked on the map) (Fig. 6). Then the current coordinates to the source can be determined by the mathematical expectation:

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Fig. 6 Graphical explanation for determining the location of the corona discharge

{ti MM =

t · f M (t) · s(t)dt. ti−1

During determining the mathematical expectation for a certain time, the coordinates of the UAV are set and the general solution is calculated from the normal of the UAV movement to the intersection with the coordinates of the power line (Fig. 7). With changing the course of the UAV in relation to the OPL, the definition of the mathematical expectation does not depend on the direction of the UAV movement (Fig. 8). There are cases when the distance between the sources of the corona discharge can be insignificant and the sound fields will be summed up. In this case, the determination of the coordinates may be shifted towards the additional source. But the coordinates of the source of this type of drones require clarification due to the error in determining the GPS coordinates. Therefore, a refining search for the location of the corona discharge will be carried out with more accurate instruments, for example, a quadrocopter-type UAV with the ability to approach the source by tens of centimeters and the possibility of hovering.

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Fig. 7 Searching the maximum amplitude with a movable scanning instrument

Fig. 8 Determining the coordinates of a corona discharge under the action of two simultaneous sources

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3 Impact of Hindrance Shielding Acoustic Radiation 3.1 Methods for Taking into Account the Reflection of Sound from Surfaces The acoustic field of any complex technical object is formed as a superposition of the acoustic fields of individual radiation sources [21, 22]. In this case, it is possible to shield the radiation of individual sources by individual elements or structural elements of the object itself. The propagation of noise in the atmosphere and near the earth’s surface (where repeated reflection present) is accompanied by a number of effects that lead to a change in the intensity of the acoustic field and, in some cases, can lead to a change in the spectral composition of the acoustic radiation of the sound source [23–25]. To determine the density of direct sound, it is necessary to know the variable sound power of the source P(t) and the curve of sound power from the sound source in space and the source shape form (point, linear, volumetric, complex), its geometric parameters, radiation inhomogeneity from surfaces, space absorption, the nature of the emitted noise, etc. The formation of the reflected noise component is influenced by many factors, which, as a rule, affect not only the occurrence of the reflected energy, but also its distribution. During evaluating these factors, it is proposed to proceed from the fact that in the process of formation at each specific point of the volume of the energy characteristic of the reflected sound field, for example, the density of the reflected sound energy, radiation previously detached from the surfaces is involved. In this case, according to the principle of superposition, the density of the reflected sound energy at each point of the volume will be determined by the sum of the density of portions of the reflected energy, taking into account the value of each portion of energy emitted by the noise source and taking into account its attenuation in the time interval between the moment of energy emission and the moment of accounting in the calculation. The nature of the distribution of the reflected sound energy is influenced by different groups of factors. The distribution of the reflected sound energy in the volume is largely determined by the proportions of the space allocated for the calculation of the volume. In some cases, the reflected sound field is taken in terms of its indicators close to the diffuse sound field, and the attenuation of sound energy occurs according to the Eyring law [26, 27], that is, the conditions for its uniformity and isotropy are observed. In cases where there are time gaps between the emitted portions of energy (for example, for impulse noise), this fact is very important in assessing the energy characteristics of non-constant reflected sound fields. This can lead to an irregular distribution of the reflected energy over the volume. Thus, in disproportionate volumes, the diffuseness of the reflected field is not observed. The reflected sound fields in this case can be quasi-diffuse or completely non-diffuse [28, 29].

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According to the definition of Schroeder [30], the reflected noise field has a quasidiffuse character, if only the isotropy condition is preserved in such a field, i.e. an equal probability of arrival at the calculated point of the energy reflected from the surfaces in all possible directions is ensured. This fact largely influences on the choice of method for calculating the energy characteristics of non-constant noise. The method must fairly objectively take into account the quasi-diffuse nature of the reflected sound field. Another group of factors that have a significant impact on the formation of reflected sound fields includes the acoustic characteristics of building envelopes [23, 31]. The main ones include the sound absorption coefficients of the enclosure and the location of the sound absorption on the enclosure. The sound-absorbing characteristics of enclosure affect on the nature of the increasing and attenuation of the reflected energy [32, 33]. This determines the absolute levels of reflected noise, as well as the temporal characteristics of non-constant noise (L max , L min —maximum and minimum noise levels, respectively, AL = L max − L min —maximum temporal level difference, L3Ke —equivalent level etc.). Great importance in this case has the placement of sound-absorbing materials with high sound absorption coefficients, and especially in disproportionate (flat and long) rooms. For example, placing sound absorption in flat rooms on the ceiling leads to a sharp degeneration of short rays in accordance with the increase in the difference AL. This is especially important for impulse noise. In this case, L 3Ke decreases due to sound absorption, but at the same time, AL also increases. The latter leads to an increase in the normalized value of noise levels for a larger area of the room, and thereby significantly reduces the effect of sound absorption as a noise control measure. Another group of factors includes factors that affect the process of scattering of reflected sound energy in the volume of premises. The main ones include the nature of the reflection of sound from surfaces, as well as the presence of sound-scattering objects in the volume. According to the nature of sound reflection, sound-protective surfaces are mirror, diffuse, mirror-diffuse (mixed) and with directionally scattered reflections (Fig. 9). Each type of reflection in its own way affects on the formation of the sound field [34, 35]. This influence essentially depends on the distance to the sound-reflecting surface. For example, during specular reflection, non-diffuse sound fields are formed, for which the processes of increasing and attenuation of the reflected energy cannot be estimated using the Sebin and Eyring formulas. At the same time, during diffuse reflection of sound, quasi-diffuse sound fields are formed, in which the processes of temporal change of sound energy can be estimated with a certain accuracy using the Eyring formula. In real conditions, the nature of reflection is closer to mixed mirrordiffuse reflection. In this case, one part of the sound energy incident on the enclosure is reflected like mirror, and the second part, respectively—diffuse. The ratio between these parts is different, and in each particular case should be determined for the corresponding surfaces in the form of ratio coefficients. The most difficult is the directed diffuse reflection. Currently, it has been little studied and, therefore, is not used in practice.

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Fig. 9 Reflection nature of sound energy from surfaces with different properties: a mirror reflection; b diffuse (scattered) reflection; c mirror-diffuse reflection; d directed-scattered reflection

All of these groups of factors have a complex effect on the energy distribution. Therefore, methods for calculating the energy characteristics of reflected sound fields should, if possible, take into account all these factors together, thereby ensuring greater reliability of calculations.

3.2 Calculation of Energy Characteristics with Reflecting Non-constant Noise Fields Based on Methods for Calculating Noise Levels Modern methods for calculating the energy characteristics of noise fields are based on the provisions of the wave [36, 37], geometric [38, 39] and statistical [40, 41] theories of acoustics. Below is an analysis of these methods from the standpoint of assessing their capabilities for the simultaneous solution of problems on the reliable spatial distribution of sound energy. The most complete theory describing acoustic processes in space is the wave theory. According to it, the air volume of space forms an oscillatory system with distributed parameters. An active sound source excites its oscillations of the air volume of space with frequencies close to the frequencies of the source spectrum. The forms of natural oscillations and the natural frequencies of the volume, excited by the source, are determined by the transmitting capacity of the space and the conditions at the boundaries. Firstly, this is due to computational difficulties for those cases when it is required to take into account many natural fluctuations in the air volume. Secondly, the wave theory is applied only to idealized premises, for which it is possible to set parameters with sufficient accuracy that characterize the behavior of the air volume of space as a complex oscillatory system at any time. For these reasons, during calculating, it is necessary to take into account a large degree of idealization in the limiting conditions, the conditions of system excitation, and the choice of geometric and acoustic characteristics of the air volume. In this regard, the methods of the wave theory of acoustics are used mainly in the study of the propagation of sound energy in empty premises of limited size, comparable with the wavelengths in the studied frequency ranges. In this case, both

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direct methods of solving the wave equation [42] and finite element methods [43] can be used. Now, during calculating the energy characteristics of noise fields, calculation methods based on the provisions of the geometric and statistical theory of acoustics are mainly used [40, 41]. The choice of specific methods is determined by the factors and conditions that affect the formation of noise fields, and in this case, during working with noise sources with variable sound power. According to the provisions of the geometric theory of acoustics, the assessment of the propagation of sound energy can be performed on the basis of ideas about the ray pattern of the sound field. The energy value at the design points of space in this case is determined as the result of the arithmetic summation of the energies brought to the calculation point by ray reflections from premises. The method of imaginary sources and methods of rays’ research are the most widespread in the practice of calculating noise fields using the principles of geometric acoustics. In the case of applying the method of imaginary sources, the reflected sound field is represented as formed by infinite chains of imaginary sources located at the nodes of the spatial lattice, the total density of direct and reflected sound is found as ⎞/ ⎛ ⎤ ⎡ m=∞ n=∞ q=∞ 6 )k j ) ( P ⎣n 1 E E E ⎝n ( 2 ⎦, 1 − αj ε= exp −m s rmnq ⎠ rmnq exp(−m s r ) + c 4π m/ =0 n/ =0 q/ =0

j=1

where P—power of the sound source; P—function that determines the nature of the radiation of the sound source; j—number of surfaces with different sound absorption coefficients aj ; k j —number of sound reflections from the j-th surface; r and r mnq — distances from the real and imaginary sources of |m| + |n| + |q| orders to the calculated point; ms —spatial attenuation coefficient of sound in air. The method is used in theoretical studies of the patterns of propagation of sound energy and practical calculations of sound pressure levels. The practice of implementing the method indicates that it does not always provide the required accuracy of calculations. This is mainly due to the differences between the calculated model and the actual process of formation of the reflected sound field. Another factor that significantly affects the accuracy of calculations is the discrepancy between the mirror reflection model and the real conditions of sound reflection from surface barriers. In most cases, diffuse or mixed reflection occurs. Scattering of sound energy on enclosure leads to its other redistribution in comparison with specular reflection. Due to scattering, the levels of reflected sound increase in the zone closest to the source and significantly decrease away from the source. At the same time, the drop in levels in the far zones can exceed 6 dB for doubled distance. Such decreasing, in principle, cannot be obtained during calculating sound pressure levels using the method of imaginary sources [44]. The presence of scattering cannot be taken into account in the method of imaginary sources. As a result, this method gives low levels of reflected sound in the zone close to the source and overestimate them in the far zone. In this regard, the method in many cases is corrected by introducing corrections and restrictions, as is done, for example, in [45].

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The principles underlying the method of imaginary sources make it possible to use it to estimate changes in sound pressure levels over time. However, in this case, it also has the same disadvantages as in assessing the distribution of sound energy over the volume from a constant source of noise. A promising method for modeling acoustic processes in space and calculating sound pressure levels is the method of studying sound rays proposed by Schroeder [30]. The essence of the method lies in the construction on a computer of the trajectories of the sound rays emitted by the source, the calculation of the energy of each ray, taking into account its losses during reflections, and in the summation of the energy of all sound rays falling into the calculation area [46, 47]. The method of studying rays has a number of advantages over the method of imaginary sources [48]. An important practical advantage of the method of studying rays is the possibility of using it in cases of not only mirror but also diffuse reflection of sound from surfaces. Since the method does not have an analytical solution, it takes a long time to perform calculations which using it. Therefore, it is advisable to use it together with other methods, for example, with simpler methods of the statistical theory of acoustics. The methods considered above make it possible to calculate noise fields only for mirror or diffuse models of sound reflection from surfaces. In real conditions, sound reflection is mirror-diffuse. This property was noted and implemented in the development of calculation methods in premises with constant noise sources. At present, there are large number of calculation methods in which attempts have been made to implement the mirror-diffuse model of sound reflection.

3.3 Acoustic Source Shielding Performing direction recognition to the corona discharge source, the presence of interference (Fig. 10) for the propagation of an acoustic wave for open spaces in the absence of additional reflective surfaces leads to a significant attenuation of the sound wave, and as a result, the determination of the coordinates (direction) to the corona discharge source will be calculated. Figure 11 shows the shift in the expected value in the presence of shielding in the scan. M1—mathematical expectation calculated without shielding and M2—mathematical expectation calculated with a shielding zone. It is obvious that the coordinates of the corona discharge source in the presence of shielding will be calculated with a random shift. Therefore, in order to carry out a measurement to determine the location of the corona discharge source, it is necessary to avoid hindrance that shields the acoustic vibrations of the sound source.

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Fig. 10 Shielding of acoustic radiation from corona discharge

Fig. 11 Mathematical expectation calculated without shielding M1 and with shielding area M2

3.4 Effect of Reflection on Localization of Corona Discharge Source In the presence of reflective surfaces, determining the coordinates will have the same effect on determining the direction to the source as well as being within a short distance of two or more sources. That is, the accuracy of determining the coordinates of the corona discharge source will have an error. In the presence of reflective interference, especially in the horizontal plane, it is necessary to perform clarifying measurements to determine the coordinates of the corona discharge source, for example, a quadcopter-type UAV (Figs. 12 and 13).

