CHAPTER 9: THEORY OF OPERATION OVERVIEWL60 LINE PHASE COMPARISON SYSTEM – INSTRUCTION MANUAL 9-299The pre-filtered instantaneous currents can be used directly in phase-segregated implementations. In mixed-modeapplications, they must be converted into a single composite current. This operation uses symmetrical components andcan seem at odds with the time-domain approach.However, the conversion can be done without introducing unnecessary delay by applying a pair of orthogonal filters.Orthogonal filters are two filters that yield phase responses shifted by 90°, and preferably have similar magnituderesponses (that is, filtering capabilities). The two filters are often labeled as direct (D) and quadrature (Q). Their outputs areinstantaneous values, but can be treated similarly to the real and imaginary parts of a phasor in the frequency domain.The L60 implementation of a phase comparison relay uses a pair of short-window FIR filters to derive the D-Q componentswhile providing for extra transient filtering. Once the D-Q components are obtained, the instantaneous negative-sequencebased composite signal (I_2 – K × I_1) is created as follows (ACB phase rotation, phase A as a reference).Eq. 9-2The equation is a linear combinations of current samples, as long as the operations of pre-filtering and deriving theorthogonal components are linear. This guarantees security on external faults regardless of any transients as long as thehardware/algorithms are the same at all line terminals. With both terminals applying the same linear processing, the twomixed currents are always out-of-phase as waveforms, regardless of their possible distortions and transients.The quadrature component of the signal is needed to estimate magnitude of the input current for fault detectors:Eq. 9-3Two levels of fast overcurrent supervision are required: fault detection low (FDL) for keying and fault detection high (FDH)for tripping. These conditions are supervisory; therefore, they do not have to be very accurate. Instead, they need to be fastenough not to slow the remainder of the 87PC algorithm.The fast magnitude is calculated as:Eq. 9-4Figure 9-21: Example of mixing current operation (relay COMTRADE record)The response of the overcurrent condition to switch off transients, including current reversal on parallel lines and heavilysaturated CTs, is important. The key design requirement is to keep the FDL and FDH picked up and resetting in a way thatensures both dependability and security in both tripping and blocking arrangements.
