Analysis and modeling of high frequency ac power distribution systems

Small signal modeling of power converters is important for analysis, fast simulation and control design. The small signal modeling based on state-space averaging method has been widely used for PWM converters since the ripples are small in the inductor current or capacitor voltage. The model becomes less accurate from the real circuit if the ripple is not ignorable. In a resonant circuit, the inductor currents and capacitor voltages are ac dominant. Therefore, the state space averaging method is not applicable to the resonant converters. Sample-data models have been studied for these converters. In the meantime, phasor modeling is also intensively investigated. The phasor dynamic modeling method maps the periodical time-varying ac state variables into stationary frame for each harmonics of interest. Correspondingly, the resonant converter is decomposed into two dc sub-circuits, the state variables of which are the time-varying Fourier Coefficients of the original ac variables. Small signal model can be derived by applying small perturbation and linearization to the Fourier Coefficients. In this paper we give the general definitions of P, Q and S in terms of the state variables in the phasor dynamics models. The physical meanings of the definitions are in accordance with the traditional ones. We present general phasor model for high frequency ac power distribution systems which are complicated because of the high order resonant tank, and parasitic and leakage components. The model can be easily derived from the topology in time-domain. Therefore this model can be easily extended to more complicated resonant topologies, and to include more parasitical components for higher accuracy of modeling. The model accuracy can also be improved by including more harmonics in the model. The model can be applied to various topologies, for instance, full-bridge and halfbridge, and a number of modulation methods, such as phase shift modulation, frequency modulation, pulse phase modulation, and pulse width modulation. It can be used for fast simulation, circuit analysis and control loop design.