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Fig. 12 Acoustic signal reception zone

Fig. 13 Determining the coordinates of a corona discharge in the presence of acoustic screens and reflective surfaces

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4 Impact of the Doppler Effect on Acoustic Measurements Acoustic measurements allow them to be made on mobile platforms. As a result of the development of microelectronics, such measuring instruments have small size and light weight, sufficient to install such equipment even on unmanned aerial vehicles [49]. If the acoustic complex is located on mobile platform, its speed can remain significant. So, the DJI Mavic Pro UAV has a speed of 65 km/h, and in sports mode—more than 80 km/h. Some exemplars, such as glider-type UAVs, have a speed of more than 150 km/h. The use of faster platforms for equipment location encourages to decrease monitoring costs and to increase the adequacy of the data obtained by such measuring equipment. The length of the OPLs is quite significant, so there are two ways—increasing the amount of equipment, or increasing the speed of data collection. In this case, the question arises about the operability of the acoustic diagnostics method with performing measurements on mobile platforms at different speeds. If the measuring equipment can have significant speeds relative to the measuring objects, then according to the Doppler law [50], the movement speeds of the equipment are critical for performing measurements of the acoustic spectrum. If the wave source is moving relative to the medium, then the distance between the wave crests (wavelength λ) depends on the speed and direction of movement. If the source moves towards the receiver, then the wavelength decreases; if it moves away from the receiver, the wavelength increases: λ=

2π (c − v) , ω0

where λ—wavelength obtained as a result of the Doppler effect, m; ω0 —angular frequency at which the source emits waves, Hz; c—speed of wave propagation in the medium, m/s; ν—speed of the wave source relative to the medium (positive if the source is approaching the receiver and negative if it is moving away). Then the frequency recorded by a fixed receiver: ω = 2π

2π (c − v) c = . λ ω0

Similarly, if the receiver moves towards the waves, it registers their crests more often. For a stationary source and a mobile receiver, we have the equation: ( u) , ω = ω0 1 + c

(5)

where u—speed of the receiver relative to the medium (positive if it moves towards the source). To calculate dependence (5), it is necessary to determine the speed of sound propagation in air.

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The sound speed in a homogeneous liquid (or gas) is calculated by the formula: / 1 , βρ

c=

(6)

where β—adiabatic elasticity of the medium; ρ—density. Formula (6) in partial derivatives has the form: / c=

( −V 2

dp dV

/

) = s

−V 2

( ) C p dp , Cv d V T

where C p —isobaric heat capacity; C v —isochoric heat capacity; p—pressure, V — specific volume, T —temperature, s—medium entropy. Dependence of the change in the wave frequency on the receiver speed is shown on Fig. 14. According to this effect, the frequency of corona discharge sound radiation, which is registered by the receiver, has the following dependence on the UAV speed [51] (Fig. 15). Only the approach of the receiver to the source is considered. According to the Doppler effect, the resulting model of acoustic radiation from a corona discharge will take the form: f (t) = A0 +

7 E i=2

) ( ( u) · t + ϕi , Ami sin 2π · i· f i · 1 + c

or in extended form ) ) ( ( ( ( u) u) t + ϕ2 + Am3 sin 2π 150 1 + t + ϕ3 (t) = A0 + Am2 sin 2π 100 1 + c c

Fig. 14 Dependence of the frequency of the receiving receiver on its speed to the source

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Fig. 15 Dependence of the source frequency displacement according to the receiver speed in the source direction

( ( + Am4 sin 2π 200 1 + ( ( + Am5 sin 2π 250 1 + ( ( + Am6 sin 2π 300 1 + ( ( + Am7 sin 2π 350 1 +

u) t c) u t c) u t c) u t c

+ ϕ4 + ϕ5 + ϕ6

) ) )

) + ϕ7 ,

where A0 —acoustic background noises; f i —frequency of the corresponding i-th harmonic; Am2 … Am7 —amplitudes from the 2-nd to the 7-th harmonic component; ϕ2 …ϕ7 —phase shift from 2-nd to 7-th harmonic component; u—speed of the receiver relative to the medium (positive if it moves towards the source).

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Prospects for the Development of Corona Discharge Detection Method by Spectral Acoustic Radiation Artur Zaporozhets , Vitalii Babak , Viktor Starenkiy , Oleg Gryb , Ihor Karpaliuk , and Roman Demianenko

Abstract The issues of the prospects for the development of method for determining the presence of corona discharge by spectral acoustic functions were considered. Since the method uses the spectral Fourier transform, which led to errors in the calculations, the literary sources devoted to the disadvantages of the Fourier transform method were analyzed. For using more suitable method, a review of the literature was carried out regarding the possibility of using other mathematical methods. A review of mathematical models and methods for monitoring the properties of dynamic processes has been carried out. The tasks of monitoring dynamic processes are described. Under the certain assumption that acoustic noise from a corona discharge will be decomposed into a time series, then a certain number of time series analysis methods can be used. An analysis of the structure of time series was carried out to identify the cause-and-effect relationships of a dynamic system. The moments of change in the properties of the time series are revealed. The moments of exit of individual process parameters beyond the permissible range of values are revealed. The method of principal components for analysis of time series is proposed. Keywords Corona discharge · Acoustic radiation · Fourier transform · Singular spectrum analysis · SSA · Time series · Dynamic processes

A. Zaporozhets (B) · V. Babak General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan, Taiwan V. Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology of the National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine O. Gryb · I. Karpaliuk · R. Demianenko National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_9

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1 Introduction 1.1 Problems of Spectral Decomposition of the Fourier Transform We consider the basic assumptions that the acoustic signal is the sum of harmonic signals with the addition of a noise component. Therefore, the use of the Fourier transform is acceptable for spectral analysis [1–5]. As a result of the spectral analysis, we obtain: • • • • •

number of harmonics in the original signal; amplitude component for each harmonic; initial phase; presence or absence of white noise; presence or absence of constant component.

During processing an acoustic signal from a corona discharge, we introduce the assumption that such an acoustic signal satisfies the basic conditions, that is, it is the sum of harmonic signals with the addition of noise component. Accordingly, it is possible to use Fourier analysis. According to the evidence provided by Jean Baptiste Joseph Fourier, it turns out that the function (corresponding to the requirements of continuity in time, periodicity and satisfying the Dirichlet conditions) can be expanded into a series, which was called the Fourier series. Fourier series decomposition allows to expand a continuous function into a sum of other continuous functions, and in general, their number will be an infinite number of terms. A further improvement of the Fourier approach is the Fourier transform, which expands the function not in discrete frequencies, but in continuous ones. The result obtained as a result of the Fourier transform is called the spectrum. The result obtained after the Fourier transform is called the spectrum. The spectrum of the Fourier transform [6, 7] is, in general terms, a complex function that describes the complex amplitudes of the corresponding harmonics. That is, the value of the spectrum is complex numbers, the modules of which are the amplitudes of the corresponding frequencies, and the arguments correspond to the initial phases. In practice, the amplitude spectrum and the phase spectrum are considered separately. General properties of the Fourier transform are given in [8, 9]. The Fourier transform is used to search for a sinusoidal signal in the spectrum. In general terms, this is a pair of delta functions, symmetrical with respect to zero frequency in the frequency band (Fig. 1). But the Fourier transform, which concerns not the entire spectrum, but only its fragment, is better described by the discrete Fourier transform. The essence of the discrete Fourier transform means that processing is performed only on some part of the infinite signal. Thus, the problem of continuity and infinity of the signal is solved. An assumption is introduced that processing is performed on a part of an infinite signal, and the rest of the time domain is filled with zero values. Mathematically, this

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Fig. 1 Amplitude spectrum of a sinusoidal signal

means that a infinite in time function f (t) is multiplied by some window function w(t), which turns to zero everywhere except for the studied interval. We consider not the initial function, but some of its multiplication with the window function. Then if the spectrum of the initial function is F(w) and the spectrum of the window function is W (w), then the multiplication spectrum will be the folding of two spectra (F × W )(w). In the graphical representation, instead of the delta function in the spectrum, the following will be presented (Fig. 2). This effect is called spectral leakage [10, 11]. And the resulting noise due to the spectral leakage, respectively, are called sidelobes [12]. The main problem of spectral leakage is the possibility of hiding other nearby harmonics by the lobes of the main spectrum (Fig. 3). As can be seen from Figs. 3 and 4 the more powerful harmonic overlaps the weaker one. There are several approaches to reduce the spectral leakage effect [10, 11]. The first one is to reduce the scattering of sidelobes, for which other non-rectangular window functions are used. The main feature of the “efficiency” of the window function is the level of sidelobes (dB) (Table 1). The second is to subtract the harmonics that create this spreading from the signal. That is, by setting the amplitude, frequency and initial phase of the harmonic, we can subtract it from the signal, while we will get the delta function corresponding to it, and with it the side lobes generated by it. Another question is how to accurately find out the parameters of the desired harmonic. It is not enough just to take the necessary data on the complex amplitude. The complex amplitudes of the spectrum are formed by integer frequencies, however, nothing prevents the harmonic from having a fractional frequency. In this

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Fig. 2 Spectral leakage effect

Fig. 3 Absorption of neighboring harmonics

case, the complex amplitude seems to spread between two neighboring frequencies, and its exact frequency, like other parameters, cannot be established. To establish the exact frequency and complex amplitude of the desired harmonic, for this, a technique is used that is widely used in many branches of engineering practice—heterodyning [13, 14]. The principle of heterodyning is as follows—if you multiply the input signal by the complex harmonic exp(I·w·t), then the signal spectrum will shift by w to the right.

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Fig. 4 Histogram of the spectral function distribution

Table 1 Sidelobe levels for some window functions №

Window function

Sidelobe levels, dB

1

Dirichlet window (rectangular window)

−13

2

Hanna window

−31.5

3

Hamming window

−42

The signal spectrum shifts to the right until the harmonic resembles a delta function (i.e., until some local signal-to-noise ratio reaches a maximum). Then the exact frequency of the desired harmonic is calculated as w0 − wren , and it is subtracted from the output signal to reduce the effect of spectral leakage. This procedure is repeated until all present harmonics will be minus and the spectrum resembles the spectrum of white noise. There is one more disadvantage of the spectral leakage effect in the Fourier spectral analysis of non-stationary signals. This disadvantage is associated with the time interval for obtaining a time series package. To obtain a significant package for analysis, a time period is needed that will fill the original information file. In our case, the duration of the measurement cannot exceed 10 s. This is due to the fact that it is planned to decompose into spectrum in terms of 65,536 frequency extension (not miss 1 Hz thin peaks). But that’s over a second for the standard 44.1 kHz sample rate. The FFT frequency grid is slightly less than 1 Hz. There is only one problem—the frequency information is averaged over more than a second of the source material. Therefore, in order to increase the reliability of determining the result, we must increase the duration of the data window to 10 s. The speed of transients processes in local branches is from 1 to 10 periods.

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Accordingly, in 10 s the operating mode of the system can change the following number of times: m = Tw × f m /Tn = 10 × 50/10 = 50, where m—maximum number of possible changes in the operating mode of the system; Tw —duration of the data collection window (10 s); f m —network frequency (50 Hz); Tn —number of periods of operation mode change (10). So, during the formation of a data packet for processing, 50-time change in the operating mode of the system is possible. That is, real operating modes cannot be considered as stationary process. Fourier transforms are traditionally used to perform harmonic and frequency analysis and evaluate slow changes in parameters: +∞ {

F( f ) =

f (t)e−itw dt.

(1)

−∞

One of the disadvantages of the Fourier transform is the so-called spectrum leakage effect, which is used in the analysis of non-stationary signals. Figure 5 shows an artificially simulated corona discharge acoustic signal, which can be described by the following system of equations: ⎧ ⎨ Am1 sin(2π f 1 t + ϕ1 ) 0 ≤ t < 0.08, a(t) = Am3 sin(6π f 1 t + ϕ3 ) 0.08 ≤ t < 0.16, ⎩ Am5 sin(10π f 1 t + ϕ5 ) 0.16 ≤ t < 0.24.

(2)

Figure 5 shows 3 frequencies of acoustic radiation 50, 150 and 250 Hz (certain frequencies are given as an example) [15, 16]. This is a case of successive replacement of one frequency by another. And when analyzing the Fourier over the full time interval, we get the frequencies of 50, 150 and 250 Hz (Fig. 6). Or we can consider another option. The acoustic signal is described by the following system of equations: ⎧ ⎪ ⎨ Am1 sin(2π f 1 t + ϕ1 ), 0 ≤ t < 0.08; a(t) = Am1 sin(2π f 1 t + ϕ1 ) + Am3 sin(6π f 1 t + ϕ3 ), 0.08 ≤ t < 0.16; ⎪ ( ) ⎩ Am1 sin(2π f 1 t + ϕ1 ) + Am3 sin(6π f 1 t + ϕ3 ) + Am5 sin 10π f 1 t + ϕ5 , 0.16 ≤ t < 0.24.

(3)

Sequential summation of frequencies over time intervals has the following form (Fig. 7). If the Fourier transform (1) is applied to the studied signal (3) over the entire time interval, then as a result we obtain information (Fig. 8) that the signal actually contains frequencies of 50, 150 and 250 Hz.

