High-Order Generalized Averaging Method for Power Electronics Modeling From DC to Above Half the Switching Frequency

Modeling power electronic converters at frequencies close to or above half the switching frequency has been difficult due to the time-variant and discontinuous switching actions. We develop a high-order generalized averaging method using the properties of moving Fourier coefficients to break though the limit of half the switching frequency. We also propose the high-order generalized average model for various switching signals, including pulsewidth modulation (PWM), phase-shift modulation, pulse-frequency modulation (PFM), and state-dependent switching signals, so that circuits and modulators-controllers can be modeled separately and combined flexibly. Moreover, using the Laplace transform of moving Fourier coefficients, the coupling of signals and their sidebands of different frequencies is clearly described as the coupling of moving Fourier coefficients of the same frequency in a linear time-invariant framework. The modeling method is applied to a PWM controlled boost converter, a V² constant on-time controlled buck converter, and a PFM controlled LLC converter, for demonstration and validation. Experimental results of the converters in different operating modes show that the proposed models have higher accuracy than exiting models, especially in the frequency range close to or above half the switching frequency. The developed method can be applied to almost all types of power electronic converters.