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Double circuit line with LR constants 38 2.4.3 Single circuit line with stray capacitance C 41 2.4.4 Double circuit line with C constants 2.5 Typical Transmission Line Constants 2.5.1 Typical line constants 2.5.2 L, C constant values derived from typical travelling-wave velocity and surge impedance 2.6 Generator by Symmetrical Components (Easy Description) 2.6.1 Simplified symmetrical equations 2.6.2 Reactance of generator 2.7 Description of Three-phase Load Circuit by Symmetrical Components 52 3 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS 53 3.1 Fundamental Concept of Symmetrical Coordinate Method 53 3.2 Line-to-ground Fault (Phase a to Ground Fault: 10G) 54 3.2.1 Condition before the fault 55 3.2.2 Condition of phase a to ground fault 56 3.2.3 Voltages and currents at virtual terminal point f in the 0-1 -2 domain 56 3.2.4 Voltages and currents at an arbitrary point under fault conditions 57 3.2.5 Fault under no-load conditions 58 3.3

SUMMARY Whenever a power transformer in a no‐load condition is manually tripped, a residual flux appears in the transformer core, which causes an inrush current when the transformer is later re‐energized. However, the true nature of residual fluxes has not yet been experimentally elucidated. The authors interpreted the residual flux as representing the ending states of transient phenomena after tripping, and tested this interpretation experimentally. In the authors' interpretation, a three‐phase balanced transient phenomenon of the voltage, current, and core flux occurs immediately after the transformer is tripped at the time top0, and it continues until time top1. The true nature of the residual flux is the core fluxes φa(t op 1), φb(t op 1), φc(t op 1) at top1. Furthermore, these residual fluxes as well as the voltages and currents during the transient interval are practically three‐phase balanced, so that they can be expressed as three‐phase balanced equilateral triangular phasors. The core flux values and waveforms cannot be directly measured but they can be digitally generated as the integrals of the voltage waveform. Thus a test of the residual flux under the above interpretation can be performed indirectly by preparing (1) measured voltage waveforms just after transformer tripping, (2) flux waveforms mathematically generated by voltage integration just after tripping, and (3) measured transient inrush current i rush 0.16ema, i rush 0.16emb, i rush 0.16emc, occurring immediately after the transformer is re‐energized at time θcl, and then comparing these three data as characteristics in the 3‐D coordinates of [θ op 0,θ cl ,i rush ] and of [θ op 1,θ cl ,i rush ]. Verification tests were performed utilizing a simulation test circuit in which large numbers of on–off switching tests of a transformer were conducted. The test results clearly indicated that the inrush current reaches its maximum whenever θcl is in antiphase with θop1 (instead of θop0), and reaches its minimum whenever θcl is in phase with θop1. These test results confirmed the authors' interpretation of the true nature of the transient phenomena and the residual flux after tripping. The test results suggest essential algorithms for inrush current restraining control in order to appropriately restrain inrush current phenomena. Field test results at a 66‐kV wind power station where commercial equipment based on the above described theory and method were in service are also presented.

SUMMARYWhenever a power transformer in a no-load condition is manually tripped, a residual flux appears in the transformer core, which causes an inrush current when the transformer is later re-energized. However, the true nature of residual fluxes has not yet been experimentally elucidated. The authors interpreted the residual flux as representing the ending states of transient phenomena after tripping, and tested this interpretation experimentally. In the authors' interpretation, a three-phase balanced transient phenomenon of the voltage, current, and core flux occurs immediately after the transformer is tripped at the time t op0 , and it continues until time t op1 . The true nature of the residual flux is the core fluxes φ a (t op1 ), φ b (t op1 ), φ c (t op1 ) at t op1 . Furthermore, these residual fluxes as well as the voltages and currents during the transient interval are practically three-phase balanced, so that they can be expressed as three-phase balanced equilateral triangular phasors. The core flux values and waveforms cannot be directly measured but they can be digitally generated as the integrals of the voltage waveform. Thus a test of the residual flux under the above interpretation can be performed indirectly by preparing (1) measured voltage waveforms just after transformer tripping, (2) flux waveforms mathematically generated by voltage integration just after tripping, and (3) measured transient inrush current i rush a , i rush b , i rush c , occurring immediately after the transformer is re-energized at time θcl, and then comparing these three data as characteristics in the 3-D coordinates ofVerification tests were performed utilizing a simulation test circuit in which large numbers of on-off switching tests of a transformer were conducted. The test results clearly indicated that the inrush current reaches its maximum whenever θ cl is in antiphase with θ op1 (instead of θ op0 ), and reaches its minimum whenever θ cl is in phase with θ op1 . These test results confirmed the authors' interpretation of the true nature of the transient phenomena and the residual flux after tripping. The test results suggest essential algorithms for inrush current restraining control in order to appropriately restrain inrush current phenomena.Field test results at a 66-kV wind power station where commercial equipment based on the above described theory and method were in service are also presented. C⃝ 2014 Wiley Periodicals, Inc. Electr Eng Jpn, 188(4): 54-67, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com).