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When referring to this work, full bibliographic details including the author, title, awarding institution and date of the thesis must be given e.g. AUTHOR (year of submission) "Full thesis title", University of Southampton, name of the University School or Department, PhD Thesis, pagination http://eprints.soton.ac.uk UNIVERSITY OF SOUTHAMPTON FACULTY OF PHYSICAL AND APPLIED SCIENCES Electronics and Computer Science Identification of Partial Discharge Sources and Their Location within High Voltage Transformer Windings by M. S. Abd Rahman Thesis for the degree of Doctor of Philosophy June 2014 UNIVERSITY OF SOUTHAMPTON ABSTRACT FACULTY OF PHYSICAL AND APPLIED SCIENCES Electronics and Computer Science Doctor of Philosophy IDENTIFICATION OF PARTIAL DISCHARGE SOURCES AND THEIR LOCATION WITHIN HIGH VOLTAGE TRANSFORMER WINDINGS by M. S. Abd Rahman This thesis is concerned with developing a new approach to high voltage transform- ers condition monitoring, which involve partial discharge (PD) measurement and lo- calisation within high-voltage transformer windings. This is an important source of information for both diagnosis and prognosis of the health of power transformers. Gen- erally, Partial discharges (PDs) existence in transformer windings are normally due to ageing processes, operational over stressing or defects introduced during manufacture. Although, the presence ofPDs does not necessarily indicate imminent failure of a trans- former, it is however, a serious insulation degradation or ageing mechanism which can be considered as a precursor of transformer failure. The initial approach taken in this thesis is based on a lumped parameter network model. The model was created and its param- eters were approximated using analytical solutions based on the geometrical dimensions of transformer windings. Based on the lumped parameter network model, theoretically the rational function should be a positive-real (PR) function and it is shown later on in this thesis that the model does hold the theoretical assumptions. Nevertheless, im- pulse response of actual transformer windings constructed for laboratory assessment was shown differently although different methods were used to find rational functions with positive-real (PR). Due to the fact that real transformer windings do not hold the characteristic of positive real transfer function, thus, this thesis finds an alternative and proposes a different approach forPD localisation which is based on energy distri- bution and features extraction methods for localisation, particularly Wavelet Transform (WT) and Principal Component Analysis (PCA). The idea of the developed approach is based on the fact that any discharge occurring at any point along windings produce an electrical signal that will propagate as a travelling wave towards both ends of the windings. During the propagation of thePD signals along transformer windings, the response with respect to the propagation path taken and termination characteristics will cause attenuation and distortion to the waveforms, ultimately produced changes in the energy characteristics of thePD pulses when they reach measurement sensors. Contents Declaration of Authorship vi Nomenclature viii Abbreviations xi Acknowledgements xiv 1 Introduction1 1.1 Research motivation..............................2 1.2 Research objectives and scope.........................3 1.3 Research contributions.............................5 1.4 Thesis organisation...............................7 1.5 Summary....................................8 2 High voltage transformer condition monitoring9 2.1 Evolution of condition monitoring systems.................. 11 2.2 Condition monitoring benefits......................... 12 2.3 Condition monitoring techniques of power transformers................................... 13 2.3.1 On-line transformers condition monitoring.............. 14 2.4 Partial discharge sources, characteristics and behaviour within transformer windings..................................... 15 2.5 Partial discharge detection and measurement systems........... 18 2.6 Transformer modelling............................. 22 2.7 Transformer winding models for partial discharge phenomena................................... 24 2.8 Localisation of partial discharge within a transformer winding....... 27 2.9 Summary.................................... 31 3 Transformer winding models and simulations 33 3.1 Transformer winding construction....................... 34 3.2 The transformer experimental model..................... 35 3.3 Transformer winding insulation system.................... 36 3.3.1 Oil-impregnated paper......................... 37 3.3.2 Transformer mineral oil........................ 38 3.4 Analytical calculations of transformer winding parameters................................... 38 ii 3.4.1 Inductances............................... 39 3.4.2 Mutual Inductance........................... 40 3.4.3 Resistances............................... 42 3.4.4 Capacitances.............................. 44 3.4.4.1 Series capacitances...................... 45 3.4.4.2 Shunt capacitances...................... 46 3.5 Equivalent models for experimental transformer winding..................................... 47 3.5.1 A transformer winding model based purely on measurement data. 47 3.5.2 A model based on vector fitting and localisation.......... 48 3.5.2.1 An implementation of the approach............ 49 3.5.3 Winding representation based on a analytical calculation of geometrical dimensions........................ 53 3.6 Simulation ofPD within a model....................... 54 3.6.1 Discharge mechanism andPD generator circuit........... 54 3.6.2 A simulation model in Matlab-Simulink .............. 58 3.6.3 Signal propagation inside a simulation model............ 60 3.6.4 Comparison of measured and simulatedPD pulses......... 63 3.7 Positive real function and validity of the transformer winding model... 66 3.8 Summary.................................... 69 4 Partial Discharge Experiments 72 4.1 Partial discharge sources............................ 72 4.1.1 Void discharge............................. 73 4.1.2 Surface discharge............................ 75 4.1.3 Corona discharge in oil......................... 77 4.1.4 Floating discharge........................... 79 4.2 Experiment design and arrangement..................... 81 4.2.1 Artificial PD source.......................... 81 4.2.2 Pulse generator............................. 82 4.3 Partial discharge (PD) measurement and signals extraction.................................... 84 4.3.1PD data and noise level........................ 87 4.3.2 DenoisingPD signals.......................... 87 4.4 Partial discharge propagation from artificialPD sources.......... 89 4.4.1PD propagations along a winding at different applied voltages... 92 4.4.2 Void discharge............................. 92 4.4.3 Surface discharge............................ 94 4.4.4 Corona discharge............................ 95 4.4.5 Floating discharge........................... 96 4.5 Signals propagation from a pulse generator................. 98 4.6 Summary.................................... 99 5 Partial discharge signal analysis 101 5.1 Pulse analysis and comparison of measurement signals........... 101 5.2 Wavelet Transform............................... 107 5.2.1 A multi-resolution analysis of Discrete Wavelet Transform..... 108 iii 5.2.2 Selection of Wavelet family and order................ 110 5.2.2.1 Energy preservation characteristic............. 110 5.2.2.2 Comparing energy of original signal............ 112 5.3 Wavelet coefficients and energy distributions................. 115 5.3.1 Wavelet coefficients........................... 115 5.3.2 Distributions of Wavelet energy.................... 116 5.3.3 Distributions of bushing tap point and neutral to earth energy.. 121 5.4 Principal Component Analysis........................ 125 5.4.1 Principal Component Analysis forPD analysis........... 126 5.5 Design and development of 3-dimensional principal component filters................................ 127 5.5.1 Wavelet filter and PCA weighting.................. 128 5.5.2 Spectral estimation........................... 132 5.6 Summary.................................... 136 6 Localisation of partial discharge 138 6.1 Dimensional reduction and clustering technique............... 138 6.1.1 Clusters for different applied voltages................ 145 6.1.2 The influence of wavelet families and presentation of clusters... 158 6.1.3 Gaussian noise representation in the principal component plot.. 163 6.2 Cluster centroid and separation distance................... 167 6.2.1 Separation distance for allPD sources................ 170 6.2.2 Cluster separation distance for different Wavelet families...... 175 6.2.3 Cluster and separation distance fromPD data bushing core bar.. 177 6.2.4 Cluster plot for all transformer winding terminals.......... 178 6.3PD localisation based on 3-dimensional filters design............ 181 6.3.1 Initial results: Clusters