GE Power ManagementL90 Line Differential Relay8-98 THEORY OF OPERATION 8.1 OVERVIEW8To correct for the roll over, subtract 256 from the round trip and subtract 128 from the phase angle. If Ti-3 is greater than Ti,add 256 to the round trip and add 128 to the phase angle. Also, if the above equations are computed using integer valuesof time stamps, a conversion to phase angle in radians is required by multiplying by π over 32.Time stamp values are snapshots of the local 256 bit sample counter taken at the time of the transmission or receipt of thefirst message in a time stamp sequence. This could be done either in software or hardware, provided the jitter is limited toless than plus or minus 130 μs. A fixed bias in the time stamp is acceptable, provided it is the same for all terminals.Another source of phase information in the case of a 2 or 3 terminal system are the current measurements. In the case of atwo terminal system, phase angle deviation at a terminal is computed as follows:Again, it is possible to use a four quadrant arctangent, in which case the minus signs are needed on the imaginary and thereal part as shown. The subscript 1 refers to the current at the local peer and the subscript 2 refers to the current at theremote peer.In the case of a three terminal system, the phase deviation at each terminal is computed as: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.In the case of 4 or more terminals, no phase information can be derived from the current measurements.Regarding timing of the computations, the latest available phase and frequency deviation information is furnished to theloop filter once per cycle in the case of a 64 Kbaud communications channel, and once every 3 cycles in the case of a 9600baud communications channel.φ1n( ) 12--- tan 1– ImIpos 2,n( )Ipos 1,n( )∗⋅( )–ReIpos 2,n( )Ipos 1,n( )∗⋅( )–--------------------------------------------------------------------- ⋅=φ1n( ) ReIpos 3,n( )Ipos 2,n( )–( )Ipos 1,n( )∗Ipos 2,n( )∗Ipos 3,n( )∗+ +( )⋅( )ImIpos 2,n( )Ipos 1,n( )∗⋅Ipos 3,n( )Ipos 2,n( )∗⋅Ipos 1,n( )Ipos 3,n( )∗⋅+ +( )------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------=
