9526142 Siljak Transient stability simulation is among the most important and frequently performed computation in power systems analysis. Accelerating this process efficiently with parallel computers is of enormous practical significance, and is the focal point of the proposed research. Our specific objective will be to design and test parallel simulation algorithms based on the balanced Border Block Diagonal (BBD) decomposition, which is ideally suited for mapping sparse matrix problems onto multiprocessor architectures, and secures both good load balancing an low intercommunication between the processors. To significantly broaden the scope of the proposed parallel transient stability simulation, well established epsilon decompositions will be applied to sparsify the Jacobian that arises in solving the discretized algebraic-differential equations by Newton's method. Preliminary results indicate that in electric power systems very significant sparsification can be achieved by discarding sufficiently small elements in blocks of matrices L and U where the fill-in is substantial. In this context, and additional objective will be to develop algorithms for identifying coherent groups of generators in large power networks via epsilon decompositions of the Jacobian, which will be linear in complexity and serve as a basis for transient stability computations. The balanced BBD and epsilon decompositions offer a new approach to the design of decentralized control of large power systems. The BBD structure will be used to parallelize the solutions of Lyapunov and Riccati matrix equations, which are of fundamental importance in the decentralized stabilization and optimization of dynamic systems. Initial experiments indicate that this method can be used to stabilize very large systems with as many as several thousand state variables. ***
