Electric Power Generation, Transmission, and Distribution

31.1.1 Voltage Sag Magnitude—Monitoring

The magnitude of a voltage sag is determined from the rms voltage. The rms voltage for the sag in
Fig. 31.1 is shown in Fig. 31.2. The rms voltage has been calculated over a one-cycle sliding window:

VrmsðÞ¼k

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

N

Xi¼k

i¼kNþ 1

viðÞ^2

v

uu

t (31:1)

withNthe number of samples per cycle, andv(i) the sampled voltage in time domain. The rms voltage
as shown in Fig. 31.2 does not immediately drop to a lower value, but takes one cycle for the transition.

1

0.8

0.6

0.4

0.2

0

0123

Time in cycles

Voltage in pu

456

−0.2

−0.4

−0.6

−0.8

− 1

FIGURE 31.1 A voltage sag—voltage in one phase in time domain.

1

0.8

0.6

0.4

0.2

0

0123

Time in cycles

Voltage in pu

456

FIGURE 31.2 One-cycle rms voltage for the voltage sag shown in Fig. 31.1.