Frequent matrix factorizations due to power electronic switch commutations are computationally expensive. This paper addresses this burden by treating power electronic switches as dependant sources instead of time-varying resistors. The resulting network matrix is constant, and does not require re-factorization when switches commutate. Three power electronic switches are presented and discussed for both nodal and mesh equation formulations. A case study at the end shows that the run-time for a power system with >200 switches when using the switching approach presented herein can reduce from 8 hours to under 15 minutes, which is a speedup of 40x.