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Chapter 1 Introduction Kenneth Pedersen Critical Voltage Distributions in the Dry Type Transformers of Large Wind Turbines when Exposed to Transients PhD thesis, February 2007 Copyright © Ørsted • DTU, Electric Power Engineering Technical University of Denmark Voltage to terminal at node 130 (outlet 7) 1 10 0 10 -1 10 Model .u.] Measurement -2 e [p 10 Voltag -3 10 U V W -4 10 Disc 1 Disc 1 Disc 1 Disc 2 Disc 2 Disc 2 Vout Disc 3 Disc 3 Disc 3 -5 Disc 14 Disc 14 Disc 14 10 1 2 3 D4isc 5 5 Dis6c 5 7 Disc 5 10 10 10 10Disc 6 10 Dis10c 6 10 Disc 6 V1 FrequencDiscy [Hz 7 ] Disc 7 Disc 7 Disc 8 Disc 8 Disc 8 Disc 39 Disc 39 Disc 39 DiDscisc 10314 DisDiscc 10314 DiscDisc 10314 DiDscisc 11145 DisDiscc 11145 DiscDisc 11145 DiDscisc 1256 DisDiscc 1256 DiscDisc 1256 DiDscisc 136 DisDiscc 136 DiscDisc 136 V14 I Preface The present PhD thesis is part of the requirements for obtaining a PhD degree. The work was carried out the at Ørsted•DTU, Power Engineering, Technical University of Denmark. The project ran from 1st of February 2004 until 14th of February 2007 and was financed by Energinet.dk. In addition DONG Energy and ABB Denmark has been part of the steering committee. I would like to thank my supervisors at Ørsted•DTU, Associate Professors Dr. Joachim Holbøll and Dr. Mogens Henriksen for guidance and encouragement. Thanks must also go to the remaining part of the steering committee constituted by Carsten Ras- mussen, Energinet.dk, Erik Koldby, ABB A/S, Denmark and Asger Jensen, DONG Energy as well as Preben Jørgensen, formerly with Energinet.dk, who participated in the steering committee at an early stage. Also thanks to Sune Grønskov Nielsen who carried out a very well documented MSc thesis in relation to this PhD. The work provided a very valuable setoff for several investigations carried out in this thesis. I am also grateful to all at Kinectrics Inc., Ontario who made my external stay possi- ble. At the section Electric Power Engineering thanks must also go to all employees, not least those at the workshop who helped with several practical issues. Finally thanks must go to family and friends, not least to my girlfriend Alice and my three boys Magnus, Sebastian and Bertram for their patience during my absence. Kgs. Lyngby, February 2007 ___________________________________ Kenneth Pedersen II III Abstract The present thesis proposes a procedure for implementing and obtaining accurate wide band models of three phase dry type power transformers so the internal as well as the external voltage response can be computed in the time domain as well as the frequency domain with good accuracy. Besides proposing a procedure, an accurate internal wide band model is developed and verified experimentally on a three phase dry type power transformer with a low voltage winding similar to those low voltage windings present in most Danish wind turbines. The high voltage winding is of the foil disc type. The majority of techniques are regarded as general so they can be applied on oil-filled transformers as well. In addition it was demonstrated how field calculations can be carried out in the time domain to examine a typical critical spot in the insulation of the high voltage winding. The resulting internal model is very general in that it can be used to model arbitrary turn connections, which is relevant for typical transformer windings with taps, parallel conductors etc. The internal model actually consists of a lumped elements model up to 20 MHz and a multiconductor transmission line (MTL) model, which takes over at 20 MHz and may produce reasonable results up to 100 MHz though this has not been verified. With the aid of vector fitting efficient reduced order models can be constructed for time domain simulation. The model takes the frequency dependence of the skin- and proximity effects into ac- count as well as the dielectric losses. The core flux and eddy currents in the core are re- garded as insignificant for the voltage distribution. All parameters were estimated with finite element computations. The model was verified with success up to 5 MHz. The resonance frequencies were es- timated very accurately. Overall the amplitudes at resonance were slightly more damped in the model than in the measurements. Overall the experience gained shows, that it is important to get the detailed information in order to produce a reliable model at higher frequencies. The main drawback of a detailed internal model is the long computation times for ob- taining the parameters. However, with the proposed simplifications for a disc winding, the computation time is estimated to be somewhere between 1 and 2 weeks. The current accuracy of the internal model is regarded as sufficient for transient simu- lations. It seems highly likely that a user-friendly piece of software can be constructed, which computes all parameters, all frequency responses and finally provides a reliable and fast reduced order model for use in simulation software such as EMTP. Such a tool would be very valuable in insulation coordination studies. IV CONTENTS PREFACE.....................................................................................................................I ABSTRACT ...............................................................................................................III CONTENTS.................................................................................................................V CHAPTER 1 INTRODUCTION.............................................................................. 