## SYSTEM IMPEDANCES AND SYMMETRICAL COMPONENTS ANALYSIS BASIC INFORMATION

The symmetrical components theory dictates that for a three-phase system, three sequence systems need, in general, to be set up for the analysis of an unbalanced fault condition. The first is the positive sequence system, which is defined by a balanced set of voltages and currents, equal in magnitude, following the normal phase sequence of a, b, and c.

The second is the negative sequence system, which is similar to the positive sequence system, but is defined by a balanced set of voltages and currents with a reverse phase sequence of a, c, and b. Finally, the zero sequence system is a system defined by a set of voltages and currents that are in phase with each other and not displaced by 120 degrees, as is the case with the other two systems.

The topology of the zero sequence system can be quite different from that of the positive and negative sequence systems due to the fact that it depends heavily on the power transformer connections (Anderson [B1], Blackburn [B3] Stevenson [B10]) and system neutral grounding, factors which are not of importance when determining the topology of the other two sequence networks.

Static system equipment like transformers, lines, cables, busways, and static loads present, under balanced conditions, the same impedances to the flow of positive and negative sequence currents. The same components present, in general, different impedances to the flow of zero sequence currents.

Rotating equipment like synchronous generators, motors, condensers, and induction motors have different impedances in all three sequence networks. The positive sequence impedances are the ones normally used for balanced power flow studies.

All sequence impedances must be either calculated, measured, provided by the equipment manufacturers, or estimated. The zero sequence impedance may not exist for some rotating equipment, depending on the machine grounding.

For a balanced three-phase fault analysis, only the positive sequence system components impedances Z1 (R1 + jX1) are required. For line-to-line faults, negative sequence impedances Z2 (R2 + jX2) are also required. For all shunt faults involving ground, i.e., line-to-ground and double line-to-ground, the zero sequence system impedances Z0 (R0 + jX0) are needed in addition to the other two. System neutral grounding equipment data like grounding resistors, reactors, transformers, etc., form an integral part of the zero sequence system impedance data.

AC decrement considerations dictate that rotating equipment impedances vary from the onset of the short circuit. This applies only to positive sequence impedances, which vary from subtransient through transient to steady-state values.

The negative and zero sequence impedances for the rotating equipment are considered unchanged. The same holds true for the impedances of the static system equipment.