Sigmoid Function–Based Discontinuous Feedforward Current Ripple Modeling for Stability Analysis of Cascaded Converter

The cascaded converter, under the switching ripple interaction between source and load converters, can be described as a high-order system with multiple switching state sequences (SSSs). This poses a hindrance to investigating the stability effects of feedforward current ripple (FCR). In general, replacing FCR with a finite Fourier series can remove this hindrance. However, this method has limitations for discontinuous FCR (DFCR). To tackle this issue, a sigmoid function–based equivalent modeling method is proposed to explore the stability effect of DFCR from the load converter operating in continuous conduction mode. Take a cascaded buck converter as an example, the effectiveness of the proposed method is demonstrated. Then, an equivalent model with only an SSS is established. By utilizing Filippov's method and Floquet theory, the monodromy matrix of the equivalent model is obtained and the corresponding eigenvalue analyses are carried out. Additionally, the stability boundaries predicted by theoretical analyses are verified by those obtained from circuit simulations. The results manifest that with the proposed method, the modeling and stability analysis of the cascaded converter with DFCR can be simplified, and the stability effects of DFCR can be investigated effectively. Finally, the correctness of the theoretical and simulation results is confirmed by the experimental results.