Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow

Abstract

Physics-informed neural networks exploit the existing models of the underlying physical systems to generate higher accuracy results with fewer data. Such approaches can help drastically reduce the computation time and generate a good estimate of computationally intensive processes in power systems, such as dynamic security assessment or optimal power flow. Combined with the extraction of worst-case guarantees for the neural network performance, such neural networks can be applied in safety-critical applications in power systems and build a high level of trust among power system operators. This paper takes the first step and applies, for the first time to our knowledge, Physics-Informed Neural Networks with Worst-Case Guarantees for the DC Optimal Power Flow problem. We look for guarantees related to (i) maximum constraint violations, (ii) maximum distance between predicted and optimal decision variables, and (iii) maximum sub-optimality in the entire input domain. In a range of PGLib-OPF networks, we demonstrate how physics-informed neural networks can be supplied with worst-case guarantees and how they can lead to reduced worst-case violations compared with conventional 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.…”

Physics-Informed Neural Networks for AC Optimal Power Flow

“…In case of a physics-informed neural network, on top of comparing the NN predictions to the AC-OPF setpoints of the training database, the validity of the physical equations governing the problem will also be accessed during NN training (see [15] [13], and our previous work [16] for DC-OPF applications). Since the optimal value should satisfy the KKT conditions given in ( 15) -( 19), the disparities in the KKT condition, denoted by , as shown in (23a)-(23d) are added to the NN training loss function (24) and minimized during training.…”