Parallel algorithm based on symplectic Radau method for transient stability simulation

The research about parallel-in-time algorithms for transient stability parallel computation focuses on the solving effectively the contradiction between parallelism-in-time and convergence, which is the main problem existed for the research topic. In this paper, the s-stage and 2s-1 order symplectic Radau method is adopted for transient stability simulation. Based on the special matrix structure of the symplectic Radau method, a simple matrix transformation technique, which is similar to the so-called Jordan decomposition, is used for the decoupling of the computational task associated with the different time-points, and thus yields a new parallel-in-time algorithm where the computational task involved in different time-points can be solved independently or parallelly. The mathematical derivations and tests in IEEE 118-bus and IEEE 145-bus power system show that, the proposed algorithm is fully parallel-in-time, and at the same time keeps the convergence characteristics of Newton method, thus presents an effi