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Enhancing Power Systems Transmission Adequacy via Optimal BESS Siting and Sizing using Benders Decomposition with Feasibility Cuts

Ginevra Larroux, Matthieu Jacobs, Keyu Jia, Fabrizio Sossan, Mario Paolone

Abstract

This work presents a general framework for the operationally driven optimal siting and sizing of battery energy storage systems in power transmission networks, aimed at enhancing their resource adequacy. The approach considers multi-period planning horizons, enforces network constraints at high temporal resolution, and targets large-scale meshed systems. The resulting computationally complex mixed-integer non-linear programming problem is reformulated as a mixed-integer second-order cone programming problem and solved via Generalized Benders Decomposition, with feasibility cuts enabling congestion management and voltage regulation under binding network limits. A tailored heuristic recovers an alternating-current power-flow-feasible operating point from the relaxed solution. The proposed formulation is parallelizable, yielding excellent computational performance, while featuring rigorous guarantees of convergence.

Enhancing Power Systems Transmission Adequacy via Optimal BESS Siting and Sizing using Benders Decomposition with Feasibility Cuts

Abstract

This work presents a general framework for the operationally driven optimal siting and sizing of battery energy storage systems in power transmission networks, aimed at enhancing their resource adequacy. The approach considers multi-period planning horizons, enforces network constraints at high temporal resolution, and targets large-scale meshed systems. The resulting computationally complex mixed-integer non-linear programming problem is reformulated as a mixed-integer second-order cone programming problem and solved via Generalized Benders Decomposition, with feasibility cuts enabling congestion management and voltage regulation under binding network limits. A tailored heuristic recovers an alternating-current power-flow-feasible operating point from the relaxed solution. The proposed formulation is parallelizable, yielding excellent computational performance, while featuring rigorous guarantees of convergence.
Paper Structure (18 sections, 19 equations, 7 figures, 6 tables, 1 algorithm)

This paper contains 18 sections, 19 equations, 7 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Grid constraints in the optimal power flow problem
  4. Optimization problem decomposition
  5. Proposed Method
  6. Optimization problem decomposition with Generalized Benders Decomposition
  7. Mathematical formulation
  8. Computational complexity and parallel solution approach
  9. Convergence
  10. Second-order cone relaxation of the optimal power flow
  11. Case studies and results
  12. Generalized Benders Decomposition convergence
  13. Solution time and scalability
  14. Tightness and AC-power flow feasibility
  15. Optimal siting and sizing
  16. ...and 3 more sections

Figures (7)

  • Figure 1: Boundary conditions: distribution of voltage (top) and branch current (bottom) magnitude over the time horizon, per bus and branch respectively.
  • Figure 2: Residuals between the optimal solutions of the centralized and Benders-decomposed integrality-relaxed problem: feasible setting. SOC-OPF state variables (left) and linking variables (right).
  • Figure 3: Residuals between the optimal solutions of the centralized and Benders-decomposed integrality-relaxed problem: infeasible setting. DC-OPF state variables (left) and linking variables (right).
  • Figure 4: Main-problem solve time per iteration (blue), total subproblem solve time per iteration (orange), maximum subproblem solve time across workers (green) and number of Benders iterations (red) as functions of the number of subproblems (left) and number of linking variables (right). Mean (solid line) and standard deviation (shaded area) across iterations.
  • Figure 5: Main problem solve-time per iteration as a function of Benders iteration count (left) and number of Benders iterations as a joint function of number of subproblems and linking variables (right).
  • ...and 2 more figures