SOFTWARE GUIDED SAFE LOADING OF TRANSFORM ERS AND ITS ECONOMICS K B M I Perera Thesis Supervisor Prof. J R Lucas A Thesis Presented to The Department of Electrical Engineering In Partial Fulfillment Of the requirement for the Degree Master of Engineering The Department of Electrical Engineering University of Moratuwa Sri Lanka September 2000 72438 CONTENTS 1. INTRODUCTIO 1.1 Software Package 1.2 Effects of Loading beyond Name Plate Rating 2. DEVELOPMENT OF THE ALGORITH FOR LINEAR -THERAML LOADING 2.1 Loading Guide 2.2 Modified Calculations 2.3 Development of the Computer Program 2.-l Variation of Hot Spot Temperature with Load Factor 2.5 Program Justification 3. CASE STUDIES- LINEAR THER1AL LOADING 3.1 Effects on Performance 4. COMPARISON OF TR..\ ~SFORMERS BASED ON EVALUATIO 4. 1 Selection of Distribution Transformer Rating 4.2 Cost of Transformer Losses 4.3 Calculation Criteria for Economic Evaluation 5. CASE STUDIES - ECONOM l C EV ALUATLON 6. TRANSFORMER CAPABILITY WITH NO:"'-SINUSOIDAL LOAD CURRENT 6.1 Transformer Losses 6.2 Harmonic Effect on Tran s former Losses 6.3 Method of Harmonic effect Calculation 6.4 Harmonic Loss Factors 6.5 Calculation of Temperature Changes 6.6 Calculation of a Transformer Derating Factor 6.7 Design Considerations for New Transformer Specification 7. CASE STUDIES- HARMONIC 8. CONCLUSIONS REFERENCES APPENDIX A- Tables in IEC 354 APPENDIX B- Definitions for Economic Evaluation APPENDIX C- Computer Program for Optimization APPENDIX D - Computer Program for Economic Evaluation ACKNOWLEDGEMENTS I wish to express my appreciation and sincere thanks to the people \\ ithout \\hose assistance this dissertation would not have been possible: Professor J R Lucas. who guided me to the topic of Loading of Transformers and its Economics and encouraged me through the \Hiting process. His guidance and insight \\as immeasurable; Mr. U 0 Jayawardana, who gave me the opportunity of engaging in a masters program \\ithout no hesitation; to my :children Umal and - Sahal for their understanding; and most of all to my wife Mrs. Samanthja Perera. for her love. patience, support and understanding. ... II CONTENTS 1. INTRODUCTIO:'l 1.1 Software Package 1.2 Effects of Loading beyond Name Plate Rating 2. DEVELOPMENT OF THE ALGORITH:\'1 FOR LINEAR -:yn:RviAL LOADING 2.1 Loading Guide 2.2 Modified Calculations 2.3 Development of the Computer Program 2.-l Variation of Hot Spot Temperature \.vith Load Factor 2.5 Program Justification ... 3. CASE ST"L'DIES- LI~EAR THER:\1AL LOADING 3.1 Effects on Performance 4. CO:viPARISO:'l OF TR..\ ~SFORMERS BASED ON ECO~O:\'liC EVALUATIO:'l 4. 1 Selection of Distribution Transformer Rating 4.2 Cost of Transformer Losses 4.3 Calculation Criteria for Economic Evaluation 5. CASE STUDIES - ECONOM lC EV ALUATLON 6. TRANSFORMER CAPABILITY WITH NO:"'-SINUSOIDAL LOAD CURREI'iT 6.1 Transformer Losses 6.2 Harmonic Effect on Transformer Losses Ill PAGE 1 2 3 5 5 10 12 17 18 21 27 29 29 31 31 35 40 41 41 6.3 Method of Harmonic effect Calculation 6.4 Harmonic Loss Factors 6.5 Calculation of Temperature Changes 6.6 Calculation of a Transformer Derating Factor 6.7 Design Considerations for New Transformer Spccitication 7. CASE STUDIES- HARMONIC LOADL~G 8. CONCLUSIONS REFERENCES APPENDIX A- Tables in IEC 354 APPENDIX B- Definitions for Economic Evaluation APPENDIX C- Computer Program for Optimization APPENDIX D - Computer Program for Economic Evaluation ... IV .. p 44 45 47 47 48 55 .I 57 58 60 61 86 LIST OF SYMBOLS 0,, =Ambient temperature 0, = Hottest-spot conductor rise over top-oil temperature (°C) e,.R =Hottest-spot conductor rise over top-oil temperature under rated conditions (°C) 8~ 1 = Hottest-spot HY conductor rise over top-oil temperature (0 C) e,,.R = Hottest-spot HV conductor rise over top-oil temperature under rated conditions (°C) Oh =Ultimate (stead: state) hot spot templ!rature Oro = Top-oil rise O\er ambient temperature (°C) Oro.R =Top-oil rise over ambient temperature under rated conditions (0 C) 02 = Power factor angle u00, =Initial top oil temperature rise f uOon =Top oi l temp. rise at end ofn'11 intenal \Oopot and top oil = Temperature difference bet\\CCll hot spot and top iJi I at rated current =Temperature difference bet,,een hot :;pot and top oil at rated current = per unit loading =peak of load cune I kVA rating · = Harmonic loss factor for\\ inding eddy currents = Harmonic loss factor for other stra) losses = Harmonic loss factor for winding I ' R loss = I Iarmonic order = RMS load current 11 = RMS fundamental load current (amperes) 111 = RMS current at harmonic "h" (amperes) IR = RMS fundamental current under rated frequency and rated load conditions (amperes) t1.R = lligh voltage (HY) rms fundamental line current under rated frequency and rated load conditions (amperes) 12-R = Lo'" voltage (I-IV) rms fundamental line current under rated frequency and rated load conditions (amperes) K ~ Load factor during t = Load Transformer capacity L =Loss of Life in per unit days LLR =Transformer rated load loss v P = I~R loss portion of the load loss (\\atts) Pf.c =Winding eddy-current loss (watts) PEe-R =Wind ing eddy-current loss under rated conditions (watts) PF.C:.o =Winding eddy-current loss at the measured current and the power frequency (watts) P~o; =nominal load losses Pu. =Load loss (watts) PLL·R - Load loss under rated condition (watts) P~'>t. =No load loss (watts) Po = idle losses PosL =Other stray loss (watts) PosL-R =Other stray loss under rated conditions (watts) PrsL-R =Total stray loss under rated conditions (watts) Pv =Losses at actual loading R = Loss ratio = Load Joss at rated current No load Joss R =DC resistance (ohms) R1 =DC resistance measured between two HY terminals (ohms) R2 =DC resistance measured between two LV terminals (ohms) R(a) =% voltage regulation =time interval of application of specific load t1, t2 =period under consideration; lr t 1 T T =total time interval of application Tp = Peak duration t 0 =Oil time constant Y = Relative ageing rate Vr = % resistance voltage at full load Y, =%leakage reactance voltage at full load x =Oil exponent y = Winding exponent . ~ VI ... .I