Piecewise broken line approximation method implementation in stability analysis of bidirectional buck/boost converters cascaded system

Closed-loop input and output impedance of converters are nonlinear functions and with too many converter parameters, which causes it very difficult to do quantitative analysis of converters cascaded system stability with Middlebrook impedance criterion. In this paper, Piecewise Broken Line Approximation Method (PBLAM) is proposed to simplify the closed-loop output and input impedances of converters. A cascaded system with two bidirectional Buck/Boost converters is used as an example. The impedances after simplification are piecewise linear and have few converter parameters in each piece. With the simplified impedances and Middlebrook impedance criterion, system stability is analyzed. Conditions to guarantee system stability are derived. With the analysis, the derived conditions in this case are not practical. Another dividing way of capacitors on the cascaded side is proposed, based on which practical conditions to guarantee system stability and corresponding system stability improvement methods are derived. To evaluate the derived conditions and system stability improvement method, calculation in Matlab and time domain simulation in Simplis of a two bidirectional Buck/Boost converters cascaded system are done. The results of the simulation approve the derived results of this paper are precise and practical.