Simultaneous Frequency and Harmonic Magnitude Estimation Using Decoupled Modules and Multirate Sampling

A number of measurement algorithms apply orthogonal signal components obtained by two orthogonal finite-impulse-response (FIR) filters. The most significant error in orthogonal FIR digital-filter-based measurement algorithms arises due to the FIR filters having different magnitude gains at frequencies other than the nominal power system frequency. In addition, although the FIR filters show complete rejection of harmonics when the power system frequency is equal to the nominal, this is not the case for other values of the power system frequency. To alleviate this drawback, the filter parameters have to be adapted during frequency estimation. Suitable implementations of adaptive filters that allow closed-form calculation of coefficients, such as cascade FIR comb filters and resonator-based filters, are present in the literature. In this paper, the advantages and pitfalls of these two techniques are addressed with regard to computational complexity, coefficient sensitivity problems, and convergence. As a result, an improved and very suitable combined algorithm based on parallel resonators with common feedback combined with an external FIR comb-filter-based module for frequency estimation that is applied on antialiasing-filtered and decimated input signal is proposed. The obtained simulation results allow us to establish the performance of the proposed algorithm by comparing its measurement precision with the results obtained using fast Fourier transform (FFT) implementations. It has been found that the proposed algorithm is suitable for real-time applications.