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Fig. 5 Example of the simplest change in the frequency of acoustic signal of corona discharge (successive change of radiation frequency)

Fig. 6 Spectral Fourier analysis of an acoustic signal with a change in the frequency of acoustic radiation (successive change in the frequency of radiation)

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Fig. 7 Change in the frequency of acoustic signal of corona discharge (multiplicative change in the emission frequency)

Fig. 8 Spectral Fourier analysis of audio signal with multiplicative change in the frequency of acoustic radiation (multiplicative change in the frequency of radiation)

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However, in this case, an error occurs in determining the amplitudes and information about the time (duration) of the presence of a particular frequency component in the studied signal is lost. The disadvantages of the fast Fourier transform (FFT) in the analysis of electrical signals are considered in detail in [17, 18]. To improve the accuracy of determining the frequency for cases where the FFT maximum does not coincide with the signal spectrum, a fast method of correlation functions is proposed. The reason for appearance of spectral leakage effect is the lack of localization in time of the sine and cosine functions used in the Fourier series. Also, the disadvantages of Fourier transforms include [19–23]: 1. The Fourier transform gives the frequency information contained in the signal, that is, it describes what the content of each frequency in the signal is, but does not allow to determine the time of occurrence and end of this frequency. 2. Limited informativeness of the analysis of non-stationary signals and the almost complete lack of opportunities for analyzing their features (singularities), since in the frequency domain, signal features (discontinuities, steps, peaks, etc.) are smeared over the entire frequency band of the spectrum. Also “parasitic” highfrequency components appear, which are clearly absent in the output signal at the presence of jumps and discontinuities in it. 3. The harmonic basis decomposition functions are not capable to display signal transitions with infinite steepness such as rectangular pulses, since this requires infinitely large number of series components. When the number of terms of the Fourier series is limited in the vicinity of jumps and discontinuities, oscillations arise during signal recovery (the Gibbs phenomenon). 4. Fourier transform displays global information about the frequencies of the studied signal and does not give an idea of the local properties of the signal with rapid temporal changes in its spectral composition. So, for example, the Fourier transform does not distinguish between a stationary signal with the sum of two sinusoids and a non-stationary signal with two sequentially subsequent sinusoids with the same frequencies, because the spectral coefficients are calculated by integration over the entire interval of the signal reference. The Fourier transform does not have the ability to analyze the frequency characteristics of the signal at arbitrary times. 5. Using the Fourier transform, it is possible to work with a signal either only in the time domain or only in the frequency domain. At the same time, it is impossible to obtain a frequency-time representation using the classical Fourier transform algorithm (there is no possibility of obtaining information about which frequencies are present in the signal at a given time). Thus, based on the foregoing, we can conclude that the use of the Fourier transform is inefficient for the harmonic analysis of non-stationary signals. The spectrum leakage effect introduces an error in determining the amplitude of the harmonic components, which make the frequency localization is more worsen. The Fourier transform does not allow to reliably determine the time of occurrence of highfrequency components in current and voltage signals. The Fourier transform does not

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allow identifying the presence of interharmonics in the voltage. Fourier analysis is not an effective tool for analyzing short-term (impulse) disturbances. All this does not allow to use the Fourier transform for digital processing of acoustic signals of corona discharge. It is possible to overcome the listed shortcomings of the Fourier transform and successfully solve the tasks set using a different mathematical apparatus. Currently, there are many problems of electrical supply of energy consumers that affect the quality indicators of power supply [24–33]. Such problems can include those arising from abrupt changes in power, those related to supplying energy to unstable consumers, and those arising from the integration of alternative (wind, solar) electrical power sources. For all of these issues, there is a common question, namely the need to monitor multiple parameters in real-time to enable appropriate actions to maintain quality performance. To solve such problems, many authors [24–33] proposed various concepts, theories and techniques. One of the possible solutions to the problem is the creation of an automated power supply quality monitoring system based on statistical analysis, which will provide complete information about the spatio-temporal structure of the power system. As a result of the development of a method for acoustic diagnostics of qualitative parameters of power supply, it became necessary to process streaming data for monitoring. As noted, the Fourier transform methods have a number of disadvantages, therefore, below will be a review of mathematical models and methods that are most suitable for dynamic processes.

2 Overview of Mathematical Models and Methods for Monitoring the Properties of Dynamic Processes 2.1 Problem of Dynamic Process Monitoring An important condition for the normal functioning of any technological process is the timely detection of failures and deviations of the process parameters from acceptable values, as well as the identification of the factors that caused these deviations [3, 34–36]. The purpose of monitoring dynamic processes is to identify deviations and prevent their consequences based on the study of time series containing information about the process parameters for a certain time period [3, 35, 37]. Statistical monitoring [38–40] can reveal the extent and periods of abnormal process flow, as well as determine the moments of deviations and diagnose their causes. The key idea behind time series performance monitoring is to monitor and, if necessary, to regulate process parameters to prevent failures or “disorders”. The task of monitoring dynamic processes can be reduced to studying the characteristics of a time series. Among these tasks are the following:

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– identification of hidden, implicit components of the time series for the analysis of cause-and-effect relationships of the dynamic system generating it; – identification of time points of changes in the properties of the studied time series; – identification of the moments of time when the values of certain process parameters go beyond a given area; – optimization of the regulation of the functioning of the considered system and control of the properties of the final product.

2.2 Analysis of the Structure of Time Series to Identify Cause-and-Effect Relationships of Dynamic System Dynamic processes, occurring in technical systems, generate time series of a complex structure containing different components, the analysis of which allows to understand the nature of the system that generates time series and can be used to develop strategies for optimal process control. The possibility of optimal control based on the study of dynamic relationships of time series of a complex structure has great practical importance. The works of many authors [40–44] are devoted to this important issue. The processing of time series generated by technical systems and production activities makes it possible to study the hidden parameters of systems and activities. The most general task of studying series should be the identification of the dynamic properties of the objects that generate them. However, in practice, researchers often confine themselves to analyzing individual components of time series. The work [45] considers two classes of problems in the analysis of time series: the problem of identifying an object, which generate a series (selection of some mathematical model that generates an adequate time series) and the problem of filtering time series, the purpose of which is to isolate and study a certain component of the series. The ultimate goal of the analysis of time series, according to the authors, is to achieve a deeper understanding of the causal mechanisms that cause the appearance of these time series, which boils down to the study of different types of behavior of individual series and the construction of models that could explain these types of behavior. In the real practice of monitoring dynamic processes, as a rule, one has to deal with series that have a complex structure. This is due to the fact that the formation of the time series is influenced by many interrelated factors, the influence of which is difficult, and sometimes impossible, for taking into account. As noted in [46], typical time series can consist of the following typical components: trend (systematic change), fluctuations relative to the trend, periodic components (seasonality effect), random (non-systematic) component. The traditional theory of time series research, as the authors note, is devoted to the decomposition of data into the indicated components, their separate study and analysis.

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A trend is a persistent, systematic change in the behavior of a series. Moreover, a situation may arise when a part of an oscillatory process with a period longer than the length of the series will be mistakenly taken as a trend. In [46] the authors proposed several ways to determine the trend. The component corresponding to the trend can be represented as a polynomial in time t. Using the method of least squares [47–49], it can be obtained a polynomial that best reflects the evolution of the series components, i.e. align the members of the series by the least squares method. At the same time, one should take into account the fact that the nature of the trend can change over time. In this case, the authors proposed to use a higher-order polynomial or a more complex function. The authors also considered an alternative approach—moving average method, in which a polynomial is searched for some part of the series (rather than the whole series) and different polynomials are used for different stages. In this case, the first n series components are taken, a polynomial with measure p, (p ≤ n − 1) is constructed from these terms, and the value of the polynomial is found within its definition domain. Next, n series component are taken, starting from the second to n + 1, and a new polynomial is built, and so on. At each stage, there is a shift by one component to the right. To extract the systematic component, the authors [46] also consider the variable differences method. One of the approaches proposed for studying the periodic component is to preliminarily exclude the trend by the method of moving averages and then study the residual characteristics of the series. Another way to analyze time series is based on the assumption that the series is formed by sinusoids and cosine waves of different frequencies [50]. The method is based on the use of periodograms used to estimate the amplitude of sinusoidal components hidden by noise. An alternative analysis of the structure of time series using information filters is considered by Kobrinsky [45]. The author calls an information filter as mathematical model for analyzing a time series obtained as a result of observing the studied process over a finite time interval. The author noted that it is possible to synthesize a set of filters for different frequencies and use them to decompose this process into elementary components. Further interest are only in those components that make a significant contribution to the dispersion of the process. The selection of such components from the series allows them to be subjected to further analysis, and their extraction from the series will significantly reduce the variance of the series. Comparison of the variance of the original series with the variance of the residual makes it possible to judge about the significance of the filtered components. The procedure for applying the information filter is as follows. The studied series enters the filter input and, depending on the frequency response of the component, either the operation of smoothing the series, or the operation of forming the differences of its members, or a combination of them is implemented. The parameters of the information (frequency) filter that extracts the “useful component of the series” are chosen so that it passes through the filter with low distortion, and different components with frequencies are suppressed.

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As noted in [45], spectral analysis in the frequency domain forms one class of time series analysis methods. The methods of spectral analysis of random processes arose in connection with the emergence of problems in the development of automatic control systems for dynamic systems, as well as problems of automated information transmission. Analysis of the frequency structure of the series allows to obtain meaningful information about the functioning of the system. Statistical methods of spectral analysis and Fourier analysis for time series are also considered in [5–9]. In the spectral analysis of a series, the evaluation of the spectrum is always made on the final frequency band. In this case, both the trend and harmonic components with frequencies close to zero are included in the first frequency band. During analyzing time series, it often becomes necessary to identify frequency bands that make a significant contribution to the variance of the process that generates the series. To separate the periodic and non-periodic components of the series, the fact that a process that does not contain periodic components has a continuous spectral density is taken into account. If there is a harmonic frequency component ω0 in the process, then a sharp peak in the spectral density will correspond to it. In [46], the author analyzes the principal components in the frequency domain, and also studies the series of principal components and their properties. X(t) vector series with r components is considered. It is assumed that it is necessary to transfer the X(t) value via communication channels from one point to another, but at the same time it has only q ≤ r channels for data transmission. In this case, the process of transmitting the X(t) series over q channels is described as filtering, which results in a q-component vector series. Such a problem can be considered as a search for a way to construct such q-dimensional ζ (t) series, which carries a significant part of the information about the initial X(t) series. Frequency filtering of the time series is performed in order to isolate and analyze a certain component or to exclude a certain frequency band. These procedures are associated with a change in the structure of the spectrum of the series and are carried out, as noted, with the help of frequency information filters. The work [45] shows the principles of filtering, namely the application of the process integration operator to suppress high frequencies and the differentiation operator to eliminate the low frequency component. The authors considers lowpass filters, as well as band-pass filters. Low-pass filters are based on averaging the components of a series. They are synthesized in the form of moving average models and implement the series smoothing procedure. By means of a set of bandpass filters, the initial time series can be divided into its constituent components by successive repeated application of the filtering procedure with different coefficients. With applying frequency filtering to extract the components of a time series, the following problem may arise: the filtered series may contain periodic fluctuations that were not in the original series. The work [45] gives some recommendations on how to prevent the introduction of side cycles into the smoothed series. There is a second problem to be noted. The selection of time series components can also be problematic due to the presence of various factors (many of which are not

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subject to direct observation and quantitative measurement) that generate different types of nonstationarity of the series and significantly aggravate the problem of dynamic identification. Despite these difficulties, frequency methods have been widely used in the study of stationary actions in automated control systems.

2.3 Identification of the Moments’ Change in the Properties of the Time Series One of the tasks of monitoring production processes is to identify failures and it comes down to solving the “disorder problem”, that is, detecting the time of a jump in the properties of the observed time series occurring at an unknown moment [51–55]. There are two classes of tasks about disorder [51, 52]. The first class was called “quick disorder detection task”. The statement of the problem is as follows: let information about a random process arrive sequentially in time (a time series is formed), at some point in time some probabilistic characteristic of the process changes. The question is how to quickly detect this change after it has occurred, and at the same time limit the erroneous signals to a certain value. That is, it is necessary to identify the disorder as soon as possible after it has occurred at a given false alarm rate, and it is not necessary to indicate the exact point in time when the disorder occurred. The second class is called “A posteriori disorder problems”. The statement of the problem here is as follows: let the implementation of a random process be presented (there is a time series). If this sample is not statistically homogeneous, that is, its probabilistic characteristics are not constant over time, the problem arises of identifying the time points of change in probabilistic characteristics and dividing the initial sample into several statistically homogeneous fragments. With such a statement, by the beginning of the solution of the problem, a finite observations’ sample of the parameters of the studied process is collected, after which it is required to estimate as accurately as possible the moment of disorder’s occurrence. Based on the foregoing, the formal statement of the disorder detection problem is as follows [51, 52]. Let a random sequence x1 , x2 , . . . , x N be given, which at some point in time t 0 changes its properties abruptly. These characteristics are uniquely determined by the θ feature vector. This means that with t ≤ t0 − 1 the vector is θ = θ1 , and with t ≥ t0 the vector is θ = θ2 . It is necessary, by observing the x1 , x2 , . . . , x N sequence, to identify the disorder’s moment t 0 . In [51], the author gives variants of criteria for optimizing the construction of algorithms for solving disorder problems. Regarding the first class of the disorder task, the following criteria are proposed.

