Power Electronics Harmonic Analysis Based on the Linear Time Periodic Modeling

This paper presents an analytical frequency-domain method for harmonics modeling and evaluation in power electronic systems. The considered system is described by a set of differential equations, which are converted in the frequency domain and presented in a matrix form. Indeed, currents and voltages are described in terms of Fourier series and arranged in a vector form. The passive elements and the switching functions are then represented by harmonic transfer matrices. The resolution of the matrix equations leads to theoretical time and frequency expressions of the system voltages and currents. This method is applied to a closed-loop three phase AC/DC/AC PWM converter. The control loop of the converter is modeled by additional equations. The spectra of the switching functions, necessary to build the corresponding harmonic transfer matrices, are calculated through a double Fourier series decomposition. The matrix equations are solved and the results are compared to those obtained by real measurements and Matlab/Simulink simulations.