Approximate sparse vector techniques for power network solutions

Four approximate sparse vector (SV) techniques to speed up power network computer applications are described. Three are approximations of established SV techniques. Skip forward is an approximation of fast forward, skip back is an approximation of fast back, and skip factor update is an approximation of factor update. Skip back by columns (SBC), an entirely new technique that has no SV counterpart, is an approximation of full back substitution by columns. Numerical examples showing the effectiveness of approximate sparse vector techniques for selected applications are presented. It is concluded that approximate SV techniques can be used to speed up solution of sparsity-oriented solution methods for large power network problems. They are most effective for large problems in which controllable speed-accuracy trade-offs are advantageous. The techniques themselves are simple, easy to implement, and can be substituted directly for their counterpart SV techniques in some applications.<>