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Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer

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Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2017 Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer Parul Kaushal University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Recommended Citation Kaushal, Parul, "Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer. " Master's Thesis, University of Tennessee, 2017. https://trace.tennessee.edu/utk_gradthes/4752 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Parul Kaushal entitled "Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Electrical Engineering. Syed Kamrul Islam, Major Professor We have read this thesis and recommend its acceptance: Yilu Liu, Benjamin J. Blalock Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Gyrator-Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Parul Kaushal May 2017 Copyright © 2017 by Parul Kaushal All rights reserved. ii DEVOTION This thesis is devoted to my husband, Vishal Sharma, and to my entire family for their sustained support throughout my educational endeavors. iii ACKNOWLEDGEMENTS It gives me immense pleasure to express my sincere and whole hearted gratitude to Dr. Syed Kamrul Islam for his endless guidance, invaluable and untiring help, encouraging attitude and supervision throughout my research work at the University of Tennessee. I am thankful to Dr. Marcus Aaron Young of Mitsubishi for endless discussions to achieve my final goal and for his indefatigable support. My heartfelt thanks go to Dr. Yilu Liu and Dr. Benjamin J Blalock in serving as a member of my thesis committee. I would also like to acknowledge Oak Ridge National Laboratory (ORNL) for providing financial support for my graduate education. iv ABSTRACT Among various approaches used for determining the behavior of power transformers to model the geomagnetically induced current (GIC), the gyrator-capacitor approach is proposed. This approach offers a better understanding of magnetic components compared to other methods, particularly for multi-winding devices and is used to model GIC in a single-phase core type power transformer. In the gyrator-capacitor approach, the gyrator acts as a bridge between the electric and the magnetic circuits making it possible to simulate the two circuits simultaneously. Under GIC conditions, the transformer core suffers a half-cycle saturation, which is the main cause of the disturbances in the power system. In addition, the design of the transformer core is one of the other important factor to analyze the impact of GIC, as the single-phase and the three- phase transformers have different core design. The single-phase transformers are known to be more susceptible to GIC than their three-phase counterparts and even a small range of DC is sufficient to drive the core of a single-phase transformer in the saturation region. The behavior of single-phase transformer is analyzed as half-cycle saturation in the fluxes, following the simulations achieved for voltages, magnetizing current, exciting current and harmonics at different levels of DC by using different magnitude of GIC (increasing order). The harmonics obtained from the proposed approach are validated with the previously published research for single-phase transformers experiencing half-cycle saturation. Since the GIC affects the current waveforms and therefore, the deviation of the current waveform is also calculated in the form of total harmonic distortion (THD).To model a transformer using the gyrator-capacitor approach, P- SPICE software tool is used.The results from the analysis reveal that, the behavior of the transformer model is dependent on the source impedance and the half-cycle saturation is dependent on the DC source setting. v TABLE OF CONTENTS CHAPTER 1 INTRODUCTION AND GENERAL INFORMATION ........................................................... 1 1.1 Overview ............................................................................................................................... 1 1.2 Thesis Outline ....................................................................................................................... 5 CHAPTER 2 SINGLE-PHASE TRANSFORMER CONCEPT AND LITERATURE REVIEW ............... 6 2.1 Single-Phase Transformer Concept ........................................................................................ 6 2.2 Literature Review.................................................................................................................... 8 CHAPTER 3 MODELING APPROACHES AND THE PROPOSED APPROACH .................................. 10 3.1 Modeling Approaches ........................................................................................................... 10 CHAPTER 4 SINGLE-PHASE TRANSFORMER MODELING USING GYRATOR-CAPACITOR APPROACH ................................................................................................................................ 22 4.1 Single-Phase Transformer Gyrator-Capacitor Model ............................................................. 22 CHAPTER 5 SIMULATION RESULTS ......................................................................................................... 29 5.1 Transformer Behavior Without GIC (DC) ......................................................................... 29 5.1.1 Input /Output Voltage Waveform in the Presence of Small Source Impedance ....... 30 5.1.2 Input /Output Current Waveform in the Presence of Small Source Impedance ........ 30 5.1.3 Input /Output Voltage Waveform in the Presence of Large Source Impedance ....... 31 5.1.4 Input /Output Current Waveform in the Presence of Large Source Impedance ........ 32 5.1.5 Flux Waveform ........................................................................................................... 33 5.1.6 Magnetizing Current Waveform ................................................................................. 34 5.2 Transformer Behavior With GIC(DC) ............................................................................... 35 5.2.1 Flux Waveform ........................................................................................................... 35 5.2.2 Exciting Current Waveform ....................................................................................... 38 5.2.3 Exciting Current Harmonics ....................................................................................... 41 5.2.4 Output Waveform ....................................................................................................... 43 vi CHAPTER 6 CONCLUSIONS AND FUTURE WORK ................................................................................ 46 REFERENCES ............................................................................................................................ 47 APPENDIX .................................................................................................................................. 51 VITA............................................................................................................................................. 55 vii LIST OF TABLES Table 3.1: Force and Flow Variables in Electric/Magnetic Domain. ........................................... 12 Table 3.2: Comparison of the Force and the Flow Variables in Electric /Magnetic Domain. ...... 14 Table 3.3: Analogs of Electric and Magnetic Quantities. ............................................................. 21 viii LIST OF FIGURES Figure 1.1.1:Transformer core operating under GIC conditions. ................................................... 4 Figure 1.1.2: Magnetizing current during half-cycle saturation. .................................................... 4 Figure 2.1.1:Schematic of a basic single-phase transformer. ......................................................... 7 Figure 3.1.1: Reluctance-resistance approach for magnetic circuit modeling. ............................. 12 Figure 3.1.2: Permeance-capacitance approach for magnetic circuit modeling. .......................... 14 Figure 3.1.3: Schematic representation of a gyrator. .................................................................... 16 Figure 3.1.4: Gyrator link. ............................................................................................................ 16 Figure 3.1.5: Gyrator-capacitor model for magnetic circuit modelling. ....................................... 18 Figure 3.1.6 : Gyrator-capacitor model with variable permeance. ..............................................
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