Areva MiCOM P441, Technical Manual

Page: 146 / 636

P44x/EN HW/E33 Relay Description
Page 18/44 MiCOM P441/P442 & P444
The following describes how to solve the above equation (determination of D fault distance
and R fault resistance). The line model used will be the 3×3 matrix of the line impedance
(resistive and inductive) of the three phases, and mutual values between phases.

Raa + j
ω
Laa Rab + j
ω
Lab Rac + j
ω
Lac


Rab + j
ω
Lab Rbb + j
ω
Lbb Rbc + j
ω
Lbc


Rac + j
ω
Lac Rbc + j
ω
Lbc Rcc + j
ω
Lcc

Where:
Raa=Rbb=Rcc and Rab=Rbc=Rac
3
. 2
0 1
X X
Lcc Lbb Laa
+
= = =
ω ω ω
and
3
1 0
X X
Lac Lbc Lab
−
= = =
ω ω ω
and
X1 : positive sequence reactance
X0 : zero-sequence reactance
The line model is obtained from the positive and zero-sequence impedance. The use of four
different residual compensation factor settings is permitted 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 " are obtained by solving the system of equations (one
equation per step of the calculation) using the Gauss Seidel method.
R fault (n) =
∑
∑ ∑
−
−
n
n
fault
n
n
Fault L
n
n
n fault fault L
I
I I Z D I V
0
0
. 1
0
) 1 ( .
)² (
) . ( . . ) (
Dfault (n) =
∑
∑ ∑
−
−
n
n
L
n
n
Fault L
n
n
n fault L L
I Z
I I Z R I Z V
0
1
0
. 1
0
) 1 ( . 1 .
)² . (
) . ( . . ) (
Rfault and Dfault are computed for every sample (12 samples per cycle).
With IL equal to I
α
+k0.3 x I0 for phase-to-earth loop or IL equal to I
αβ
for phase-to-phase
loop.