This paper introduces for the first time a framework to obtain provable worst-case guarantees for neural network performance, using learning for optimal power flow (OPF) problems as a guiding example. Neural networks have the potential to substantially reduce the computing time of OPF solutions. However, the lack of guarantees for their worst-case performance remains a major barrier for their adoption in practice. This work aims to remove this barrier. We formulate mixed-integer linear programs to obtain worst-case guarantees for neural network predictions related to (i) maximum constraint violations, (ii) maximum distances between predicted and optimal decision variables, and (iii) maximum sub-optimality. We demonstrate our methods on a range of PGLib-OPF networks up to 300 buses. We show that the worst-case guarantees can be up to one order of magnitude larger than the empirical lower bounds calculated with conventional methods. More importantly, we show that the worst-case predictions appear at the boundaries of the training input domain, and we demonstrate how we can systematically reduce the worst-case guarantees by training on a larger input domain than the domain they are evaluated on.
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Deep decarbonization of the energy sector will require massive penetration of stochastic renewable energy resources and an enormous amount of grid asset coordination; this represents a challenging paradigm for the power system operators who are tasked with maintaining grid stability and security in the face of such changes. With its ability to learn from complex datasets and provide predictive solutions on fast timescales, machine learning (ML) is well-posed to help overcome these challenges as power systems transform in the coming decades. In this work, we outline five key challenges (dataset generation, data pre-processing, model training, model assessment, and model embedding) associated with building trustworthy ML models which learn from physics-based simulation data. We then demonstrate how linking together individual modules, each of which overcomes a respective challenge, at sequential stages in the machine learning pipeline can help enhance the overall performance of the training process. In particular, we implement methods that connect different elements of the learning pipeline through feedback, thus "closing the loop" between model training, performance assessments, and re-training. We demonstrate the effectiveness of this framework, its constituent modules, and its feedback connections by learning the N-1 small-signal stability margin associated with a detailed model of a proposed North Sea Wind Power Hub system.
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.
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