Toshiba GRL100-701B Instruction Manual page 154

Distance calculation for earth fault (in the case of A-phase earth fault)
x
=
1
⋅ α ⋅ ⋅
{I (R I I α " + R I
m 1 0 0S
where,
V a = fault voltage
I α = fault current = (2I a − I b − I c )/3
I α " = change of fault current before and after fault occurrence
=
I a , I b , I c = fault current
I La , I Lb , I Lc = load current
I 0s = zero sequence current
I 0m = zero sequence current of parallel line
R 1 = resistance component of line positive sequence impedance
X 1 = reactance component of line positive sequence impedance
R 0 = resistance component of line zero sequence impedance
X 0 = reactance component of line zero sequence impedance
R 0m = resistance component of line mutual zero sequence impedance
X 0m = reactance component of line mutual zero sequence impedance
K a = impedance imbalance compensation factor
I m ( ) = imaginary part in parentheses
R e ( ) = real part in parentheses
L = line length (km)
Equations (1) and (2) are general expressions when lines are treated as having lumped constants
and these expressions are sufficient for lines within 100 km. For lines exceeding 100 km,
influences of the distributed capacitance must be considered. For this fault locator, the following
equation is used irrespective of line length to find the compensated distance x
distance x which was obtained in equation (1) or (2).
1
x = x
2 1
where,
k = propagation constant of the protected line = 0.001km
⋅
I (V I
α
m a
⋅ ⋅ ⋅
I α " + R I I α ") + R (X
0m 0m e
− − −
2I a I b I c 2I La I Lb
−
3 3
3
x
1
2
− ⋅
k (3)
3
 153 
×
") L
⋅ α ⋅ ⋅ ⋅
I I α " + X I I α " + X
1 0 0S
−
I Lc
6 F 2 S 0 8 5 0
⋅ ⋅ ×
I I α ")} K
0m 0m a
with respect to
2
-1
(fixed)
(2)