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case of three-terminal application, the distance measurement equation varies according to which
zone the fault is in, this side or beyond the junction. Terminal A measures the distance using
Equations (5), (6) or (7).
Terminal A
V A
I A
Z A
Figure 2.17.4.2 Three-terminal Model
χ A = (V A − V B + Z A (I B + I C ) + Z B I B ) / Z A I d (5)
χ JB = (V A − V B + Z B I B − Z A I A ) / Z B I d (6)
χ JC = (V A − V C + Z C I C − Z A I A ) / Z C I d (7)
where,
I d = I A + I B + I C
V C = voltage at terminal C
I C
= current at terminal C
χ A = distance from terminal A to fault point as a ratio to line length from terminal A to
junction
χ JB , χ JC = distance from junction to fault point as a ratio to line length from junction to
terminal B or C
Z A ,Z B ,Z C = impedance from each terminal to junction
Firstly, χ A is calculated using Equation (5) assuming that the fault is between terminal A and the
junction. If the result does not match the input line data, then χ JB is calculated using Equation (6)
assuming that the fault is between the junction and terminal B. If the result does not match the
input line data, the calculation is repeated using Equation (7) assuming that the fault is between the
junction and terminal C.
Calculation Method
In the calculation, the sequence quantities of voltages and currents are employed instead of the
phase quantities. Thus, equation (4) is combined with Equation (8) to give:
−
V
V
A
1
B
χ =
Z I
11
where,
V A1 = positive sequence voltage at terminal A
V B1 = positive sequence voltage at terminal B
Junction
Z C
V C , I C
Terminal C
+
+
+
(
Z I
Z I
Z I
1
11
B
1
12
B
2
10
+
+
Z I
Z I
d
d
d
1
12
2
10
0
151
Terminal B
V B
I C
Z B
)
B
0
(8)
6 F 2 S 0 8 5 0
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