A new formulation and its solution method for a maximum loading point in electric power systems

Abstract

This paper proposes a new efficient formulation and its solution method for a maximum loading point or saddle node bifurcation point in electric power systems. This point, corresponding to a tip of the P (Q)-V curve, is characterized by singularity of the load flow Jacobian. The proposed formulation is of dimension n+1, instead of 2n+1 in the standard formulation, for n-dimensional load flow equations. The proposed method uses 1-dimensional singularity condition, obtained from a reduction of the standard n+1-dimensional singularity conditions. For this reduction, one of the diagonal elements of the load flow Jacobian is selected. We also propose an index for this selection to make the proposed method reliable. The solution for the proposed formulation can effectively be obtained based on the Newton-Raphson method with sparse matrix techniques. The computational performance of the proposed method is demonstrated on 6, 14, and 118 bus test systems.