Optimal base frequency estimation of an electrical signal based on Prony's estimator and a FIR filter

In the frequency domain modeling of power supplying networks, it is usually necessary to determine the frequency spectrum of the currents flowing through the nonlinear devices (Arrillaga and Watson, 2003; Das, 2015; Lewandowski and Walczak, 2014). The spectrum estimation can be done in many different ways (Lewandowski and Walczak, 2014; Łobos and Rezmer, 1997; Ray et al., 2016). In work (Lewandowski and Walczak, 2014) a spectrum estimation method has been proposed, which has better accuracy in comparison with other competitive methods like WIFTA (Window Interpolated Fourier Transform) or TDQS (Time Domain Quasi-Synchronous Sampling), while maintaining a low demand for computing power. The accuracy of this method depends on two main factors: the accuracy of the fundamental frequency estimation and the accuracy of the signal interpolation in the resampling process. For the estimation of the fundamental frequency, the method uses a first order Prony's estimator (Łobos and Rezmer, 1997) and a band-pass FIR (Finite Impulse Response) filter. In the paper, an attempt was made to find the optimal parameters for both: the Prony's estimator and the FIR filter. First, an analysis of the measurement window size of the Prony's estimator and the number of the FIR filter coefficients was performed. Then, the optimization problem was defined, which is not trivial, since the Prony's estimator is highly nonlinear and some of the parameters (the window size and the number of filter coefficients) are integers. The research allowed to determine the optimal values of the considered parameters of the frequency estimation method. Along with the results presented in Lewandowski and Walczak (2015) it is now possible to implement the spectrum estimation method from Lewandowski and Walczak (2014) using the optimal set of parameters.