8 THEORY OF OPERATION
The rotational rate of phasors is equal to the difference between the power system frequency and the ratio of the sampling
frequency divided by the number of samples per cycle. The correction is computed once per power system cycle at each
relay. For conciseness, we use a phasor notation:
I n ( )
(
)
=
Re Phasor
+
j Im Phasor
n
n ( )
I n ( )
I
for phase a from the k th terminal at time step n
=
a k ,
n ( )
I n ( )
I
for phase b from the k th terminal at time step n
=
b k ,
n ( )
I n ( )
I
for phase c from the k th terminal at time step n
=
c k ,
Each terminal computes positive sequence current:
1
n ( )
(
n ( ) I
I
-- - I
=
+
pos k ,
a k ,
b k ,
3
Each relay computes a quantity derived from the positive sequence current that is indicative of the amount of rotation from
one cycle to the next, by computing the product of the positive sequence current times the complex conjugate of the posi-
tive sequence current from the previous cycle:
n ( )
n ( ) I
Deviation
I
=
pos k ,
k
The angle of the deviation phasor for each relay is proportional to the frequency deviation at that terminal. Since the clock
synchronization method maintains frequency synchronism, the frequency deviation is approximately the same for each
relay. The clock deviation frequency is computed from the deviation phasor:
f ∆
FrequencyDeviation
=
---- -
Note that a four quadrant arctangent can be computed by taking the imaginary and the real part of the deviation separately
for the two arguments of the four quadrant arctangent. Also note that the input to the loop filter is in radian frequency which
is two pi times the frequency in cycles per second:
∆
ω
⋅
f ∆
2π
=
So the radian frequency deviation can be calculated simply as:
1
–
∆
ω
f ∆ tan
⋅
(
(
=
Im Deviation
There are two separate sources of clock phase information; exchange of time stamps over the communications channels
and the current measurements themselves (although voltage measurements can be used to provide frequency information,
they cannot be used for phase detection). Current measurements can generally provide the most accurate information, but
are not always available and may contain large errors during faults or switching transients. Time stamped messages are
the most reliable source of phase information but suffer from a phase offset due to a difference in the channel delays in
each direction between a pair of relays. In some cases, one or both directions may be switched to a different physical path,
leading to gross phase error.
For two or three terminal systems, the approach is:
•
The primary source of phase information is current measurements (when available) and the secondary source is the
time-tagged messages. The filter uses a single input that is switched back and forth between the two sources of phase
angle information. This makes the system immune to changes in communications delays as long as current informa-
tion is available. The rules for switching between the sources are:
•Phase angle deviations from both current information and ping-long information are always computed. The ping-pong
algorithm has a wider range of validity, and is used to help decide which source of phase angle information is to be
used by the filter.
•Phase angle deviation computed from currents is used whenever it is valid. Otherwise, phase angle information from
the ping-pong algorithm is used.
•Phase angle deviation computed from currents is deemed valid whenever the currents are large enough, and when
the deviation computed from the ping-pong information is below a fixed threshold (this threshold is ± half-cycle.)
GE Power Management
⋅
(
)
n
j 2π 3 ⁄
j 2π 3 ⁄
n ( ) e
⋅
n ( ) e
⋅
I
+
c k ,
) ∗
(
n N
–
–
pos k ,
–
1
(
(
) Re Deviation
⁄
tan
Im Deviation
=
------------------------------------------------------------------------------------------------ -
f
2π
) Re Deviation
⁄
(
)
)
L90 Line Differential Relay
)
(
)
)
8.1 OVERVIEW
8.1.11 PHASE DETECTION
8-7
8
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