Damping and relative mode-shape estimation in near real-time through phasor approach
A technique for estimating damping and electromechanical mode-shape in near real-time as oscillations develop under transient condition is presented. At each sampling instant, measured signals are expressed as phasors using corrected values of modal frequencies. Damping is obtained from the exponential variation of estimated phasor magnitude using a moving window least squares (LS) algorithm. The relative mode-shape is computed directly from the magnitude and phase angle of the phasors. Random variations in loads are considered to examine possible impact on phasor estimation, especially the frequency correction loop. Accuracy and speed of convergence is validated by comparing the time variation of estimated dampings and relative mode-shapes against the actual values obtained from the linearized models under respective operating conditions. Besides the well-known four-machine, two-area test system, a 16-machine, five-area system is considered for illustration of the concept. Monte Carlo simulations are used to capture the statistical variability in estimation as a result of persistent disturbances (e.g., random fluctuations in loads) leading to different signal-to-noise ratios (SNRs). Results from a commercial real-time simulator illustrate the practical feasibility of the proposed approach.