GE L90 Instruction Manual page 340

8.1 OVERVIEW
Again, it is possible to use a four quadrant arctangent, in which case the minus signs are needed on the imaginary and the
real part as shown. The subscript 1 refers to the current at the local peer and the subscript 2 refers to the current at the
remote peer.
In the case of a three terminal system, the phase deviation at each terminal is computed as:
φ n ( )
1
Numbering of the terminals is not critical. Subscript 1 refers to the local peer. Subscripts 2 and 3 refer to the other 2 peers.
Swapping 2 and 3, flips the sign of both the numerator and the denominator.
Regarding timing of the computations, the latest available phase and frequency deviation information is furnished to the
loop filter once per cycle in the case of a 64 Kbaud communications channel, and once every 3 cycles in the case of a 9600
baud communications channel.
Capture T2 T1
8
( T1
i-3,
Calculate 1, 1.
Figure 8–2: ROUND TRIP DELAY AND CLOCK OFFSET COMPUTATION FROM TIME STAMPS
8-8

1
1
–
φ n ( ) -- - tan ⋅

=
1
2

( ( n ( ) I n ( )
Re I
–
, ,
pos 3 pos 2
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -
=
n ( ) ∗
( n ( ) I ⋅
Im I
+
, ,
pos 2 pos 1
Relay 1
Send T1
i-3
Store T1
i-3
8.3 ms
Capture T1
i-2
T1
i-2
Send T1
i-2
8.3 ms
Store T2
i-2
T1
Send T1 i-1
i-1
8.3 ms
T1
i
i-1, i
T2 T2 T1 )
i-2, i -1, i
δ θ
Slow down
t 1
L90 Line Differential Relay
n ( ) ∗
( n ( ) I ⋅ ) 
Im I
–
, ,
pos 2 pos 1
---------------------------------------------------------------------

n ( ) ∗

( n ( ) I ⋅ )
Re I
–
, ,
pos 2 pos 1
n ( ) ∗ n ( ) ∗
) ⋅ (
I I
+ +
, ,
pos 1 pos 2
n ( ) ∗
n ( ) I ⋅ n ( ) I
I I
+
, , ,
pos 3 pos 2 pos 1
COMMUNICATION PATH
T2
i-2
T2
i-1
T2
i
t 2
8 THEORY OF OPERATION
n ( ) ∗
) )
I
,
pos 3
n ( ) ∗
⋅ )
,
pos 3
Relay 2
Clocks mismatch
Send T2
i-3
Store T2
i-3
Capture T2
i-2
8.3 ms
Send T2
i-2
Store T1
i-2
8.3 ms
Send T2
i-1
Capture T1 T2
i-1, i
( T2 T1 T1 T2 )
i-3, i -2, i-1, i
δ θ
Calculate 2, 2.
Speed up
831729A2.CDR
(EQ 8.18)
(EQ 8.19)
GE Multilin