GE UR Series C70, Instruction Manual

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GE Multilin C70 Capacitor Bank Protection and Control System 9-7
9 THEORY OF OPERATION 9.1 OVERVIEW
9
Figure 9–3: COMPENSATED BANK NEUTRAL OVERVOLTAGE APPLICATION
b) BALANCED CASE
To understand neutral voltage unbalance protection, we can start with Kirchhoff's current law for the neutral node of the
bank:
(EQ 9.27)
This expression can be rearranged as follows.
(EQ 9.28)
Multiplying both sides by –1 / C
A
and substituting the sum of the phase voltages with 3 V
0
yields:
(EQ 9.29)
As the left hand side of this equation is equal to zero, we can subtract it from the expression inside the absolute value
brackets in equation 8.25 to get:
(EQ 9.30)
The unbalance ratio k -values that reflect the initial or inherent bank unbalance are chosen as:
(EQ 9.31)
Therefore, as seen from the previous two equations, the initial operating signal will be zero.
834745A1.CDR
V
A
-V
X
V
A
A
B
C
V
X
I
C
I
B
I
A
I
A
+ I
B
+ I
C
= 0
C
C
C
B
C
A
I
A
I
B
I
C
+ +
j
ω
C
A
V
A
V
X
–
( )
j
ω
C
B
V
B
V
X
–
( )
j
ω
C
C
V
C
V
X
–
( )
+ +
0
= =
V
X
C
A
C
B
C
C
+ +
( )
– V
A
C
A
V
B
C
B
V
C
C
C
+ + + 0 =
V
X
C
A
C
B
C
C
+ +
( )
–
V
A
C
A
V
B
C
A
V
C
C
A
V
B
C
B
V
B
C
A
–
V
C
C
C
V
C
C
A
– + + + + +
0
=
⇒
V
X
C
A
C
B
C
C
+ +
( )
– C
A
V
A
V
B
V
C
+ +
( )
V
B
C
B
C
A
–
( )
V
C
C
C
C
A
–
( )
+ + + 0 =
⇒
V
X
1
C
B
C
C
+
C
A
--------------------- +
⎝ ⎠
⎛ ⎞
3 V
0
– V
B
1
C
B
C
A
------- –
⎝ ⎠
⎛ ⎞
V
C
1
C
C
C
A
------- –
⎝ ⎠
⎛ ⎞
+ + 0 =
V
OP
1
3
--- V
X
1 k
AB
k
AC
+ +
( )
3 V
0
–
V
B
1 k
AB
–
( )
V
C
1 k
AC
–
( )
V
–
X
1
C
B
C
C
+
C
A
--------------------- +
⎝ ⎠
⎛ ⎞
3 V
0
V
B
–
1
C
B
C
A
------- –
⎝ ⎠
⎛ ⎞
V
C
–
1
C
C
C
A
------- –
⎝ ⎠
⎛ ⎞
+ + + =
1
3
---
V
X
k
AB
C
B
C
A
------- – k
AC
C
C
C
A
------- – +
⎝ ⎠
⎛ ⎞
V
B
C
B
C
A
------- k
AB
–
⎝ ⎠
⎛ ⎞
V
C
C
C
C
A
------- k
AC
–
⎝ ⎠
⎛ ⎞
+ + =
k
AB
C
B
C
A
------- , k
AC
C
C
C
A
------- = =