Solving large-scale reactive optimal power flow problems by a primal–dual M2BF approach

• Published in: Optimization and engineering 2020, Vol.21 (2), p.485-515
• Main Authors: Pinheiro, Ricardo B. N. M., Nepomuceno, Leonardo, Balbo, Antonio R.
• Format: Article
• Language: English
• Subjects: Algorithms; Control; Engineering; Environmental Management; Financial Engineering; Hessian matrices; Mathematics; Mathematics and Statistics; Numerical methods; Operations Research/Decision Theory; Optimization; Penalty function; Power flow; Reactive power; Research Article; Systems Theory
• ISSN: 1389-4420; 1573-2924
• DOI: 10.1007/s11081-019-09451-4

In this paper, we propose a predictor–corrector primal–dual approach for the doubly modified logarithmic barrier function ( M 2 BF ) method in order to solve Optimal Reactive Power Flow (ORPF) problems. The M 2 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 M 2 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.