GE C70 Instruction Manual page 434

8.1 OVERVIEW
In the above equations, I
the same per-unit base used by the relay. Voltages are in primary volts, capacitances in Farads, and frequency in radians
per second.
The two neutral currents can be derived from the above equations:
The differential current is the vector difference between the two currents. By subtracting I
At the same time the total currents in each phase are driven by the total admittance of the two banks in each phase:
Inserting the equations above into equation 8.58 so as to eliminate the voltages:
Label k , k , and k as follows:
A B C
8
Also, convert from phase coordinates into sequence components as follows, and equation 8.60 becomes:
Substituting this into equation 8.54, we get:
8-14

V jC
A
----------------------------- -
I
=
A1
I
base

V jC
B
----------------------------- -
I
=
B1
I
base

V jC
C
I ----------------------------- -
=
C1
I
base
represents the differential CT primary current rating, inserted here to put the string currents on
base
I I I I
= + + =
N1 A1 B1 C1
I I I I
= + + =
N2 A2 B2 C2
I I I
= –
DIF N1 N2
  
j V C C
–
A A1 A2
--------------------------------------------------------------------------------------------------------------------------------------------- -
=
I I I
= +
A A1 A2
I I I
= +
B B1 B2
I I I
= +
C C1 C2
  
j V C C
–
A A1 A2
--------------------------------------------------------------------------------------------------------------------------------------------- -
I
=
DIF
C C
–
A1 A2

-------------------------- -
I I
= +
A B
C C
+
A1 A2
C C
–
A1 A2

-------------------------- -
k k
=
A B
C C
+
A1 A2
a ˆ
  
I k I I I k
= + + +
DIF A 1 2 0 B
2
a ˆ a ˆ k
 
I k k
= + + +
1 A B C
C70 Capacitor Bank Protection and Control System

V jC
A1 A A2
----------------------------- -
I
; =
A2
I
base

V jC
B1 B B2
----------------------------- -
I
; =
B2
I
base

V jC
C1 C C2
I ----------------------------- -
; =
C2
I
base
jC V jC V jC
+ +
A1 A B1 B C1
-------------------------------------------------------------------------------------
I
base
jC V jC V jC
+ +
A2 A B2 B C2
-------------------------------------------------------------------------------------
I
base
  
V C C V C
+ – + –
B B1 B2 C C1
I
base
 
jV C C
+
A A1 A2
---------------------------------------------
=
I
base
 
jV C C
+
B B1 B2
---------------------------------------------
=
I
base
 
jV C C
+
C C1 C2
--------------------------------------------- -
=
I
base
  
V C C V C
+ – + –
B B1 B2 C C1
I
base
C C C C
– –
B1 B2 C1 C2
 
-------------------------- - -------------------------- -
I
+
C
C C C C
+ +
B1 B2 C1 C2
C C C C
–
–
B1 B2 C1

-------------------------- - -------------------------- -
k
= =
C
C C C C
+ +
B1 B2 C1
2 2
a ˆ I a ˆ I a ˆ
 
I I k I
+ + + +
1 2 0 C 1 2
2
a ˆ k a ˆ
  
I k k I k
+ + + +
2 A B C 0 A
8 THEORY OF OPERATION
V
C
V
C
from I , one obtains:
N2 N1
 
C
C2
 
C
C2
C2
C2

I
+
0

k k
+
B C
GE Multilin
(EQ 8.56)
(EQ 8.57)
(EQ 8.58)
(EQ 8.59)
(EQ 8.60)
(EQ 8.61)
(EQ 8.62)