AC Optimal Power Flow: a strengthened SDP relaxation and an iterative MILP scheme for global optimization
Résumé
The Alternating-Current Optimal Power Flow (ACOPF) is a fundamental optimization problem for power system analysis. Due to the nonconvexity of power flow equations, the ACOPF is a difficult problem both in theory and in practice. Thanks to Interior Point (IP) algorithms, developed starting in the 90s, the computation of ACOPF feasible solutions and local optima is accessible, even for instances of several thousand nodes. During the last decade, researchers have been focusing on the design and solution of convex relaxations to bound the optimality gap of feasible solutions found by IP algorithms. Despite these advances, finding global optima of ACOPF instances with several hundreds of buses is challenging for state-of-the-art algorithms, mostly branch-and-bound solvers based on Second-Order Cone Programming (SOCP), Quadratic Convex (QC) or Semidefinite Programming (SDP) relaxations.
In this quest towards global optimality, our contribution is threefold: (i) we propose a new strengthening of the SDP relaxation based on angle difference limits on lines (ii) we combine feasibility and optimality bound-tightening methods with a dynamic programming algorithm to propagate the angles domain reduction (iii) we propose an original global optimization algorithm that proceeds by solving a sequence of dynamically generated Mixed-Integer Linear Programming (MILP) problems. We apply our global optimization algorithm on the IEEE PES PGLib benchmark and compare the optimality gaps with other recent and state-of-the-art global optimization approaches [5,9] that use this reference benchmark. Our algorithm closes the optimality gap for 19 over 30 instances. For 7 of these 19 instances, it is the only one among the three benchmarked algorithms to reach global optimality. For 25 over 30 instances, our approach has the lowest optimality gap.
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