  Simulation is an efficient tool in the design and control of power electronic
systems. However, quick and accurate simulation of them is still challenging,
especially when the system contains a large number of switches and state
variables. Conventional general-purpose integration algorithms assume
nonlinearity within systems but face inefficiency in handling the piecewise
characteristics of power electronic switches. While some specialized algorithms
can adapt to the piecewise characteristics, most of these methods require
systems to be piecewise linear. In this article, a numerical derivative-based
flexible integration algorithm is proposed. This algorithm can adapt to the
piecewise characteristic caused by switches and have no difficulty when
nonlinear non-switching components are present in the circuit. This algorithm
consists of a recursive numerical scheme that obtains high-order time
derivatives of nonlinear components and a decoupling strategy that further
increases computational efficiency. The proposed method is applied to solve a
motor derive system and a large-scale power conversion system (PCS) to verify
its accuracy and efficiency by comparing experimental waveforms and simulated
results given by commercial software. Our proposed method demonstrates
several-fold acceleration compared to multiple commonly used algorithms in
Simulink.
