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DER Day-Ahead Offering: A Neural Network Column-and-Constraint Generation Approach

Weiqi Meng, Hongyi Li, Bai Cui

TL;DR

The paper tackles the day-ahead offering problem for DER aggregators under price and generation uncertainty by formulating a two-stage hybrid adaptive robust stochastic optimization (2S-ARSO) model. It combines stochastic programming for price trajectories with robust optimization for DER uncertainty, and introduces a neural network-accelerated column-and-constraint generation (NN-CCG) method to efficiently solve the resulting max-min recourse problem. A tailored neural architecture with set-based encoders learns to approximate the recourse value and worst-case realization, enabling MILP-compatible surrogate master and subproblem formulations. Numerical tests on a 1028-bus synthetic distribution network show up to 100x speedups over Gurobi and about 33x over classical CCG, while preserving solution quality, demonstrating strong scalability and practical potential for industrial DER day-ahead offering. The approach advances the tractability of complex, network-constrained 2S-ARSO problems and provides a framework for integrating learned surrogates into large-scale optimization pipelines.

Abstract

In the day-ahead energy market, the offering strategy of distributed energy resource (DER) aggregators must be submitted before the uncertainty realization in the form of price-quantity pairs. This work addresses the day-ahead offering problem through a two-stage robust adaptive stochastic optimization model, wherein the first-stage price-quantity pairs and second-stage operational commitment decisions are made before and after DER uncertainty is realized, respectively. Uncertainty in day-ahead price is addressed using a stochastic programming, while uncertainty of DER generation is handled through robust optimization. To address the max-min structure of the second-stage problem, a neural network-accelerated column-and-constraint generation method is developed. A dedicated neural network is trained to approximate the value function, while optimality is maintained by the design of the network architecture. Numerical studies indicate that the proposed method yields high-quality solutions and is up to 100 times faster than Gurobi and 33 times faster than classical column-and-constraint generation on the same 1028-node synthetic distribution network.

DER Day-Ahead Offering: A Neural Network Column-and-Constraint Generation Approach

TL;DR

The paper tackles the day-ahead offering problem for DER aggregators under price and generation uncertainty by formulating a two-stage hybrid adaptive robust stochastic optimization (2S-ARSO) model. It combines stochastic programming for price trajectories with robust optimization for DER uncertainty, and introduces a neural network-accelerated column-and-constraint generation (NN-CCG) method to efficiently solve the resulting max-min recourse problem. A tailored neural architecture with set-based encoders learns to approximate the recourse value and worst-case realization, enabling MILP-compatible surrogate master and subproblem formulations. Numerical tests on a 1028-bus synthetic distribution network show up to 100x speedups over Gurobi and about 33x over classical CCG, while preserving solution quality, demonstrating strong scalability and practical potential for industrial DER day-ahead offering. The approach advances the tractability of complex, network-constrained 2S-ARSO problems and provides a framework for integrating learned surrogates into large-scale optimization pipelines.

Abstract

In the day-ahead energy market, the offering strategy of distributed energy resource (DER) aggregators must be submitted before the uncertainty realization in the form of price-quantity pairs. This work addresses the day-ahead offering problem through a two-stage robust adaptive stochastic optimization model, wherein the first-stage price-quantity pairs and second-stage operational commitment decisions are made before and after DER uncertainty is realized, respectively. Uncertainty in day-ahead price is addressed using a stochastic programming, while uncertainty of DER generation is handled through robust optimization. To address the max-min structure of the second-stage problem, a neural network-accelerated column-and-constraint generation method is developed. A dedicated neural network is trained to approximate the value function, while optimality is maintained by the design of the network architecture. Numerical studies indicate that the proposed method yields high-quality solutions and is up to 100 times faster than Gurobi and 33 times faster than classical column-and-constraint generation on the same 1028-node synthetic distribution network.

Paper Structure

This paper contains 13 sections, 1 theorem, 12 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Hybrid Adaptive Robust Stochastic Optimization Formulation
  3. Neural Network-Accelerated Column-and-Constraint Generation Algorithm
  4. Column-and-Constraint Generation Algorithm
  5. NN-Accelerated Column-and-Constraint Generation
  6. Master Problem
  7. Subproblem
  8. Numerical Study
  9. Experiment Setup
  10. Structure and Accuracy of Neural Network
  11. Effectiveness of NN-Accelerated CCG
  12. Conclusion
  13. Finite-Termination of NN-Accelerated CCG

Key Result

Proposition 1

Suppose $\mathcal{X}$ is a polytope with $N$ extreme points, and assume that the master problem selects an optimal extreme point of $\mathcal{X}$ at each iteration. Then Algorithm alg:neuraro-ccg-obj terminates in at most $N+1$ iterations.

Figures (1)

  • Figure 1: Neural architecture of NN-accelerated CCG

Theorems & Definitions (2)

  • Proposition 1
  • proof