Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods

Abstract

The Optimal Power Flow (OPF) problem is a fundamental building block for the optimization of electrical power systems. It is nonlinear and nonconvex and computes the generator setpoints for power and voltage, given a set of load demands. It is often solved repeatedly under various conditions, either in real-time or in large-scale studies. This need is further exacerbated by the increasing stochasticity of power systems due to renewable energy sources in front and behind the meter. To address these challenges, this paper presents a deep learning approach to the OPF. The learning model exploits the information available in the similar states of the system (which is commonly available in practical applications), as well as a dual Lagrangian method to satisfy the physical and engineering constraints present in the OPF. The proposed model is evaluated on a large collection of realistic medium-sized power systems. The experimental results show that its predictions are highly accurate with average errors as low as 0.2%. Additionally, the proposed approach is shown to improve the accuracy of the widely adopted linear DC approximation by at least two orders of magnitude.

Recent Developments in Machine Learning for Energy Systems Reliability Management

“…More recently, several papers proposed to exploit Deep Learning (DL) for this purpose. Pan et al [153] use deep learning to predict the decision of a DC-OPF while in [154], [155] the authors predict the decision of an AC-OPF. In all these papers a post-processing method ensuring the feasibility of the solution is described.…”

“…In [155], the output of the DL model is constrained with a sigmoid function to adhere to active power generation and voltage magnitude constraints and a power flow problem is then solved based on the predictions. Finally, in [154], the authors take advantage of previous optimal power flow solutions computed at previous time steps as well as a dual Lagrangian method to improve the solution and enforce physical and operational constraints.…”

A Data-driven Method for Fast AC Optimal Power Flow Solutions via Deep Reinforcement Learning

“…Step 6 gets a batch size of data from the training dataset; Steps 7-9 refer to the interactions between the DRL agent and the power grid environment such that the trajectories are collected; Steps 10-13 imply the training of the actor NN, and (8), (10) (the outputs of the critic NN), and (11) are calculated according to the previously collected trajectories, then Adam optimizer [39] is applied to maximize (12); and Steps 14-16 indicate the training of the critic NN, and (8) is calculated from the previously collected trajectories, then Adam optimizer is applied to minimize the objective function (13).…”

“…In [9], a graph neural network (NN) has been applied to approximate the solutions of PF solvers. Deep NNs (DNN) are similarly utilized to solve the DC OPF [10], [11] and AC OPF problems [12], [13]. A commonality among all these methods is that they primarily depend on supervised learning techniques to train the NNs while using massive simulations that must be obtained ahead of time for approximating optimal solutions.…”

Machine learning for ranking day-ahead decisions in the context of short-term operation planning

“…Closer to the subject of the present work, several papers propose to use machine learning to learn the outputs of a SCOPF. For instance, [11]- [13] exploit deep learning to predict the generators set-points. Finally, several other papers propose machine learning approaches to build proxies of shorter-term decision-making contexts to be used when solving longer-term reliability assessment problems, but in other contexts than short-term operation.…”