Interior–exterior point method with global convergence strategy for solving the reactive optimal power flow problem

• We propose a predictor–corrector primal–dual nonlinear rescaling method with global convergence strategy.
• We apply the proposed method for solving the reactive optimal power flow.
• We propose a novel updating rule for the Lagrange multiplier estimates.
• We show the efficiency of the method for systems having up to 300 buses.

This paper proposes a predictor–corrector primal–dual modified log-barrier interior–exterior point method with global convergence and cubic fitting strategies for solving the Reactive Optimal Power Flow (ROPF) problem. The interior–exterior approach is a variant of the primal–dual nonlinear rescaling method, recently proposed. The application of the global convergence strategy produces only descent directions, even if the optimization problem is non-linear and non-convex. The application of a cubic fitting strategy for modified log-barrier functions preserve the continuity and also the first and second-order derivatives of the logarithm near the boundary of the feasible set. Some updating rules for the Lagrange multiplier estimates are theoretically and numerically evaluated. Numerical tests and comparisons with classical interior point methods, involving the electrical systems of 3, 9, IEEE-14, IEEE-30, IEEE-57, IEEE-118, IEEE-162 and IEEE-300 buses, are performed, which demonstrate the robustness and efficiency of the method.