For four or more terminals, the approach is:
The only source of phase information is the time tagged message exchange, which is used for clock adjustment.
During start up, the relays measure the minimum round trip channel delay. Channel delay in each direction is assumed
to be 1/2 the round trip delay.
During operation, the phase error is estimated as half the absolute value of the difference between the round trip chan-
nel delay and the start-up value.
In both cases, frequency deviation information is also used whenever available. The phase difference between a pair of
clocks is computed by an exchange of time stamps. Each relay exchanges time stamps with all other relays that can be
It is not necessary to exchange stamps with every relay, and the method works even with some of the channels failed. For
each relay that a given relay can exchange time stamps with, the clock deviation is computed each time a complete set of
time stamps arrives. The net deviation is the total deviation divided by the total number of relays involved in the exchange.
For example, in the case of two terminals, each relay computes a single time deviation from time stamps, and divides the
result by two. In the case of three terminals, each relay computes two time deviations and divides the result by three. If a
channel is lost, the single deviation that remains is divided by two.
Four time stamps are needed to compute round trip delay time and phase deviation. Three stamps are included in the mes-
sage in each direction. The fourth time stamp is the time when the message is received. Each time a message is received
the oldest two stamps of the four time stamps are saved to become the first two time stamps of the next outgoing message.
The third time stamp of an outgoing message is the time when the message is transmitted. A fixed time shift is allowed
between the stamp values and the actual events, provided the shift for outgoing message time stamps is the same for all
relays, and the shift incoming message time stamps is also identical.
To reduce bandwidth requirements, time stamps are spread over 3 messages. In the case of systems with 4 messages per
cycle, time stamps are sent out on three of the four messages, so a complete set is sent once per cycle. In the case of sys-
tems with 1 message per cycle, three time stamps are sent out each cycle in a single message. The transmit and receive
time stamps are based on the first message in the sequence.
One of the strengths of this approach is that it is not necessary to explicitly identify or match time stamp messages. Usually,
two of the time stamps in an outgoing message are simply taken from the last incoming message. The third time stamp is
the transmittal time. However, there are two circumstances when these time stamps are not available. One situation is
when the first message is transmitted by a given relay. The second is when the exchange is broken long enough to invali-
date the last received set of time stamps (if the exchange is broken for longer than 66 ms, the time stamps from a given
clock could roll over twice, invalidating time difference computations). In either of these situations, the next outgoing set of
time stamps is a special start-up set containing transmittal time only. When such a message is received, nothing is com-
puted from it, except the message time stamp and the received time stamp are saved for the next outgoing message (it is
neither necessary nor desirable to "reset" the local clock when such a message is received).
Error analysis shows that time stamp requirements are not very stringent because of the smoothing behavior of the phase
locked loop. The time stamp can be basically a sample count with enough bits to cover the worst round trip, including chan-
nel delay and processing delay. An 8 bit time stamp with 1 bit corresponding to 1/64 of a cycle will accommodate a round
trip delay of up to 4 cycles, which should be more than adequate.
The computation of round trip delay and phase offset from four time stamps is as follows:
The Ts are the time stamps, with Ti the newest. Delta is the round trip delay. Theta is the clock offset, and is the correct sign
for the feedback loop. Note that the time stamps are unsigned numbers that wrap around while 'a' and 'b' could be positive
or negative. Delta must be positive. Theta could be positive or negative. Some care must be taken in the arithmetic to take
into account possible roll over of any of the time stamps. If Ti-2 is greater than Ti-1, there was a roll over in the clock
responsible for those two time stamps.
L90 Line Differential Relay
8 THEORY OF OPERATION
GE Power Management