Corrective device protection
A control system for an electrical power system includes an electrical corrective device, a voltage measuring device coupled to each phase of the electric power system, a current measuring device connected between each phase of the electric power system and the electrical corrective device, and a protective device connected to outputs of the voltage measuring device and the current measuring device. The protective device includes a controller configured to detect an imbalance using the measured voltages and currents output from the voltage measuring device and the current measuring device without using or independently of other recent voltage or current measurements for other points in the electrical corrective device and independently of a neutral-ground measurement at the electrical corrective device.
1. A method of detecting imbalances in an electrical corrective device, connected to an electric power system, the method comprising:
measuring a voltage V A , V B , and V C of each phase A, B, C of an electric power system;
measuring a current I A , I B , and I C between each phase A, B, C of the electric power system and an electrical corrective device connected to the electric power system;
calculating positive-sequence, negative-sequence, and zero-sequence device currents I 1 , I 2 , and I 0 , respectively, and positive-sequence, negative-sequence, and zero-sequence voltages V 1 , V 2 , and V 0 , respectively, on the basis of the currents I A , I B , and I C and the voltages V A , V B , and V C ;
determining a predetermined negative-sequence current I 2un of an undamaged electrical corrective device;
calculating a negative-sequence current difference by comparing the calculated negative-sequence current I 2 with the predetermined negative-sequence current I 2un ;
comparing the negative-sequence current difference to a predetermined threshold;
if the negative-sequence current difference exceeds the predetermined threshold, determining that an imbalance exists in the electrical corrective device; and
de-energizing the electrical corrective device when an imbalance exists in the electrical corrective device.
2. The method of claim 1 , wherein the predetermined negative-sequence current I 2un is calculated based on the positive-sequence and negative-sequence voltages V 1 , and V 2 , respectively, at the electrical corrective device and the positive-sequence current I 1 at the electrical corrective device for an ungrounded electrical corrective device.
3. The method of claim 1 , wherein:
I
2
un
=
[
(
G
21
C
+
j
B
21
C
)
V
1
+
(
G
11
C
+
j
B
11
C
)
V
2
]
×
I
1
V
1
G
11
C
2
+
B
11
C
2
,
for an ungrounded electrical corrective device, wherein:
G
11
C
=
V
1
C
I
1
rC
+
V
2
rC
I
2
rC
+
V
2
i
C
I
2
i
C
V
1
C
2
+
(
V
2
r
C
2
+
V
2
i
C
2
)
,
B
11
C
=
V
1
C
I
1
iC
+
V
2
iC
I
2
rC
+
V
2
r
C
I
2
i
C
V
1
C
2
-
(
V
2
r
C
2
+
V
2
i
C
2
)
,
G
21
C
=
I
2
rC
-
G
11
C
V
2
rC
+
B
11
C
V
2
iC
V
1
C
,
B
21
C
=
I
2
iC
-
G
11
C
V
2
iC
-
B
11
C
V
2
r
C
V
1
C
,
and
V
1
C
=
V
1
C
,
V
2
C
=
V
2
rC
+
j
V
2
i
C
,
I
1
C
=
I
1
rC
+
jI
1
iC
,
I
2
C
=
I
2
rC
+
j
I
2
i
C
,
where V 1C , I 1C , V 2C , and I 2C are, respectively, a positive-sequence voltage, a positive-sequence current, a negative-sequence voltage, and a negative-sequence current that were measured when the electrical corrective device was commissioned; I 1rC , I 1iC are, respectively, real and imaginary components of I 1C ; V 2rC , V 2iC are, respectively, real and imaginary components of V 2C ; and I 2rC , I 2iC are, respectively, real and imaginary components of I 2C .
4. The method of claim 1 , wherein the predetermined negative-sequence current I 2un is calculated based on the positive, negative, and zero-sequence voltages V 1 , V 2 , V 0 , respectively, at the electrical corrective device, and the positive-sequence current I 1 at the electrical corrective device for a grounded electrical corrective device.
5. The method of claim 1 , wherein:
I
2
un
=
I
2
un
=
[
Y
10
C
V
1
+
Y
11
C
V
2
+
Y
12
C
V
0
]
×
I
1
V
1
Y
11
C
;
Y
11
C
=
g
11
I
1
C
+
g
12
I
2
C
+
g
13
I
0
C
,
Y
12
C
=
g
12
I
1
C
+
g
13
I
2
C
+
g
11
I
0
C
,
Y
10
C
=
g
13
I
1
C
+
g
11
I
2
C
+
g
12
I
0
C
;
and
g
11
=
(
V
1
C
)
2
-
V
2
C
V
0
C
(
V
1
C
)
3
+
(
V
2
C
)
3
+
(
V
0
C
)
3
-
3
V
1
C
V
2
C
V
0
C
,
g
12
=
(
V
2
C
)
2
-
V
1
C
V
0
C
(
V
1
C
)
3
+
(
V
2
C
)
3
+
(
V
0
C
)
3
-
3
V
1
C
V
2
C
V
0
C
,
g
13
=
(
V
0
C
)
2
-
V
1
C
V
2
C
(
V
1
C
)
3
+
(
V
2
C
)
3
+
(
V
0
C
)
3
-
3
V
1
C
V
2
C
V
0
C
;
for a grounded electrical corrective device.
6. The method of claim 1 , wherein the negative-sequence current difference is I 2 −I 2un .
7. The method of claim 6 , wherein I 2 −I 2un is proportional to an internal asymmetry of the electrical corrective device caused by a failure of a discrete component included in the electrical corrective device.
8. The method of claim 1 , wherein the imbalance in the electrical corrective device exists due to a failure of a discrete corrective component included in the electrical corrective device.
9. The method of claim 1 , wherein the electrical corrective device includes a capacitor bank.
10. The method of claim 1 , wherein the electrical corrective device includes a reactor bank.
11. The method of claim 1 , wherein the electrical corrective device is shunt connected.
12. The method of claim 1 , further comprising:
if the predetermined threshold is exceeded, determining in which phase A, B, C the imbalance occurred.
13. The method of claim 12 , wherein determining in which phase A, B, C the imbalance occurred comprises accessing data that defines a correlation between a phase angle of the imbalance and the positive-sequence voltage.
14. A method of detecting imbalances in an electrical corrective device connected to an electric power system, the method comprising:
measuring a current I A , I B , and I C between each phase of an electric power system and an electrical corrective device connected to the electric power system;
calculating a negative-sequence current I 2 on the basis of the currents I A , I B , and I C ;
determining a predetermined negative-sequence current I 2un of an undamaged electrical corrective device;
calculating a negative-sequence current difference by comparing the calculated negative-sequence current I 2 with the predetermined negative-sequence current I 2un ;
comparing the negative-sequence current difference to a predetermined threshold;
if the negative-sequence current difference exceeds the predetermined threshold, determining that an imbalance exists in the electrical corrective device; and
de-energizing the electrical corrective device when an imbalance exists in the electrical corrective device.
15. The method of claim 14 , wherein the electrical corrective device includes a capacitor bank.
16. The method of claim 14 , wherein the electrical corrective device includes a reactor bank.
17. The method of claim 14 , wherein the electrical corrective device is shunt connected.
18. The method of claim 14 , wherein the negative-sequence current difference is I 2 −I 2un .
19. The method of claim 18 , wherein I 2 −I 2un is proportional to an internal asymmetry of the electrical corrective device caused by a failure of a discrete component included in the electrical corrective device.
20. The method of claim 14 , wherein the imbalance in the electrical corrective device exists due to a failure of a discrete component included in the electrical corrective device.