Stepwise quadratic state-space modeling technique for simulation of power electronics circuits

A fast and accurate technique for simulation of power electronics circuits is presented. The methodology begins by using Chebyshev polynomials to derive an adaptive stepwise quadratic state-space model for each piecewise-linear circuit topology. The state-space equation sets are integrated with modified nodal equations. The key feature of this algorithm is that it gives an approximate value of the optimum simulation step size for analysis of each circuit topology in order to achieve a desired accuracy in calculating the state transition matrix of the topology. Moreover, the algorithm hybridizes the advantages of calculating the circuit responses at circuit level and determining switching instants at device level. The switching instants are calculated directly by solving simple quadratic equations. Furthermore, it is unnecessary to have prior knowledge of the circuit operations, such as the topology sequence and duration. The algorithm automatically looks for a valid topology at any time instant. The proposed method is illustrated with the examples of a practical induction heater and a boost DC/DC regulator. The theoretical predictions are verified with the results obtained in experiment and available literature.