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It is necessary to develop an algorithm for signaling a disorder that has occurred, minimizing the average delay time of its detection for a given mathematical expectation of the number of false alarms received by the time the disorder occurs, i.e. τ=M

M ( N˜ ) τ −→ min, ta ≥ t0

(4)

where τ = ta − t0 + 1; τ —mean delay time in the detection of a disorder; ta — time of report’s receipt about the disorder; t0 —time moment of disorder; M( N˜ )— mathematical expectation of the number of false alarms. It is necessary to minimize the average delay time in the detection of a disorder, with given probability of false alarms: τ

P(ta n → min,

(8) c

where Pn —the probability of an estimate going out of tolerance; t 0 —assessment of the moment’s occurrence of the disorder; t0 —time moment of disorder; n ≥ 0. In [51] the author gives a general classification and review of methods for detecting the disorder. One of the algorithms of greatest practical interest is the cumulative sum algorithm. Its idea is to analyze the behavior of the cumulative sum: ( ( / )/ ( / )) S(t) = St−1 + ln ω xt θ2 ω xt θ1 ,

(9)

( / ) where ω xt θ2 —probability distribution of random variables xt0 , . . . , xt ) ( / density since the disorder’s occurrence (t 0 ); ω xt θ1 —probability distribution density of random variables x1 , . . . , xt0 −1 before the onset of the disorder (t0 − 1). The relevance of the disorder’s tasks is associated with the possibilities of controlling production processes. However, there are difficulties in solving the disorder problem, which are associated with the need for accurate knowledge of the distribution functions of the studied data sequences before and after the disorder moment and the distribution function of the disorder moment, which is practically impossible under the conditions of studying real processes. The disorder task has particular interest for solving the problems of current control of the production process. The essence of such task may lie in the sequential control and early detection of changes in the parameters of the controlled process based on changes in the structure of the time series generated by the process, with a certain set level of erroneous signals about the disorder. At the same time, it is important not only to identify the fact of a failure or failure as quickly as possible, but also to determine the cause of their occurrence.

2.4 Optimization of Regulation and Quality Control To develop a strategy for optimal control of a complex system, it is necessary to identify the nature and structure of the relationship between process variables (X) that affect some characteristics of the quality of the final product and the resulting indicator (y). As a result, it is possible to control the y indicator by adjusting the X parameters to prevent or minimize deviations of the resulting indicator from the set nominal value. Adjustment in this case is an attempt to compensate for the perturbations introduced into the system, and some of these perturbations are available for direct

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measurements, others are not, and appear as inexplicable deviations from the set value of the controlled characteristic of the process. The work [56] considers the correlation-regression dependence between random vectors of resulting indicators (quality or efficiency indicators) and vectors of predictor (exogenous) variables. In this type of models, the components of the vector of the resulting quality indicator and the components of the exogenous vectors of variables depend on many uncontrolled factors and, in fact, are random variables fluctuating randomly around the established nominal values. The works [57, 58] consider an expert-statistical method for constructing a single summary indicator of the effectiveness of the system functioning (the quality of the final product). In [58] the model is presented as follows. The summary generalized characteristic of the final product (y—output parameter) is determined by a set of some criteria (x i —input variables): y = f (X ) + δ(X ),

(10)

where y—summary quality indicator, presented as an expert opinion; f (X )— summary quality indicator as a function of input variables; δ(X )—distortion, which is random in nature, includes the error of an expert opinion and a number of unaccounted for (possibly external) factors that were not included in X = {xi }. In [58] the problem is reduced to finding the target function of the generalized studied property—the “initial quality” of the final product. The authors in [58] also proposed to solve this problem as the task of constructing an integral indicator of the efficiency of the system functioning according to specified criteria X = {xi } based on methods for reducing the dimension of the feature studied space (to a single “summary feature”). One of the effective methods for reducing the dimension is the method of principal components, considered by different authors for solving a wide range of problems in different literature [51–58]. Another approach for determining the quality of the final product is presented in [59]. The author notes that the data on the technological parameters of the process, collected for the entire period of the process, contain essential information regarding the quality of the final product. However, regulation and quality control is complicated by the fact that the process is characterized by a huge number of variables. These variables correlate with each other, not all measured parameters are significant, many of them only indirectly reflect important, hidden properties of the process. It is assumed here that there is a matrix of these measurements of process parameters over a certain period of time X (n × k) and a matrix of product quality data Y (n × m). The data is excessive and only a subset of the indicators (perhaps implicit) are really informative and contain potentially important information about the quality of the final product. Compared to the original high-dimensional data matrix, the matrix of implicit variables has a low dimension. The model looks like this:

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X = T P T + E; Y = T Q T + F,

(11)

where X (n × k)—matrix of measurements of technological parameters; Y (n × m)— product quality data matrix; T (n × A)—matrix of implicit variables; P(k × A), Q(m × A)—load matrices; E, F—“noise”. The transition to the model of implicit variables implies a significant reduction in the dimension of the data array, and it also becomes possible to purposefully control the process parameters due to their influence on the final result of the process (the quality of the final product). With this approach, control can be carried out even when direct measurements of product quality are not available at certain production stages. Therefore, in industrial processes, in order to maintain some resulting quality characteristic as close as possible to the established level, it is possible to control product quality by regulating process parameters through the use of models and methods of component analysis. The use of component analysis for quality control is most relevant in cases where: • individual quality indicators are not directly measured; • some data on the process parameters that affect the quality of the final result are missing (for example, at some points in time the sensor did not work, as a result of which data with gaps were obtained); • quality is a complex indicator for which there is no measurement scale; • the quality of the final product is latent at some stages of the production process. For problems of analysis of dynamic systems, it is proposed to apply the method of singular-spectral analysis.

3 Method of Singular Spectrum Analysis (SSA) To study the structure of time series, the SSA method is considered, which is based on the selection of the main components of the considered time series [60–64]. The idea of the SSA method is to turn a one-dimensional time series into a matrix, study it by analyzing the principal components (singular value decomposition) and restore (approximate) the series using the selected principal components. The purpose of the SSA method is to decompose the time series into additive components that allow meaningful interpretation. The method is based on the singular value decomposition of the trajectory matrix, whose columns are fragments of length L of the studied time series (i.e., the embedding vector), where L is the main parameter of the method (“window length”). The analysis of the terms of the singular value decomposition allows to first classify them as belonging to one of the components of the series, and then isolate this component.

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The result of applying the method is the decomposition of the time series into simple components: trend, periodic components, noise. Formally, the SSA [60] method can be represented as two parts: decomposition and recovery. The decomposition includes the stage of embedding (formation of the trajectory matrix) and singular value decomposition (formation of tracks and decomposition of the trajectory matrix into a sum of elementary matrices). Recovery includes grouping (grouping of own tracks, distribution of additive components of the series) and diagonal averaging (a formal procedure for transforming matrices into a time series). The algorithm of the SSA method described in [60] is as follows: there is a X N = {x0 , . . . , x N −1 } time series of length N (N > 2). The first step is the decomposition stage, that is, the formation of the trajectory matrix. The main step here is to choose an integer L, the length of the window, 2 ≤ L ≤ N − 1. When choosing the parameter L, it is advisable to take into account the fact that if the window length is chosen large enough, then all vectors of the trajectory matrix will contain a significant part of the information about the behavior of the initial time series. Since the trajectory matrix has a symmetry property, and the singular value decomposition of trajectory matrices with window length L and window length N − L + 1 are equivalent, then choosing the value L, the length of the time series, greater than half, does not make sense. Thus, to form a trajectory matrix, it is advisable / to choose a window length approximately equal to half the row length—L ≈ N 2. If the time series is supposed to have a periodic component with a certain period, it is recommended to choose a window length proportional to the value of this period. Taking into account the above recommendations on the choice of the parameter L during studying the structure of the time series, it is advisable to use several options for the length of the window. After choosing the parameter L, the columns of the X ∗ trajectory matrix are sequentially filled with the values of the initial time series. In this case, the first column contains the elements of the series from x0 to x L−1 , the second—from x1 to x L , and so on, until the series is finished. So, the first stage consists in the formation of the X ∗ (L × M) trajectory matrix from the time series X N , where M = N − L + 1 is formed by successive selection of segments of length L from the X N series, that is, the transformation of the initial onedimensional series into a sequence of L-dimensional vectors, the number of which )T ( is equal to M, where X ∗j = x j−1 , . . . , x j+L−2 , 1 ≤ j ≤ M. The X ∗ matrix looks like this:

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⎛

x0 x1 x2 ⎜ x1 x2 x3 ⎜ ⎜ X ∗ = ⎜ x2 ⎜ . .. .. ⎝ .. . . x L−1 x L x L+1

⎞ . . . x M−1 . . . xM ⎟ ⎟ ⎟ ⎟. ⎟ .. .. ⎠ . . . . . x L+M−2

(12)

The next step is the singular value decomposition. The singular value decomposition of the matrix X ∗ is performed according to the following scheme. First, the R = X ∗ X ∗T matrix is calculated. Next, the eigenvalues λ1 , . . . , λ L of the matrix R are found. All eigenvalues are in descending order (λ1 ≥ . . . ≥ λ L ≥ 0). Next, the eigenvectors U1 , . . . , U L of the matrix R(L × L) corresponding to these eigenvalues are found. {U1 , . . . , U L } is the system of orthonormal eigenvectors of the R matrix, √ Ui vectors are left singular vectors. Next, λi singular numbers are calculated and factor vectors are found: 1 Vi = √ X ∗T Ui , i = 1, . . . , d, λi

(13)

where d = max{i, λi > 0}; V i —factorial vectors (right singular vectors). Next, the vector of i-th principal components is calculated: Zi =

v λi Vi = X ∗T Ui , i = 1, . . . , d.

(14)

As a result of the above, we obtain the singular value decomposition of the trajectory matrix X ∗ : X ∗ = X 1∗ + . . . + X i∗ + . . . + X d∗ , i = 1, . . . , d, where X i∗ =

(15)

√ λi Ui ViT , or d E v λi Ui ViT . X = ∗

(16)

i=1

√ For this singular value decomposition, the set λi , Ui , Vi is the i-th own triple of the singular value decomposition; X i∗ —elementary matrices (with rank equal to 1). Each λi eigenvalue characterizes the contribution of the X i∗ matrix to the singular value decomposition. Singular value decomposition can be interpreted by analogy with the method of principal components in statistics, as the expansion of all columns of the X ∗ matrix over a basis of their principal vectors. At the next stage of SSA method, the decomposition components are grouped. The purpose of this grouping step is to divide the time series into additive components.

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The grouping procedure allows to divide the entire set of (i = 1, . . . , d) indices into m non-overlapping subsets: I1 , . . . , Im . That is, the procedure for combining the indices into groups or the distribution of the terms of the singular value decomposition into groups is carried out. Each I j subset corresponds to the resulting X ∗I j matrix, defined as the sum of the matrices included in the subset. Having calculated the resulting matrices for each of the m subsets, we can represent the singular value decomposition of the X ∗ matrix in a grouped form as the sum of the resulting matrices of each subset: X ∗ = X ∗I1 + X ∗I2 + · · · + X I∗m .

(17)

In the SSA method, the grouping step is difficult to fully formalize. This procedure is based on the analysis of the λi eigenvalues, as well as the Ui and Vi vectors—left and right singular vectors in the singular value decomposition, with each matrix component of the singular value(√ decomposition ) being completely λi , Ui , Vi . determined by the corresponding singular triplet Analyzing the shape of the singular vectors of one of the proper triples, one can predict the behavior of the corresponding component of the series, restored using this triple, since the restored component will have a similar shape. The larger the singular value in a proper triple, the greater the contribution of the component of the series reconstructed from this proper triple. As noted by the authors in [60], in order to extract a trend from a time series, it is necessary to group all proper triples with slowly changing singular vectors, and if the series has a pronounced trend, then the proper triples corresponding to the trend will have the first positions in the singular value decomposition of the trajectory matrix. If this time series contains pronounced fluctuations, then the first triplets will correspond to harmonic components, and each harmonic component generates two own triplets with close singular values. One harmonic component of the series corresponds to two main components with eigenvalues close in value [60]. The principle of grouping for identifying noise can be to assign to the group own triples that do not contain either a trend or fluctuations. Useful information for detecting noise components can also be a sharp jump in the decrease in eigenvalues, in this case, the signal corresponds to large eigenvalues, and the noise to small ones. ( j) The last step of the SSA method is diagonal averaging. At this stage, the X N rows ∗ ∗ are restored from the grouped X I j matrices, that is, each X I j matrix is translated into a new row of length N. Since it is assumed that any X ∗I j matrix is a trajectory matrix of some time series, the side diagonals of such matrices must consist of the same elements. However, in practice this is not often the case. There is a need to apply a procedure that formally transforms an arbitrary X ∗I j matrix into a Hankel matrix containing the same elements on the side diagonals. As such a transformation, diagonal averaging is used, by which ( j) the value of the X N series is given as the average of the values of the elements of ∗ the X I j matrix along the respective side diagonals.

