GE C70 Instruction Manual page 466

OVERVIEW
The derivative is thus:
Substituting equation 9-17 into equation 9-13, we have:
Therefore:
Substituting this value into equation 9-19, we get:
Or alternately,
The value can be expressed as:
In this equation, ΔC
ground voltage, and V
per-unit of nominal bus phase-to-ground voltage, so V
however that under external fault conditions sensitivity can be much different from the non-fault sensitivity.
In practice, k is no less than 2.0 as the tap is no more than half way up the phase string. Comparing equation 9-16 with
A
equation 9-24, it can be seen that V
a operating signal no smaller than the same failure in the upper sub-string. Thus V
sensitivity. A failure resulting in a 0.01 pu capacitance change in the leg capacitance results in an operating signal of at
least 0.01 pu of bus phase-to-ground voltage.
9.1.3.4 Auto-setting
While a capacitor bank can be designed to have a tap at say the mid-point or the one-third point, manufacturing
tolerances result in the actual tap ratio being slightly different from the design target. To prevent a spurious component in
the operating signal, the match factor settings must correspond to the actual rather than the design tap ratio. As a
convenient alternative to manually determining the optimum match factor settings, the relay can automatically calculate
these settings from its own measurements while the capacitor is in-service, as described in the Commands chapter. The
9
C70 sets the operate signal to zero in equation 9.7 or 9.8 and solves for the match factor k
successive voltage measurements. This technique has the further advantage that it to a large degree compensates for
instrumentation error. However, the assumption made here is that when the auto-set command is executed, the capacitor
is in an acceptably balanced state, wherein the operating signal ought to be zero. Following the auto-set command, the
protection measures changes from the state that existed at the time the auto-set command executed.
9-6
d
-------- - V =
OP 2A ( )
dC
A
=
=
C
2A
k = ------- - = ------------------ -
A
C C
A 1A
d
-------- - V
dC
A
dV
OP 2A (
V ( pu ) =
OP 2A ( )
(pu) is the capacitance change as a per-unit of the leg capacitance, V
A
(pu) is the operating signal resulting from the failure in the lower sub-string. Both voltages are in
OP(2A)
(pu) ≥ V
OP(2A) OP(1A)
C C
d –
 
1A A
V × -------- - 1 k ------------------ -
–
 
Spg A
dC C
A 1A
k
A
V ×
------- -
Spg
C
1A
k
A
------- -
V ×
Spg
C
1A
C
1A
or C = k C k C
–
1A A 1A A
C
–
A
k C
A A
C = ------------ -
1A
k 1
–
A
k
A
------- -
= V ×
OP 2A ( ) Spg
C
1A
k 1
–
A
× ------------ -
= V
Spg
C
A
dC
A
= V × ( k 1 ) × -------- -
–
) Spg A
C
A
V ( pu ) × ( k 1 ) × Δ C ( pu
–
Spg A A
can be taken as 1 when the system is normal (not faulted). Note
Spg
(pu), and thus that an element failure in the lower substring produces
C70 CAPACITOR BANK PROTECTION AND CONTROL SYSTEM – INSTRUCTION MANUAL
CHAPTER 9: THEORY OF OPERATION
A
)
is the system phase-to-
Spg
(pu) represents the worse case
OP(1A)
using the average of several
A
Eq. 9-19
Eq. 9-20
Eq. 9-21
Eq. 9-22
Eq. 9-23
Eq. 9-24