Relaxation-Newton methods for transient stability analysis on a vector/parallel computer

In this paper, the implementation of transient stability analysis programs on a vector/parallel computer is considered. The windowing technique is adopted. The parallelism-in-time is exploited by using the Gauss-Jacobi or the Gauss-Seidel methods to relax the dependency between time steps within a time window; the Newton method is employed to solve the discretized equations corresponding to each time step exploiting the parallelism-in-space. The computation of the bus voltage and state variables pertaining to different time steps is carried out in parallel by the processors available. A reordering of the operations relative to the synchronous machine equations is introduced to obtain an efficient use of the vector hardware of the computer. The W-matrix method is employed to solve the network equations. Test case simulations are performed for the IEEE 118 bus system and two US networks with 662 and 904 buses using a 4-processor CRAY Y-MP8/464 computer. The proposed vector/parallel programs achieve substantial speed-ups over a scalar reference program based on the Very Dishonest Newton method. The synergy between vector and parallel processing allows speed-ups in excess of 22 to be attained for the US 904 bus network; run times are always shorter than the simulation interval. Best results are obtained by implementing the proposed travelling window approach. Thanks to a suitable task partitioning, the apparently sequential Gauss-Seidel approach is demonstrated to be an effective alternative to the Gauss-Jacobi relaxation scheme