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Computationally Enhanced Approach for Chance-Constrained OPF Considering Voltage Stability

Yuanxi Wu, Zhi Wu, Yijun Xu, Huan Long, Wei Gu, Shu Zheng, Jingtao Zhao

TL;DR

This work tackles chance-constrained voltage-stability-constrained OPF under renewable uncertainty by embedding a neural-network surrogate for the voltage-stability index (VSI) and employing adaptive polynomial chaos expansion (APCE) for distribution-free uncertainty propagation. A dimensionally decomposed APCE (DD-APCE) and a partial least squares NN (PLS-NN) framework are introduced to scale the approach to large systems, followed by an iterative scheme that updates the operation point to satisfy chance constraints. The framework is validated on multiple test systems, demonstrating accurate VSI surrogate performance, faithful uncertainty quantification, and significant computational gains while enhancing voltage stability. The method is data-driven and distribution-free, making it applicable to real-world networks, with potential extensions to joint chance constraints and high-dimensional uncertainties.

Abstract

The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained voltage-stability-constrained optimal power flow (CC-VSC-OPF) problem, which is hindered by the implicit voltage stability index and intractable chance constraints Leveraging a neural network (NN)-based surrogate model, the stability constraint is explicitly formulated and directly integrated into the model. To perform uncertainty propagation without relying on presumptions or complicated transformations, an advanced data-driven method known as adaptive polynomial chaos expansion (APCE) is developed. To extend the scalability of the proposed algorithm, a partial least squares (PLS)-NN framework is designed, which enables the establishment of a parsimonious surrogate model and efficient computation of large-scale Hessian matrices. In addition, a dimensionally decomposed APCE (DD-APCE) is proposed to alleviate the "curse of dimensionality" by restricting the interaction order among random variables. Finally, the above techniques are merged into an iterative scheme to update the operation point. Simulation results reveal the cost-effective performances of the proposed method in several test systems.

Computationally Enhanced Approach for Chance-Constrained OPF Considering Voltage Stability

TL;DR

This work tackles chance-constrained voltage-stability-constrained OPF under renewable uncertainty by embedding a neural-network surrogate for the voltage-stability index (VSI) and employing adaptive polynomial chaos expansion (APCE) for distribution-free uncertainty propagation. A dimensionally decomposed APCE (DD-APCE) and a partial least squares NN (PLS-NN) framework are introduced to scale the approach to large systems, followed by an iterative scheme that updates the operation point to satisfy chance constraints. The framework is validated on multiple test systems, demonstrating accurate VSI surrogate performance, faithful uncertainty quantification, and significant computational gains while enhancing voltage stability. The method is data-driven and distribution-free, making it applicable to real-world networks, with potential extensions to joint chance constraints and high-dimensional uncertainties.

Abstract

The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained voltage-stability-constrained optimal power flow (CC-VSC-OPF) problem, which is hindered by the implicit voltage stability index and intractable chance constraints Leveraging a neural network (NN)-based surrogate model, the stability constraint is explicitly formulated and directly integrated into the model. To perform uncertainty propagation without relying on presumptions or complicated transformations, an advanced data-driven method known as adaptive polynomial chaos expansion (APCE) is developed. To extend the scalability of the proposed algorithm, a partial least squares (PLS)-NN framework is designed, which enables the establishment of a parsimonious surrogate model and efficient computation of large-scale Hessian matrices. In addition, a dimensionally decomposed APCE (DD-APCE) is proposed to alleviate the "curse of dimensionality" by restricting the interaction order among random variables. Finally, the above techniques are merged into an iterative scheme to update the operation point. Simulation results reveal the cost-effective performances of the proposed method in several test systems.
Paper Structure (28 sections, 2 theorems, 26 equations, 11 figures, 4 tables, 2 algorithms)

This paper contains 28 sections, 2 theorems, 26 equations, 11 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Formulation of CC-VSC-OPF
  4. Surrogate Model for Voltage Stability Index
  5. Practical Uncertainty Propagation Approach
  6. Motivation
  7. Adaptive Polynomial Chaos Expansion
  8. Gram Matrix
  9. Orthogonal Basis
  10. APCE Approximation
  11. Dimensionally Decomposed APCE
  12. The Integrated Data-driven Scheme
  13. PLS-NN Framework
  14. The Iterative Scheme
  15. Simulations and Results
  16. ...and 13 more sections

Key Result

Proposition 1

For any distinct $i,j\in\mathbb{N}\cap[1,L_{m}]$, the $i$-th and $j$-th element of the polynomial vector $\boldsymbol{\Psi}_m(\boldsymbol{\xi})$ are mutually orthonormal w.r.t. the probability measure of $\boldsymbol{\xi}$.

Figures (11)

  • Figure 1: Flowchart for establishing NN-based model
  • Figure 2: Comparison between MC simulations and: (a) PCE; (b) APCE
  • Figure 3: Accuracy of NN-based surrogate model: left column for IEEE 14-bus system, and right column for IEEE 30-bus system
  • Figure 4: Comparison between MC simulations and APCE metamodel: top row for IEEE 14-bus system, and bottom row for IEEE 30-bus system
  • Figure 5: Probability distribution of the VSI with and without voltage stability constraint in small cases
  • ...and 6 more figures

Theorems & Definitions (9)

  • Remark 1
  • Definition 1: Gram matrix
  • Proposition 1: Orthonormality
  • proof
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Remark 4