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Joint Chance-constrained Game for Coordinating Renewable Microgrids with Service Delivery Risk: A Bayesian Optimization Approach

Yifu Ding, Benjamin Hobbs

TL;DR

The paper tackles coordinating renewable microgrids in two-settlement electricity markets under reserve deliverability risk due to forecast errors. It develops a distributionally robust joint chance-constrained (DRJCC) Stackelberg game that combines a two-stage Wasserstein DRO for microgrid bidding with a joint constraint on reserve performance. To solve the problem under unknown correlation among players, it introduces an end-to-end Bayesian optimization procedure to approximate optimal individual violation rates, ensuring the joint constraint is met. Case studies on a 30-bus network with CAISO data show the method can regulate the joint violation rate and maintain microgrid profits, offering a scalable, data-driven alternative to conservative or grid-search approaches.

Abstract

Microgrids incorporate distributed energy resources (DERs) and flexible loads, which can provide energy and reserve services for the main grid. However, due to uncertain renewable generations such as solar power, microgrids might under-deliver reserve services and breach day-ahead contracts in real-time. If multiple microgrids breach their reserve contracts simultaneously, this could lead to a severe grid contingency. This paper designs a distributionally robust joint chance-constrained (DRJCC) game-theoretical framework considering uncertain real-time reserve provisions and the value of lost load (VoLL). Leveraging historical error samples, the reserve bidding strategy of each microgrid is formulated into a two-stage Wasserstein-metrics distribution robust optimization (DRO) model. A JCC is employed to regulate the under-delivered reserve capacity of all microgrids in a non-cooperative game. Considering the unknown correlation among players, a novel Bayesian optimization method approximates the optimal individual violation rates of microgrids and market equilibrium. The proposed game framework with the optimal rates is simulated with up to 14 players in a 30-bus network. Case studies are conducted using the California power market data. The proposed Bayesian method can effectively regulate the joint violation rate of the under-delivered reserve and secure the profit of microgrids in the reserve market.

Joint Chance-constrained Game for Coordinating Renewable Microgrids with Service Delivery Risk: A Bayesian Optimization Approach

TL;DR

The paper tackles coordinating renewable microgrids in two-settlement electricity markets under reserve deliverability risk due to forecast errors. It develops a distributionally robust joint chance-constrained (DRJCC) Stackelberg game that combines a two-stage Wasserstein DRO for microgrid bidding with a joint constraint on reserve performance. To solve the problem under unknown correlation among players, it introduces an end-to-end Bayesian optimization procedure to approximate optimal individual violation rates, ensuring the joint constraint is met. Case studies on a 30-bus network with CAISO data show the method can regulate the joint violation rate and maintain microgrid profits, offering a scalable, data-driven alternative to conservative or grid-search approaches.

Abstract

Microgrids incorporate distributed energy resources (DERs) and flexible loads, which can provide energy and reserve services for the main grid. However, due to uncertain renewable generations such as solar power, microgrids might under-deliver reserve services and breach day-ahead contracts in real-time. If multiple microgrids breach their reserve contracts simultaneously, this could lead to a severe grid contingency. This paper designs a distributionally robust joint chance-constrained (DRJCC) game-theoretical framework considering uncertain real-time reserve provisions and the value of lost load (VoLL). Leveraging historical error samples, the reserve bidding strategy of each microgrid is formulated into a two-stage Wasserstein-metrics distribution robust optimization (DRO) model. A JCC is employed to regulate the under-delivered reserve capacity of all microgrids in a non-cooperative game. Considering the unknown correlation among players, a novel Bayesian optimization method approximates the optimal individual violation rates of microgrids and market equilibrium. The proposed game framework with the optimal rates is simulated with up to 14 players in a 30-bus network. Case studies are conducted using the California power market data. The proposed Bayesian method can effectively regulate the joint violation rate of the under-delivered reserve and secure the profit of microgrids in the reserve market.
Paper Structure (19 sections, 51 equations, 8 figures, 2 tables, 1 algorithm)

This paper contains 19 sections, 51 equations, 8 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. DRJCC market game considering uncertain reserve provision
  3. Model formulation
  4. Wasserstein-metric ambiguity set to model the worst-case reserve performance
  5. ISO's optimization for the energy and reserve joint dispatch
  6. Data-driven bidding strategy considering the worst-case reserve performance
  7. Complementarity model for market equilibrium
  8. Approximating the optimal solutions using Bayesian optimization
  9. Summary of the algorithm
  10. Evaluation of the black-box function
  11. Sample selection using the acquisition function
  12. Case studies
  13. Numerical results
  14. The optimal radius of Wasserstein-metrics ambiguity sets
  15. Game convergence with the increasing number of players
  16. ...and 4 more sections

Figures (8)

  • Figure 1: Bilevel Stackelberg game framework for coordinating renewable microgrids in two-settlement electricity markets
  • Figure 2: The solar power forecast error distribution between day-ahead and real-time markets at 11:00 a.m. california_iso_oasis_nodate
  • Figure 3: (a) The total amount of under-delivered reserve and (b) the empirical contract violation rates with an increasing radius of the ambiguity set
  • Figure 4: The convergence of Bayesian optimization in games with increasing players. All the games converge to points with a deviation less than 0.05, highlighted in black dashed line; Colored dash lines show the convergence of games in the repeating experiments with different starting points
  • Figure 5: The total amount of under-delivered reserve and empirical joint violation rates in three scenarios
  • ...and 3 more figures