The allure of parallel processing is that this technology has the potential to be cost effective on computationally intense problems, which are typical of many power systems analysis. But in reality, the formulation of most power system problem's in use today are not readily applicable to parallel computing. For these problems, parallel (or near-parallel) formulations have to be found to adapt each of them to the intended parallel architecture to achieve the best computational efficiency.; Various power system problems are characterized by the solution of a large set of non-linear algebraic equations. The most popular sequential solution scheme to date is to linearize the nonlinear functions and obtain the solution by iteratively applying matrix factorization and forward and backward substitutions. This algorithm is greatly speeded up by incorporating sparse matrix techniques, but these are thought by many to be almost unparallelizable because of the strong precedence relations among the computations. Two alternative parallel linear matrix equation solution methods are developed. One is based on the partial matrix inversion concept enhanced by a new, high performance node reordering and partitioning scheme, which converts the substitutions into parallelizable matrix-vector product series. The other is a complete parallel factorization and substitution algorithm which achieves parallelism through the swapping of independent operations. It is as efficient as the sparse factorization and substitution algorithms on sequential computers, but adaptable to a change in the number of processors. Performance analysis is presented and a parallel overhead model is proposed to help improve the speedup gain estimation.; The first application of the proposed parallel matrix equation algorithms is the power flow, which is the most used power system computation and is often embedded in other problems. Test results using the popular Newton and Fast Decoupled methods with actual power system data are presented to show the effectiveness of the proposed algorithms.; Transient stability analysis is the most time consuming power system problem, and is also the one to have attracted most attention for the application of parallel computing mostly because of the need for on-line security analysis. The network solution part in time domain simulation requires repetitively solving sparse matrix equations, which is the main obstacle to parallel computing, while the machine equation part is readily parallelizable. The proposed parallel matrix equation algorithms are applied and shown to be very effective.; The research work has for the first time demonstrated, with a range of power flow and transient stability analysis programs, that a magnitude speedup gain can be obtained not only in theory, but in real practice for power system computations on presently available parallel computers. The major factors affecting the speedup gains in the parallel computing are also studied. The new parallel techniques apply to existing algorithms making it possible to easily modify production grade codes in use today; this is demonstrated on a transient stability program from a large electric utility.
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