Embedding spatial decomposition in parareal in time power system simulation

We propose an approach for combining two decompositions in power system simulation, temporal and spatial, with a goal to achieve faster simulation time than utilizing either one of them alone. The proposed approach builds upon the structure of the Parareal algorithm for temporal decomposition and explores an efficient way of embedding the spatial decomposition into its coarse and fine solutions. This introduces two types of simultaneous parallelism in power system simulations - parallelism between system areas and between coarse integration intervals for time integration. The results from the application of the proposed approach are shown on a two-area system comprised of the IEEE 16-machine, 68-bus, and the IEEE 50-machine, 145-bus system.