Piecewise Newton-Raphson load flow ߞAn exact method using ordered elimination

Abstract

Based on the Diakoptic Equation, an algorithm is developed for block diagonalizing and solving any given set of linear simultaneous equations. This algorithm is then applied to block diagonalize and solve the Jacobian matrix and hence the load flow problem. The algorithm is perfectly general and can be appliedto any set of linear simultaneous equations, symmetrical or asymmetrical and hence can be applied to other fields as well. Applied to the load flow problem, it requires to consider a few more additional right hand side vectors to the Jacobian, and further an inter-subdivision matrix is to be formed and solved. No matrix inversion is required in this method and hence sparsity can be exploited to the maximum extent. Practical steps are given, so that the algorithm can be implimented by others.