Frequency responses of phasor-based microprocessor relaying algorithms

The magnitude and phase estimate algorithms in phasor-based microprocessor relaying are nonlinear. The characteristics of the nonlinear relay algorithms cannot be analyzed using the frequency response concept defined for studying linear time-invariant (LTI) systems. The term "frequency response" needs to be clarified when it is used to characterize nonlinear relay algorithms. The paper clarifies and then investigates the magnitude responses of deterministic relay algorithms and Kalman filter relay algorithms. The deterministic relaying algorithms studied in the paper include Mann-Morrison, Prodar, full cycle DFT, half cycle DFT, Cosine filter, and least square. In the Kalman filter relay algorithms, two-state and three-state Kalman filter models are considered. Finally, the effect of the signal statistic property on the frequency responses of the Kalman filter relay algorithms is studied.