GPU-accelerated Poincaré map method for harmonic-oriented analyses of power systems

A parallel Poincaré map method based on graphic processing units (GPU), suitable for harmonic-oriented studies, is presented in this paper. It relies on a Newton method and a transition matrix computed by columns on the GPU. A parallel kernel for the Trapezoidal Rule integration routine allows solving the set of ordinary differential equations, whilst sparse matrices involved in the Trapezoidal Rule are stored at the GPU using a Compressed Sparse Row (CSR) format. Direct and iterative solvers based on LU decomposition and Krylov subspace methods are used to solve system of equations arising from the Newton-Raphson algorithm. Results in terms of convergence to the periodic steady-state and speedup factors of order 7 confirm that this novel GPU-based approach is an efficient parallel version of the Poincaré map method. An advanced memory optimization approach based on pinned memory and asynchronous transfers provides further computational savings of the order of 20%.