Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Variable aggregation-based formulations for pumped storage hydro model in the day-ahead unit commitment problem

Shaoze Li, Junhao Wu, Zhibin Deng

TL;DR

This work tackles the computational challenges of incorporating PSH into day-ahead UC by addressing symmetry from multiple PSH units sharing a reservoir. It introduces two symmetry-breaking approaches: an Aggregated PSH formulation for fully identical units and a Presolved PSH formulation based on disjoint-interval representations to handle partial symmetry, with a preprocessing step to merge intervals. Numerical experiments show substantial improvements in solve times and solvability, especially as the count of identical units increases, and demonstrate the Presolved method’s effectiveness even for nonidentical units with the same efficiencies. The methods are simple to implement and extend, and are applicable across solvers beyond the tested environment, offering practical gains for PSH-integrated UC models.

Abstract

Pumped storage hydro (PSH) plants can improve the flexibility of power systems. A well-designed formulation for a PSH model is essential when incorporating the PSH units into a day-ahead unit commitment model. In the literature, the formulation of a PSH model is generally based on the individual PSH unit. This formulation is tight if there is only one PSH unit in the reservoir. However, when there are multiple units sharing the same reservoir in a PSH plant, the existing formulation may introduce some symmetric structures which degrade the efficiency of a mixed-integer programming solver significantly. In this paper, to cope with the symmetric structure in the PSH plants that have multiple units, we propose two new formulations. The first formulation considers the case in which there are multiple identical units sharing the same reservoir. The second formulation considers a general case in which the units sharing the same reservoir have the same generating and pumping efficiency. Using the new formulations, the symmetric structures in the problem can be effectively broken. Numerical results are presented to study the computational efficiency of the new formulations.

Variable aggregation-based formulations for pumped storage hydro model in the day-ahead unit commitment problem

TL;DR

This work tackles the computational challenges of incorporating PSH into day-ahead UC by addressing symmetry from multiple PSH units sharing a reservoir. It introduces two symmetry-breaking approaches: an Aggregated PSH formulation for fully identical units and a Presolved PSH formulation based on disjoint-interval representations to handle partial symmetry, with a preprocessing step to merge intervals. Numerical experiments show substantial improvements in solve times and solvability, especially as the count of identical units increases, and demonstrate the Presolved method’s effectiveness even for nonidentical units with the same efficiencies. The methods are simple to implement and extend, and are applicable across solvers beyond the tested environment, offering practical gains for PSH-integrated UC models.

Abstract

Pumped storage hydro (PSH) plants can improve the flexibility of power systems. A well-designed formulation for a PSH model is essential when incorporating the PSH units into a day-ahead unit commitment model. In the literature, the formulation of a PSH model is generally based on the individual PSH unit. This formulation is tight if there is only one PSH unit in the reservoir. However, when there are multiple units sharing the same reservoir in a PSH plant, the existing formulation may introduce some symmetric structures which degrade the efficiency of a mixed-integer programming solver significantly. In this paper, to cope with the symmetric structure in the PSH plants that have multiple units, we propose two new formulations. The first formulation considers the case in which there are multiple identical units sharing the same reservoir. The second formulation considers a general case in which the units sharing the same reservoir have the same generating and pumping efficiency. Using the new formulations, the symmetric structures in the problem can be effectively broken. Numerical results are presented to study the computational efficiency of the new formulations.

Paper Structure

This paper contains 9 sections, 1 theorem, 47 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. The Standard Formulations
  3. Two New Formulations
  4. A Formulation for Identical Units in One Reservoir
  5. A Formulation via Presolving
  6. Numerical Experiments
  7. Unit Commitment with Identical PSH Units
  8. Unit Commitment with Nonidentical PSH units
  9. Conclusion

Key Result

Proposition 1

The intervals $[l^\prime_1,u^\prime_1],\cdots,[l^\prime_{k^\prime},u^\prime_{k^\prime}]$ returned by Algorithm 1 satisfy $l^\prime_1\leq u^\prime_1<l^\prime_2\leq u^\prime_2<\cdots<l^\prime_{k^\prime}\leq u^\prime_{k^\prime}$.

Figures (2)

  • Figure 1: The performance profile of using different formulations. From top to bottom, the three figures illustrate the case in which there are 2, 3 and 4 identical PSH units being incorporated, respectively.
  • Figure 2: The performance profile of using different formulations. From top to bottom, the three figures illustrate the case in which there are 2, 3 and 4 PSH units being incorporated, respectively.

Theorems & Definitions (2)

  • Proposition 1
  • proof