Uses of signal derivatives in analysis voltage sags

The paper investigates the use of first and second derivatives of voltage waveforms as estimators of the times of initiation and recovery of voltage sags. Discrete-time approximations of the derivatives of continuous-time voltages are investigated. It is shown that the simple backward difference derivative approximation yields acceptable results when the voltage waveforms are pure sinusoids, although its effectiveness is lessened when the voltage waveforms are distorted and noisy. An improved derivative approximation which incorporates averaging is shown to be superior to the backward difference for the purpose of sag initiation and recovery time estimation. The proposed derivative approximation contains prominent impulses which can be used to identify voltage sag initiation and recovery.