Scalability of Parareal for Large Power Grid Simulations

The Parareal in time algorithm belongs to a class of temporal decomposition for a time parallel solution of differential equations. This paper investigates the approaches through which the Parareal algorithm can be deployed under a Message Passing Interface (MPI) environment. A state space model of a 10 state cascaded π network model of a transmission line, representing the computational load and nature of ordinary differential equations (ODE) in an electrical power grid/system, is used for experimentation. Two types of implementation approaches, Master Worker and Distributed, are discussed and scaling tests are performed. Analytical expressions for each approach based on the idling and non-idling processor deployment are derived. Using the expressions, weak scaling is performed to show the conditional scalability of Parareal under growing state size and integration steps.