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From the principle of diagonal averaging, stated in [60], it follows that diagonal averaging for an arbitrary matrix X ∗ with dimension (L × M) (at L < M) will be performed according to the formula: ⎧ k+1 ⎪ 1 E ⎪ ⎪ xi,k−i+2 for 0 ≤ k ≤ L − 1 ⎪ k+1 ⎪ ⎪ i=1 ⎪ ⎨ E L xi,k−i+2 for L − 1 ≤ k ≤ M xk = L1 , ⎪ i=1 ⎪ ⎪ ⎪ N −M+1 E ⎪ ⎪ 1 ⎪ xi,k−i+2 for M ≤ k ≤ N ⎩ N −k

(18)

i=k−M+2

where xk —elements of the X N = (x0 , . . . , x N −1 ) series; N = L + K − 1—series’s length; xi j —X ∗ matrix elements ( j = k − i + 2). Therefore, diagonal averaging transforms the X ∗ matrix into a X N = (x0 , . . . , x N −1 ) series. As a result of applying the method of singular spectral analysis, the initial X N = ( j) (x0 , . . . , x N −1 ) series is decomposed into the sum of m of X N series, i.e. it is possible to achieve a partition of the time series into additive components. The next question that may arise in the analysis of time series concerns the interpretation of the recovered components and relates to the subject area of the study. The advantages of the described method are the absence of the need for an a priori problem of the series model, as well as the ability to work with modulated harmonics (in contrast to methods using the Fourier transform).

4 Development of a Technique for Applying Singular Decomposition to Analyze Changes in the Properties of Time Series To diagnose the disorder, a method is proposed for identifying the moments of change in the structure of the time series based on SSA. Let the time series X N = (x0 , . . . , x N −1 ) of length N (N > 2) be researched for structural changes. To do this, it first needs to select the viewing range of the studied time series—D parameter (D < N). The choice of the range is made on the basis of a preliminary analysis of the time series or the use of a priori information about the structural components of the series. Further, according to the algorithm of the SSA method, a singular decomposition of a fragment of the time series that fell inside the viewing range is performed, and the resulting set of proper triples as a result of decomposition is analyzed. At each next step, the viewing limits are shifted by one element of the time series (Fig. 9).

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Fig. 9 Setting of view range limits

View range limits are set as follows: at the first step—t ∈ [1; D], at the i-th step—t ∈ [i; D + i − 1]. Since each proper triple uniquely determines the decomposition component, the analysis of changes in the structure of proper triples of the singular value decomposition of series’ fragment within the viewing range makes it possible to identify structural changes in the time series. So the appearance of new triples indicates that new structural components have appeared in the time series. It should be taken into account that each harmonic component gives rise to two proper triples with close singular values, so the appearance of a new harmonic component in the series structure is evidenced by a new pair of proper triples in the singular-spectral decomposition of the next fragment of the series within the viewing range. The disappearance of eigentriples in the singular spectral decomposition indicates that the corresponding structural components are no longer present in the time series. An increase or decrease in the values of singular numbers in proper triples indicates a change in the significance of the corresponding decomposition components. If we are talking about the harmonic structural components of the time series, then a change in the values of singular numbers may indicate a change in the amplitude of oscillations (an increase or decrease in the effect of the factor, which causes the appearance of a component in the (√ ) structure of the time series). Singular triples λ , U , V of singular value decomposition at SSA consist i i i (√ ) √ λi , Ui , Vi —factorial of λi —singular numbers, Ui —left singular vectors and vectors (right singular vectors), where λi are eigenvalues of the matrix R = X ∗ X ∗T . Therefore, instead of analyzing singular values, one can analyze the set of eigenvalues of the R = X ∗ X ∗T covariance matrix. The change in the spectrum of the R matrix at the next shift in the viewing range suggests that at this moment there are structural changes in the X N = (x0 , . . . , x N −1 ) time series. Extraction from a number of structural components that have a high diagnosable level of significance makes it possible to obtain a number of residues, the analysis of which allows obtaining additional information about the moment of structural disorder. To achieve the best results in identifying structural disturbances in time series, it is recommended to use several viewing ranges with different lengths.

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For express analysis, only observations of changes in the values of the eigenvalues of the covariance matrix are sufficient. Moreover, it does not matter which component corresponds to which eigenvalues and, accordingly, which eigentriples. For a deeper analysis, in addition to the analysis of the values of the eigenvalues of the covariance matrix, it is necessary to analyze the eigentriples, since the behavior of V and U can be used to determine the behavior of the structural component of the series reconstructed from this eigentriple. After that, it is possible to determine which structural component of the series corresponds to which group of eigenvalues and, accordingly, judge about the level of significance of each component in the new structure of the time series.

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15. Gryb, O.G., Karpaliuk, I.T., Zaporozhets, A.O., Shvets, S.V., Rudevich, N.V.: Acoustic diagnostics for determining the appearance of corona discharge. In: Control of Overhead Power Lines with Unmanned Aerial Vehicles (UAVs), pp. 127–157 (2021) 16. Gryb, O., Karpaliuk, I., Shvets, S., Zaporozhets, A.: Recognition of corona discharge presence by acoustic system installed on unmanned aerial vehicle. Proc. Natl. Aviat. Univ. 85(4), 46–53 (2020) 17. Goda, K., Jalali, B.: Dispersive Fourier transformation for fast continuous single-shot measurements. Nat. Photonics 7(2), 102–112 (2013) 18. Polat, K., Güne¸s, S.: Classification of epileptiform EEG using a hybrid system based on decision tree classifier and fast Fourier transform. Appl. Math. Comput. 187(2), 1017–1026 (2007) 19. Smith, B.C.: Fundamentals of Fourier Transform Infrared Spectroscopy. CRC Press (2011) 20. McLoughlin, F., Duffy, A., Conlon, M.: Evaluation of time series techniques to characterise domestic electricity demand. Energy 50, 120–130 (2013) 21. Bell, R.: Introductory Fourier Transform Spectroscopy. Elsevier (2012) 22. Barducci, A.: Information-theoretic approach to Fourier transform spectrometry. JOSA B 28(4), 637–648 (2011) 23. Asimopolos, L., Pestina, A.M., Asimopolos, N.S.: Considerations on geomagnetic data analysis. Chin. J. Geophys. 53(3), 765–772 (2010) 24. Armaroli, N., Balzani, V.: The future of energy supply: challenges and opportunities. Angew. Chem. Int. Ed. 46(1–2), 52–66 (2007) 25. Omer, A.M.: Energy, environment and sustainable development. Renew. Sustain. Energy Rev. 12(9), 2265–2300 (2008) 26. Pérez-Lombard, L., Ortiz, J., Pout, C.: A review on buildings energy consumption information. Energy Build. 40(3), 394–398 (2008) 27. Kaboli, S.H.A., Selvaraj, J., Rahim, N.A.: Long-term electric energy consumption forecasting via artificial cooperative search algorithm. Energy 115, 857–871 (2016) 28. Soytas, U., Sari, R.: Energy consumption, economic growth, and carbon emissions: challenges faced by an EU candidate member. Ecol. Econ. 68(6), 1667–1675 (2009) 29. Drewnowski, A., Specter, S.E.: Poverty and obesity: the role of energy density and energy costs. Am. J. Clin. Nutr. 79(1), 6–16 (2004) 30. Figueiredo, V., Rodrigues, F., Vale, Z., Gouveia, J.B.: An electric energy consumer characterization framework based on data mining techniques. IEEE Trans. Power Syst. 20(2), 596–602 (2005) 31. Stern, D.I.: The role of energy in economic growth. Ann. N. Y. Acad. Sci. 1219(1), 26–51 (2011) 32. Grub, O., Krapalyuk, I., Shvets, S., Luka, O., Kaurkin, Y.: Relationship between coronal discharge and harmonious component and their influence on electricity quality indicators. In: Bulletin of the National Technical University “KhPI”. Series: Hydraulic Machines and Hydraulic Units, vol. 2, pp. 60–65 (2022) 33. Gapon, D.A., Gryb, O.G., Karpaliuk, I.T., Rudevich, N.V.: (2021). Automated metering and power quality systems in power supply systems. In: Bulletin of the National Technical University «KhPI». Series: Energy, Reliability and Energy Efficiency, vol. 2, no. 3, pp. 54–58 34. Eremenko, V., Babak, V., Zaporozhets, A.: Method of reference signals creating in nondestructive testing based on low-speed impact. Tekhnichna Elektrodynamika 4, 070 (2021) 35. Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M., Babak, V.P., et al.: Methods and models for information data analysis. In: Diagnostic Systems for Energy Equipments, pp. 23–70. (2020) 36. Babak, V.P., Babak, S.V., Myslovych, M.V., Zaporozhets, A.O., Zvaritch, V.M., Babak, V.P., et al.: Principles of construction of systems for diagnosing the energy equipment. In: Diagnostic Systems for Energy Equipments, pp. 1–22 (2020) 37. Babak, V., Zaporozhets, A., Kulyk, M., Kuts, Y., Scherbak, L.: Application of discrete Hilbert transform to estimate the characteristics of cyclic signals: information provision. In: Systems, Decision and Control in Energy IV: Volume I. Modern Power Systems and Clean Energy, pp. 93–115. Springer Nature, Cham, Switzerland (2023)

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38. Shiavi, R.: Introduction to Applied Statistical Signal Analysis: Guide to Biomedical and Electrical Engineering Applications. Elsevier (2010) 39. Yin, S., Ding, S.X., Xie, X., Luo, H.: A review on basic data-driven approaches for industrial process monitoring. IEEE Trans. Ind. Electron. 61(11), 6418–6428 (2014) 40. Lewis, F.L., Vrabie, D., Syrmos, V.L.: Optimal Control. Wiley (2012) 41. Naidu, D.S.: Optimal Control Systems. CRC Press (2002) 42. Athans, M., Falb, P.L.: Optimal Control: An Introduction to the Theory and Its Applications. Courier Corporation (2013) 43. Wang, G., Wang, L., Xu, Y., Zhang, Y.: Time optimal control of evolution equations. Birkhäuser, Cham (2018) 44. Vinter, R.B., Vinter, R.B.: Optimal Control, vol. 2, no. 1. Birkhäuser, Boston (2010) 45. Kobrynskiy, N.E.: Information filters in the economy. Analysis of univariate time series. Statistics (1978) 46. Kendall, M.J., Stewart, A.: Multivariate Statistical Analysis and Time Series. Nauka (1976) 47. Mehmood, T., Liland, K.H., Snipen, L., Sæbø, S.: A review of variable selection methods in partial least squares regression. Chemom. Intell. Lab. Syst. 118, 62–69 (2012) 48. Gavin, H.P.: The Levenberg-Marquardt Algorithm for Nonlinear Least Squares Curve-Fitting Problems, p. 19. Department of Civil and Environmental Engineering, Duke University (2019) 49. Sarstedt, M., Henseler, J., Ringle, C.M.: Multigroup analysis in partial least squares (PLS) path modeling: alternative methods and empirical results. In: Measurement and Research Methods in International Marketing, vol. 22, pp. 195–218. Emerald Group Publishing Limited (2011) 50. Box J., Jenkins H.: Analysis of Time Series. Forecast and Management. Mir (1974) 51. Nikiforov, I.V.: Sequential Detection of Change in Time Series Properties. Nauka (1983) 52. Shyryaiev, A.N.: Statistical Sequential Analysis. Optimal Stopping Rules. Nauka (1976) 53. Shyryaiev, A.N.: About optimal methods in problems of early detection. Probab. Theory Appl. 8(1), 26–51 (1963) 54. Shyryaiev, A.N.: About the detection of defects in the production process. Probab. Theory Appl. 8(3), 264–281 (1963) 55. Darhovskyi, B.S.: Nonparametric methods in random sequence disorder problems. In: Statistics and Control of Random Processes, pp. 57–70 (1989) 56. Zaporozhets, A.O.: Correlation analysis between the components of energy balance and pollutant emissions. Water Air Soil Pollut. 232, 1–22 (2021) 57. Aivazyan, S.A., Enyukov, I.S., Meshalkin, L.D. et al.: Applied statistics: dependency research. Financ. Stat. (1985) 58. Aivazyan, S.A., Buchstaber, V.M., Enyukov, I.S., Meshalkin, L.D.: Applied statistics: classification and dimension reduction. Financ. Stat. (1989) 59. Kourti, T.: Process analysis and abnormal situation detection: from theory to practice. IEEE Control Syst. Mag. 22(5), 10–25 (2002) 60. Hassani, H.: Singular Spectrum Analysis: Methodology and Comparison (2007) 61. Kumar, U., Jain, V.K.: Time series models (Grey-Markov, Grey model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India. Energy 35(4), 1709– 1716 (2010) 62. Miranian, A., Abdollahzade, M., Hassani, H.: Day-ahead electricity price analysis and forecasting by singular spectrum analysis. IET Gener. Transm. Distrib. 7(4), 337–346 (2013) 63. Vitanov, N.K., Hoffmann, N.P., Wernitz, B.: Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA. Chaos Solitons Fractals 69, 90–99 (2014) 64. Stoica, P., Moses, R.L.: Spectral Analysis of Signals, vol. 452, pp. 25–26. Pearson Prentice Hall, Upper Saddle River, NJ (2005)

Economic Effect of the Use of the Method of Diagnosing the State of Power Lines at the Expense of UAVs Oleg Gryb , Ihor Karpaliuk , Vitalii Babak , Viktor Starenkiy , Artur Zaporozhets , and Yevgen Kaurkin

