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:

with N the number of samples per cycle, and v(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.

FIGURE 31.2 One-cycle rms voltage for the voltage sag

This is due to the finite length of the window used to calculate the rms value. We also see that the rms value during the sag is not completely constant and that the voltage does not immediately recover after the fault.

There are various ways of obtaining the sag magnitude from the rms voltages. Most power quality monitors take the lowest value obtained during the event. As sags normally have a constant rms value during the deep part of the sag, using the lowest value is an acceptable approximation.

The sag is characterized through the remaining voltage during the event. This is then given as a percentage of the nominal voltage. Thus, a 70% sag in a 230-V system means that the voltage dropped to 161 V.

The confusion with this terminology is clear. One could be tricked into thinking that a 70% sag refers to a drop of 70%, thus a remaining voltage of 30%. The recommendation is therefore to use the phrase ‘‘a sag down to 70%.’’

Characterizing the sag through the actual drop in rms voltage can solve this ambiguity, but this will introduce new ambiguities like the choice of the reference voltage.

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