A Recursive Maximum Likelihood Estimator for the Online Estimation of Electromechanical Modes With Error Bounds

Accurate and near real-time estimates of electromechanical modes are of great importance since the modal damping is a key indicator of the stability of the power system. If the estimates of the electromechanical modes are to be useful, knowing the variability in the estimates is critically important. This paper presents a method of directly estimating the variance of each mode estimate in addition to estimating the frequency and damping of each mode in an online setting using a recursive maximum likelihood (RML) estimator. The variance estimates are achieved using two closed-form multidimensional Taylor series approximations, the details of which are fully derived here. The proposed method is validated using a Monte Carlo simulation with a low order model of the Western Electricity Coordinating Council (WECC) power system under both ambient and probing conditions, with multiple modes closely spaced in frequency, and is compared to the regularized robust recursive least squares (R3LS) method. It is also successfully applied to phasor measurement unit (PMU) data collected from the actual WECC system, also under both ambient and probing conditions.