Parameter determination of a nonsinusoidal periodic signal harmonic based on the modified sine transform

Abstract

An algorithm is presented for determining the amplitude and the initial phase of the oscillations of the kth harmonic included in the structure of the nonsinusoidal periodic signal. The algorithm differs from the well-known Euler–Fourier method based on sine and cosine transforms. The qualitative difference of the proposed method consists in the use of the cosine function, which is an analytic solution of a modified sine transform, the structure of which includes a sinusoidal factor with a complex argument that contains a variable phase angle. The coordinates of the maximum of this functional dependence, which is raised to a positive integer power to improve the accuracy of determining the parameters, are uniquely associated with the amplitude and the initial phase of oscillations of the kth harmonic of the nonsinusoidal signal. The considered method minimizes the use of nonlinear operations and at its core has the element inherent in the selective filter. The possibility of obtaining information on the parameters of the first voltage and current harmonics with the required accuracy enhances the reliability of the evaluation of processes occurring in the power system in the conditions of interference in the form of higher harmonics. An example problem is solved in the MS Excel environment