Relaxation/Newton methods for concurrent time step solution of differential-algebraic equations in power system dynamic simulations

A class of algorithms that exploits the concurrent solution of many time steps is presented. By applying a stable integration method, the overall algebraic-differential set of equations can be transformed into a unique algebraic problem at each time step. The dynamic behavior of the system can be obtained by solving an enlarged set of algebraic equations relative to the simultaneous solution of many time steps. A class of relaxation/Newton algorithms can be used to solve this problem efficiently. This formulation permits easy implementation of multigrid techniques. The convergence rates and computational complexity of the algorithms are discussed. Test results for realistic power systems confirm theoretical expectations and show the promise of a several-fold increase in speed over that obtainable by traditional parallel-in-space approaches. The synergism obtainable by parallelism in time and in space can provide speed-up adequate for online implementations of transient stability analysis.>