Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Learning to Pursue AC Optimal Power Flow Solutions with Feasibility Guarantees

Damola Ajeyemi, Yiting Chen, Antonin Colot, Jorge Cortes, Emiliano Dall'Anese

TL;DR

The paper tackles real-time AC OPF for distribution feeders with DERs by merging a safe gradient flow with a neural-network surrogate that approximates the QP update. The approach delivers practical feasibility guarantees and exponential convergence to a neighborhood of a strict local optimizer, while enabling both online feedback-based and offline PF-based deployments. The authors prove theoretical stability and forward-invariance under bounded errors, and demonstrate superior voltage regulation and computational speed on a 93-bus SimBench system using Open Power System Data. This yields a scalable, reliable framework for fast, guaranteed-feasible OPF solutions in modern power distribution networks.

Abstract

This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected gradient flow - referred to as the safe gradient flow - that incorporates voltage and current information obtained either through real-time measurements or power flow computations. These two setups enable both online and offline implementations. The safe gradient flow involves the solution of convex quadratic programs (QPs). To enhance computational efficiency, we propose a novel framework that employs a neural network approximation of the optimal solution map of the QP. The resulting method has two key features: (a) it ensures that the DERs' setpoints are practically feasible, even for an online implementation or when an offline algorithm has an early termination; (b) it ensures convergence to a neighborhood of a strict local optimizer of the AC OPF. The proposed method is tested on a 93-node distribution system with realistic loads and renewable generation. The test shows that our method successfully regulates voltages within limits during periods with high renewable generation.

Learning to Pursue AC Optimal Power Flow Solutions with Feasibility Guarantees

TL;DR

The paper tackles real-time AC OPF for distribution feeders with DERs by merging a safe gradient flow with a neural-network surrogate that approximates the QP update. The approach delivers practical feasibility guarantees and exponential convergence to a neighborhood of a strict local optimizer, while enabling both online feedback-based and offline PF-based deployments. The authors prove theoretical stability and forward-invariance under bounded errors, and demonstrate superior voltage regulation and computational speed on a 93-bus SimBench system using Open Power System Data. This yields a scalable, reliable framework for fast, guaranteed-feasible OPF solutions in modern power distribution networks.

Abstract

This paper focuses on an AC optimal power flow (OPF) problem for distribution feeders equipped with controllable distributed energy resources (DERs). We consider a solution method that is based on a continuous approximation of the projected gradient flow - referred to as the safe gradient flow - that incorporates voltage and current information obtained either through real-time measurements or power flow computations. These two setups enable both online and offline implementations. The safe gradient flow involves the solution of convex quadratic programs (QPs). To enhance computational efficiency, we propose a novel framework that employs a neural network approximation of the optimal solution map of the QP. The resulting method has two key features: (a) it ensures that the DERs' setpoints are practically feasible, even for an online implementation or when an offline algorithm has an early termination; (b) it ensures convergence to a neighborhood of a strict local optimizer of the AC OPF. The proposed method is tested on a 93-node distribution system with realistic loads and renewable generation. The test shows that our method successfully regulates voltages within limits during periods with high renewable generation.

Paper Structure

This paper contains 17 sections, 3 theorems, 51 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation and Proposed Model
  3. Distribution System Model
  4. AC OPF Formulation
  5. Proposed Mathematical Framework and Implementations
  6. Motivations and Rationale
  7. Neural Network-based OPF Pursuit
  8. Algorithmic Design
  9. Online and Offline Implementations
  10. Experimental Results in a Distribution Feeder
  11. Dataset Generation and Training
  12. Voltage regulation and over-voltage duration
  13. Computational times
  14. Theoretical Analysis
  15. Conclusions
  16. ...and 2 more sections

Key Result

Lemma 5.1

Let Assumption as:Regularity hold, and assume that $\boldsymbol{u} \mapsto C_p(\boldsymbol{u})$, $\boldsymbol{\nu} \mapsto C_v(\boldsymbol{\nu})$ are twice continuously differentiable over $\mathcal{B}(\boldsymbol{u}^*,r_1)$ and for any $\boldsymbol{\nu}$ Then: (i) For any $\boldsymbol{n} \in \mathc

Figures (5)

  • Figure 1: (Left) Feedback-based online implementation leveraging measurements from the network. (Center) Offline implementation with power-flow solver. (Right) Design process.
  • Figure 2: Distribution network used in the simulations SimBench.
  • Figure 3: Overvoltage events and number of nodes impacted with the considered simulation setup, when no control actions are implemented.
  • Figure 4: Highest voltage profile and number of nodes experiencing overvoltages with different optimization methods : (a) Batch optimization (BO) using IPOPT; (b) the proposed NN-SGF \ref{['eq:main_NN']}, implemented in an online feedback configuration as in Figure \ref{['fig:proposed_arch']}(left); (c) method where a neural network is trained to emulate BO solutions (NN-BO).
  • Figure 5: Overvoltage duration for the three strategies (s1)--(s3) compared in Figure \ref{['fig:voltage_comparison']}. Additionally, we consider the no control (NC) setup as in Figure \ref{['fig:voltage_nc']} and the SFG.

Theorems & Definitions (4)

  • Remark 2.1: Model and notation
  • Lemma 5.1: Lipschitz continuity
  • Theorem 5.2: Stability and convergence
  • Proposition 5.3: Practical forward invariance