Validating the use of stochastic models for power electronic converters

One of the drawbacks of using averaging models in the analysis and design of power electronic systems has been the uncertainty in determining the stability of the system since these techniques necessitate a small-signal restriction and thus cannot account for nonlinearities. This paper addresses this problem. It presents the replacement of the averaging models by stochastic models. The stochastic models for pulse-width modulated (PWM) converters are developed based on recent techniques employed from the theory of stochastic differential equations. An important feature of these stochastic models is the representation of perturbations in the duty ratio of switching converters as Gauss-Markov processes (or colored noises) keeping the nonlinear model intact. In these type of studies, the dynamics of the electronic system (switching converters) are modeled as a diffusion process, indicating that the system will exhibit transitions between stable states. This has lead to the introduction of the mean first passage time (MFPT) of the dynamic electronic system from a certain domain of attraction which can be used as an index of system stability