Power Flow of Unsolvable Power Systems using Combination of Jacobian and Nonsingular Diagonal Matrices

Based on the determinant of the Jacobian matrix in the power flow (PF) problem, power systems are categorized to well-conditioned, ill-conditioned and unsolvable systems. In this paper, a novel and simple approach based on Newton technique is presented to solve the PF problems in the unsolvable power flow cases in the power systems. The presented method is based on combination of the inverse of Jacobian matrix to a nonsingular diagonal matrix. Application of the proposed method causes to change the zero eigenvalues to new values in their neighborhoods. The application of the presented algorithm in various scale power systems (2-bus, 11-bus, 14-bus and 118-bus) indicates that the proposed formulation decreases the computation time and number of iterations in comparison with benchmark methods.