Suggestions: References:
1. Stevenson, Jr. W. D., "Elements of Power System Analysis," Third Edition, McGraw-Hill Book Co., 1975
2. Wadhwa C. L., "Electrical Power Systems," Second Edition, John Wiley & Sons, New York, 1991
3. IEEE Std 399-1990 "IEEE Recommended Practice for Industrial and Commercial Power Systems Analysis"
4. Gross C. A., "Power System Analysis," John Wiley & Sons, New York, 1979
5. Bergen A. R., "Power Systems Analysis," Prentice-Hall, Inc., Englewood Cliffs, NJ, 1986
6. Gungor B. R., Power Systems," Harcourt Brace Jovanovich, Publishers, New York, 1988
1) Reference 1 covers three-phase faults on pages 282-289 without use of symmetrical components. Chapter 13 "Unsymmetrical Faults" covers Line-to-Line Fault, Double-Line-to-Ground Fault, and Line-to-Ground Fault. It appears that Prof. and Dr. Stevenson treated symmetrical components what they are worth.
2) Reference 2 covers three-phase-to-phase-to-ground fault under symmetrical components; however, no sign of the ungrounded three-phase-to-phase treatment. This is a fairly meety book on Electrical Power System otherwise, authored by Professor of Electrical Engineering Delhi College of Engineering in Delhi, India, and Dean of Faculty of Technology at University of Delhi, Delhi, India.
3) Reference 3 par 3.2.9 "The Symmetrical Component Analysis," pages 52-56 does not include three-phase faults.
4) Reference 4 only addresses in Section 8-2 "The Balanced Three Phase Fault" that is a general balanced three-phase-to-phase-to-ground fault treated by symmetrical components. Dr. Gross biography includes Professor of Electrical Engineering at Auburn University in Alabama. Dr. Gross received the Outstanding Teacher Award for three consecutive years.
5) Reference 5 includes the symmetrical three-phase-to-phase-to-ground short circuit in Example 13.10 on page 449. Else, it includes Single-Line-to-Ground fault, Double-Line-to-Ground fault, and Line-to-Line Fault treated by symmetrical components. Dr. Bergen is a Professor in Department of Electrical Engineering and Computer Science at University of California, Berkeley, CA.
6) Reference 6 Chapter 10 covers "Conventional Fault Studies" including Three-phase-to-phase (balanced) fault. Paragraph 10.2 states that a three-phase fault is an unbalanced condition. Rather, it is a condition wherein all three lines of a system are shorted (a-b-c) or grounded (a-b-c-g) at a point. However, this is where the fallacy is, namely, the approach to those points is different. The a-b-c approaches to that point over the delta connection where there are phase-to-phase ungrounded voltages, while the a-b-c-g approaches to the point over the y-connection and the voltages are always grounded. Obviously, both approaches may be balanced. One needs a good understanding of the infinitesimal calculus (limits, limiting processes) and some background, how to treat the infinity (oo), since the equations for the power (and current, when voltage is kept constant and different from zero) included Z impedance in the denominator. Once the Z is approaching to zero the power is approaching to 3**0.5 x oo for delta (perhaps motor, could be heater, load bank, etc.) and to the oo for the y-connection. Whenever, the Z is different from zero, e.g. 0.01 or 0.0001 or etc., the power (current) for the delta connection will be 3**0.5 x oo, and the oo for the y-connection.
The symmetrical components. Luckily, one may notice a puzzling remark in Reference 6 on a page 207, which states "Note that the zero-sequence line voltage is always zero, even though zero-sequence phase voltages may exist. For this reason, it is not possible to construct a complete set of symmetrical components of phase voltages even when the unbalanced system of line voltages is know." This may be interpreted as a weakness of the symmetrical component approach, and a potential answer to the missing treatment or the three-phase-to-phase-to-ground faults in Reference 1 through 5 and a dubious treatment of this fault in the Reference 6 about a-b-c and a-b-c-g, which seems to be adhered to in some of the above postings without any proofs or references. Professor and Dr. Gungor is with Department of Electrical Engineering, University of South Alabama, Mobile, AL.
The referenced ANSI/IEEE Standard C37.010-1979 "American National Standard Application Guide for AC High-Voltage Circuit Breakers Rated on a Symmetrical Current Basis" is in agreement with my "motor delta and y-winding concept of proof" by stating that "In general, the three-phase ungrounded fault imposes the most severe duty on a circuit breaker, since the first phase to interrupt has a normal-frequency recovery voltage of approximately 87 % of system phase-to-phase voltage.
