Harmonic analysis of hysteresis controlled grid-connected inverters

This paper proposes an analytical harmonic model for the hysteresis-controlled inverter. The model expresses the triangular-like error current signal in the time and frequency domains. First, time domain analysis derives the instantaneous expression of the error signal and then it applies analogue frequency modulation theory (FM) to the first term of the error Fourier series to obtain the analytical harmonic representation of the error. The harmonic spectrum of the error is closely approximated by the Bessel functions of the first kind. The instantaneous switching frequency resulting from the hysterisis controller is expressed in terms of the coupling reactance, the relay band, and the amplitude modulation index of the inverter. MATLAB\Simulink
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studies are used to validate the proposed model.