A Fast and Stable Method for Modeling Generalized Nonlinearities in Power Electronic Circuit Simulation and Its Real-Time Implementation

Nonlinearities have been the major obstructions that limit the computational efficiency in power electronic circuit simulation for a long time. Yet there is no standard way for dealing with them. This paper presents a new method that makes the handling of nonlinearities fast and stable. In the proposed method, nonlinearities are transformed into a uniform representation - a constant resistor in parallel with a companion current source, thus making the system admittance matrix constant for fixed time-step simulation. To solve for the corresponding companion current source, nonlinearities are treated as either current or voltage sources and a diagonal time-varying matrix equation is developed. Three methods are proposed for solving the matrix equation - precomputed inversion or factorization, modified Gaussian elimination, and updating inverse using the Sherman-Morrison formula - that can fit different system sizes and applications. The proposed method is validated by two common power electronic converter topologies, both in offline and real-time simulation. Offline tests show that the proposed method achieved the same accuracy with the mature simulation software while being more than ten times faster. The same test cases are also implemented into field programmable gate arrays based real-time simulation experiments for verification.