A Computationally Efficient Method for Solving Mixed-Integer AC Optimal Power Flow Problems

TL;DR

The paper tackles the challenging mixed-integer AC-OPF problem arising from stepwise controllable devices, which makes exact solutions intractable for real-time use. It introduces an iterative deflation algorithm that solves a continuously relaxed version of the problem and progressively eliminates discrete setpoints one at a time, achieving linear growth in computational effort with the number of integer variables. Simulation on a large HV grid (SimBench HV) demonstrates that deflation substantially reduces required curtailment compared with a standard two-step approach while maintaining feasible computation times. The method offers a scalable, practical path for congestion management in distribution HV/MV grids with legacy stepwise-controllable equipment.

Abstract

Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is generally hard to solve optimally. Existing methods for solving MI-AC-OPF problems usually suffer from either limited accuracy or computational intractability, making them impractical for real-world applications. To address these challenges, we propose an efficient iterative deflation approach providing high-quality approximate solutions. In each iteration, a continuously relaxed version of the MI-AC-OPF problem is solved and one candidate integer value is systematically eliminated based on the evaluation of a simple power flow result. The computational complexity of the proposed algorithm grows linearly with the number of integer optimization variables, ensuring scalability. Simulations demonstrate that the proposed approach achieves significant improvements in solution accuracy compared to a state-of-the-art approach. Thus, the proposed method is promising for solving practical MI-AC-OPF problems.

Figures (6)

• Figure 1: Flowchart of the state-of-the-art two-step algorithm
• Figure 2: Flowchart of the proposed deflation algorithm
• Figure 3: Evolution of objective function value
• Figure 4: Power curtailment vs. number of stepwise controllable generators
• Figure 5: Visualisation of improvement achieved by deflation method