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In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods. [ABSTRACT FROM AUTHOR]

This manuscript presents a complete framework for the development and verification of physics-informed neural networks with application to the alternating-current power flow (ACPF) equations. Physics-informed neural networks (PINN)s have received considerable interest within power systems communities for their ability to harness underlying physical equations to produce simple neural network architectures that achieve high accuracy using limited training data. The methodology developed in this work builds on existing methods and explores new important aspects around the implementation of PINNs including: (i) obtaining operationally relevant training data, (ii) efficiently training PINNs and using pruning techniques to reduce their complexity, and (iii) globally verifying the worst-case predictions given known physical constraints. The methodology is applied to the IEEE-14 and 118 bus systems where PINNs show substantially improved accuracy in a data-limited setting and attain better guarantees with respect to worst-case predictions. • An end-to-end framework to design, train, and validate scalable PINNs is proposed. • We formally validate the performance advantages of PINNs over traditional NNs. • We demonstrate this framework on the AC power flow problem for grid operations. [ABSTRACT FROM AUTHOR]

• Deep Neural Networks applied to estimate solar panel size, tilt and azimuth. • Solar panel size estimate with mean percentage error of 3.98%. • Tilt and azimuth estimated with absolute error of 2.55 and 4.71 degrees respectively. • Net load data resolution does not heavily impact accuracy. • Proposed approach is robust to mislabeled training data. There is an ever-growing number of photovoltaic (PV) installations in the US and worldwide. Many utilities do not have complete or up-to-date information of the PVs present within their grids. This research presents a deep neural network approach for estimating PV size, tilt, and azimuth using only behind-the-meter data. It is found that the proposed deep neural network (DNN) method can estimate PV size with an error of 2.09% in a data set with fixed tilt and azimuth values and 3.98% in a data set with varying tilt and azimuths. This is a lower error than the benchmark linear regression approach. A net load data resolution of 1 min provides the lowest error when estimating the PV size. The proposed DNN is also reasonably robust to erroneous training data. When applied to estimate PV tilt and azimuth, the proposed method achieves a mean absolute percentage error of 10.1% and 2.8% respectively. These error metrics are 2.0 × and 3.7 × lower, respectively, than the benchmark linear regression achieves. It was observed that a higher data resolution (1 min) does not provide significant gains in accuracy. It is recommended that a data resolution of 60 min is used to reduce the effects of phenomena such as cloud enhancements. The proposed deep neural network approach is also highly robust, maintaining reasonable accuracy with high levels of mislabeled training data. [ABSTRACT FROM AUTHOR]