Widely linear adaptive frequency estimation for unbalanced three-phase power systems with multiple noisy measurements

Abstract

We address the problem of adaptive frequency estimation of unbalanced three-phase power systems in practical situations when the voltage samples are contaminated with measurement noise. The complex-valued-transformed voltages are used in order to utilise all the available information in the three-phase reference channels, at the expense of modest addition in computational complexity. A widely linear predictive model is established over multiple noisy voltage measurements to cater for the system unbalance conditions, which are manifested in noncircular empirical distributions. To obtain frequency estimates in an adaptive manner, the total least-squares fitting and gradient descent optimisation techniques are adopted based on the augmented complex statistics. The so introduced augmented complex total least mean square (ACTLMS) algorithm is shown to enable, by design, more reliable frequency estimates over its augmented complex least mean square (ACLMS) counterpart. The ACTLMS is also shown to provide the user with a choice in the degrees of freedom to control the trade-off between tracking speed and estimation accuracy. Simulations on both synthetic and real-world noisy unbalanced power systems support the analysis.