This article proposes a method of phasor estimation called the Morlet wavelet-based two-point finite-impulse response (FIR) filter (MW-FIR), showing advantages on algorithm complexity, customizability, and zero overshoot. The method focuses on amplitude and frequency estimation, while phase and rate of frequency of change (ROCOF) estimation can be performed using the standard signal processing model with an FIR filter. The mathematical principle behind the method is presented. The causes of error are discussed, and the parameter selection procedure is introduced to minimize error and adjust algorithm performance according to different application requirements. The proposed method has been discussed and compared with the three-point interpolated discrete Fourier transform (ipDFT) method and the FIR method using a flat-top (FT) windowing function, under the static and dynamic situations given by the IEC/IEEE 60255-188-1 and noise immunity evaluation. Finally, the major advantages of the proposed frequency estimation method compared with the conventional FIR-based method using the derivative of angular position are discussed. It can be concluded that this method becomes a substitute for ipDFT in most cases and shows several advantages over the FIR-based method with an FT sequence.

The paper is related to the problem of modeling and optimizing power systems supplying, among others, nonlinear loads. A software solution that allows the modeling and simulation of power systems in the frequency domain as well as the sizing and allocation of active power filters has been developed and presented. The basic assumptions for the software development followed by the models of power system components and the optimization assumptions have been described in the paper. On the basis of an example of a low-voltage network, an analysis of the selection of the number and allocation of active power filters was carried out in terms of minimizing losses and investment costs under the assumed conditions for voltage total harmonic distortion (THD) coefficients in the network nodes. The presented examples show that the appropriate software allows for an in-depth analysis of possible solutions and, furthermore, the selection of the optimal one for a specific case, depending on the adopted limitations, expected effects, and investment costs. In addition, a very high computational efficiency of the adopted approach to modeling and simulation has been demonstrated, despite the use of (i) element models for which parameters depend on the operating point (named iterative elements), (ii) active filter models taking into account real harmonics reduction efficiency and power losses, and (iii) a brute force algorithm for optimization.

Purpose: – A highly accurate method of current spectrum estimation of a nonlinear load is presented in this paper. Using the method makes it possible to evaluate the current injection frequency domain model of a nonlinear load from previously recorded time domain voltage and current waveforms. The paper aims to discuss these issues. Design/methodology/approach: – The method incorporates the idea of coherent resampling (resampling synchronously with the base frequency of the signal) followed by the discrete Fourier transform (DFT) to obtain the frequency spectrum. When DFT is applied to a synchronously resampled signal, the spectrum is free of negative DFT effects (the spectrum leakage, for example). However, to resample the signal correctly it is necessary to know its base frequency with high accuracy. To estimate the base frequency, the first-order Prony's frequency estimator was used. Findings: – It has been shown that the presented method may lead to superior results in comparison with window interpolated Fourier transform and time-domain quasi-synchronous sampling algorithms. Research limitations/implications: – The method was designed for steady-state analysis in the frequency domain. The voltage and current waveforms across load terminals should be recorded simultaneously to allow correct voltage/current phase shift estimation. Practical implications: – The proposed method can be used in case when the frequency domain model of a nonlinear load is desired and the voltage and current waveforms recorded across load terminals are available. The method leads to correct results even when the voltage/current sampling frequency has not been synchronized with the base frequency of the signal. It can be used for off-line frequency model estimation as well as in real-time DSP systems to restore coherent sampling of the analysed signals. Originality/value: – The method proposed in the paper allows to estimate a nonlinear load frequency domain model from current and voltage waveforms with higher accuracy than other competitive methods, while at the same time its simplicity and computational efficiency is retained.

Purpose: – In most applications the active power filters (APFs) are used to reduce harmonic distortion of a nonlinear load which is located near the APF installation point. This classic approach allows to reduce the distortion introduced to the power system but do not guarantee that the cost of the APFs installation is optimal. The purpose of this paper is to compare the classic approach to harmonic compensation with an optimization method of sizing and placement of the APFs in an existing distributed power network. Design/methodology/approach: – An exemplary real-life power system with distributed nonlinear loads was modeled using PCFLO power analysis software. Next, Matlab was used to implement the classic method and the optimization algorithm. Between Matlab and PCFLO a specially written Java middleware was used to provide a seamless workflow integration. Findings: – It was shown that the presented optimization method may lead to superior results in comparison with the classic approach. Simulation results clearly showed that the APFs installation cost can be significantly reduced when the optimization algorithm is used. Moreover, the proposed optimization method can overcome some problems connected with the nonlinearity and discontinuity of the APF's price/current function. Research limitations/implications: – There are two main limitations of the presented method. First, the method needs much more computing power then the classic approach. Second, according to the authors’ knowledge, currently there are no commercially available APFs, which allow to directly apply the optimization method in industrial applications. Practical implications: – The presented results showed that the approach, which is the most popular in the industry, is far from being optimal from the cost perspective. As it has been shown in the investigated example, it might be possible to significantly reduce the total cost of APFs installed in the power system. Originality/value: – The optimization method presented in the paper as well as all simulation results are the original authors work. It was shown that the existing harmonic compensation strategies can be significantly upgraded and the proposed optimization method may be a basis and a reference point for future commercial solutions.