Schweitzer Engineering Laboratories SEL-311L, Instruction Manual, Page: 724 / 734

J-2 Example Calculations for 87L Settings Date Code 20010625
SEL-311L Instruction Manual
Calculating I
AR
/I
AL
for Phase Faults
We can use positive-sequence currents from each line terminal to evaluate three-phase faults (see
Equation J.1 and Equation J.2). Equation J.3 shows the ratio of remote to local positive-
sequence currents. Note that I
1R
/ I
1L
= I
AR
/ I
AL
for balanced faults.
L 1 S 1
S
S 1
mZ Z
E
I
+
° δ ∠
=
Equation J.1
( )
L 1 R 1
R
R 1
Z • m 1 Z
0 E
I
− +
° ∠
=
Equation J.2
[ ]
( )
[ ]
L 1 R 1
L 1 S 1
S
R
AL
AR
S 1
R 1
Z • m 1 Z
Z • m Z
•
E
0 E
I
I
I
I
− +
+
° δ ∠
° ∠
= =
Equation J.3
From Equation J.3, we conclude the following:
1. If the system is homogeneous (i.e.,
∠
Z
1S
=
∠
Z
1L
=
∠
Z
1R
), then
∠
(I
1R
/ I
1S
) is zero when
δ
= 0°. In our default settings, we assumed
δ
= 10°. Given the following system:
•
System Voltage: 230 kV
LL
•
Line Length: 10 miles
•
Line Impedance: 0.8
Ω
/mi (8.0
Ω
primary total)
•
Source S and R Impedance: ½ Z
LINE
•
Current Transformer Ratio: 1200/5 (240:1)
Increasing
δ
greater than 10° causes the secondary line current to exceed 6 A. In actual
practice, we expect the source impedances to be much lower. From this we conclude
that 10° is a reasonable maximum value for
δ
.
2. If the system is non-homogeneous, this too can create an angle difference between I
1R
and I
1S
. The extent of the angle difference depends in part on the fault location. For
example, if Source R and the Line have the same angle and
∠
Z
1S
is 10° less than
∠
Z
1R
, a
fault at m = 0 creates a 10° difference between the remote and local currents. Moving
the fault location to m = 1 creates a 3.3° difference between the phase currents. As a
worst case study, the non-homogeneous angle difference can add with the angle
difference caused by
δ
= 10°. If the
∠
Z
1S
is 10° greater than
∠
Z
1R
for the fault at m = 0,
the non-homogenous system angle and system load angle errors cancel: I
AR
and I
AL
are
then in-phase.