PER UNIT CALCULATION - FAULT CALCULATION TOOL

Power system calculations can be done using actual voltages and currents or using per-unit representations of actual quantities. While performing a calculation in actual quantities makes sense occasionally, the vast majority of calculations are done in per-unit.

The discussion in this assumes a familiarity with the per-unit method; but, to avoid confusion, definitions of important parameters are given in Table 1. Equivalent three-phase values are usually used in practice, but an understanding of the mathematics presented in Table 1 relies on a careful interpretation of base values as single-phase quantities.

Table 1 - Per unit base parameters


Example A: Calculate the maximum three-phase current measured by an instantaneous relay, fuse, or series trip device on the 13.8 kV feeder serving the 2 Mvar power factor capacitor on Bus 4.

Figure 2 depicts a portion of the system one-line diagram and shows a fault in the 13.8 kV, 2 Mvar capacitor feeder on Bus 4. The calculated current magnitudes are

Distribution of instantaneous currents for fault on capacitor feeder in sample system

— 19 203 A, rms asymmetrical
— 12 410 A, rms symmetrical

A moderate asymmetrical offset (X/R = 15.65) is present due primarily to the close proximity of the generator, which contributes 4080 A of symmetrical current. The largest contributor, of course, is the utility, with other sources making up the difference.

The capacitor itself does not contribute current to the fault. Present practice ignores any capacitor contribution to system short-circuit currents on the basis that it occurs so quickly and is out of phase with system currents.

In this instance, also, a protective device in the capacitor feeder would detect currents flowing from the system to a fault on the feeder, or current flowing from the capacitor to the system, but not both, again illustrating that the analyst should carefully consider what constitutes the branch current measured by the protective device of interest.

Figure 3 shows this same fault condition, but with the impedances adjusted to calculate the long-time fault magnitude. The current has decayed to less than 9185 A symmetrical and the generator contribution is down to 2721 A. Also, the contributions from motors on the system have dropped to zero.

Figure 3 Calculated distribution of long-time relay current to fault on capacitor feeder in sample system

NOTE—The current is purely symmetrical and the contributions from sources other than the generator and utility have decayed away.

HIGH RESISTANCE GENERATOR GROUNDING PROTECTION METHOD

Method I: High-resistance grounded (distribution-transformer grounded)
Grounding method I utilizes a distribution transformer with a primary-voltage rating equal to, or greater than, the line to- neutral voltage rating of the generator, with a secondary rating of 120 V or 240 V. The distribution transformer should have sufficient overvoltage capability so that it does not saturate on phase-to ground faults with the machine operated at 105% rated voltage.

Secondary resistors are usually selected so that for a single-phase-to-ground fault at the terminals of the generator, the power dissipated in the resistor is equal to, or greater than, the zero-sequence reactive volt amperes in the zero-sequence capacitive reactance of the generator windings, its leads, and the windings of the transformers that are connected to the generator terminals.

This arrangement is considered to be high-resistance grounding, and it limits the maximum single-phase-to ground fault current to a value in the range of approximately 3 to 25 primary amperes. This is not of sufficient magnitude to operate standard generator differential relays.

In general, the W-Z current transformer will have a ratio of unity and the R-S current-transformer ratio is usually selected so that its secondary current will be approximately equal to the primary current in the generator neutral.

A generator system grounded through a distribution transformer with a secondary resistor has certain characteristics that may have the following desirable features:

a) Mechanical stresses and fault damage are limited during phase-to-ground faults by restricting fault current.

b) Transient overvoltages are limited to safe levels.

c) The grounding device is more economical than direct insertion of a neutral resistor.

A disadvantage of this grounding scheme is that surge protective equipment must be selected on the basis of higher temporary overvoltages during ground faults.

Method II: High-resistance grounded (neutral-resistor grounded)
Grounding method II is functionally equivalent to that of method I. In method II, the resistor is sized directly to limit the single-phase-to-ground fault current to the same magnitude as in method I without the use of a distribution transformer.

However, the voltage-transformer voltage ratings are selected on the same basis as those for the distribution transformer in method I. The W-Z current-transformer ratio is generally selected to be unity.