Deep Neural Networks for AC-OPF under Flexible Topology and Two-Stage Stochastic AC-OPF

Abstract

The Optimal Power Flow (OPF) problem is a cornerstone in ensuring the eco-nomic efficiency and operational reliability of modern power grids. However, in many practical applications, conventional iterative solvers often struggle to produce timely solutions. To tackle this challenge, this thesis explores the development of deep neural network (DNN)-based solvers to solve OPF problems more efficiently. The contributions of this work are two-fold:

We first develop DeepOPF-FT as an embedded training approach to design one DNN for solving multiple alternating current optimal power flow (AC-OPF) problems under flexible topology and line admittances, addressing a critical limitation of learning-based OPF schemes. The idea is to embed the discrete topology representation into the continuous admittance space and train a DNN to learn the mapping from (load, admittance) to the corresponding AC-OPF solution. We then employ the trained DNN to solve AC-OPF problems over any power network with the same bus, generation, and line capacity configurations but different topology and/or line admittances. Simulation results over IEEE 9-/57-bus and synthetic 2000-bus test cases demonstrate the effectiveness of our design and highlight the training efficiency improvement of DeepOPF-FT over training one DNN for every combination of power network topology and line admittances.

We then propose DeepOPF-Stoc as a neural network approach to efficiently solve a critical two-stage stochastic AC-OPF problem, which emphasizes reliable and cost-effective grid operation while accounting for uncertainties in renewable energy generation and load demand. We identify a crucial partial permutation-invariance property of the mapping from load to first-stage solution. We then leverage this property in DeepOPF-Stoc to design (i) a novel partially permutation-invariant neural network (PPNN) to learn such mappings, and (ii) a PPNN-aware sampling algorithm to prepare training data efficiently. DeepOPF-Stoc effectively addresses the dimensionality explosion issue inherent in vanilla designs, significantly reducing both the required number of neurons and the volume of training data. Our theoretical analysis confirms the universal approximation capability of PPNNs for our application. We further prove that the PPNN-aware sampling algorithm improves sampling efficiency by a factor of K! compared to uniform sampling, where K represents the number of second-stage scenarios. Simulation results on IEEE 118-bus and synthetic 793-bus test systems demonstrate the superiority of DeepOPF-Stoc over state-of-the-art alternatives. It achieves two orders of magnitude speedup compared to iterative solvers while generating feasible first-stage solutions, comparable second-stage out-of-sample feasibility, within 0.95% cost gap.

In summary, this work establishes a framework for deploying learning-based solvers in practical power grid operations by overcoming two critical deployment barriers: the inability of existing models to handle topology changes without retraining, and the dimensionality explosion associated with stochastic AC-OPF. By resolving these bottlenecks, our methods remain highly applicable to real-world grids subject to frequent scheduled maintenance, network reconfiguration, and contingencies, while efficiently managing renewable energy uncertainties. Looking forward, potential directions for future research include extending these designs to multi-stage OPF frameworks, incorporating security-constrained OPF (SC-OPF) to further enhance grid resilience against N-1 contingencies, and applying the proposed embedded training and PPNN architectures to high-dimensional constrained optimization problems in other critical infrastructures, such as gas and water networks.

Date of Award	18 Mar 2026
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Minghua CHEN (Supervisor)