GE P444

P
44x/EN AP/Hb6
Application Notes
(AP) 5
-12 MiCOM P40 Agile
P442, P444
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
Rab + jω Lab Rbb + jω Lbb Rbc + jω Lbc
Rac + jω Lac Rbc + jω Lbc Rcc + jω Lcc
Where:
Raa=Rbb=Rcc and Rab=Rbc=Rac
ωLaa = ωLbb = ωLcc =
10
2.
3
xx+
and ωLab = ωLbc = ωLac =
01
3
xx
+
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.
Rfault (n) =
∑
∑ ∑
−
−
n
n0
fault
n
n0
n
n0
faultl1faultfaultL
)²(I
).I.I(Z . 1).(nD
).I(V
Dfault (n) =
∑
∑ ∑
−−
n
n0
l1
n
n0
n
n0
faultl1faultl1L
)².I(Z
).I.I(Z .
1).(nR ).I.Z(V
Rfault and Dfault are computed for every sample (24 samples per cycle).
Note: See also in § 2.3.1 the Rn and Dn (Xn) conditions of convergence.
With IL equal to Iα + k0 x 3I0 for phase-to-earth loop or IL equal to Iαβ for phase-to-phase
loop.