Alternating Methods for Large-Scale AC Optimal Power Flow with Unit Commitment

TL;DR

This paper tackles large-scale SCUC-ACOPF by introducing a spatial-temporal decomposition that splits MILP unit-commitment decisions per bus from nonlinear, time-separable ACOPF subproblems. It then applies a penalty alternating direction method (pADM) to coordinate the two blocks, with convergence to a partial optimum and practical heuristics including a second-order cone (SOC) relaxation, contingency screening, and ramp/energy restrictions to enable fast, scalable solving. The authors develop a tailored algorithm that fixes discrete decisions in a final subproblem to guarantee feasibility, while preserving flexibility through ramp-based bounds and energy-violation relaxations, achieving an average optimality gap of about 1.33% to a SOC-derived dual bound on GO Challenge 3 data (up to 8,000 buses and 48 periods) within tight time limits. The approach also yields a computable dual bound and demonstrably improves upon relevant benchmarks in both solution quality and runtime, indicating strong practical impact for security-constrained UC with AC power flows in modern grids.

Abstract

Security-constrained unit commitment with alternating current optimal power flow (SCUC-ACOPF) is a central problem in power grid operations that optimizes commitment and dispatch of generators under a physically accurate power transmission model while encouraging robustness against component failures. SCUC-ACOPF requires solving large-scale problems that involve multiple time periods and networks with thousands of buses within strict time limits. In this work, we study a detailed SCUC-ACOPF model with a rich set of features of modern power grids, including price-sensitive load, reserve products, transformer controls, and energy-limited devices. We propose a decomposition scheme and a penalty alternating direction method to find high-quality solutions to this model. Our methodology leverages spatial and temporal decomposition, separating the problem into a set of mixed-integer linear programs for each bus and a set of continuous nonlinear programs for each time period. To improve the performance of the algorithm, we introduce a variety of heuristics, including restrictions of temporal linking constraints, a second-order cone relaxation, and a contingency screening algorithm. We quantify the quality of feasible solutions through a dual bound from a convex second-order cone program. To evaluate our algorithm, we use large-scale test cases from Challenge 3 of the U.S. Department of Energy's Grid Optimization Competition that resemble real power grid data under a variety of operating conditions and decision horizons. The experiments yield feasible solutions with an average optimality gap of 1.33%, demonstrating that this approach generates near-optimal solutions within stringent time limits.

Figures (3)

• Figure 7.1: (top) Empirical cumulative distribution function of the optimality gap. Distributions are shown for feasible solutions obtained from the tailored pADM, tailored pADM without adding contingencies, tailored pADM without the ramping restriction, and the benchmark algorithm. (left) Distribution on the gap interval of $0\% - 2\%$, corresponds to the leftmost shaded region of (top). (right) Distribution on the upper quintile, corresponds to the uppermost shaded region of (top).
• Figure 7.2: Empirical cumulative distribution function of solution time by division and network.
• Figure 7.3: Proportion of runtime allocated to UC iterations, SOC iterations, and final models on cases for which the time limit is not binding and 10 iterations are run ($N = 457$). Runtime is totaled across cases with the same network and across iterations for UC and SOC models. Average runtime for each network is given in parentheses.

Theorems & Definitions (28)

• Lemma 3.1
• Proposition 3.1
• Proposition 4.1
• Theorem 1
• Theorem 2
• Proposition 5.1
• Proposition 5.2
• Proposition 5.3
• Proposition 5.4
• Proposition 5.5