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The purpose of this paper is to study variation regularization with a positive sequence extraction-normalized least mean square (VRP-NLMS) algorithm for frequency estimation in a three-phase electrical distribution system. A simulation test is provided to validate the performance and convergence rate of the proposed estimation algorithm.

Least mean square (LMS) algorithms for frequency estimation encounter problems when voltage contains unbalance, sags and harmonic distortion. The convergence rate of the LMS algorithm is sensitive to the adjustment of the step-size parameter used in the update equation. This paper proposes VRP-NLMS algorithm for frequency estimation in a power system. Regularization parameter is variable in the NLMS algorithm to adjust step-size parameter. Delayed signal cancellation (DSC) operator suppresses harmonics and negative sequence component of the voltage vector in a two-phase Î ± β plane. The DSC part is placed in front of the NLMS algorithm as a pre-filter and a positive sequence of the grid voltage is extracted.

By adapting of the step-size parameter, speed and accuracy of the LMS algorithm are improved. The DSC operator is augmented to the NLMS algorithm for more improvement of the performance of this adaptive filter. Simulation results validate that the proposed VRP-NLMS algorithm has a less misalignment of performance with more convergence rate.

This paper is a theoretical support to simulated system performance.