Multiple Fourier Series Method for Amplitude-Frequency Characteristics of PWM Pulses With Amplitude-Frequency Time-Varying Modulation Signals

With increasing penetration of renewable energy generation and power electronic converters, waveform distortion and resonance related to high-frequency harmonics and interharmonics increasingly affect power grid quality and stability. The generation and characteristics of high-frequency grid harmonics and interharmonics are correlated with pulse width modulation (PWM) of grid-integrated converters with amplitude–frequency (A–F) interfered modulation signals. However, due to the applicability and precision, prior PWM analysis methods cannot effectively deal with A–F time-varying modulation signals. To solve this issue, focusing on small harmonic and interharmonic disturbances near the steady operating state, the PWM modeling and characteristic analysis are carried out for A–F time-varying modulation signals in this article. Multiple Fourier series PWM analysis method based on decomposition principle of multivariate periodic function is proposed, which can explicitly characterize the impact mechanism of modulation signal components and carrier signal on the PWM amplitude and frequency. Coupling characteristics among fundamental, small A–F interference and carrier frequencies are clarified. To enhance applicability of this method, an improved multiple Fourier series coefficient calculation method is further proposed, which does not require multiple integrals, and has lower computational burden compared with traditional method. Finally, effectiveness of proposed method is verified by experiment.