Sparsity analysis and optimization for state-space-based simulation of power electronic systems

Computer-aided analysis tool is playing an important role in the design of power electronics converters. However, with the increase of system scale and complexity, the existing simulation tools show lack of efficiency, especially when taking parasitic elements into account to analyze their influences on the system reliability. The challenges of simulating such systems mainly come from the high-dimension stiff mathematical equations and variable topologies brought by switching events. This paper derives the block sparsity of the state equation matrices of large-scale power electronic systems by exploiting their topological characteristics. Thus it can work as a general tool to accelerate the state-space-based simulations of such systems by greatly reducing the computational cost of both matrix updating and numerical integration process at each simulation step without sacrificing accuracy. Especially, for stiff problems where implicit solvers are involved, a subsystem reordering strategy is adopted to make better use of the sparsity in optimizing numerical integration. A four-port solid-state transformer for the integration of renewable energy into distribution network, with in total 87 submodules, hundreds of switching devices, and pF/nH-level parasitic elements is simulated with the proposed method. About 4-fold acceleration contributed by the proposed method independently is observed and the high-frequency oscillation observed in experiments is reproduced, which verifies its efficiency and accuracy.