Wide band modelling of an air-core power transformer winding B.J van Jaarsveld Thesis presented in partial fulfilment of the requirements for the degree Master of Science in Engineering in the Faculty of Engineering at Stellenbosch University Supervisor: Prof H.J Vermeulen Department of Electrical & Electronic Engineering December 2013 Stellenbosch University http://scholar.sun.ac.za DECLARATION By submitting this thesis electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the sole author thereof (save to the extent explicitly otherwise stated), that reproduction and publication thereof by Stellenbosch University will not infringe any third party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification. B. J. van Jaarsveld December 2013 Copyright © 2013 Stellenbosch University All rights reserved i Stellenbosch University http://scholar.sun.ac.za ABSTRACT The objective of this project is to develop an electromagnetic model that can be used to accurately calculate the voltage distribution in a transformer winding structure when excited with standard impulse excitation waves. This voltage distribution is required during the design stage of a power transformer to ensure that the insulation is capable of withstanding the occurring electric field stresses during these tests. This study focuses on the modelling of a single disk-type power transformer winding without the presence of an iron-core. Methods of calculating self- and mutual-inductances of transformer windings are presented and validated by means of finite element method software simulations. The same is done for the calculation methods used for calculating the capacitances in and around the winding structure. The calculated and FEM-simulated results are compared to measured values as a final stage of validation. The methods used to calculate the various model parameters seem to produce results that agrees well with measured values. The non-linear frequency dependant dissipative nature of transformer windings is also investigated and a methodology to take this into account is proposed and implemented. The complete modelling methodology proposed in this thesis, which includes the calculation of the model parameters, model synthesis and solver algorithm, are applied to an actual case study. The case study is performed on an air-core reactor manufactured using a disk-type power transformer winding. The reactor is excited with standard lightning impulse waves and the voltages along the winding are measured. The calculated and measured voltage wave forms are compared in both the frequency and time-domain. From the comparison it is found that the model accurately represents the actual transient voltage response of the test- unit for the frequency range of interest during standard factory acceptance tests. ii Stellenbosch University http://scholar.sun.ac.za OPSOMMING Die doel van hierdie projek is om 'n elektromagnetiese model te ontwikkel wat gebruik kan word om die spanningsverspreiding in 'n transformatorwindingstruktuur te bereken as standaard weerligimpulstoetse toegedien word. Hierdie spanningsverspreiding word vereis tydens die ontwerpstadium van ‘n kragtransformator om te verseker dat die isolasie in staat is om die elektriese veldsterkte tydens hierdie toetse te weerstaan. Hierdie studie fokus op die modelering van 'n enkele skyftipe-kragtransformatorwinding sonder die teenwoordigheid van 'n ysterkern. Metodes van berekening van self- n wedersydse-induktansie van transformatorwindings word aangebied en getoets deur middel van Eindige-Element-Metode (EEM) simulasies. Dieselfde word gedoen vir die metodes wat gebruik word vir die berekening van die kapasitansies in en rondom die windingstruktuur. Die berekende en EEM-gesimuleerde resultate word vergelyk met die gemeete waardes as 'n finale vlak van bekragtiging. Die metodes wat gebruik word om die verskillende modelparameters te bereken vergelyk goed met gemete waardes. Die nie-lineêre frekwensie-afhanklike verliese van transformatorwindings word ook ondersoek en 'n metode om hierdie in ag te neem is voorgestel en geïmplementeer. Die volledige voorgestelde modeleringsmetodiek in hierdie tesis, wat die berekening van die modelparameters, modelsintese en oplosingsalgoritme insluit word toegepas op 'n werklike gevallestudie. Die gevallestudie is uitgevoer op 'n lugkern-reaktor wat 'n skyftipe-kragtransformatorwinding. Die reaktor word onderwerp aan die standaard weerligimpuls golwe en die spanning al langs die winding word gemeet. Die berekende en gemete spanning golf vorms word met mekaar vergelyk in beide die frekwensie- en tyd-vlak. Uit die vergelyking blyk dit dat die model die werklike oorgangspanningsweergawe van die toetseenheid akkuraat verteenwoordig vir die frekwensie reeks van belang tydens standaard fabriekaanvaardingstoetse. iii Stellenbosch University http://scholar.sun.ac.za ACKNOWLEGEMENTS During research I have done in this project, I have had the privilege in being guided and mentored by renowned experts in this field of study. Without their help and the grace of my God this work would not have been possible. My sincerest gratitude goes to Robert Degeneff - president of Utility Systems Technologies (UST) - for sharing his knowledge gained by years of experience and his constant words of encouragement. I will treasure our casual discussions at the dinners in Albany. You have been a great mentor and friend – may God bless you and your family. I thank my supervisor at Powertech Transformers Pty. (Ltd) Nico Günter and the rest of the Technology team for creating a resourceful, productive and friendly environment at the office where I could focus on my research. Many thanks to Angélica Rocha and the other members of the Cigré joint workgroup A2/C4.39 for creating a platform for sharing knowledge and experience. I have learned a considerable amount from my interaction with this group of experts and hope that my contribution to the Cigré organisation and similiar entities will grow in value over time. A special thanks to my supervisor at the University of Stellenbosch, Johan Vermeulen. Your passion for the science of engineering and your philosopical discussions ensured that my time spent with you was insightful and enjoyable. I want to extend my gratitude to Baudilio Valecillos from TrafoExperts for his assistance and guidance in my research. Thank you for your positive attitude during the long hours we spent in the laboratory. To my wive Elsje, you have been a great friend and spouse to me. I love you dearly. Thank you for your patience and support with my research. To my mother Renette, thank you for your help in proofreading my work. Your support means a lot to me and I treasure your love with all my heart. Without the grace of my God and Saviour all my work in life would be of no value. I thank you Lord for your love and guidance through your Spirit, and your constant encouragement. iv Stellenbosch University http://scholar.sun.ac.za In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not. - John1:5 King James Bible, Cambridge Edition v Stellenbosch University http://scholar.sun.ac.za TABLE OF CONTENTS Declaration ......................................................................................................................... i Abstract .........................................................................................................................ii Opsomming ........................................................................................................................ iii Acknowlegements .................................................................................................................iv Table of contents ..................................................................................................................vi List of tables ........................................................................................................................xi List of figures ....................................................................................................................... xii Symbols and abreviations ....................................................................................................xv Chapter 1 Project description and motivation ................................................................... 1 1.1 Introduction ............................................................................................................ 1 1.2 Project motivation .................................................................................................. 2 1.3 Project description ................................................................................................. 4 1.3.1 Project objective .............................................................................................. 4 1.3.2 Research objectives......................................................................................... 4 1.4 Thesis outline ........................................................................................................ 6 Chapter 2 Literature review .............................................................................................. 8 2.1 Overview ............................................................................................................... 8 2.2 Power transformer anatomy..................................................................................