GE C70 Instruction Manual page 469

CHAPTER 9: THEORY OF OPERATION
Differentiating this gives:
dV
-------- - 1
dC
Substituting for V from equation 9.34 gives:
X
This can be substituted into equation 9.33 to obtain:
For our purposes,
C ≅ C ≅ C
A B
Under normal system conditions (non-fault), V
V , which by convention is on the bus voltage base, converted to the base of nominal value of the neutral-point VT used
Spg
in these equations, is:
This gives:
This can be written as:
In these equations, ΔC(pu) is the capacitance change as a per-unit of the leg capacitance, and V
signal resulting from the failure in per-unit of the nominal value of the neutral-point VT. V
voltage in per-unit of the nominal system phase-to-ground voltage, so can be taken as 1 when the system is normal (not
faulted). Note however that under external fault conditions sensitivity can be much different from the non-fault sensitivity.
n and n are the VT ratios of the phase VT bank of the bus source and of the auxiliary VT channel of the neutral
bus_phs ntrl_aux
source, respectively.
Note that under external fault conditions sensitivity can be much different form the non-fault sensitivity. To prevent mis-
operation, use a restraint and/or coordinating time delay.
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
C + C
1
    V
X B C
---- -
+ ---------------- - + V
–
   
X C
C
C
C A A

-------- - V
dC

-------- - V
dC
(
3V V 1 k
d – –
0 B
-------- - V = ------------------------------------------------------------------------ -
X
dC
C ( 1 k +
C
A
d 1
-------- - V = -- 1 k ( + + k
OP AB
dC 3
C
3V V ( 1 k
–
1
0 B
=
------------------------------------------------------------------------ -
--
(
C 1 k
3
A
, so and . This results in:
k ≅ 1 k ≅ 1
C AB AC
V
d 1
C
-------- - V ≅ --
--------------- -
OP
dC 3
C
C
1 1
-- × ---- -
=
3 C
>> V , and V
C 0
n
bus_phs
----------------- -
×
n
ntrl_aux
1 1
d
-- ---- -
-------- - V ≅ × ×
OP
3 C
dC
C C
n
1
bus_phs
dV ≅ -- × ----------------- -
OP
3 n
ntrl_aux
n
1
bus_phs
-- ----------------- -
V ( pu ) ≅ ×
OP
3 n
ntrl_aux
1
 
---- -
= 0
 
C
A
V V
–
d
X C
------------------------------------ -
=
–
X
C + C
 
B C
C
C 1 + ---------------- -
 
A
C
A
V V
–
d
X C
= --------------------------------------- -
–
X
( )
C 1 k + + k
A AB AC
C
) ( )
V 2 k +
–
AB C AB
2
+ k )
AB AC
dV
X
) -------- -
AC
dC
C
) V ( 2 k + )
– –
AB C AB
)
+ + k
AB AC
V
–
0
C
×
V V
–
C 0
C
is the system phase-to-ground voltage. The system voltage
C
V
Spg
n
bus_phs
----------------- -
× V
Spg
n
ntrl_aux
dC
C
× V × -------- -
Spg
C
C
× V × Δ C pu ( )
Spg
Spg
OVERVIEW
Eq. 9-35
Eq. 9-36
Eq. 9-37
Eq. 9-38
Eq. 9-39
Eq. 9-40
Eq. 9-41
(pu) is the operating
OP
is the system phase-to-ground
9-9
9