Abstract A brief history of approaches to the quality of electricity supply is given. The main parameters of electric power supply quality, which were grouped according to various factors, are shown. Attention was drawn to the fact that the quality of electrical energy can be considered as one of the elements of quality indicators of electricity supply. The results of the research of quality parameters of electric power in the Ukrainian energy system are presented. The presence of deviations in quality parameters of electric power is shown. Keywords UAV · Energy objects · Monitoring · Diagnostics · Power lines · Power networks · Economic analysis

1 Analysis of the Status of Energy Objects of Ukraine In Ukraine, there is a significant number of energy objects that require constant monitoring. Telemetry systems and bypass brigades are used to perform these duties. In recent years, updating of technical systems has been carried out at a slow pace. Therefore, the level of equipment wear is increasing. The current level of wear leads to an increase in the probability of emergency conditions, and as a result of system shutdowns. The situation is further aggravated by the fact that the staff of operational O. Gryb · I. Karpaliuk · Y. Kaurkin National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine V. Babak · A. Zaporozhets (B) General Energy Institute of NAS of Ukraine, Kyiv, Ukraine e-mail: [email protected] V. Starenkiy State of Organization “Grigoriev Institute for Medical Radiology and Oncology of the National Academy of Medical Sciences of Ukraine”, Kharkiv, Ukraine A. Zaporozhets Green Technology Research Center, Yuan Ze University, Taoyuan, Taiwan © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024 Y. Sokol et al. (eds.), Detection of Corona Discharge in Electric Networks, Studies in Systems, Decision and Control 509, https://doi.org/10.1007/978-3-031-44025-0_10

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personnel needs to be increased to service worn-out systems, but energy companies do not increase staff, but even reduce it [1–5]. Among all the Ukrainian energy objects we can distinguish the following: • generation facilities (hydropower plants, thermal power plants, nuclear power plants; • energy conversion stations; • electrical networks. A number of terms are used to characterize the equipment’s suitability. The established service life is the calendar duration of the operation of the object, upon reaching which its further use for its intended purpose is possible only after a special confirmation of operability (paragraph 3.11 of State Building Regulations (SBR) V.1.2-14-2009). Limit state—a state according to which the further operation of the construction object is unacceptable, associated with difficulties or impractical (paragraph 3.13 of SBR V.1.2-14-2009). The residual resource of the equipment is determined according to the organizational and methodological documents. The actual value of the resource is confirmed by the appropriate measuring equipment. When the deadline for the operation of the equipment has expired, the authorized organization develops a procedure for technical inspections for an extended period of safe operation. It is stored along with the equipment passport. For buildings and structures, the service life is determined after its examination and assessment of the technical condition in accordance with paragraph 5.3.2 of SBR V.1.2-14-2009 “General principles for ensuring the reliability and structural safety of buildings, structures, building structures and foundations”, approved by order Ministry of Regional Development and Construction of Ukraine dated December 30, 2008 No. 709. The procedure for assessing the technical condition of buildings and structures is determined by the State Standard of Ukraine (SSU) V.1.218:2016 “Guidelines for the inspection of buildings and structures to determine and assess their technical condition” (approved by order of the Ministry of Regional Development dated 02.07.2016 No. 213). Nuclear power plants (NPPs). Among the 15 operating power units of the NPP of Ukraine [6, 7], the operating period has already been extended for 6 units: • Rivnenska NPP (blocks №1,2)—on December 10, 2010, the period of operation was extended until 2030, 2031, respectively; • South Ukraine NPP (block №1)—on November 28, 2013, the period of operation was extended until December 2, 2023; • Zaporizhzhia NPP (block №1)—on September 14, 2016, the period of operation was extended until December 23, 2025; • Zaporizhzhia NPP (block №2)—on October 4, 2016, the period of operation was extended until February 19, 2026.

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To extend the life of existing NPPs, when predicting the long-term development of the energy sector in Ukraine, the calculated cost of extending the life of 20 years will be $504 (~e467) million per 1000 MW of installed capacity [8]. Hydroelectric power plants (HPPs). According to the use of water resources and the pressure concentration, HPPs are divided into: channel, burial, diversion, pumped storage and supply. HPPs are divided into large, medium and small. For all scenarios, the development of large HPPs is almost not expected, since this type of generation is recognized as an unsustainable renewable energy source. As for small HPPs, on the one hand, according to public environmental organizations, there is not a single example of a small hydropower plant in Ukraine [9–11] that would meet environmental criteria, and they bring significantly more environmental harm than potential benefits can be obtained, for example, reduction greenhouse gas emissions. At the same time, there are examples of HPPs in Austria [12] and Norway [13] that are quite safe for the environment. Therefore, in this work, a compromise option was chosen: the use of 50% of the available potential while meeting the most stringent environmental criteria. As of 2016, the capacity of small hydropower plants is 90 MW. The maximum capacity of small HPPs by 2030, according to the Institute of Renewable Energy of the National Academy of Sciences of Ukraine, is 250 MW. That is, the addition to the existing potential is 180 MW. Assuming that 50% of new small HPPs will meet all environmental criteria, the additional increase is 90 MW. At the same time, it was assumed that a significant part of this potential should be realized as a result of the modernization and increase in the efficiency of existing small HPPs. The construction of new small HPPs can only be carried out if strict environmental criteria are met, which must be introduced at the legislative level (such as those applied by the International Rivers Network, WWF, Greenpeace, Bankwatch). In addition, after 2030, the “green” tariff will be canceled, so the construction of new small HPPs after 2030 is very doubtful, because the latter will significantly lose in terms of cost to rapidly depreciating WPPs and SPPs. Total electricity consumption (production) in Ukraine. According to the National Statistical Office, the dynamics of electricity generation and consumption in Ukraine has recently been distributed in the following way (Fig. 1). Consumption by the industrial sector is declining. At the same time, the percentage of consumption by the population is growing. The requirements for the quality of power supply are also increasing [14–16]. In recent years, the consumption of fuel and energy resources (FER) has significantly decreased (Tables 1 and 2), which is due to the previously indicated political and economic factors, and not the active policy of increasing energy efficiency in the country, which illustrates the change in macroeconomic indicators and volumes of FER consumption in period 2012–2016 [17–19]. According to consumption data, production volumes by types of generating capacities are also proposed (Table 3). Such a strategic forecast shows that a gradual shutdown of traditional generation capacities is not planned. Although it is planned to increase the production of

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Fig. 1 Energy flows in Ukraine

Table 1 FER consumption Type

Unit

2012

2013

2014

2015

2016

Electricity

109

187.70

182.60

167.50

148.30

147.10

kW/h

Table 2 Final FER consumption by sector (with forecast), ktoe Year

2012

2015

2020

2025

2030

2035

2040

2045

2050

Sector Industry

24,844 16,408 18,212 21,797 24,539 27,684 29,883 31,532 32,756

Population

23,467 16,555 20,390 21,069 21,482 22,130 22,817 23,570 24,067

Transport

11,448

Service Agriculture Total

8749 10,964 11,976 12,839 13,893 14,991 15,946 16,709

5037

3838

5986

6541

6916

7429

7762

8054

8283

2195

1960

2245

2480

2694

2899

3058

3186

3292

66,991 47,510 57,797 63,862 68,469 74,036 78,511 82,288 85,107

electricity from renewable sources (solar, wind, bio, geothermal). But most of the generated electricity will still come from traditional types of generation [20, 21]. In addition, the generation will use existing capacities, that is, objects that have significant wear and tear. And in order to maintain such facilities in working order, it is necessary to allocate additional funds for the prevention of emergency conditions and the maintenance of electricity quality indicators in an appropriate state.

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Table 3 Electricity generation (with forecast), billion kWh Year

2012

2015

2020

2025

2030

2035

2040

2045

2050

NPPs (existing)

90

88

65

52

32

20

13

13

13

NPPs (new)

0

0

0

7

20

34

34

34

34

TPPs (existing)

79

58

89

96

100

98

97

97

97

TPP (new, caol)

0

0

11

28

45

67

87

105

121

TPP (new, gas)

0

0

0

7

11

14

18

13

1

CHP and block stations

18

8

22

27

32

32

35

34

35

HPPs and PSPPs (large)

11

7

10

11

12

12

12

12

12

HPP (new, small)

0.3

0.2

0.5

0.6

0.6

0.7

0.8

0.8

0.9

WPP

0.3

1.1

3

4.3

4.4

4.5

4.6

4.6

5

SPP (ground)

0.3

0.5

0.2

0.2

0.5

0.6

0.5

0.5

0.5

SPP (roof)

0

0

0.1

0.4

0.4

0.4

0

0

0

Geothermal energy

0

0

0

0.3

0.7

0.9

0.9

0.9

0.9

Bio HPP/CHP

0

0.1

0.9

1

1

1.1

1.2

1.3

1.4

Total

199

162

202

235

260

285

304

315

322

% RES

6.00

5.40

7.30

7.70

7.70

7.20

6.70

6.50

6.50

Type

2 Calculation of Losses from Emergency Modes The valuation of the damage caused due to the interruption of the process of production, transmission and supply of electrical energy or deviation of the quality indicators of electrical energy from the normalized values is made by direct calculation using economic dependencies according to formulas (3)–(24). Quantitatively, the main types of damage (D) are defined as follows.

2.1 Damage Definition Structure The total damage from the occurrence of an event (accident, failure, shutdown) arising from the interruption of the process of production, transmission and supply of electrical energy or the deviation of electrical energy quality indicators from normalized values can be generally expressed by the formula: Dt = Dd + El + Di ,

(1)

where Dt —total damage from the occurrence of the event, $; Dd —direct damage to the consumer, $; E l —expenses for localization (liquidation) and investigation of the incident, $; Di —indirect damage, $.

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Direct damage from the occurrence of an event is calculated by the formula: Dd = L b f + L i + L p ,

(2)

where L bf —consumer losses from destruction, damage of basic funds (industrial and non-industrial), $; L i —losses from destruction, damage to inventory items, $; L p —losses from destruction, damage of property of third parties, $. The costs of localization (liquidation) and investigation of an event (E l ) can be determined by the formula: El = E c + E i ,

(3)

where E c —expenses associated with the localization (liquidation) of the consequences of the incident, $; E i —incident investigation expenses, $. Indirect damage (Di ) from the occurrence of an event is recommended to be defined as part of the profit lost by the enterprise as a result of downtime (Ddown ), wages and semi-fixed costs of the enterprise during downtime (Dw ) and losses caused by the payment of various penalties (Dp ), as well as losses of third parties (Dtp ). Di = Ddown + Dw + D p + Dt p .

(4)

2.2 Components of Economic Damage Direct damage (direct loss). The components of direct damage from the occurrence of an event included in formula (2) are recommended to be determined as follows. Direct losses from destruction, damage to fixed assets: L b f = L b f.des + L b f.dam ,

(5)

where L b f.des —losses from the destruction of basic funds, $; L b f.dam —losses from the damage of basic funds, $. At the same time, L b f.des can be calculated using the formula ( ) L b f.des = Cb f.rr − C gm − Cb f.ut ,

(6)

where Cb f.rr —cost of replacing or reproducing the type of destroyed basic funds, $; C gm —cost of goods and material values, suitable for further use, $; Cb f.ut —utilization cost of destroyed official funds, $. If there are several types of basic funds, then the total loss (L tot ) is the sum for each type of destroyed or damaged fixed assets. The losses from damage of basic funds and other property is determined by the formula:

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L b f.dam = Ccat · Ddam + Ceq + Coth ,

207

(7)

where C act —actual (residual) value of estimated basic funds, $; Ddam —degree of damage of basic funds, %; C eq —cost of equipment damage, $; C oth —cost of damage to other property, $. The degree of damage Ddam of basic funds is determined by the formula Ddam =

n E

i i Ddam · Wcon ,

(8)

i=1 i where Ddam —degree of damage of a separate structure, element, %; n—number of i —specific weight of a separate structure, element. separate structures, elements; Wcon In case of partial damage of property, it is recommended to determine the value of the damage in the amount of costs for its restoration (recovery costs) to the state in which the property was immediately before the occurrence of the event (accident, failure, stoppage), while it is recommended to take into account:

• • • •

costs for materials and spare parts for repairs, $; costs of paying for the services of third-party repair organizations, $; cost of electricity and other energy required for restoration, $; costs of materials delivery to the repair place and other costs necessary to restore the object to the state in which it was immediately before the occurrence of the event, $; • salary increments for overtime work, night work, official holidays, $. Losses from the destruction, damage of goods and material values of C gm can be determined by the sum of the losses of each type of values as follows C gm =

n E i=1

C gm i +

m E

C gm j ,

(9)

j=1

where C gm i —damage caused to the i-th type of products manufactured by the enterprise, $ (it is determined based on the production costs necessary for their repeated manufacture, but not higher than their market value); n—number of types of goods that were damaged as a result of the event (accidents, failures, shutdowns); C gm j — damage caused to the j-th type of products purchased by the enterprise, as well as raw materials and semi-finished products, $ (it is recommended to be determined based on the value at the prices necessary for their repurchase, but not higher than the prices at which they could be sold on the date of the event, as well as the costs of their transportation and packaging, customs duties and other fees); m—number of types of raw materials that were damaged as a result of the event (accidents, failures, shutdowns). The amount and value of goods and material values that were at the time of the event (accident, failure, shutdown) can be determined based on accounting data.

