Multiple Fourier Series-Based Modeling and Stability Analysis of the Three-Phase Pulsewidth-Modulated VSC

Pulsewidth modulators in the digital control system of the voltage source converter (VSC) are used to generate switching signals. However, their complex multifrequency characteristics may lead to middle- and high-frequency oscillations. There are currently limited studies on the three-phase pulsewidth modulation (PWM) VSC considering modulator's sideband harmonics, and the modeling methods proposed for other kinds of PWM converters are not applicable to the three-phase VSC. Therefore, to investigate the sideband harmonic stability of three-phase VSCs, the multiple Fourier series-based modeling method of the digital PWM modulator is proposed in this article. First, the analytic expressions of switching signals when the modulator is perturbed by harmonics are derived based on the proposed method. Then, this article summarizes the selection principles of the dominant harmonic components of the perturbed modulator. Finally, complex analytic expressions are simplified and approximated linearly to provide easy-to-use analytic results for other researchers. Then, based on the proposed modeling method, the impedance model of the VSC with a symmetric regular sampled sinusoidal pulsewidth modulation (SPWM) modulator is derived. Based on the derived model, the influences of the key parameters on the system stability are investigated. Finally, the theoretical analysis results are validated through both simulations and hardware experiments.