The Time-Invariant Polynomial Model of Fixed-Frequency PWM DC–DC Converter Applying Normalized Coordinate Transformation

In this article, a time-invariant polynomial model of fixed-frequency pulsewidth modulation dc-dc converter is proposed. Through normalized coordinate transformation, the time-varying model of the converter is transferred into a time-invariant model, whose state matrix and input matrix are obtained by the addition and multiplication of matrices simply and expressed by the polynomial of duty cycle concisely. The proposed model has the following advantages. Compared with the state-space average (SSA) model, the ripple of the state vector and the switching period are considered, thereby improving the accuracy. Contrary to other time-invariant models, the state matrix and input matrix instead of the state vector are expanded into series. Therefore, neither the number of state vectors nor the order of the matrices increases, and the proposed model has a simple structure similar to the SSA model. In addition, as a time-invariant polynomial model, the calculation and analysis of the proposed model are much simpler than the time-variant exact model. In order to prove the above advantages of the proposed model, the general expression of the proposed model is derived and the proposed model is compared with other models. These analyses and comparisons are verified through the simulation and experimental results.