A comparison amongst sub-optimal ordering schemes for power systems accompanied with a GA-based optimal ordering method

This paper presents a review over famous methods of solving sparse linear equations and a comparison amongst the most famous sub-optimal ordering schemes in order to speed up the calculations needed for power systems analysis. A GA-based algorithm is also proposed to verify the efficiency of the existing methods whose goal is to reach the optimal reordering to minimize the number of fill-ins, the number of added nonzero elements created during so called elimination process. A remarkable comparison is, then, made between different reordering schemes using several IEEE standard power networks based on number of fill-ins, and calculation time for DC load flow, fast decoupled load flow, and LU factorization. Approximate minimum degree, for the first time, is used in power systems analysis, and has been shown to be the best method amongst the others.