Electric Power Generation, Transmission, and Distribution

Vsag¼

ZF

ZSþZF

(31:2)

where it is assumed that the pre-event voltage is
exactly 1 pu, thusE¼1. The same expression can
be derived for constant-impedance load, whereEis
the pre-event voltage at the pcc. We see from
Eq. (31.2) that the sag becomes deeper for faults
electrically closer to the customer (whenZFbe-
comes smaller), and for weaker systems (whenZS
becomes larger).
Equation (31.2) can be used to calculate the sag magnitude as a function of the distance to the fault.
Therefore, we writeZF¼zd, withzthe impedance of the feeder per unit length anddthe distance
between the fault and the pcc, leading to:

Vsag¼

zd

ZSþzd

(31:3)

This expression has been used to calculate the sag magnitude as a function of the distance to the
fault for a typical 11 kV overhead line, resulting in Fig. 31.5. For the calculations, a 150-mm^2
overhead line was used and fault levels of 750 MVA, 200 MVA, and 75 MVA. The fault level is used
to calculate the source impedance at the pcc and the feeder impedance is used to calculate the
impedance between the pcc and the fault. It is assumed that the source impedance is purely
reactive, thusZS¼j 0.161Vfor the 750 MVA source. The impedance of the 150 mm^2 overhead
line isz¼0.117þj 0.315V=km.

31.1.4 Propagation of Voltage Sags

It is also possible to calculate the sag magnitude directly from fault levels at the pcc and at the fault
position. LetSFLTbe the fault level at the fault position andSPCCat the point-of-common coupling. The
voltage at the pcc can be written as:

E

ZS

VSag Z

F

pcc

load

fault

FIGURE 31.4 Voltage divider model for a voltage sag.

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 102030

750 MVA

200 MVA

75 MVA

Distance to the fault in km

Sag magnitude in pu

40 50

FIGURE 31.5 Sag magnitude as a function of the distance to the fault.