Learning-based optimal power flow : addressing feasibility, adaptability, and scalability issues

Abstract

The Optimal Power Flow (OPF) problem has been studied for many years. The aim is to determine the most efficient operating condition while meeting grid demand and physical constraints. However, due to the nonconvexity and nonlinearity of power flow equations, this problem has proved to be NP-hard. To obtain a solution within polynomial time, it is common to solve a simplification problem or use a non-linear optimization solver. However, these methods often face issues in providing real time and high quality solutions in modern power grids. Thanks to the universal approximation capability of machine learning models and the fact that they can provide a solution in real time, leveraging such models to solve OPF has become a hot topic. Even though a large number of learning models are validated in computational speed and solution quality, three primary issues are hindering their practical applicability. In this thesis, we would like to improve the applicability of learning-based OPF models by addressing feasibility, adaptability, and scalability issues. To address the feasibility issue, we propose an OptNet-embedded approach for OPF proxy to provide a feasible solution efficiently. It is achieved by designing a three-stage neural network architecture with an embedded optimization problem to approximate the original OPF problem solving. Finally, to expedite the solving process, a two-step pruning method is proposed to remove the unnecessary inequality constraints and values. Numerical experiments on the IEEE 4- and 14-bus test systems validate that the proposed approach can provide a "good enough" feasible solution. To address the adaptability issue for topology changes, we propose a topology change-aware two-stage approach. It is achieved by designing a topology transfer framework and by dynamically ensembling well-trained models obtained from the framework. Numerical experiments on the modified IEEE 14- and TAS 97-bus test systems demonstrate that the proposed approach can provide optimality-enhanced and equality function-satisfied OPF solutions as compared to other learning-based approaches. To address the adaptability issue for environmental changes, we propose a multi-task learning approach. It is achieved by utilizing multi-task learning to model multiple scenarios simultaneously by sharing network parameters. Meanwhile, to balance the training process, an error-focused up-sampling method and an adaptive-weight algorithm are proposed. Simulation results based on the IEEE 14- and 118-bus systems show that the proposed framework can provide optimality and feasibility-enhanced OPF solutions in near real time compared to existing methods. To address the scalability issue of Graph Neural Networks (GNN), we propose a multi-fidelity OPF learning framework and a clustering training algorithm from data and space aspects, respectively. It is achieved because of the sample efficiency and memory efficiency for the proposed framework and training algorithm, respectively. Simulation results based on the IEEE 14- to GOC 10000-bus systems validate that the proposed method can be scalable and efficient compared to existing graph-based methods. In summary, this thesis aims to improve the applicability of learning-based OPF models. We also believe that our proposed methods can be further extended to other learning-based optimization problems in or beyond power systems, e.g., multi-energy systems.