Adaptive frequency estimation of three-phase power systems

• We show that the recursive least-squares (RLS) estimate of the frequency of a three-phase power system using the second-order autoregressive (AR2) linear predictive model for the complex-valued αβ signal is biased when the voltage readings are noisy.
• We show that the frequency estimation bias can be evaluated and subtracted from the RLS estimate to yield a bias-compensated RLS (BCRLS) estimate if the noise variance is known a priori.
• We also utilize the concept of total least-square (TLS) estimation and calculate a recursive TLS (RTLS) estimate of the system frequency by employing the inverse power method with no need for the prior knowledge of the noise variance.
• We prove mean convergence and asymptotic unbiasedness of the BCRLS and RTLS algorithms.
• Simulation results show that the RTLS algorithm outperforms the RLS and BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm in estimating the frequency of both balanced and unbalanced three-phase power systems.

The frequency of a three-phase power system can be estimated by identifying the parameter of a second-order autoregressive (AR2) linear predictive model for the complex-valued αβ signal of the system. Since, in practice, both input and output of the AR2 model are observed with noise, the recursive least-squares (RLS) estimate of the system frequency using this model is biased. We show that the estimation bias can be evaluated and subtracted from the RLS estimate to yield a bias-compensated RLS (BCRLS) estimate if the variance of the noise is known a priori. Moreover, in order to simultaneously compensate for the noise on both input and output of the AR2 model, we utilize the concept of total least-square (TLS) estimation and calculate a recursive TLS (RTLS) estimate of the system frequency by employing the inverse power method. Unlike the BCRLS algorithm, the RTLS algorithm does not require the prior knowledge of the noise variance. We prove mean convergence and asymptotic unbiasedness of the BCRLS and RTLS algorithms. Simulation results show that the RTLS algorithm outperforms the RLS and BCRLS algorithms as well as a recently-proposed widely-linear TLS-based algorithm in estimating the frequency of both balanced and unbalanced three-phase power systems.