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Modeling to Generate Alternatives for Robustness of Mixed Integer DC Optimal Power Flow

Constance Crozier

TL;DR

This work addresses the gap where linearized DC-OPF-based MILP formulations fail to produce AC-feasible solutions for discrete transmission decisions. It proposes Modeling to Generate Alternatives (MGA), a framework that explicitly searches for multiple near-optimal solutions using HSJ, Random Vector, and novel HSJ variants to improve AC feasibility through topology exploration. Application to transmission switching (OTS) and unit commitment (UC) across 13 challenging networks shows MGA can produce AC-feasible solutions in cases where DC-OTS cannot, often with orders-of-magnitude faster convergence than greedy heuristics. The results demonstrate that MGA can provide operators with diverse, high-quality alternatives, enabling practical, robust decision support for real-time power system operation.

Abstract

Transmission system operators face a variety of discrete operational decisions, such as switching of branches and/or devices. Incorporating these decisions into optimal power flow (OPF) results in mixed-integer non-linear programming problems (MINLPs), which can't presently be solved at scale in the required time. Various linearizations of the OPF exist, most famously the DC-OPF, which can be leveraged to find integer decisions. However, these linearizations can yield very poor integer solutions in some edge cases, making them challenging to incorporate into control rooms. This paper introduces the use of modeling to generate alternatives (MGA) to find alternative solutions to the linearized problems, reducing the chance of finding no AC feasible solutions. We test this approach using 13 networks where the DC linearization results in infeasible integer decisions, and MGA finds a solution in all cases. The MGA search criteria selected drastically affects the number and quality of solutions found, so network specific search functions may be necessary.

Modeling to Generate Alternatives for Robustness of Mixed Integer DC Optimal Power Flow

TL;DR

This work addresses the gap where linearized DC-OPF-based MILP formulations fail to produce AC-feasible solutions for discrete transmission decisions. It proposes Modeling to Generate Alternatives (MGA), a framework that explicitly searches for multiple near-optimal solutions using HSJ, Random Vector, and novel HSJ variants to improve AC feasibility through topology exploration. Application to transmission switching (OTS) and unit commitment (UC) across 13 challenging networks shows MGA can produce AC-feasible solutions in cases where DC-OTS cannot, often with orders-of-magnitude faster convergence than greedy heuristics. The results demonstrate that MGA can provide operators with diverse, high-quality alternatives, enabling practical, robust decision support for real-time power system operation.

Abstract

Transmission system operators face a variety of discrete operational decisions, such as switching of branches and/or devices. Incorporating these decisions into optimal power flow (OPF) results in mixed-integer non-linear programming problems (MINLPs), which can't presently be solved at scale in the required time. Various linearizations of the OPF exist, most famously the DC-OPF, which can be leveraged to find integer decisions. However, these linearizations can yield very poor integer solutions in some edge cases, making them challenging to incorporate into control rooms. This paper introduces the use of modeling to generate alternatives (MGA) to find alternative solutions to the linearized problems, reducing the chance of finding no AC feasible solutions. We test this approach using 13 networks where the DC linearization results in infeasible integer decisions, and MGA finds a solution in all cases. The MGA search criteria selected drastically affects the number and quality of solutions found, so network specific search functions may be necessary.
Paper Structure (20 sections, 16 equations, 11 figures, 2 tables)

This paper contains 20 sections, 16 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Mixed Integer Optimal Power Flow Problems
  3. DC Optimal Power Flow
  4. AC Power Flow Constraints
  5. Common Mixed Integer Problems
  6. Transmission Switching
  7. Unit Commitment
  8. Limitations of Mixed-Integer DC Decisions
  9. Modeling to Generate Alternatives
  10. Hop, Skip, and Jump
  11. Random Vectors
  12. HSJ with Negative Weights
  13. HSJ with Zero Bias
  14. Proposed use of MGA for solution exploration
  15. Simulation & Testing Platforms
  16. ...and 5 more sections

Figures (11)

  • Figure 1: Solutions to the linearized problem lie on vertices, the distance from the feasible non-linear region will vary.
  • Figure 2: Solutions to the linearized DC-OTS problem exist at the vertices of the feasible polygon. However the AC-OTS problem is higher dimension and bounded by non-linear constraints. Fixing a topology can be thought of as taking a slice of the AC-OTS space. Taking multiple slices increases the chance of finding a good solution to the AC-OTS problem.
  • Figure 3: Visualization of the process to find AC feasible solutions
  • Figure 4: The chosen topologies for the first five iterations using each MGA method. The background color demonstrates whether the solution was: infeasible, had small unavoidable overloads, or was safe after an AC OPF.
  • Figure 5:
  • ...and 6 more figures