Load flow solution for ill-conditioned power systems by quadratically convergent Newton-like method

This paper presents an application of mathematician K.M. Browns method to load-flow solution. The method is particularly effective for the solution of ill-conducted systems of nonlinear algebraic equations. It is a variation of Newtons method incorporating Gaussian elimination in such a way that the most recent information is always used at each step of the algorithm; similar to what is done in the Gauss-Seidal process. The iteration converges locally and the convergence is quadratic in nature. It is not necessary for the user to provide partial derivatives of load-flow equations in the computer program. A general discussion of ill-conditioning of a system of algebraic equations is given, and it is also shown by fixed- point formulation that the proposed method falls in the general category of successive approximation methods. Digital computer solutions by the proposed method are given for several ill-conditioned power systems for which the standard load-flow methods failed to converge. A comparison of this method with the standard load-flow methods is also presented for the well-conditioned AEP 30 and 57 bus systems.