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Robust Microgrid Dispatch with Real-Time Energy Sharing and Endogenous Uncertainty

Meng Yang, Rui Xie, Yongjun Zhang, Yue Chen

TL;DR

This paper tackles robust microgrid dispatch in the presence of endogenous uncertainty caused by the on/off decisions of renewable generators and the need for real-time energy sharing among prosumers. It develops a two-stage robust optimization framework where day-ahead decisions on renewable connections shape the uncertainty set, and a real-time energy-sharing mechanism among customers resolves deviations through a generalized Nash equilibrium. A centralized-equivalent reformulation of the energy-sharing game is shown to exist and be unique in a social-optimum sense, enabling a projection-based C&CG algorithm to efficiently solve the endogenous-uncertainty problem. Numerical results on benchmark and larger networks demonstrate the approach’s effectiveness, with energy sharing improving prosumer welfare, energy storage enabling online operation, and the proposed algorithm outperforming traditional C&CG in handling endogenous uncertainty. The work provides a practical pathway to scalable, secure, and economically efficient microgrid operation under uncertainty, with clear implications for future distributed energy systems and market design.

Abstract

With the rising adoption of distributed energy resources (DERs), microgrid dispatch is facing new challenges: DER owners are independent stakeholders seeking to maximize their individual profits rather than being controlled centrally; and the dispatch of renewable generators may affect the microgrid's exposure to uncertainty. To address these challenges, this paper proposes a two-stage robust microgrid dispatch model with real-time energy sharing and endogenous uncertainty. In the day-ahead stage, the connection/disconnection of renewable generators is optimized, which influences the size and dimension of the uncertainty set. As a result, the uncertainty set is endogenously given. In addition, non-anticipative operational bounds for energy storage (ES) are derived to enable the online operation of ES in real-time. In the real-time stage, DER owners (consumers and prosumers) share energy with each other via a proposed energy sharing mechanism, which forms a generalized Nash game. To solve the robust microgrid dispatch model, we develop an equivalent optimization model to compute the real-time energy sharing equilibrium. Based on this, a projection-based column-and-constraint generation (C&CG) method is proposed to handle the endogenous uncertainty. Numerical experiments show the effectiveness and advantages of the proposed model and method.

Robust Microgrid Dispatch with Real-Time Energy Sharing and Endogenous Uncertainty

TL;DR

This paper tackles robust microgrid dispatch in the presence of endogenous uncertainty caused by the on/off decisions of renewable generators and the need for real-time energy sharing among prosumers. It develops a two-stage robust optimization framework where day-ahead decisions on renewable connections shape the uncertainty set, and a real-time energy-sharing mechanism among customers resolves deviations through a generalized Nash equilibrium. A centralized-equivalent reformulation of the energy-sharing game is shown to exist and be unique in a social-optimum sense, enabling a projection-based C&CG algorithm to efficiently solve the endogenous-uncertainty problem. Numerical results on benchmark and larger networks demonstrate the approach’s effectiveness, with energy sharing improving prosumer welfare, energy storage enabling online operation, and the proposed algorithm outperforming traditional C&CG in handling endogenous uncertainty. The work provides a practical pathway to scalable, secure, and economically efficient microgrid operation under uncertainty, with clear implications for future distributed energy systems and market design.

Abstract

With the rising adoption of distributed energy resources (DERs), microgrid dispatch is facing new challenges: DER owners are independent stakeholders seeking to maximize their individual profits rather than being controlled centrally; and the dispatch of renewable generators may affect the microgrid's exposure to uncertainty. To address these challenges, this paper proposes a two-stage robust microgrid dispatch model with real-time energy sharing and endogenous uncertainty. In the day-ahead stage, the connection/disconnection of renewable generators is optimized, which influences the size and dimension of the uncertainty set. As a result, the uncertainty set is endogenously given. In addition, non-anticipative operational bounds for energy storage (ES) are derived to enable the online operation of ES in real-time. In the real-time stage, DER owners (consumers and prosumers) share energy with each other via a proposed energy sharing mechanism, which forms a generalized Nash game. To solve the robust microgrid dispatch model, we develop an equivalent optimization model to compute the real-time energy sharing equilibrium. Based on this, a projection-based column-and-constraint generation (C&CG) method is proposed to handle the endogenous uncertainty. Numerical experiments show the effectiveness and advantages of the proposed model and method.
Paper Structure (28 sections, 4 theorems, 29 equations, 14 figures, 7 tables, 1 algorithm)

This paper contains 28 sections, 4 theorems, 29 equations, 14 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Abbreviation
  2. Indices and Sets
  3. Parameters
  4. Decision Variables
  5. Introduction
  6. Mathematical Models
  7. Real-Time Stage with Energy Sharing
  8. Endogenous Uncertainty Set
  9. Two-Stage Robust Microgrid Dispatch
  10. Solution Approach
  11. Transformation of the Energy Sharing Game
  12. Linearization of the Objective Function
  13. Projection-based C&CG Algorithm
  14. Case Studies
  15. Benchmark Case
  16. ...and 13 more sections

Key Result

Proposition 1

For each period $t \in \mathcal{T}$, suppose the charging power $p_{et}^c$ and discharging power $p_{et}^d$ satisfy eq:Fc.10 and eq:Fc.11, respectively, where the parameters ($\underline{p}_{et}^{DA,c}$, $\overline{p}_{et}^{DA,c}$, $\underline{p}_{et}^{DA,d}$, $\overline{p}_{et}^{DA,d}$) are determi

Figures (14)

  • Figure 1: Overview of the control architecture in a microgrid.
  • Figure 2: The proposed two-stage decision-making framework.
  • Figure 3: Uncertainty sets under different disconnection strategies.
  • Figure 4: Illustration of the objective function linearization.
  • Figure 5: Illustration of the projection operation.
  • ...and 9 more figures

Theorems & Definitions (5)

  • Definition 1
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4