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Losses from the destruction and damage of the property of third parties are recommended to be determined similarly to the determination of losses of the property of the enterprise (for legal entities), as well as on the basis of the market value that belongs to them by the right of ownership or possession of the property (for individuals) and (or) taking into account the data of insurance companies (in case of insured property). Indirect damage. Loss from labor downtime is determined as follows: L ld = td · (1 + αad ) · (1 + αsoc ) · K d ·

n E

Sav · Nk ,

(10)

k=1

where td —duration of downtime of workers, hours; αad —the average percentage of additional wages in the form of deductions for vacation pay from the amount of additional accrued basic wages, %; αsoc —deduction for social insurance, %; K d — constant coefficient that takes into account the peculiarities of the company’s costs when workers don’t work; n—number of ranks of workers; Sav —average hourly salary of a first class worker, $; Nk —number of workers of the first category who don’t work. Also K d = K 1 · K 2 · K 3 , where K 1 —coefficient that takes into account the reduction of payment to workers for idle time, as a rule, 0.5; K 2 —coefficient takes into account that part of the workers (approximately 10%) are used for other jobs during the break, as a rule, 0.9; K 3 —coefficient takes into account that during outages, the power system, as a rule, preserves the power supply of emergency and technological armor loads (up to 30%), as a rule, 0.7–1. The loss from production downtime (L pd ) is calculated according to the formula: L pd = At · th · C f pu ,

(11)

where At—production process downtime, h; th —hourly productivity, units/h; C f pu —fixed unit costs, $/units. Production process downtime At is calculated by the following formula: At = tel + ttech ,

(12)

where tel —duration of power interruption, hours; ttech —amount of time required to restore the technological process after the restoration of the power supply, hours. Unearned profit is determined by the formula Pun =

n E

( ) Fun Paw − Pap ,

(13)

i=1

where n—number of types or names of products, units; F un —underproduction of the i-th type of products due to a simple enterprise, units; Paw —average wholesale price

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(sale price) of a unit of the i-th type of unfinished product (service), $; Pap —average planned cost of i-th type of non-produced product (service), $. There is another way to calculate Pun : Pun =

n E

( ) Fun Paw − C pv ,

(14)

i=1

where C pv —planned variable costs per unit of production, i-th type of product (service), $. Variable costs include mostly direct costs that are accurately calculated per unit of production. Fixed costs, as a rule, are indirect, and when calculating in multi-product production, they are distributed between products quite roughly depending on the selected distribution base. The volume of the i-th type of unfinished product (service) due to the occurrence of an event (accident, failure, stoppage) is determined by the formula ) ( Fun = Fi0 − Fi1 Tel.d ,

(15)

where Fi0 —average daily (monthly, quarterly, annual) production volume of the i-th type of product (service) before the accident; Fi1 —average daily (monthly, quarterly, annual) production volume of the i-th type of product (service) after the accident; Tel.d —amount of time required to eliminate damage and destruction and restore the volume of production (services) to the pre-accident level. Damage from overtime work Dow is calculated as follows [( Dow =

] ) K iop − 1 · Fm + K iop · Fa tc , To

(16)

where K iop —coefficient of increase in overtime pay; F m —annual salary fund for the main production workers who work overtime, $; F a —annual salary fund for auxiliary personnel servicing the equipment during overtime work, $; t c —duration of overtime work caused by the need to compensate for underproduction of products, hours; T o —amount of hours of operation of the enterprise per year, hours. The loss from the forced operation mode L fom is calculated by the formula ( ) L f om = Cvp · V pnm · K f ms − 1 · γ · T f m ,

(17)

where C vp —variable part of production operating costs per unit of production, $; V pnm —volume of temporary output of products at the nominal mode of operation of the consumer, units; K fms —coefficient of increase in salary in the forced mode per unit of production; γ —multiplicity of the forced mode, equal to the ratio of the output of products in the forced mode to the output of products in the nominal mode during the period of the forced time; T fm —time of operation of the enterprise in the forced mode, hours.

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If the intensification of production during forced operation requires additional costs that can be calculated and documented, they must also be included in the amount of the losses. The amount of the loss also includes the costs of paying sanctions to counterparties (as a result of violation of product delivery terms (schedule), other reasons). Then the amount of damage will be determined by the formula: ) ( L f om = Wit + P f wm · (1 + αad ) · (1+soc ) + Cad + Psan ,

(18)

where W it —wages of main production workers for idle time, $; Pfwm —additional payment to employees for forced work mode, $; C ad —additional operating costs, $; Psan —volume of sanctions to counterparties, $. Replacement of labor intensity Drli (during replacing raw materials, materials and components, etc.). Additional costs due to changes in the price and quantity of materials and components are calculated as the difference between the cost of the materials actually used and those replaced, taking into account transport and procurement costs. At the same time, additional labor costs (in case of increased labor intensity of operations) and other operational needs (electricity, tools, preparation of materials, etc.) are possible: Drli = Cmat.u − Cmat.r + Pad (1 + αad )(1 + αsoc ) + Cad .

(19)

where C mat.u , C mat.r —costs of materials, respectively, actually used and replaced, $; Pad —additional payments to employees for increased labor intensity of work with using other materials, $. Lossed from the release of products L plq of low quality: ( ) L plq = N plq Pu − Pplq ,

(20)

where Pu —price of a unit of products (works, services) of nominal quality, $; Pplq — price of a unit of low-quality products (works, services), $; N plq —number of units of products (works, services) of low quality, units. Defective product. The loss from the defective product is expressed in losses from the destruction of a certain amount of resources and losses due to the underproduction of products, which are not compensated, or are compensated for those that was defective. The amount of the loss excludes the value of the finally rejected products pos at the price of their possible use (Cde f ), $, (for example, if it is a metallurgical industry, then the value of scrap (1 ton.) is used as a defective product), but to it are liq added costs for the liquidation or disposal of defective products (Cde f ), $, if any. Damage from defective products Ddp during a power outage is calculated as: Ddp =

] [( ) pos liq C L I + C pp + (1 + K tran ) + Er f (1 + K we ) − Cde f + Cde f · Nde f , (21)

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where C LI —costs of labor items (raw materials, energy, etc.), $; C pp —cost of purchased products (related to finishing products to nominal quality), $; K tran — average ratio of transport and procurement costs at the enterprise. If transport and procurement costs are insignificant or their determination is impossible or not documented, then K tran = 0; E rf —employee remuneration fund of the enterprise, which is spent on the correction of a unit of production, $; K we —coefficient expressing the ratio of workshop costs and equipment maintenance costs to the basic salary of workers; N def —number of defective products, units; or ) ( pos Ddp = C ppu − C gen − Cde f · Nde f ,

(22)

where C ppu —production cost per unit of production, $; C gen —general production costs of general economic purpose, $. If there are several types of defective products, then the total loss (L tot ) is the sum for each type of defective products: L tot = L 1 + L 2 + · · · + L n , where n—number of types of defective products. The given ratio refers to the case of delivery of low-quality products to consumers. But in a number of cases, the manufacturing company has the opportunity, if it is economically feasible, to finalize the product in order to increase its quality to the nominal level. Then the loss consists in non-productive (without the release of additional volume of products) costs of material and labor resources for correction and refinement of products. In the case of elimination of defects in products (performed work) by the forces of a third-party organization, the amount of damage is determined by the cost of works to eliminate defects performed by a third-party organization. If the specified products were delivered to the location of a third-party organization to eliminate defects, the cost of its transportation is also included in the amount of damage. The expenses also include expenses related to the need to send employees of the enterprise to carry out work to eliminate product defects at the consumer (transportation, business trip, etc.), or costs for transporting these products from the consumer and back to carry out the specified work at the supplier’s location. Costs for payment of sanctions are calculated as the sum of all sanctions paid by the company to counterparties for improper product quality (decreased grade, technical and economic level, etc.) due to the fault of the defendant. The losses in the finalization of products (L fp ) to the nominal level in the field of production is calculated as follows: ] [ L f p = C L' I + C 'pp + Er' f · (1 + K we )Nlq p ,

(23)

where C L' I —cost of labor items (raw materials, energy, etc.) included in the unit cost of production, $; C 'pp —cost of purchased products (related to finishing products to nominal quality), attributed to the unit cost of production, $; Er' f —remuneration fund

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of the company’s employees, which is spent on the correction of a unit of production, $; N lqp —number of units of low-quality products, which need to correction, units. Economic damage is caused not only by a decrease in the quality of labor items, labor tools or spoilage of products, but also by electricity costs. This loss is determined by the amount of electricity L el spent on the production process (provided that the product completely loses its properties and quality): L el =

Teq.o · Cel , tu

(24)

where T eq.o —duration of equipment operation before the start of the event, hours; C el —cost of one kW/h of electricity, $/h; t u —time period during which the processed products become unusable, hours.

3 Measures to Reduce Losses from Emergency Modes Due to the Use of UAVs Costs related to monitoring the technical condition of the facility in the power supply system are included in operating costs and general production costs [22, 23]. Therefore, in order to calculate the costs, it is necessary to study the following: • production management costs; • costs for maintenance, operation and repair, insurance, operating lease of fixed assets, other non-current assets of general production purpose; • costs for improving technology and organization of production; • maintenance costs of the production process; • costs for labor protection, safety equipment and environmental protection; • other expenses. It should be noted that the distribution of costs for monitoring the technical condition of facilities will differ for different types of energy enterprises [24–26]. Thus, for generating enterprises, monitoring should include measures to control the technological cycles of electricity production. For enterprises engaged in energy conversion (transformer substations), such companies need to monitor the operating modes of the energy system in addition to monitoring the technical condition of the equipment. For network companies, monitoring of the technical condition of lines and control of insulation means is the main type of monitoring. Therefore, the total monitoring costs can be calculated using the following formula: Bmon = B1 + B2 + B3 ,

(25)

where B1 —costs associated with monitoring the state of fixed assets and technological modes at generating facilities; B2 —costs of monitoring electric energy conversion stations; B3 —monitoring costs of network companies.

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In accordance with cost calculations, only such components are considered, the sizes of which have bits approved by the relevant decisions of the commissions, ministry or government. In this case, the state of depreciation of equipment is not taken into account in the amount of deductions. For example, according to the regulations, the bypass of the lines must be carried out once a year (for the permitted periods of operation). In this case, it is not taken into account that worn equipment requires additional monitoring. Therefore, the occurrence of a failure can occur “unexpectedly”, at an unpredictable time. The limiting state of an object can be characterized by [27]: • the transition of a non-renewable object into an inoperable state; • the decrease in the efficiency of the use of the object due to the deterioration of reliability; • economic impracticality of further operation; • moral aging of equipment. The DM distribution [28, 29] can be used to calculate the run-up to the limit state: ( F(t) = D M(t, μ, ν) = q where q(z) =

√1 2π

{z −∞

) t −μ , √ ν μt

(26)

( 2) exp − U2 dU – normal distribution.

The distribution density of the residual resource can be calculated by the formula: ] [ 2 (t + μ) exp − (t−μ) 2 2ν μt ). ( r (t) = √ √ 2νt 2π μtq νμ−τ μτ

(27)

at t ≥ τ . The mathematical expectation of the residual resource is calculated according to the formula: [ ( ) ] ( ) ( 2 ) ( μ+τ ) 2 μν 2 √ μ 1 + ν2 − τ q νμ−τ + q − ν √μτ exp μτ 2 ν2 ) ( M= + √ q νμ−τ μτ ] [ (28) √ ν μτ (τ −μ)2 √ exp − 2 μt 2ν 2π ) ( + . √ q νμ−τ μτ The density of failures constructed in graphic form corresponds to the model (Fig. 2). According to regulations, there is a required number of inspections and repairs for equipment. The standardized number of inspections is based on reliability requirements.

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Fig. 2 Classification of problems by three stages

The required number of service personnel for the given system or equipment is calculated from these standard labor costs. Calculation of the number of inspections is carried out according to normative documents (e.g., GOST 27.502-83). During the calculation, the minimum amount of statistical information is determined, for which the reliability indicators of elements can be obtained with the necessary accuracy. In accordance with GOST 27.502-83 methods of determining the minimum number of monitoring objects can be parametric (with a known type of distribution law of the investigated incidental value) and non-parametric (type of distribution law is not known). If the law of distribution of the chosen quantity is known, it is possible to set a relative (or absolute) error with confidence probability β. In addition, it is necessary to have an estimate of the random value x res obtained based on investigations or by selections from the multiplicity of values of the random value. For two-parameter distribution laws, the sample mean square deviation σ res is also required. So, with the exponential law, the probability density function is given in the form f (t) = λe−λt at t ≥ 0. The number N of observation objects depends on the relative error δ of determining the average value of t av of the studied random variable t with a confidence probability β. The relative error is defined as δ=

(t u − tav ) , tav

where t u —upper one-sided confidence limit. It is recommended to use the following confidence probabilities β: 0.80, 0.90, 0.95, 0.99. The number N of observation objects is determined from the formula: δ+1=

2N , 2 χ1−γ (2N )

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2 where χ1−γ (2N )—quantile of the χ2 distribution with the number of degrees of freedom 2N, which corresponds to the probability 1 − γ . The probability of failure-free operation is the probability that the product will not fail during a given period of time t under given operating conditions. The probability of failure-free operation is expressed in terms of the probability density f (t) in the following way

{∞ Rel(t) =

f (t)dt. t

An event that is opposite to the probability of failure-free operation is called the probability of failure during a given time interval t under given operating conditions: {t Emer (t) =

f (t)dt. −∞

Since the events are opposite and represent a complete group of events, then. Rel(t) + Emer (t) = 1. Let’s consider the variability of the harmonicity of the vibration for the time interval t, assuming that the harmonicity follows to the normal law of distribution {t Emer (t) = −∞

1 f (t)dt = √ σ σ 2π

{t e

−(ti −tcp )2 2σ 2

· dt.

