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Data-Driven Stochastic AC-OPF using Gaussian Processes

Mile Mitrovic

TL;DR

This work tackles stochastic AC-OPF under uncertainty by introducing a data-driven framework that replaces the nonlinear AC-PF balance equations with Gaussian Process Regression (GPR). The full GP-CC-OPF forms an analytical reformulation enabling uncertainty propagation via Taylor or Exact Moment Matching and is demonstrated on IEEE 9, 39, and 118-bus systems, outperforming scenario-based CC-OPF in accuracy and speed. To improve robustness and scalability, a fast hybrid sparse GP CC-OPF is proposed, combining a linear DC-PF balance with a GP learned on AC-DC residuals, and evaluated with sparse inducing points. Across extensive experiments, the GP-based approaches deliver reliable chance-constrained feasibility with competitive costs, while requiring no explicit grid-parameter knowledge, and the hybrid/sparse variant offers up to substantial speedups and robustness to data gaps. The work provides open-source software and a pathway for deploying data-driven, CC-OPF techniques in real-time TSO operations, promising substantial efficiency gains in grids with high Renewable Energy Source penetration.

Abstract

The thesis focuses on developing a data-driven algorithm, based on machine learning, to solve the stochastic alternating current (AC) chance-constrained (CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been successful in academic circles, it is highly nonlinear and computationally demanding, which limits its practical impact. The proposed approach aims to address this limitation and demonstrate its empirical efficiency through applications to multiple IEEE test cases. To solve the non-convex and computationally challenging CC AC-OPF problem, the proposed approach relies on a machine learning Gaussian process regression (GPR) model. The full Gaussian process (GP) approach is capable of learning a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The proposed approach uses various approximations for GP-uncertainty propagation. The full GP CC-OPF approach exhibits highly competitive and promising results, outperforming the state-of-the-art sample-based chance constraint approaches. To further improve the robustness and complexity/accuracy trade-off of the full GP CC-OPF, a fast data-driven setup is proposed. This setup relies on the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty.

Data-Driven Stochastic AC-OPF using Gaussian Processes

TL;DR

This work tackles stochastic AC-OPF under uncertainty by introducing a data-driven framework that replaces the nonlinear AC-PF balance equations with Gaussian Process Regression (GPR). The full GP-CC-OPF forms an analytical reformulation enabling uncertainty propagation via Taylor or Exact Moment Matching and is demonstrated on IEEE 9, 39, and 118-bus systems, outperforming scenario-based CC-OPF in accuracy and speed. To improve robustness and scalability, a fast hybrid sparse GP CC-OPF is proposed, combining a linear DC-PF balance with a GP learned on AC-DC residuals, and evaluated with sparse inducing points. Across extensive experiments, the GP-based approaches deliver reliable chance-constrained feasibility with competitive costs, while requiring no explicit grid-parameter knowledge, and the hybrid/sparse variant offers up to substantial speedups and robustness to data gaps. The work provides open-source software and a pathway for deploying data-driven, CC-OPF techniques in real-time TSO operations, promising substantial efficiency gains in grids with high Renewable Energy Source penetration.

Abstract

The thesis focuses on developing a data-driven algorithm, based on machine learning, to solve the stochastic alternating current (AC) chance-constrained (CC) Optimal Power Flow (OPF) problem. Although the AC CC-OPF problem has been successful in academic circles, it is highly nonlinear and computationally demanding, which limits its practical impact. The proposed approach aims to address this limitation and demonstrate its empirical efficiency through applications to multiple IEEE test cases. To solve the non-convex and computationally challenging CC AC-OPF problem, the proposed approach relies on a machine learning Gaussian process regression (GPR) model. The full Gaussian process (GP) approach is capable of learning a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The proposed approach uses various approximations for GP-uncertainty propagation. The full GP CC-OPF approach exhibits highly competitive and promising results, outperforming the state-of-the-art sample-based chance constraint approaches. To further improve the robustness and complexity/accuracy trade-off of the full GP CC-OPF, a fast data-driven setup is proposed. This setup relies on the sparse and hybrid Gaussian processes (GP) framework to model the power flow equations with input uncertainty.
Paper Structure (82 sections, 100 equations, 29 figures, 6 tables)

This paper contains 82 sections, 100 equations, 29 figures, 6 tables.

Table of Contents

  1. General Introduction
  2. Contributions
  3. Thesis Structure
  4. Corresponding papers
  5. Power System Description and Optimal Power Flow
  6. Introduction
  7. Power System Description
  8. Power Flow
  9. DC Approximation
  10. Optimal Power Flow
  11. Deterministic OPF
  12. Interior-point method
  13. Convex relaxations
  14. Linearized DC-OPF
  15. Stochastic OPF
  16. ...and 67 more sections

Figures (29)

  • Figure 2.2.1: Fundamental concept of the power systems; the figure is taken from https://engineeringnotesonline.com/power-system-structure/.
  • Figure 2.2.2: Graph representation of the power system (IEEE5 bus example).
  • Figure 2.2.3: Illustration of Kirchoff’s bus law.
  • Figure 3.2.1: Types of machine learning tasks; the figure is taken from https://medium.com/almabetter/machine-learning-fundamentals-for-beginners-70f409b1197e.
  • Figure 3.2.2: Illustration of the ERM properties on a regression problem using a toy function.
  • ...and 24 more figures