Parallel processing in dynamic simulation of power systems

The dynamic behaviour of a large interconnected electric power system is characterized by a simultaneous set of nonlinear algebraic and ordinary differential equations. The solution is obtained by numerical methods and the simulation of the transient behaviour for a few seconds after a fault is the standard analytical procedure used in planning and operational studies of the system. The need for on-line simulation in near real time for more efficient operation has encouraged the search for faster solution methods and the use of parallel computers for this purpose has attracted the attention of many researchers. The success of parallelization depends on three factors: the problem structure, the computer architecture, and the algorithm that takes maximum advantage of both. In this problem, the generator equations are only coupled through the electrical network providing some parallelization in (variable) space, and a solution is needed at each time step leading to some parallelization in time (waveform relaxation). However, since the problem formulation is not completely decoupled, parallel algorithms can only be developed by trading off any relaxation with a degradation in convergence. The fastest sequential algorithm used today is the combination of implicit trapezoidal integration with a dishonest Newton solution. The Newton algorithm is not parallel at all but has the fastest convergence while a Gauss-Jacobi algorithm is completely parallel but converges very slowly. A relaxation of the Newton algorithm appears to be a good compromise. As for the parallel hardware, the coupling seems to require significant communication between processors thus favouring a data-sharing architecture over a message-passing hypercube. Special architectures to match the problem structure have also been an area of investigation. This paper elaborates on the above issues and assesses the present state-of-the-art.