An Explicit and Unconditionally Stable Finite Difference Scheme for the Fast Transient Analysis of a Power Distribution Network

Generally, an explicit difference scheme has the numerical stability condition which constrains the time step size, and this condition depends on the lowest reactance component. If the time step size that does not fulfill the numerical stability condition is used, unstable modes arise, and we fail the transient analysis. In this paper, we propose an explicit and unconditionally stable finite difference scheme in which the constraint of time step size is overcome by removing the unstable modes. Numerical results show that the proposed method is quite effective to perform the fast transient simulation of power distribution networks with extremely small apertures.