A Disturbed Grid Voltage Interharmonic Analysis with Fourier Series of Several Variables

Abstract

Increasing the range of electronic devices, especially nonlinear impulse loads worsen the parameters of electricity quality. One of the most negative factors for the electricity quality are low-frequency interharmonics, which have a negative impact on electric motors, transformers and other AC equipment. The interharmonics generated by disturbances forming by grid loads which operates with frequency that is not multiple with the electric grid one. The interharmonics detection is a complex problem because of their permanent frequency fluctuation. The common numerical methods implementation for interharmonic analysis leads to large number of the mathematical operation, therefore analytical methods are more attractable. Usually, interharmonics forming is researched in wide range of disturbance parameters for further analysis and their suppression. Often, for math operation reducing, interharmonic analysis is performed by probabilistic approach in several points of parameters range with subsequent expanding its result on all parameter values that cause to inaccurate results. In the paper is proposed a fully analytical method based on a Fourier series of several variables, which allows: describe the voltage model immediately in the frequency domain; calculate the interharmonics of the voltage in all disturbance parameter range directly with a minimum number of mathematical operation due to representing the parameters in final analytical formula for interharmonics calculation; minimize error. In considered case the electric grid model consists of active-inductive internal resistance and a batch of nonlinear loads: AC system which operates on different frequency comparing with the grid frequency; pulse loads that switches with different frequency than grid frequency; parametric load with non-multiple period to the grid frequency. The properties of Fourier series of several variable are analyzed and advantages of describing signals with several components are shown. Principle of projection of multidimensional spectrum to one variable is demonstrated. The grid voltage disturbance for each load are analyzed and voltage model in frequency domain of several variable are obtained. The shape of each disturbance for batch of the input parameters are constructed and total grid voltage shape and its spectrum are built. The nature of interharmonic forming as combinational harmonics are shown. The mathematical operation elimination is analyzed for general case and shown the total advantage of the proposed method in comparing with numerical Fourier series of one variable.