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Fast and Certified Bounding of Security-Constrained DCOPF via Interval Bound Propagation

Eren Tekeler, Xiangru Zhong, Huan Zhang, Samuel Chevalier

TL;DR

This work addresses the computational bottleneck of security-constrained DCOPF (SC-DCOPF) problems arising in GO3 by casting the SC-DCOPF into a GPU-accelerated computational graph and applying Interval Bound Propagation (IBP) to compute certified bounds efficiently. By leveraging a PTDF-based DCOPF formulation, rank-1 contingency updates via the Sherman–Morrison identity, and a loop-free graph representation compatible with $\alpha,\beta$-CROWN, the approach yields fast, certified solution bounds and the ability to identify infeasibility without full dispatch solves. Empirical results show mean IBP gaps below $3\%$ and a maximum of $6.53\%$ on test cases up to 73 buses, with scalability to 8,316-bus systems and runtimes near $0.07$ seconds per time index, plus speedups up to $8.97\times 10^{6}$ over CPU LP solvers. The findings indicate that IBP can provide high-quality, rapid bounds and guide infeasibility detection, with potential integration into Branch-and-Bound frameworks for global optimality in large, contingency-rich power-system problems.

Abstract

Security-Constrained DC Optimal Power Flow (SC DCOPF) is an important tool for transmission system operators, enabling economically efficient and physically secure dispatch decisions. Although CPU-based commercial solvers (e.g., Gurobi) can efficiently solve SC-DCOPF problems with a reasonable number of security constraints, their performance degrades rapidly as both system size and the number of contingencies grow into thousands, leading to a significant computational burden. This introduces a bottleneck for system operators who seek timely decision-making across a wide range of potential threats. In this paper, we design a computational graph representation of the SC-DCOPF-based market-clearing problem, inspired by the third ARPA-E Grid Optimization Competition (GO3). We are able to quickly bound the optimal solution of large-scale SC-DCOPF problems using a GPU-accelerated Neural Network verification tool called Interval Bound Propagation (IBP). Using IBP, we compute certified bounds with a maximum gap of 6.53% for instances up to 617 buses, while demonstrating scalability on challenging systems up to 8,316 buses with a runtime of approximately 0.07 seconds. These results demonstrate that IBP can provide high-quality solution bounds at very fast speeds, and it can help identify infeasibility drivers in challenging SC-DCOPF instances.

Fast and Certified Bounding of Security-Constrained DCOPF via Interval Bound Propagation

TL;DR

This work addresses the computational bottleneck of security-constrained DCOPF (SC-DCOPF) problems arising in GO3 by casting the SC-DCOPF into a GPU-accelerated computational graph and applying Interval Bound Propagation (IBP) to compute certified bounds efficiently. By leveraging a PTDF-based DCOPF formulation, rank-1 contingency updates via the Sherman–Morrison identity, and a loop-free graph representation compatible with -CROWN, the approach yields fast, certified solution bounds and the ability to identify infeasibility without full dispatch solves. Empirical results show mean IBP gaps below and a maximum of on test cases up to 73 buses, with scalability to 8,316-bus systems and runtimes near seconds per time index, plus speedups up to over CPU LP solvers. The findings indicate that IBP can provide high-quality, rapid bounds and guide infeasibility detection, with potential integration into Branch-and-Bound frameworks for global optimality in large, contingency-rich power-system problems.

Abstract

Security-Constrained DC Optimal Power Flow (SC DCOPF) is an important tool for transmission system operators, enabling economically efficient and physically secure dispatch decisions. Although CPU-based commercial solvers (e.g., Gurobi) can efficiently solve SC-DCOPF problems with a reasonable number of security constraints, their performance degrades rapidly as both system size and the number of contingencies grow into thousands, leading to a significant computational burden. This introduces a bottleneck for system operators who seek timely decision-making across a wide range of potential threats. In this paper, we design a computational graph representation of the SC-DCOPF-based market-clearing problem, inspired by the third ARPA-E Grid Optimization Competition (GO3). We are able to quickly bound the optimal solution of large-scale SC-DCOPF problems using a GPU-accelerated Neural Network verification tool called Interval Bound Propagation (IBP). Using IBP, we compute certified bounds with a maximum gap of 6.53% for instances up to 617 buses, while demonstrating scalability on challenging systems up to 8,316 buses with a runtime of approximately 0.07 seconds. These results demonstrate that IBP can provide high-quality solution bounds at very fast speeds, and it can help identify infeasibility drivers in challenging SC-DCOPF instances.

Paper Structure

This paper contains 13 sections, 19 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Market Clearing DCOPF
  4. Formulation of Soft-Constrains
  5. Formulation of Security-Constrains
  6. Objective Function Formulation
  7. Proxy NN Model
  8. Formal Verification of Neural Networks
  9. Interval Bound Propagation
  10. Computational Graph Formulation
  11. Cost Function Implementation
  12. Results
  13. Conclusion

Figures (3)

  • Figure 1: Complexity dimensions of the largest GO3 test case (8,316-bus) solved in this paper.
  • Figure 2: IBP gap statistics across different benchmarked system sizes. Negative IBP upper bound scenarios are excluded.
  • Figure 3: Distribution of IBP mean runtimes in log scale across different system sizes.