Contents I. Introduction
Unbalanced conditions of three-phase power systems along with injection of multiple order harmonics due to nonlinear loads increase the losses and affect the overall operation of practical power system. Monitoring of unbalanced voltage/current parameters and harmonics can protect the sensitive equipment used in transmission and distribution networks. To measure the unbalanced voltages and currents, symmetrical components should be estimated correctly across all the phases. To reduce the effects of harmonics, accurate estimation of amplitude and phase parameters is crucial to design harmonic elimination filters. Signal processing algorithms play a vital role for estimation of power quality (PQ) disturbances and adaptive filters are popular signal processing models used for easy implementation in both software and hardware. Different implementation methods have been proposed for measurement of harmonic and sequence components [1]–[4], which includes transform based approaches, such as discrete Fourier transform, short time Fourier transform [5]–[7]. But, these transforms suffer from spectral leakage effects and highly nonstationary nature of the signals. Similarly neural networks [8]–[10] and fuzzy models [11] are also frequently used to estimate the time-varying power signal parameters. But, these models require efficient adaptive algorithms for training. Thus, choice of proper adaptive algorithm is important to achieve faster convergence of the model. Adaptive filtering, such as least mean square (LMS) [12], [13], least square [14]–[17], Kalman filters [7], [18]– [20] are elegant and powerful techniques to track short duration and time varying PQ disturbances. Among adaptive filters LMS has simplest and low complexity structure offering good convergence behavior in case of stationary signals. But, the performance degrades in a situation where the signal statistics are time varying. In this paper, a new adaptive structure is proposed with Volterra expansions [21], [22] of input samples to estimate harmonic and sequence components simultaneously of three-phase power system. The new structure is a compromise between LMS and least mean fourth (LMF) [23] which is modeled as LMS/F [24] having a modified cost function. Section II represents the mathematical formulation of estimation models to track both Harmonics and sequence components. Section III describes the implementation steps of Volterra LMS/F (VLMS/F) algorithm. Estimation results with discussions are presented in Section IV. Section V presents an overall conclusion of the paper.
