10-8 L90 LINE CURRENT DIFFERENTIAL SYSTEM – INSTRUCTION MANUALOVERVIEW CHAPTER 10: THEORY OF OPERATION10Normally each relay detects frequency deviation, but if there is no current flowing nor voltage measurement available at aparticular relay, it is not be able to detect frequency deviation. In that case, the frequency deviation input to the loop filteris set to zero and frequency tracking is still achieved because of phase locking to the other clocks. If frequency detection islost at all terminals because there is no current flowing, then the clocks continue to operate at the frequency present at thetime of the loss of frequency detection. Tracking resumes as soon as there is current.The rotational rate of phasors is equal to the difference between the power system frequency and the ratio of thesampling frequency divided by the number of samples per cycle. The correction is computed once per power system cycleat each relay. For conciseness, we use a phasor notation:Eq. 10-21Each terminal computes positive sequence current:Eq. 10-22Each relay computes a quantity derived from the positive sequence current that is indicative of the amount of rotationfrom one cycle to the next, by computing the product of the positive sequence current times the complex conjugate of thepositive sequence current from the previous cycle:Eq. 10-23The angle of the deviation phasor for each relay is proportional to the frequency deviation at that terminal. Since the clocksynchronization method maintains frequency synchronism, the frequency deviation is approximately the same for eachrelay. The clock deviation frequency is computed from the deviation phasor:Eq. 10-24Note that a four-quadrant arctangent can be computed by taking the imaginary and the real part of the deviationseparately for the two arguments of the four-quadrant arctangent. Also note that the input to the loop filter is in radianfrequency which is two pi times the frequency in cycles per second; that is, .So the radian frequency deviation can be calculated simply as:Eq. 10-2510.1.11 Phase detectionThere are two separate sources of clock phase information: exchange of time stamps over the communications channelsand the current measurements themselves (although voltage measurements can be used to provide frequencyinformation, they cannot be used for phase detection). Current measurements can generally provide the most accurateinformation, but they are not always available and can 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 inthe channel delays in each direction between a pair of relays. In some cases, one or both directions can be switched to adifferent physical path, leading to gross phase error.The primary source of phase information is CPU time-tagged messages. If GPS compensation is enabled, GPS time stampsare used to compensate for asymmetry. In all cases, frequency deviation information also is used when available. Thephase difference between a pair of clocks is computed by an exchange of time stamps. Each relay exchanges time stampswith all other relays that can be reached.
