Page 307 - Handbook of Electrical Engineering

FAULT CALCULATIONS AND STABILITY STUDIES 293

X-to-R ratio of generators is high, e.g. between 20 (for LV generators) and 100 (for HV generators).
However, the value of armature resistance is of most importance when considering the downstream
circuit-breaker fault clearance capabilities. This aspect is described in sub-sections 7.2.7 and 7.2.11.
The calculation of current magnitudes may be carried out in several ways depending upon the amount
and accuracy of the data available.

11.8.2 Simplest Case

Assume that only X is given, and that this figure is only accurate to about ±15% accuracy. Hence,
d
assume that the X-to-R ratio is infinity; this means that full current doubling will occur (the doubling
factor from Table H.1b is 2.848).

Take the X figure and deduct 15% of its value. Calculate I f using the method of sub-
d
section 11.5.2. This will give a safe estimate of the situation.
11.8.3 The Circuit X-to-R Ratio is Known

The method of sub-section 11.8.2 may be used, but an allowance for fault current decrement needs
to be made (because the X-to-R ratio is known). Table H.1b gives the appropriate ‘doubling factor’
for the situation at one-quarter of a cycle for a known X-to-R ratio.
If, for example, the X-to-R ratio happened to be 25 for the numerical example in sub-
section 11.8.2 then the ‘doubling factor’ would be 2.663 instead of 2.848.

11.8.4 Detailed Generator Data is Available

A more exact result may be obtained by using equation (7.2). However, all the necessary data must
be available, e.g. X , X , X d , R a , T , T , T a . It is also advisable to consider the worst-case situation

d d d d
where the reactances take their low tolerance values.
In this method the rms value of the asymmetrical fault current is calculated from the symmet-
rical rms value and the DC offset value by using the following equation:

(rms value of symmetrical fault current during the
rms value of asymmetrical fault current = 2 2
first half-cycle) + (DC offset current)
Note: This equation is based on the theory used for calculating the rms value of waveforms that
contain harmonic components.

The peak asymmetrical value may be found directly from (7.2) when t = 0.005 sec (for 50 Hz
systems) or 0.00417 sec (for 60 Hz systems).

11.8.5 Motor Contribution to Fault Currents

During a fault condition, the load side of the power system can contribute currents to the fault. The
origin of such contribution is motors, which can be either induction or synchronous machines.