A primal–dual interior-point method to solve the optimal power flow dispatching problem

This paper presents a primal–dual path-following interior-point method for the solution of the optimal power flow dispatching (OPFD) problem. The underlying idea of most path-following algorithms is relatively similar: starting from the Fiacco–McCormick barrier function, define the central path and loosely follow it to the optimum solution. Several primal–dual methods for OPF have been suggested, all of which are essentially direct extensions of primal–dual methods for linear programming. Nevertheless, there are substantial variations in some crucial details which include the formulation of the non-linear problem, the associated linear system, the linear algebraic procedure to solve this system, the line search, strategies for adjusting the centring parameter, estimating higher order correction terms for the homotopy path, and the treatment of indefiniteness. This paper discusses some of the approaches that were undertaken in implementing a specific primal–dual method for OPFD. A comparison is carried out with previous research on interior-point methods for OPF. Numerical tests on standard IEEE systems and on a realistic network are very encouraging and show that the new algorithm converges where other algorithms fail.