Page 297 - Handbook of Electrical Engineering

FAULT CALCULATIONS AND STABILITY STUDIES 283

The oscillating term reaches its first maximum value when wt + θ − φ equals + π/2, or,

1 π
t m1 = − θ + φ seconds
ω 2
There are two important cases to consider. Firstly when the resistance is much smaller than
the inductive reactance and secondly when it is much greater, Tables 11.3 and 11.4 show the peak
maximum and minimum values of the instantaneous current when the maximum value of V is 1.414
per unit,
Z = 1.0 per unit, and the ratio of X to R has different values over a wide range.

11.6.1.1 Resistance smaller than inductive reactance

This case often represents a circuit in which a circuit breaker or a contactor is subject to its most
onerous duty, because ‘current doubling’ occurs.
The angle φ approaches π/2, and θ approach zero. The first maximum value then occurs at,

1 π π π
t m1x = − 0 + = seconds
ω 2 2 ω
Which is half the periodic time of the sinusoidal forcing function v.

Table 11.3. Values of maximum and minimum currents for a 50 Hz power system
X-to-R ratio I 1 (pu) I 2 (pu) I 3 (pu) I 4 (pu) I 5 (pu) I 6 (pu)
500.0000 2.8196 −.0177 2.8020 −.0351 2.7847 −.0523
100.0000 2.7845 −.0864 2.7011 −.1672 2.6227 −.2432
50.0000 2.7418 −.1680 2.5850 −.3151 2.4467 −.4449
30.0000 2.6863 −.2697 2.4459 −.4859 2.2509 −.6612
25.0000 2.6593 −.3176 2.3825 −.5612 2.1672 −.7507
20.0000 2.6196 −.3861 2.2944 −.6631 2.0570 −.8655
16.0000 2.5714 −.4661 2.1952 −.7737 1.9413 −.9816
14.0000 2.5378 −.5197 2.1310 −.8428 1.8716 −1.0493
12.0000 2.4943 −.5868 2.0533 −.9237 1.7926 −1.1235
10.0000 2.4355 −.6729 1.9581 −1.0182 1.7041 −1.2028
8.0000 2.3520 −.7864 1.8406 −1.1275 1.6084 −1.2834
6.0000 2.2246 −.9402 1.6971 −1.2474 1.5133 −1.3556
5.0000 2.1327 −1.0368 1.6172 −1.3064 1.4719 −1.3835
4.0000 2.0105 −1.1475 1.5369 −1.3585 1.4397 −1.4026
3.0000 1.8444 −1.2667 1.4664 −1.3959 1.4206 −1.4120
2.0000 1.6267 −1.3710 1.4232 −1.4123 1.4146 −1.4141
1.0000 1.4341 −1.4134 1.4143 −1.4142 1.4142 −1.4142
.5000 1.4143 −1.4142 1.4142 −1.4142 1.4142 −1.4142
.2000 1.4142 −1.4142 1.4142 −1.4142 1.4142 −1.4142
.1000 1.4142 −1.4142 1.4142 −1.4142 1.4142 −1.4142