Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

Zachary Kilwein, Jordan Jalving, Michael Eydenberg, Logan Blakely, Kyle Skolfield, Carl Laird and Fani Boukouvala ()
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Zachary Kilwein: Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Jordan Jalving: Sandia National Laboratories, Albuquerque, NM 87185, USA
Michael Eydenberg: Sandia National Laboratories, Albuquerque, NM 87185, USA
Logan Blakely: Sandia National Laboratories, Albuquerque, NM 87185, USA
Kyle Skolfield: Sandia National Laboratories, Albuquerque, NM 87185, USA
Carl Laird: Sandia National Laboratories, Albuquerque, NM 87185, USA
Fani Boukouvala: Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Energies, 2023, vol. 16, issue 16, 1-17

Abstract: 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.

Keywords: optimal power flow; security; neural networks; optimization (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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