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Transient Stability-Constrained OPF: Neural Network Surrogate Models and Pricing Stability

Manuel Garcia, Nicole LoGiudice, Robert Parker, Russell Bent

TL;DR

The paper tackles transient stability in economic dispatch by enforcing frequency constraints through a neural-network surrogate within a Transient Stability-Constrained OPF ($TSC-OPF$). It introduces a model-driven active sampling algorithm that iteratively generates training data near the stability boundary, embedding an explicit NN representation inside the AC-OPF framework. The work analyzes how NN input choices affect market pricing, highlighting a trade-off between accuracy and pricing efficacy, including discriminatory versus uniform pricing patterns. Validation on a Hawaii test case shows substantial stability improvements at low computational and financial cost, with the potential to stabilize all load scenarios for certain NN inputs and threshold settings. These findings offer practical guidance for deploying stability-constrained OPF in wholesale markets and emphasize the importance of input selection for pricing and incentive compatibility.

Abstract

A Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem is proposed that enforces frequency stability constraints using Neural Network (NN) surrogate models. NNs are trained using a novel model-driven active sampling algorithm that iteratively generates NN training data located near the stability boundary and contained within the feasible set of the Alternating Current Optimal Power Flow (AC-OPF) problem. In the context of wholesale electricity markets, pricing structures are analyzed along with their dependencies on the selected input features to the NN surrogate model. An important insight identifies a trade-off between the accuracy of the NN surrogate model and sensible locational pricing structures. NN surrogate models for frequency stability are validated by ensuring the resulting TSC-OPF solution is stable over randomly generated load samples using a small Hawaii test case. The proposed TSC-OPF problem is shown to significantly enhance frequency stability at low computational cost and low financial cost to the system. For certain selections of NN inputs, the TSC-OPF problem is able to stabilize all load scenarios for which the solution to the AC-OPF problem resulted in instability.

Transient Stability-Constrained OPF: Neural Network Surrogate Models and Pricing Stability

TL;DR

The paper tackles transient stability in economic dispatch by enforcing frequency constraints through a neural-network surrogate within a Transient Stability-Constrained OPF (). It introduces a model-driven active sampling algorithm that iteratively generates training data near the stability boundary, embedding an explicit NN representation inside the AC-OPF framework. The work analyzes how NN input choices affect market pricing, highlighting a trade-off between accuracy and pricing efficacy, including discriminatory versus uniform pricing patterns. Validation on a Hawaii test case shows substantial stability improvements at low computational and financial cost, with the potential to stabilize all load scenarios for certain NN inputs and threshold settings. These findings offer practical guidance for deploying stability-constrained OPF in wholesale markets and emphasize the importance of input selection for pricing and incentive compatibility.

Abstract

A Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem is proposed that enforces frequency stability constraints using Neural Network (NN) surrogate models. NNs are trained using a novel model-driven active sampling algorithm that iteratively generates NN training data located near the stability boundary and contained within the feasible set of the Alternating Current Optimal Power Flow (AC-OPF) problem. In the context of wholesale electricity markets, pricing structures are analyzed along with their dependencies on the selected input features to the NN surrogate model. An important insight identifies a trade-off between the accuracy of the NN surrogate model and sensible locational pricing structures. NN surrogate models for frequency stability are validated by ensuring the resulting TSC-OPF solution is stable over randomly generated load samples using a small Hawaii test case. The proposed TSC-OPF problem is shown to significantly enhance frequency stability at low computational cost and low financial cost to the system. For certain selections of NN inputs, the TSC-OPF problem is able to stabilize all load scenarios for which the solution to the AC-OPF problem resulted in instability.

Paper Structure

This paper contains 36 sections, 1 theorem, 8 equations, 11 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contributions
  4. Transient Stability-Constrained OPF
  5. General Problem Formulation
  6. Transmission Constraints
  7. Generator Model
  8. Explicit NN Representation
  9. Choice of NN Input and Pricing Implications
  10. Defining Prices
  11. Incentive Alignment
  12. Choice of NN Input Features
  13. Active Sampling Algorithm
  14. Algorithm Intuition
  15. Algorithm Description
  16. ...and 21 more sections

Key Result

Proposition 1

Consider a KKT point from Definition KKTdef. If prices are chosen as in pprice-hprice and reserve prices are non-negative $\alpha\geq \bold{0}$, then the dispatch $(\bold{g}_j^{\star},\bold{r}_j^{\star},\bold{h}_j^{\star})$ represents a globally optimal solution to the profit maximization problems P

Figures (11)

  • Figure 1: Toy example illustrating the intuition of the active sampling algorithm.
  • Figure 2: Histogram illustrating the distribution of total system load drawn from a Gamma distribution.
  • Figure 3: Fraction of unstable load samples versus threshold parameter $c$ for different input selections.
  • Figure 4: Optimal objective value of TSC-OPF (dispatch cost) versus threshold parameter $c$.
  • Figure 5: Optimal objective value of TSC-OPF (dispatch cost) versus the fraction of unstable load samples.
  • ...and 6 more figures

Theorems & Definitions (2)

  • Definition 1
  • Proposition 1