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A Hybrid Decomposition Approach for Stochastic Unit Commitment with Combined-Cycle Generators

Rosemary Barrass, Harsha Nagarajan, Mathieu Tanneau, Russell Bent, Pascal Van Hentenryck

Abstract

The U.S. power grid is undergoing a major paradigm shift with the increased development of renewable generators, electric vehicles, and data centers. In response to this growing need, the U.S. has ramped up the construction of combined-cycle generators (CCs). CCs are fast-ramping generators that utilize variable configurations of combustion turbines (CTs) and steam turbines (STs) to achieve much higher efficiency than traditional CTs alone. For schedule optimization, this requires the addition of a large number of binary constraints and variables in Unit Commitment (UC) problem formulations. This paper presents a novel hybrid Benders' (BD) and Dantzig-Wolfe (DW) decomposition algorithm for stochastic UC problems with CCs. The algorithm exploits the separability of the linear constraints in UC through BD and the integer CC constraints through DW. Results are presented for the 935-generator FERC test data set, modified to include mode data for CCs. The algorithm demonstrates a significant speed-up over traditional BD across all cases. It also demonstrates better convergence rates on cases with 25 or more scenarios than both BD and Gurobi's branch-and-bound solver. These cases show that the proposed algorithm is a scalable approach for solving stochastic UC.

A Hybrid Decomposition Approach for Stochastic Unit Commitment with Combined-Cycle Generators

Abstract

The U.S. power grid is undergoing a major paradigm shift with the increased development of renewable generators, electric vehicles, and data centers. In response to this growing need, the U.S. has ramped up the construction of combined-cycle generators (CCs). CCs are fast-ramping generators that utilize variable configurations of combustion turbines (CTs) and steam turbines (STs) to achieve much higher efficiency than traditional CTs alone. For schedule optimization, this requires the addition of a large number of binary constraints and variables in Unit Commitment (UC) problem formulations. This paper presents a novel hybrid Benders' (BD) and Dantzig-Wolfe (DW) decomposition algorithm for stochastic UC problems with CCs. The algorithm exploits the separability of the linear constraints in UC through BD and the integer CC constraints through DW. Results are presented for the 935-generator FERC test data set, modified to include mode data for CCs. The algorithm demonstrates a significant speed-up over traditional BD across all cases. It also demonstrates better convergence rates on cases with 25 or more scenarios than both BD and Gurobi's branch-and-bound solver. These cases show that the proposed algorithm is a scalable approach for solving stochastic UC.
Paper Structure (14 sections, 18 equations, 2 figures, 1 table, 1 algorithm)

This paper contains 14 sections, 18 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contributions and Outline
  4. Methodology
  5. Full UC with CC Formulation
  6. General formulation
  7. Benders' Decomposition
  8. Dantzig-Wolfe Decomposition
  9. Column-Row Generation Algorithm
  10. Stabilization Techniques
  11. Computational Results
  12. Conclusion
  13. Acknowledgments
  14. Appendix: CRG Algorithm

Figures (2)

  • Figure 1: Sensitivity analysis on the 30-load scenario case terminated after 120s using varying $\alpha$ and $\beta$ values. The heatmap shows the optimality gap (%) for each $(\alpha,\beta)$ pair, with grid lines (grey) indicating the evaluated combinations. Setting $\alpha$ and $\beta$ to $1$ is equivalent to not using in–out separation in Section \ref{['subsec:stabilization']}.
  • Figure 2: Convergence of incumbent solutions and lower bounds for B&B, BD, and CRG. Each plot shows a test case with a different number of load scenarios.