Optimal pivot strategies for load-flow calculation - Wendel, H. (International journal of electrical power & energy systems, 1987)
The determination of optimal sequences of pivots for a matrix M is a well-known but open problem in load-flow calculation. Optimal means that the system Mx = b can be solved by Gauss's algorithm, where the number of arithmetic operations is minimal; the space to store the triangular factors of M should also be minimal. This problem is commonly studied by considering the equivalent (general) minimum fill-in problem. This graph-theoretical optimization problem is the subject of this paper. A valuable tool to attack it is the Initial Theorem due to Bertele and Brioschi. We demonstrate the feasibility of this method by calculating optimal orderings for the well-known AEP test networks. The Initial Theorem can be generalized to a special class of graphs which represents the zero, non-zero pattern of the Jacobian matrix, derived from the nonlinear network equations. Additionally, a separation approach is presented, producing (if necessary assumptions are satisfied) optimal orderings of the global network which are composed of optimal orderings of the (local) sub-networks.