Abstract: An Adaptive Kalman Filtering scheme for statistically predicting the occurence and type of a fault on a three phase power transmission line. Additionally, estimations of the steady-state postfault phasor quantities, distance protection and fault location information is provided. Current and voltage data for each phase is processed in two separate Adaptive Kalman Filtering models simultaneously. One model assumes that the phase is unfaulted, while the other model assumes the features of a faulted phase. The condition of the phase, faulted or unfaulted, is then decided from the computed a posteriori probabilities. Upon the secure identification of the condition of the phase, faulted or unfaulted, the corresponding Adaptive Kalman Filtering model continues to obtain the best estimates of the current or voltage state variables. Thus, the Adaptive Kalman Filtering model having the correct initial assumptions adapts itself to the actual condition of the phase faulted or unfaulted.

Abstract: Methods for determining magnitude, phase angle and frequency deviation in the sinusoid waveform output of electrical power generation equipment are disclosed. The first method uses a two-state linear Kalman filter to calculate the magnitude and phase angle from which the frequency deviation is calculated using the linear relationship between frequency deviation and the average rate of change of phase angle. In a second method, a three-state extended Kaman filter is employed. The frequency deviation is considered a third state variable and is recursively computed on-line.

Abstract: Digital distance relaying of a three-phase electric power transmission line depends on accurate estimation of the postfault voltage and current phasors during the first postfault electrical cycle, when the line voltages and currents are corrupted by noise and transients. The digital relay herein responds to each postfault sample as it arrives and recursively electronically estimates the postfault phasors before the next sample arrives. The method involves a powerful state variable approach which for the voltages provides at least two state variables per voltage, and for the currents provides at least three state variables per current. Parallel processing of the samples equalizes computer burden, and an additional processor classifies the fault, computes faulted line resistance and reactance, relays the fault by tripping a circuit breaker, and documents the fault including its distance.

Abstract: Waveform frequency measuring apparatus and methods utilizing zero-crossing triggered analog-to-digital conversion apparatus combined with Discrete Fourier Transform (DFT) digital computing apparatus accomplish measurement of waveform fundamental frequency using hitherto disadvantageous leakage of the Discrete Fourier Transform.In an example, the frequency measuring apparatus and methods are used in an alternating current (AC) electrical power system for measuring and monitoring frequency deviation .DELTA.f from the nominal system frequency f and actuating protective relaying when the frequency deviation is excessive.