Maximum likelihood frequency estimation in smart grid applications

Abstract

International audienceThis paper focuses on the estimation of the fundamental frequency in balanced three-phase power systems. Specifically, we propose a Maximum Likelihood Estimator (MLE) that exploits the multidimensional nature of electrical signals. For perfectly sinusoidal signals, we show that the MLE can be expressed according to the periodogram of the instantaneous positive component. For harmonic signals, we demonstrate that the MLE can be approximated by a cumulated periodogram of the zero, positive and negative sequence components. As compared to single-phase estimators, statistical analysis and simulation results prove that the proposed estimator decreases the Mean Square Error by a factor of three, whatever the Signal to Noise Ratio (SNR) or data length. Furthermore, simulations with experimental data show that the proposed technique outperforms classical spectral estimators such as MUSIC

Three-phase electrical signals analysis for mechanical faults monitoring in rotating machine systems

“…By the same way, if the fundamental component of the three-phase current contains an unbalanced part, this part is entirely projected onto i − (t) and/or i 0 (t) depending on the type of unbalance. This result is to be related to the one mentioned in [17], where it is shown that for perfectly balanced three-phase signals the Cramer Rao Bound of the frequency estimator is three times lower for the positive-sequence ISC than for single phase approaches.…”

“…The current signal formulation given in Eq. (16) can be rewritten in a more compact form using phasor notations, leading to Equation (17).…”