−∞

Let’s make a substitution z0 =

(ti − tav ) . y

(29)

Then we can write. z 0 · y = ti − tav , and dt = y · dz 0 . Taking into account substitution (29), we get 1 Emer (t) = √ σ σ 2π

{z0 e

−z 02 2

−∞

Let this integral be represented by two integrals

· dz 0 .

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1 Emer (t) = √ 2π

{0 e −∞

−z 02 2

1 · dz 0 + √ 2π

{z0 e

−z 02 2

· dz 0 .

0

The first integral of the sum is equal to 0.5, i.e. 1 · √ 2π

{0

z 02

e− 2 · dz 0 = 0.5.

−∞

The other integral of the sum is not taken by analytical methods, but is calculated by numerical methods and is often designated as O (z 0 )—Laplace integral, i.e. A

1 O (z 0 ) = √ 2π

A

{z0 e

−z 02 2

· dz 0 .

0

Then the probability of withdrawal in the interval of time can be written as A

Emer (t) = 0.5 + O (z 0 ). Figure 3 shows the change in the probability of system failure-free operation depending on the time of operation. According to the Fig. 3, we get that the probability of failures increases gradually. The technical indicators of the increase in the probability of failure are the gradual deterioration of the reliability of the system blocks. And with a load that exceeds the capabilities of the worn element, the failure of the element (link) occurs and, as a result, the performance deteriorates, or the failure of the entire system.

Fig. 3 Changes in the probability of failure-free operation

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217

Fig. 4 Graph of equipment failures and periodic inspections of equipment with significant wear and tear

For options when the equipment has not reached the condition of group 3 (Fig. 2), if a surface inspection is carried out once a year, it is possible to assess the condition and predict weakly fluid wear processes of the equipment. But more often it is possible to record the normal working condition of the equipment. It is clear that the inspections are designed to detect a sharp increase in AEmer(t) or to detect a level of Emer(t) that can correspond to the emergency values. Thus, it is necessary to increase the frequency of annual inspections to achieve the required values of AEmer(t). The more worn the equipment, the more often inspections should be carried out (Fig. 4). Let’s determine the required number of inspections to ensure reliability by preventing failure due to wear and tear. The time interval between the inspections (frequency of the inspections) must ensure the increment of the function of the admissions by a certain value AQ(t) ≤ const. Let us write down the incremental function of the inputs for the initial time t 0 : AEmer(t0 ) = Emer(t0 + At) − Emer(t0 ). But this growth has to take place within a certain period of time At: Emer(t0 + At) − Emer(t0 ) AEmer(t0 ) = . At At If we do not set At to be specific (year or month), but direct it to zero, we will get ( lim

At→0

AEmer(t0 ) At

)

( = lim

At→0

) Emer(t0 + At) − Emer(t0 ) . At

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Fig. 5 Inspection schedule according to the standard and according to the calculation

Thus, we get that the number of inspections should depend on the derivative of the rejection function: ( N = lim

At→0

Emer(t0 + At) − Emer(t0 ) At

)

'

= Emer(t).

In the graphic presentation, the number of inspections will look as shown in Fig. 5. It is clear that the number of inspections to maintain (prevent) failures at a given level should increase in accordance with the growth of the failure function. And the number of inspections significantly exceeds the normative values for worn equipment. The Ukrainian energy system has significant equipment wear. And the existing inspection system currently does not allow to ensure the required level of trouble-free operation. A way out of this situation is offered by the implementation of overhead power line (OPL) monitoring using UAVs. The frequency of overflights of the line can be much more frequent than the rounds of inspections of line personnel, which reduces AEmer(t) and achieves the required level of system continuity. Ensuring the reduction of accidents due to the prevention of mechanical damage. Indicators of element wear can be various parameters [2, 30]: • electric; • mechanical; • chemical. In electrical systems, control of electrical parameters is performed using sensors of relay protection systems or additional emergency equipment. And the control of the mechanical condition is carried out only by a superficial inspection. Chemical parameters are evaluated only during the analysis of the occurrence of an accident. We do not consider chemical indicators for current monitoring. Mechanical parameters monitoring is essential on both new and worn electrical systems. The main causes of accidents on OPLs [31–33]: • • • •

breakage of OPLs due to icing; destruction of wires and cables from vibration near the clamps; wind load (breakage of wires, overturning of supports); destruction of supports (wind, water, human activity);

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Fig. 6 Distribution of automatic shutdowns of OPLs with downtime for more than an hour

• • • •

frequent cases of short circuits or prolonged action of short circuit currents; switching overvoltage (insulation breakdown); overvoltage (lightning); chemical action of polluted air.

The frequency of disconnections of OPLs, depending on the reasons, was considered by various researchers. Figure 6 shows the distribution of outages followed by downtime of the OPLs for more than an hour due to various reasons on the example of the Kharkiv region. From the given data, it is clear that the mechanical reasons for disconnection of OPLs are the main ones.

4 Calculating the Economic Effect of UAV’s Implementation We will perform the calculation according to the following algorithm, calculate the loss from outages and separate the frequency that can be prevented by the implementation of UAVs. We will consider it as the income (I) part of the economic effect: I = 0.42 · L dis tot ,

(30)

where—L dis tot total losses from disconnections, $; 0.42—share of outages that can be prevented by the UAVs implementation, units. Let’s calculate the costs of implementing the UAV complex (C imp ):

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Cimp = CU AV + C year ,

(31)

where CU AV —costs for the purchase of UAVs’ complex, $; C year —annual costs for maintaining the complexes, $. After finding the break-even point, we will determine the economic effect of the UAV complex implementation in the electric power system of one region (using the example of Kharkiv region).

4.1 Determination of the Income Part from the Implementation According to statistical data, the balance of energy companies includes network and station equipment. Let’s describe the situation with the state of the equipment using the example of a real energy company. JSC “Kharkivoblenergo” has overhead and cable lines on its balance (Table 4). On the balance of JSC “Kharkivoblenergo” there are substations, the amount of which is presented in Table 5. The electrical equipment of JSC “Kharkivoblenergo” has significant operational wear and tear, which is 60% on average. The equipment and its rate of wear and tear are presented in the Table 6. Such wear and tear of equipment leads to forced emergency shutdowns. Table 4 OPLs on the balance of JSC “Kharkivoblenergo” for 2019

Table 5 Amount of substations on the balance of JSC “Kharkivoblenergo” for 2019

№

OPLs, kV

Length, km

1

154

16,600

2

110

3505,993

3

35

3478,679

4

10

12,975,375

5

6

1020,861

6

0.4

19,448,058

№

Substation

Quantity, units

1

110

93

2

35

195

3

6–10

11,159

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221

Table 6 Amount of elements of substations and their rate of wear №

Name

Quantity, units

1

110 kV power transformers

173

88

2

35 kV power transformers

332

93

3

6–10 kV power transformers

12,947

64

4

6–110 kV switches

7435

22

5

110 kV short-circuit separator kits

84

100

6

35 kV short-circuit separator kits

63

100

7

6–10 kV distribution substation

272

82

Wear, %

4.2 Loss of Energy Companies from Unearned Profit The calculation was carried out according to the data of JSC “Kharkivoblenergo”. According to statistics on the energy sector for 2019, there were 139 cases of disconnection of various sections of the network on electric networks. Data of disconnections are given in the Tables 7, 8, and 9. If we separate only the 110 kV OPLs, which mostly supply energy for industrial enterprises, and among them we consider only disconnections due to mechanical damage, then such losses of electricity are shown in Table 10. Considering that the average cost of a kilowatt-hour of electric energy in 2019 was UAH 2.24 with VAT, then the energy company’s losses in monetary terms directly from unreleased electricity are: 7, 721 · 2.24 ≈ 17, 295 UAH. Table 7 Reasons for disconnecting high-voltage lines in 2019 №

Reason of disconnection

1

Weather conditions (precipitation, wind)

74

2

Mechanical damage

65

Number of disconnections

Total number of disconnections

139

Table 8 Disconnection time depends on the line voltage and the cause №

Voltage, kV

1

110

2

110

3

35

4

35 Total

Number of disconnections

Disconnection time, min

Reason for disconnection

38

5702

Precipitation

41

6065

Mechanical

37

14,510

Precipitation

23

8894

Mechanical

139

34,340

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Table 9 Volume of unreleased electrical energy due to disconnections №

Voltage, kV

1

110

2 3

Unreleased electricity, MW*hour

Reason for disconnection

5,702

Precipitation

110

7,721

Mechanical

35

38,387

Precipitation

4

35

8,623

Mechanical

5

Total

59,891

Table 10 Consequences of 110 kV OPLs’ disconnection due to mechanical damage №

Number of disconnections

Disconnection time, min

Unreleased electricity, MW*hour

1

41

6065

7,721

4.3 Consumer Losses from Destruction, Damage of Basic Funds and Property of Third Parties As a quantitative assessment of damage from voltage drops in various industries, data (Table 11) from the practical guide on the quality of electric energy within the framework of the European Commission’s “Leonardo” program can be used [34]. These data are caused, first of all, by a violation of the technological process due to voltage drops. According to statistical data, the number of disconnects on 110 kV lines is 41 per year (Table 10), 11 disconnects were due to outages of networks supplying responsible enterprises. Enterprises that use complex scientific and technological production cycles, financial institutions, IT companies, telecommunications firms, manufacturers with continuous cycles were selected for the calculation. The loss for each group of companies is presented in Table 12. So, the total losses of consumers of JSC “Kharkivoblenergo” is more than 130 mln. UAH. Table 11 Quantitative estimates of damage from voltage drops in various industries

Economy sector

Financial losses for the period

Production of semiconductors

3,800,000 euro

Financial sector

6,000,000 euro/h

Computer center

750,000 euro

Telecommunications

30,000 euro/min

Production of steel

350,000 euro

Production of glass

250,000 euro

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Table 12 Estimated losses of consumers from drops of electric energy №

Name of group of companies

Losses from inadequate energy

Indicator of electric power shortage

Sum, mln. UAH

Value

Units Thous. UAH. for voltage drop

11 Voltage drops

63.80

34.77

1

Enterprises with complex scientific and technological production cycles

5800

2

Financial institutions

570

Thous. UAH. per hour

61 h of non-delivery of electricity

3

IT companies

890

Thous. UAH. for voltage drop

11 Voltage drops

4

Telecommunications companies

230

Thous. UAH. 61 h of per hour without non-delivery of electicity electricity

5

Producers with non-interruptible cycles

750

Thous. UAH. for voltage drop

11 Voltage drops

Total

9.79 14.03

8.25 130.64

4.4 Total Losses The total losses are calculated as follows L dis tot = 17, 295 +130, 640, 000 = 130, 657, 295 UAH. Let’s calculate the income part of the measures in accordance with (30): I = 0.42 · 130, 657, 295 ≈ 54, 876, 064 UAH.

4.5 Costs for the Purchase of UAV Complexes In accordance with the planned scope of OPLs maintenance, the estimated need for UAVs is 1 complex per 150 km of OPLs. Table 13 shows calculations regarding the amount of required UAV complexes. Table 13 Calculation of the amount of UAV complexes

№

Power line

1

154 kV

16.6

0.1

2

110 kV

3505.993

23.4

Length, km

UAVs amount, units

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Fig. 7 DJI Matrice 210 RTK V2 Combo

The cost of one DJI Matrice 210 RTK V2 Combo UAV complex (Fig. 7) in 2019 was 326,400 UAH. It can be seen from Table 13 that the total number of necessary complexes is about 23 units. Thus, the costs of acquiring UAV complexes are CU AV = 23 · 326, 400 UAH ≈ 7.507 mln UAH.

4.6 Current UAV Maintenance Costs To perform work using a UAV, it is necessary to hire (retrain) an employee with the f skills of piloting and servicing such equipment. The monts salary fund (Smon ) of the UAV operator engineer will be (including taxes) 16.78 thous. UAH per month. f Accordingly, the annual salary fund S year of one UAV operator will be: f f S year = 12 · Smon = 12 · 16.78 = 201.36 thous UAH.

The total Stot salary fund for all 23 UAV operators will be: f Stot = 23 · S year = 23 · 201.36 ≈ 4.631 mln UAH.

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4.7 UAV Implementation Efficiency According to the technical regulations, the UAV has a resource of 10,000 h of operation, which corresponds to 5 years of operation. Then the total costs on UAV complexes for five years will be CUtotAV = 5 · Stot + CU AV = 5 · 4.631+7.507 = 30.662 mln UAH. The income part for 5 years (on the example of Kharkiv region) will be: I 5 = 5 · I = 5 · 54.876 = 274.38 mln UAH.

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