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Neural Risk Limiting Dispatch in Power Networks: Formulation and Generalization Guarantees

Ge Chen, Junjie Qin

TL;DR

This paper designs a data-driven formulation for the RLD problem and proposes neural RLD, a novel solution method that leverages an L2-regularized neural network to learn the decision rule, thereby transforming the data-driven formulation into a training task that can be efficiently completed by stochastic gradient descent.

Abstract

Risk limiting dispatch (RLD) has been proposed as an approach that effectively trades off economic costs with operational risks for power dispatch under uncertainty. However, how to solve the RLD problem with provably near-optimal performance still remains an open problem. This paper presents a learning-based solution to this challenge. We first design a data-driven formulation for the RLD problem, which aims to construct a decision rule that directly maps day-ahead observable information to cost-effective dispatch decisions for the future delivery interval. Unlike most existing works that follow a predict-then-optimize paradigm, this end-to-end rule bypasses the additional suboptimality introduced by separately handling prediction and optimization. We then propose neural RLD, a novel solution method to the data-driven formulation. This method leverages an L2-regularized neural network to learn the decision rule, thereby transforming the data-driven formulation into a neural network training task that can be efficiently completed by stochastic gradient descent. A theoretical performance guarantee is further established to bound the suboptimality of our method, which implies that its suboptimality approaches zero with high probability as more samples are utilized. Simulation tests across various systems demonstrate our method's superior performance in convergence, suboptimality, and computational efficiency compared with benchmarks.

Neural Risk Limiting Dispatch in Power Networks: Formulation and Generalization Guarantees

TL;DR

This paper designs a data-driven formulation for the RLD problem and proposes neural RLD, a novel solution method that leverages an L2-regularized neural network to learn the decision rule, thereby transforming the data-driven formulation into a training task that can be efficiently completed by stochastic gradient descent.

Abstract

Risk limiting dispatch (RLD) has been proposed as an approach that effectively trades off economic costs with operational risks for power dispatch under uncertainty. However, how to solve the RLD problem with provably near-optimal performance still remains an open problem. This paper presents a learning-based solution to this challenge. We first design a data-driven formulation for the RLD problem, which aims to construct a decision rule that directly maps day-ahead observable information to cost-effective dispatch decisions for the future delivery interval. Unlike most existing works that follow a predict-then-optimize paradigm, this end-to-end rule bypasses the additional suboptimality introduced by separately handling prediction and optimization. We then propose neural RLD, a novel solution method to the data-driven formulation. This method leverages an L2-regularized neural network to learn the decision rule, thereby transforming the data-driven formulation into a neural network training task that can be efficiently completed by stochastic gradient descent. A theoretical performance guarantee is further established to bound the suboptimality of our method, which implies that its suboptimality approaches zero with high probability as more samples are utilized. Simulation tests across various systems demonstrate our method's superior performance in convergence, suboptimality, and computational efficiency compared with benchmarks.
Paper Structure (34 sections, 5 theorems, 47 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 34 sections, 5 theorems, 47 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions and paper organization
  3. Other related literature
  4. Learning-based stochastic dispatch
  5. Sample average approximation
  6. Direct learning
  7. Problem Formulation
  8. Classic network risk limiting dispatch
  9. Data-driven limiting dispatch
  10. Neural Risk Limiting Dispatch
  11. Neural network for data-driven RLD
  12. NN training
  13. Generalization performance guarantee
  14. Case Study
  15. Simulation setup
  16. ...and 19 more sections

Key Result

Proposition 1

The gradient $\nabla_{\mathbf{u}} Q$ can be expressed as liang2022operation: where $\bm \lambda^\star$ is the optimal dual variable of constraint eqn_DCOPF.

Figures (10)

  • Figure 1: Steps for deriving the proposed neural RLD formulation.
  • Figure 2: Unit generation costs used in different test cases. Note the first-stage unit generation cost $\bm \alpha$ is always smaller than the second-stage one $\bm \beta$.
  • Figure 3: Standardized training losses of the NNs trained by different methods.
  • Figure 4: Normalized suboptimality given by different methods.
  • Figure 5: Times for solving one and 5,000 instances with different methods.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Remark 1: VOLL interpretation
  • Proposition 1: Expression of gradients
  • Theorem 1: PAC bound of excess cost
  • Corollary 1: Asymptotic optimality
  • Lemma 1: Vector contraction inequality mangasarian1987lipschitz
  • Lemma 2: Generalization bound via uniform convergence bartlett2002rademacher