For the first fault scenario, the relay at A is observed when a three phase to ground fault (ABC- g) is placed at B (referring to Figure 4.1). The results of this end of line fault are displayed in Figures 6.1 and 6.2. For an ideally transposed transmission line where no mutual coupling is present, one would expect to see all impedance loci settling perfectly at the edge of the line characteristic for both the phase and ground impedance loop plots for this fault.
Figure 6.1: Phase to ground impedance plots for a three phase to ground fault at 100% of the line with ideally-transposed transmission lines and no mutual coupling present between the transmission lines with both transmission lines in service
Figure 6.2: Phase to phase impedance plots for a three phase to ground fault at 100% of the line with ideally-transposed transmission lines and no mutual coupling present between the transmission lines with both lines in service
As expected, the impedance locus in each measurement loop settled at the end of the line characteristic as it should under ideal conditions. The impedance plots in Figures 6.1 and 6.2 will be referred back to for comparison purposes in all future fault studies.
Applying exactly the same three phase to ground fault on the system, but now with mutual coupling present between the transmission lines and with the transmission lines untransposed, the response of the impedance protection relay is shown in Figures 6.3 and 6.4. The deviation from the ideal case can be clearly noted when comparing each impedance locus to the corresponding locus in Figures 6.1 and 6.2.
Figure 6.3: Phase to ground impedance plots for a three phase to ground fault at 100% of the line with untransposed transmission lines and mutual coupling present between the lines with both lines in service
Figure 6.4: Phase to phase impedance plots for a three phase to ground fault at 100% of the line with untransposed transmission lines and mutual coupling present between the lines with both lines in service
Note now that as a result of the combined effects of mutual coupling (which affected only the phase to ground impedance loci for ground faults) and non-transposition of transmission lines (which affected primarily the phase to phase impedance loci for phase faults) both the phase to ground and the phase to phase impedance loci seen by the distance protection relay show noticeable changes. The fault applied on the system in this case is a three phase to ground fault which, ideally, behaves like a three phase fault, since the fault itself is balanced (fault current in all phases normally summing to zero) [11], so one would expect to see no change in the phase to ground impedance loci, but Figure 6.3 shows a contrary image. Chapter 5 showed that in the case of untransposed transmission lines, there exists coupling between the sequence networks for all fault types, which will introduce an associated unbalanced voltage drop in each phase.
This unbalanced voltage drop, combined with the presence of mutual coupling, which in
Chapter 4 was shown to affect the zero sequence volt drop, causes the phase to ground impedance loci to deviate from the ideal impedance plots shown in Figure 6.1.
The most significant impact of the fault scenario presented above on the distance protection relay appears in the phase A to ground impedance loop in Figure 6.3: for this particular fault and complex operating condition, the A-g impedance locus settles at the edge of the zone 2 characteristic which is set to protect 120% of the line, indicating a 20% error in the A-g impedance loop measurement. Fortunately, for this fault scenario, the B-g and C-g impedance loops see the fault in zone 2 since their impedance loci settle within the zone 2 boundary of the reach of this relay so the relay will issue a three pole time delayed trip, provided that no POTT scheme is implemented.
The complex environment of the study was extended further by taking one transmission line out of service and grounding it at both ends and repeating the same fault study. The impedance loci are shown in Figures 6.5 and 6.6 for an ABC-g fault.
Figure 6.5: Phase to ground impedance plots for a three phase to ground fault at 100% of the line with untransposed transmission lines and mutual coupling present between the lines and with one line out of service and grounded at both ends
Figure 6.6: Phase to phase impedance plots for a three phase to ground fault at 100% of the line with untransposed transmission lines and mutual coupling present between the lines and with one line out of service and grounded at both ends
The results in Figure 6.5 show that with one line out of service and grounded at both ends, the phase to ground impedance loci move closer (when compared to Figure 6.3) toward the ideal locus trajectories seen in Figure 6.1. Recall that when one line was taken out of service and grounded at both ends in Chapter 4, the relay at A changed from under-reaching for single phase ground faults, when both lines were in service, to over-reaching when one line was taken out of service and grounded at each end (Figures 4.17 and Figure 4.18 illustrate this behaviour). In this case, for three phase to ground faults, the effect of taking one line out of service in the presence of both mutual coupling and untransposed lines is to cancel out some of the under-reaching effects seen in Figures 6.3 and 6.4. The impedance seen by the distance protection relay is now the combined result of both of these effects (under-reaching due to mutual coupling when one line is taken out of service and grounded at both ends, and over-reaching due to the transmission lines being untransposed).