A Study Of Precise Modeling And Stability Analysis Methods For DC-DC Switching Converters

DC-DC switching converter is very important in power electronics systems, the development of the theoretical research lags far behind its practical application. As modern society requires higher performance of switching converter day by day, the traditional modeling and analysis methods can’t satisfies the design demands of switching converter. The switching link of the converter is averaged in the modelling of single converter by the traditional small signal modelling method, consequently the strong nonlinearity is ignored, so the model is not accurate. And the Middlebrook impedance criterion, which is used for the stability analysis of cascaded converters, is based on the engineering experience, and the solution for impedance is too complicated, it cannot guarantee the accuracy as well. So, this thesis takes DC-DC switching converter as an example, studies the precise modeling and stability analysis methods for both single and cascaded DC-DC switching converters.For single DC-DC converter, the thesis takes describing function method to do the modelling and stability analysis. Taken a boost converter as an example, the describing function of the switching link is deduced, the model based on describing function is established and the stability criterion is given. According to the simulation and experimental results, it can be concluded that the stability analysis based on the proposed model with describing function method is more accurate and effective in the transition interval from stable region to unstable region than that base on traditional small signal method, and the transition interval is further verified by bifurcation diagram. Finally, the low frequency oscillation phenomenon appeared in the transition interval is analyzed.For cascaded DC-DC converters, the Floquet theory is taken to do the modelling and stability analysis. Firstly, the feasibility and advantages of that Floquet theory is applied into DC-DC converter are analyzed. Further, taken a two-stage cascaded buck converter as an example, the transfer matrix based on Floquet theory is deduced and stability criterion is given. the simulation and experiment verifies the correctness and accuracy. Finally, a unified form of the transfer matrix based on Floquet theory for multiple cascaded buck converters is deduced after that the stability of a three-stage cascaded buck converter is analyzed based on Floquet theory, which is the first step of the application for Floquet theory used in multi-stage cascaded buck converters.