GE MiCOM P40 Agile Technical Manual page 164

P44x/EN AP/Hb6
(AP) 5-12
The following describes how to solve the above equation (determination of D fault distance
and R fault resistance). The line model used is the 3×3 matrix of the symmetrical line
impedances (resistive and inductive) of the three phases, and mutual values between
phases.
Raa + jω Laa
Rab + jω Lab
Rac + jω Lac
Where:
Raa=Rbb=Rcc and Rab=Rbc=Rac
ωLaa = ωLbb = ωLcc =
and
X1: positive sequence reactance
X0: zero-sequence reactance
The line model is obtained from the positive and zero-sequence impedance. Four different
residual compensation factor settings can be used on the relay, as follows:
kZ1: residual compensation factor used to calculate faults in zones 1 and 1X.
kZ2: residual compensation factor used to calculate faults in zone 2.
kZp: residual compensation factor used to calculate faults in zone p.
kZ3/4: residual compensation factor used to calculate faults in zones 3 and 4.
The solutions "Dfault" and "Rfault" solutions are obtained by solving the system of equations
(one equation per step of the calculation) using the Gauss Seidel method.
n
∑
n0
Rfault (n) =
n
∑
n0
Dfault (n) =
Rfault and Dfault are computed for every sample (24 samples per cycle).
Note:
With IL equal to Iα + k0 x 3I0 for phase-to-earth loop or IL equal to Iαβ for phase-to-phase
loop.
Rab + jω Lab
Rbb + jω Lbb
Rbc + jω Lbc
+
2. x x
1 0
3
− −
(V .I ) D .(n 1)
L fault fault
n
∑
(I )²
fault
n0
− −
(V .Z ) .I R .(n 1)
L 1 l fault
n
∑
(Z .I )²
1 l
n0
See also in § 2.3.1 the Rn and Dn (Xn) conditions of convergence.
Rac + jω Lac
Rbc + jω Lbc
Rcc + jω Lcc
and ωLab = ωLbc = ωLac =
n
∑
. (Z .I .I )
1 l fault
n0
n
∑
. (Z .I .I )
1 l fault
n0
Application Notes
MiCOM P40 Agile P442, P444
+
x x
0 1
3