Solving large-scale reactive optimal power flow problems by a primal–dual $$\hbox {M}^{2}\hbox {BF}$$ approach

Abstract

In this paper, we propose a predictor–corrector primal–dual approach for the doubly modified logarithmic barrier function ($$\hbox {M}^{2}\hbox {BF}$$) method in order to solve Optimal Reactive Power Flow (ORPF) problems. The $$\hbox {M}^{2}\hbox {BF}$$ is a modification of the Polyak’s modified logarithmic barrier function (MBF) and is also a particular element of a recent family of nonquadratic penalty functions for augmented Lagrangian methods for handling convex problems only with inequality constraints. We also propose a global convergence strategy to be inserted in the proposed algorithm, which is developed over weak assumptions concerning the primal Hessian matrix. The resulting predictor–corrector primal–dual $$\hbox {M}^{2}\hbox {BF}$$ approach is applied for solving ORPF problems involving power systems with 57, 89, 118, 200, 300, 1354, 2007 and 2869 buses. A comparison with two state-of-the-art methods is performed. Numerical results show that the proposed approach is competitive and capable of solving ORPF problems for small to large-scale power systems.