To quantify sag magnitude in radial systems, the voltage divider model, shown in Fig. 31.4, can be used, where ZS is the source impedance at the point of- common coupling; and ZF is the impedance between the point-of-common coupling and the fault.
The point-of-common coupling (pcc) is the point from which both the fault and the load are fed. In other words, it is the place where the load current branches off from the fault current.
In the voltage divider model, the load current before, as well as during the fault is neglected. The voltage at the pcc is found from:
Vsag = ZF / (ZS + ZF)
where it is assumed that the pre-event voltage is exactly 1 pu, thus E = 1. The same expression can be derived for constant-impedance load, where E is the pre-event voltage at the pcc. We see from the Eq. that the sag becomes deeper for faults electrically closer to the customer (when ZF becomes smaller), and for weaker systems (when ZS becomes larger).
Equation can be used to calculate the sag magnitude as a function of the distance to the fault. Therefore, we write ZF = zd, with z the impedance of the feeder per unit length and d the distance between the fault and the pcc, leading to:
Vsag = zd / (ZS + zd)
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. For the calculations, a 150-mm2 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, thus ZS = j 0.161 V for the 750 MVA source. The impedance of the 150 mm2 overhead
line is z = 0.117 + j 0.315 V/km.
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