Small-Step Discretization Method for Modeling and Stability Analysis of Cascaded DC–DC Converters With Considering Different Switching Frequencies

Cascaded dc–dc converter is the main component of the dc distributed power system. It is valuable to establish the accurate model for studying the stability of cascaded dc–dc converters. However, the cascaded dc–dc system has many operating modes, such that the existing classic methods, e.g., state-space average model and discrete-mapping model, are difficult to explore to analyze cascaded dc–dc converter system, especially that with different switching frequencies. To overcome this drawback, this article promulgates a new modeling and stability analysis method for cascaded dc–dc converter. Small-step method, discretization method, and Euler method are exploited to modeling. All stages of the system are considered, therefore, accurate; and stability is divided into three categories according to the different definitions. Then, the cascaded systems with the same or different switching frequencies are studied using the presented method. As an example, two-stage peak current-mode controlled boost converter is scrutinized. Finally, simulations and experiments are manipulated to verify the correctness of the new method.