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Data-Driven Two-Stage Distributionally Robust Dispatch of Multi-Energy Microgrid

Xunhang Sun, Xiaoyu Cao, Bo Zeng, Miaomiao Li, Xiaohong Guan, Tamer Başar

TL;DR

This work tackles MEMG dispatch under uncertainty by formulating a two-stage distributionally robust optimization problem with a Wasserstein ambiguity set around an empirical data distribution. The authors develop a novel C&CG-DRO(CG) algorithm that combines a finite-step worst-case expectation solver with a column-and-constraint framework to achieve exact, scalable solutions. Numerical results show that the DRO-based DRD reduces load shedding, energy not supplied, and emissions relative to stochastic programming and robust optimization while maintaining computational tractability through parallelized subproblems. Overall, the approach provides a practical, data-driven mechanism for robust MEMG operation that bridges classical SP and RO paradigms and supports scalable deployment in real-world microgrid environments.

Abstract

This paper studies adaptive distributionally robust dispatch (DRD) of the multi-energy microgrid under supply and demand uncertainties. A Wasserstein ambiguity set is constructed to support data-driven decision-making. By fully leveraging the special structure of worst-case expectation from the primal perspective, a novel and high-efficient decomposition algorithm under the framework of column-and-constraint generation is customized and developed to address the computational burden. Numerical studies demonstrate the effectiveness of our DRD approach, and shed light on the interrelationship of it with the traditional dispatch approaches through stochastic programming and robust optimization schemes. Also, comparisons with popular algorithms in the literature for two-stage distributionally robust optimization verify the powerful capacity of our algorithm in computing the DRD problem.

Data-Driven Two-Stage Distributionally Robust Dispatch of Multi-Energy Microgrid

TL;DR

This work tackles MEMG dispatch under uncertainty by formulating a two-stage distributionally robust optimization problem with a Wasserstein ambiguity set around an empirical data distribution. The authors develop a novel C&CG-DRO(CG) algorithm that combines a finite-step worst-case expectation solver with a column-and-constraint framework to achieve exact, scalable solutions. Numerical results show that the DRO-based DRD reduces load shedding, energy not supplied, and emissions relative to stochastic programming and robust optimization while maintaining computational tractability through parallelized subproblems. Overall, the approach provides a practical, data-driven mechanism for robust MEMG operation that bridges classical SP and RO paradigms and supports scalable deployment in real-world microgrid environments.

Abstract

This paper studies adaptive distributionally robust dispatch (DRD) of the multi-energy microgrid under supply and demand uncertainties. A Wasserstein ambiguity set is constructed to support data-driven decision-making. By fully leveraging the special structure of worst-case expectation from the primal perspective, a novel and high-efficient decomposition algorithm under the framework of column-and-constraint generation is customized and developed to address the computational burden. Numerical studies demonstrate the effectiveness of our DRD approach, and shed light on the interrelationship of it with the traditional dispatch approaches through stochastic programming and robust optimization schemes. Also, comparisons with popular algorithms in the literature for two-stage distributionally robust optimization verify the powerful capacity of our algorithm in computing the DRD problem.

Paper Structure

This paper contains 21 sections, 6 theorems, 29 equations, 8 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Stage-Wise Dispatch Formulation
  4. Pre-Dispatch Stage
  5. Re-Dispatch Stage
  6. Integrated Formulation based on DRO
  7. Finite-Step Solution of WCEP via CG
  8. Solving DRD-MEMG via C&CG-DRO(CG)
  9. Numerical Studies
  10. MEMG's Dispatch Results
  11. Dispatch Scheme
  12. Out-of-Sample Performance
  13. Analysis on ELZ's model
  14. Impact of Wasserstein Radius
  15. Computational Performance
  16. ...and 6 more sections

Key Result

Proposition 1

For $r_1<r_2$, i.e., $\mathcal{P}_1\subseteq\mathcal{P}_2$, we have $w_1\leq w_2$.

Figures (8)

  • Figure 1: Typical structure of multi-energy microgrid.
  • Figure 2: Three-state model for electrolyzer.
  • Figure 3: MEMG's dispatch scheme.
  • Figure 4: ELZ's dispatch schemes by using three- and two-state models.
  • Figure 5: Impact of Wasserstein radius.
  • ...and 3 more figures

Theorems & Definitions (19)

  • Remark 1
  • Remark 2
  • Proposition 1
  • Theorem 1
  • Remark 3
  • Proposition 2
  • proof
  • Corollary 1
  • Corollary 2
  • Remark 4
  • ...and 9 more