Sel 411L - Page 130

P.3.22
SEL-411L Relay Protection Manual Date Code 20151029
Protection Functions
87L Theory of Operation
Relay 1 receives the packet after the channel delay (a few milliseconds to tens
of milliseconds). It uses its own clock to capture the time of reception as t
3
.
From the sequence number it receives, Relay 1 knows that this is a reply to the
message it sent at time t
0
.
At this point, Relay 1 can finish the key calculations related to channel delay,
clock offset, and data alignment.
Assuming symmetrical channel delay, the one-way channel delay is as
follows.
Equation 3.26
Note that the difference between t
3
and t
0
is the time elapsed at the local relay,
and the hold time is the time the remote relay measures and communicates
back explicitly. Therefore, Equation 3.26 makes sense even though its
components come from two asynchronously running clocks.
Backdating t
3
by the channel delay time, we get the transmission time at
Relay 2 expressed in the local time of Relay 1.
Equation 3.27
Backdating further by the known delay in transmitting a packet after capturing
the data (see t
TX
in Figure 3.14), we obtain the data time stamp expressed in
time of Relay 1.
Equation 3.28
The data time stamp expressed in Relay 2 time is included in the packet. This
allows calculation of the time offset (i.e., the difference in time between the
two relays).
Equation 3.29
Positive values of the offset time mean that the local clock (Relay 1) is leading
the remote clock; negative offset means that the remote clock is ahead.
Inserting (3.26) into (3.29) gives the following key equation.
Equation 3.30
In the above equation, t
0
and t
3
are local time stamps, t
H
and t
DATA
are
included in the received packet, and t
TX
is a design constant.
Note that the clock offset value is a very stable number because it reflects a
difference between clocks of the two relays, regardless of data latency and
therefore regardless of the channel delay at any given moment. This means
that the raw calculations per Equation 3.30 are already very stable. Further
averaging improves accuracy and provide for ride-through capability.
We then use the clock offset t
OFFSET
to shift the received t
DATA
time stamp to
align it with the local time stamp of the relay.
Equation 3.31
Differences in the channel latency in the transmit and receive directions
(channel asymmetry) result in synchronization errors when using the channel-
based synchronization method. Note that, because of raw clock offset
calculation averaging, the relay is immune to temporary (transient) channel
asymmetry. Only prolonged (standing) channel asymmetry would propagate
t
CH
t
3
t
0
–t
H
–
2
------------------------------=
t
2@Relay1
t
3
t
CH
–=
t
DATA @Relay1
t
3
t
CH
– t
TX
–=
t
OFFSET
t
DATA @Relay1
t
DATA
t
3
t
CH
– t
TX
– t
DATA
–=–=
t
OFFSET
1
2
--- t
0
t
3
t
H
++t
TX
t
DATA
––=
t
DATA @Relay1
t
DATA
t
OFFSET
+=