Handbook of Electrical Engineering

FAULT CALCULATIONS AND STABILITY STUDIES 283

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

tm 1 =

1

ω

(π

2

−θ+φ

)

seconds

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 angleφapproachesπ/2, andθapproach zero. The first maximum value then occurs at,

tm1x=

1

ω

(π

2

− 0 +

π

2

)

=

π

ω

seconds

Which is half the periodic time of the sinusoidal forcing functionv.

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