Power Grid Simulation using Matrix Exponential Method with Rational Krylov Subspaces

Abstract: One well adopted power grid simulation methodology is to factorize matrix once and perform only backward forward substitution with a deliberately chosen step size along the simulation. Since the required simulation time is usually long for the power grid design, the costly factorization is amortized. However, such fixed step size cannot exploit larger step size for the low frequency response in the power grid to speedup the simulation. In this work, we utilize the matrix exponential method with the rational Krylov subspace approximation to enable adaptive step size in the power grid simulation. The kernel operation in our method only demands one factorization and backward forward substitutions. Moreover, the rational Krylov subspace approximation can relax the stiffness constraint of the previous works. The cheap computation of adaptivity in our method could exploit the long low frequency response in a power grid and significantly accelerate the simulation. The experimental results show that our method achieves up to 18X speedup over the trapezoidal method with fixed step size.