Physics-Informed Neural Networks for AC Optimal Power Flow

Abstract

This paper introduces, for the first time to our knowledge, physics-informed neural networks to accurately estimate the AC-OPF result and delivers rigorous guarantees about their performance. Power system operators, along with several other actors, are increasingly using Optimal Power Flow (OPF) algorithms for a wide number of applications, including planning and real-time operations. However, in its original form, the AC Optimal Power Flow problem is often challenging to solve as it is non-linear and non-convex. Besides the large number of approximations and relaxations, recent efforts have also been focusing on Machine Learning approaches, especially neural networks. So far, however, these approaches have only partially considered the wide number of physical models available during training. And, more importantly, they have offered no guarantees about potential constraint violations of their output. Our approach (i) introduces the AC power flow equations inside neural network training and (ii) integrates methods that rigorously determine and reduce the worst-case constraint violations across the entire input domain, while maintaining the optimality of the prediction. We demonstrate how physics-informed neural networks achieve higher accuracy and lower constraint violations than standard neural networks, and show how we can further reduce the worstcase violations for all neural networks.

Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems

“…Though end-to-end methods have been actively studied for constrained optimizations with promising speedups, the lack of feasibility guarantees presents a fundamental barrier for practical application, e.g., infeasibility due to inaccurate active/inactive limits identification. Infeasible solutions from the end-to-end approach are also observed [5], [13], especially considering the DNN worst-case performance under adversary input with serious constraints violations [14], [45], [46]. This echoes the critical challenge of ensuring the DNN solutions feasibility.…”

“…Though the inequality limits are considered as penalty during training, the DNN solution could still be infeasible due to approximation errors. In [45], [46], the Physics-Informed Neural Networks (PINNs) are applied to predict the optimization problem solutions while incorporating the problem Karush-Kuhn-Tucker (KKT) conditions during training. Though the PINNs present better worst-case performance, the constraints satisfaction is not guarantted by the obtained DNN solution.…”

“…In the previous work, the training (test) set is generally obtained by sampling the input data according to some distribution to train (evaluate) the DNN performance [6], [13]. However, the DNN model obtained from such approaches may not achieve good feasibility performance over the entire input domain D especially considering the worst-case scenarios [14], [45], [46]. In the following, we study the worst-case performance of DNN and determine the sufficient DNN size so that for any possible input from the input region, the resulting DNN solution is guaranteed to be feasible w.r.t.…”

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

“…They have since additionally been used for system identification [35], transient stability predictions [36], and for learning grid dynamics without simulation data [37]. Beyond ODE simulation and trajectory prediction, physics and sensitivity informed methods have also been utilized for regularizing models related to power distribution grid optimization [38], ACOPF [39], [40], DCOPF [41], parameter estimation [42], and risk-aware voltage optimization via "riskregularization" [43].…”

“…This approach was first applied to power systems in [62], where the authors computed formal guarantees for the performance of classification NNs in the context of security assessment. This method was extended in [23] and [40], where the authors computed worst-case performance guarantees for a regression NN which was trained to solve the DC-and AC-OPF problems, respectively. A feedback procedure is developed in [41], which finds the worst-case performing input point, and then adds this points (and its true ground-truth output) into the training set.…”