Parareal in Time for Fast Power System Dynamic Simulations

Recent advancements in high-performance parallel computing platforms and parallel algorithms have significantly enhanced the opportunities for real-time power system protection and control. This paper investigates application of Parareal in time algorithm for fast dynamic simulations. Parareal algorithm belongs to the class of temporal decomposition methods which divide the time interval into sub-intervals and solve them concurrently. Time-parallel algorithms face the difficulty of providing correct initial conditions for all the sub-intervals which impact the convergence rates. Parareal overcomes this difficulty by using an approximate trajectory. It has become popular in recent years for long transient simulations (e.g., molecular dynamics, fusion, reacting flows). This paper presents an approach for reliable implementation of Parareal with detailed models of power systems including saturation. Windowing approach is proposed for improving the convergence. Parareal is compared with the Newton-based time-parallel method. Effectiveness of the algorithm is analyzed by parallel emulation using extensive case studies on 10-generator 39-bus system and 327-generator 2383-bus system for various disturbances. Parareal with simulation windows of 1 s have shown convergence in 1 to 3 iterations for majority of the simulated cases, irrespective of the size of the system and nature of the disturbance. All the cases tested have converged with the proposed implementation.