1 1.1 BACKGROUND.................................................................................................. 1 1.2 SCOPE OF THE PRESENT THESIS ........................................................................ 1 1.2.1 Overview ................................................................................................. 1 1.2.2 Critical voltage distributions and electrical fields.................................. 2 1.2.3 Linear frequency domain models and influence of the core.................... 3 1.2.4 Time domain response via frequency domain ......................................... 5 1.2.5 Influence of other factors ........................................................................ 5 1.2.6 Other effects ............................................................................................ 5 1.3 CHAPTER SUMMARY........................................................................................ 6 CHAPTER 2 OVERVIEW OF TRANSFORMER MODELS .............................. 7 2.1 MODELLING MUTUAL IMPEDANCE ................................................................... 7 2.1.1 Mutual inductance and corresponding equivalent circuits ..................... 7 2.2 OVERVIEW OF MODELS IN THE LITTERATURE ................................................. 12 2.2.1 Linear and nonlinear models ................................................................ 12 2.2.2 Frequency domain or time domain ....................................................... 13 2.2.3 Lumped or distributed parameters ........................................................ 15 2.2.4 Circuit description ................................................................................ 15 2.2.5 Physical interpretation.......................................................................... 17 2.2.6 Mathematical description...................................................................... 17 2.3 CHAPTER SUMMARY ...................................................................................... 19 CHAPTER 3 THEORY .......................................................................................... 21 3.1 ON THIS CHAPTER .......................................................................................... 21 3.2 NONLINEAR VOLTAGE DISTRIBUTION IN SIMPLE COIL MODEL ........................ 21 3.2.1 Coil models consisting of Π, T and Γ sections...................................... 21 3.3 ON THE USE OF LUMPED AND DISTRIBUTED PARAMETER MODELS.................. 28 3.3.1 Reflection modelling with Π-sections.................................................... 28 3.3.2 On the validity of transmission line models .......................................... 29 3.3.3 The nodal admittance matrix of a lumped circuit.................................. 30 3.3.4 The nodal impedance matrix of an MTL ............................................... 32 3.4 CHAPTER SUMMARY ...................................................................................... 39 CHAPTER 4 MODELLING APPROACH........................................................... 41 4.1 PREFERRED MODEL SPECIFICATIONS .............................................................. 41 4.2 MODELLING APPROACH - OVERVIEW ............................................................. 42 4.2.1 Core influence on internal and external response................................. 42 4.2.2 Fundamentals of the internal model...................................................... 46 4.2.3 Connecting the nodes ............................................................................ 49 4.2.4 From Circuit Description to Model Response....................................... 49 4.2.5 Obtaining the frequency response......................................................... 50 4.2.6 From nodal admittance matrix to frequency response.......................... 51 4.2.7 Accounting for probe capacitance ........................................................ 53 4.2.8 From frequency response to transient response.................................... 57 4.3 PARAMETER ESTIMATION..............................................................................
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