Newton-Homotopy Algorithm of Ill-Conditioned Load-Flow

The ill-condition of the load-flow is caused by a variety of reasons. Among them, heavy load and a long line of radiation type slip(large r/x) are the two important reasons. In connection with the ill-conditon above, Newton-homotopy algorithm is introduced in this paper. The algorithm mixes the locally quadratic convergence of Newton-raphison with wide range convergence of homopoty algorithm, so it improves the ill-condition of Jacobian matrix in the process of load-flow calculating, and speeds the convergence. Finally, several examples show the efficiency of the algorithm.