Optimal pivot strategies for load-flow calculation

• Published in: International journal of electrical power & energy systems Vol. 9; no. 2; pp. 66 - 82
• Main Author: Wendel, H.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.1987; Elsevier
• Subjects: Applied sciences; Electrical engineering. Electrical power engineering; Electrical power engineering; Exact sciences and technology; load flow; network analysis; Operation. Load control. Reliability; Power networks and lines; power system element modelling; power system element modelling; load flow; network analysis; Power system load; Electrical network; Calculating method; Optimization; Load flow
• ISSN: 0142-0615; 1879-3517
• DOI: 10.1016/0142-0615(87)90027-5

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.