Efficient Transient Analysis of Power Grids

An efficient technique to establish a constant matrix with variable step-size multi-step formulas is presented for transient analysis of linear power grids. Instead of deriving new formulas with a constant leading coefficient, it is shown that, if the step change is relatively small, a constant matrix can also be obtained by carefully allocating the integration points and using the existing variable step-size multi-step formulas with proven accuracy and stability. Thus, with the technique proposed in this paper, LU decompositions are needed only for large step changes, and the computational efficiency of variable step methods can, therefore, be improved by effectively reducing the number of LU decompositions in transient analyses.