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5.1.1 Assumptions: Short-Circuit Calculations

The source voltage or prefault voltage is the system-rated voltage, though a higher or lower voltage can be used in the calculations. The worst short-circuit conditions occur at maximum loads, because the rotating loads contribute to the short-circuit currents. It is unlikely that the operating voltage will be above the rated voltage at maximum loading. Under light load conditions, the operating voltage may be higher, but the load contributions to the short-circuit currents will also be reduced. The effect of higher voltage at a reduced load is offset by the reduced short-circuit contributions from the loads. Therefore, the short-circuit calculations are normally carried out at the rated voltage. Practically, the driving voltage will not remain constant; it will be reduced, and varies with the machine loading and time elapsed subsequent to short-circuit. The fault current source is assumed sinusoidal; all harmonics and saturation are neglected. All circuits are linear; the nonlinearity associated with rotating machines, transformer, and reactor modeling is neglected. As the elements are linear, the theorem of superim- position is applicable.Loads prior to short-circuit are neglected; short-circuit occurs at zero crossing of the voltage wave. At the instant of fault, the DC current value is equal in magnitude to the AC fault current value, but opposite in sign.



5.1.2 Short-Circuit Currents for Arc Flash Calculations

For calculations of the short-circuit currents, the IEEE 1584 Guide states that only symmetrical short-circuit currents need be considered. The short-circuit currents are asymmetrical by nature (see Chapter 6). There is always an exponentially decaying DC component associated with a three-phase symmetrical fault, which makes the short- circuit current wave asymmetrical about the zero axis. Both the AC and DC components decay. However, for arc ash calculations, we need not consider the DC component.Fault arc resistance varies nonlinearly with the current, and due to its erratic nature, it is not a constant resistance during any one cycle. An expression for arc resistance per centimeter of the arc length is: 50P1/16 I3/4, where P is the pressure in atmospheres and I is the current in kA. The voltage across the arc is more constant. A discussion of the arc ash calculations vis--vis IEEE Guide 1584 is in Chapter 3.


This can be summarized in the following steps:

1. A single-line diagram of the system to be studied is required. It identies imped- ances of all system components as pertinent to the short-circuit calculations. For hand calculation, a separate impedance diagram may be constructed, which follows the pattern of a single-line diagram with impedances and their X/R ratios calculated on a common MVA base. The transformer voltage ratios may be different from the base voltages considered for data reduction. The transformer impedance can be adjusted for transformer voltage adjustment taps and voltage ratios.2. Appropriate impedance multiplying factors are applied from Table 5.1, depend- ing on the type of calculation. For HV circuit breakers, at least two networks are required to be constructed, one for the rst-cycle (close and latch) calcula- tions and the other for the interrupting duty calculations.3. A fault-point impedance positive sequence network (for three-phase faults) is then constructed, depending on the location of the fault in the system. Both resistances and reactances can be shown in this network, or two separate net- works, one for resistance and the other for reactance, can be constructed. Table5.2 shows the resistance values to be used. Typical curves for estimating X/R ratios are provided in ANSI/IEEE standard [2]. All commercially available computer programs have built-in data for the X/R ratios for generators, motors, and transformers; though manufacturers data can be used where available.



TABLE 5.2. Resistance of System Components for Short-Circuit Calculations

System Component Approximate Resistance

Turbine generators and condensers Effective resistanceSalient pole generators and motors Effective resistanceInduction motors 1.2 times the DC armature resistancePower transformers AC load loss resistance (not including no-load losses or auxiliary losses)Reactors AC resistanceLines and cables AC resistance

The effective resistance = X2V/(2fTa3), where X2V is the rated-voltage negative-sequence reactance and Ta3is the rated voltage generator armature time constant in seconds.Source: IEEE Reference [2].

4. For E/Z complex calculation, the fault-point positive sequence network is reduced to single impedance using complex phasors. Alternatively, the resis- tance and reactance values obtained by reducing separate resistance and reac- tance networks to a single-point network to calculate the fault-point X/R ratio can also be used for E/Z calculation. This considerably simplies hand calcula- tions, compared with complex impedance reduction, but is not accurate.5. If there are many sources in the network, NACD is required to be calculated, and this sets a limit to the complexity of networks that can be solved by hand calculations. The currents from NACD sources have to be traced throughout the system to the faulty node to apply proper weighting factors, and this may not be an easy calculation in interconnected networks. The calculation of the rst-cycle duty does not require considerations of remote or local.6. The adjusted short-circuit currents, thus calculated, can be used to compare with the short-circuit ratings of the existing switching equipment or selection of new equipment.

. 33, pp. 10731082, 1997.




The situation with respect to accurate calculations of short-circuit currents for arc ash is demonstrated with respect to a simple system conguration in Figure 6.7. This shows a generator of 40 MVA operating in parallel with a 50-MVA utility transformer. The motor loads in the system are lumped together on equivalent transformers. The

Figure 6.7. A 13.8 kV bus with multiple sources of short-circuit currents.



impedance data and utility source impedance is shown in this gure, based on which the three-phase short-circuit current at 13.8-kV bus is 37.9 kA symmetrical.It is interesting to note that in the industrial distribution environment, much larger transformers and generators have been interconnected, and the application of 13.8-kV circuit breakers is limited to an interrupting rating of 40.2 kA (earlier 15 kV, K = 1.3,37 kA breakers). Following is a real-world example of a large distribution system:

Four utility tie transformers each of 30/50 MVA, 11013.8 kV, six plant generators having a total installed capacity of 270 MVA, total running load 190 MVAthe excess power generated is supplied into the utility system, full stream production can be maintained on forced or maintenance outage of one or more generators and one utility tie transformer, yet,13.8 kV circuit breakers with interrupting rating of 40.2 kA at 13.8 kV have been applied.

6.9.1 Available Computer-Based Calculations

The commercially available software programs use the short-circuit calculations as the base to which the arc ash routines are added. With respect to the calculations of short- circuit currents for arc ash analysis, there are two situations:

1. There is no algorithm in the available computer program to account for the decay from the generators or motors. A user can select either the rst cycle (momentary) or interrupting (1.55 cycle) symmetrical rms currents.2. Some programs facilitate knocking out the motor contribution after a user- selectable time delay, and similarly reduce the generator short-circuit current, after a selectable time delay.

The calculation to follow demonstrates that though situation 2 is better, it is still not accurate.

6.9.2 Accumulation of Energy from Multiple Sources

Consider a fault on the 13.8 kV bus of Figure 6.7. With no decay from the generator or motors, the incident energy accumulation prole is shown in Figure 6.8a. The gen- erator circuit breaker is tripped prior to tripping the utility tie circuit breaker. The motor contributions continue for the entire period, until the fault is ultimately cleared. The gure shows energy release from the individual sources and then sums these to give an overall energy accumulation graphic representation.Now, assume that the motor contributions are dropped in six cycles, and generator contribution is reduced to 300% of its full load current in 0.5 second. This situation is depicted in Figure 6.8b. The total energy accumulated is reduced, as shown in the shaded area, compared with the situation shown in Figure 6.8a.Yet the total energy accumulations shown in Figure 6.8b are not accurate. In the real world situation, it is not the step reduction, but the decay at a certain rate given by the transient parameters