A multi-level graded-precision model of large scale power systems for fast parallel computation - Huang, G.; Abur, A.; Tsai, W.K. (Mathematical and computer modelling, 1988)
A novel approach to the large electric power flow analysis is introduced and evaluated. The approach is novel in various ways. It exploits the degree of “criticality” of the power system by constructing their M-level model and the associated algorithmic arrangement as one unit. Conventionally, engineers supply the models and problem statement, and then experts in numerical methods design algorithms to solve this numerically. Elimination of this interface creates a truly engineering computational approach, which has been found, in our preliminary work, to speed up computation several folds. Systems of larger sizes with more levels should produce even larger savings. Solution algorithms are executed parallelly from node to node of a set of the ith level criticality with a detailed model on the critical portion and an aggregated model describing the less critical part. This solution is then passed down to the (i + 1)th level - the solution is disaggregated and is used as the initial estimate for the (i + 1)th level. This aggregation/disaggregation procedure can be top-down only (i.e. one-pass), or can be run iteratively (i.e. multi-pass). This procedure is independent of numerical algorithm used at each level. To simplify the parallel implementation, a Jacobi type numerical algorithm is employed at each level. The supporting argument for the choice of Jacobi type numerical methods is discussed. The advantage of this method is that approximate solutions are available continually with improving degree of accuracy, and these approximate solutions converge to the exact solution; while the traditional methods do not provide a meaningful solution unless the overall computation is completed. This feature is very attractive when the speed of obtaining a reasonable solution in part of the system is critical. Also, this approach accelerates the convergence of the overall system solution and can be implemented parallelly.