(476b) Deep Neural Network As Surrogates for Intractable Constraints and Problem Dimension Reduction: Security Constrained AC Optimal Power Flow

Optimal power flow (OPF) problems are frequently used in industry and academia to find economically optimal generator setpoints that balance given load demands (Cain 2012). Ideally, optimal solutions must also be “N-1 secure”, which means that the system can absorb contingency events (e.g., transmission line or generator failures) without loss of service. Current practice is to solve the OPF problem and then check a subset of contingencies against heuristic values, resulting in suboptimal solutions. Unfortunately, online solution of the full OPF including N-1 contingencies, leads to a two-stage stochastic programming formulation, which is intractable for even modest sized electrical grids. To address this challenge, we present an efficient method to replace N-1 security constraints with a Neural Network (NN) classification model that maps the feasible space.

The first challenge towards training an accurate NN representation of the secure operation is sampling, due to non-convexity, high dimensionality (10,000’s of variables) and large variable ranges of the system state space. Our approach introduces an optimization-based adaptive sampling technique (Dias 2019, Metta 2021) which aims to find informative sampling locations for our NN classifier (i.e., boundary points and points with high prediction error). This is distinct from existing sampling approaches for this problem which use hyperspheres (Venzke et al. 2019). We will present a non-linear programming formulation, that when solved using multistart approaches, leads to targeted addition of boundary samples that improve the classification accuracy of the NN models. Moreover, the availability of a full OPF N-1 contingency formulation enables us to solve an optimization problem that leads to new samples in regions where the classifier has maximum deviations from the full model. These two metrics combined lead to accurate NN classifiers of the security region, with reduced sampling requirements.

Once the NN classifier model is trained and validated, it is embedded as a constraint into the original OPF formulation, which is a nonlinear, nonconvex problem with equations that are based on mechanistic knowledge. Hence, the overall OPF+NN formulation is a hybrid model (i.e., comprised of both physics-based and data-based constraints). We show that solving this hybrid optimization problem to get secure solutions is accurate and efficient when compared to the full OPF with N-1 contingency problem. We also investigate the performance of different NN models including non-linear sigmoid activation functions and linear ReLU networks. The former naturally lead to an overall non-linear program (NLP) formulation, while the latter can be approximated using complementarity formulations into NLPs. We show that solutions found with the hybrid formulation have marginally increased computational time when compared to unconstrained OPF but are much more secure to contingency events. Finally, through this work we address important challenges in hybrid modeling including the effects of surrogate complexity vs accuracy, hybrid sampling techniques using physics-based formulations and surrogates, and how to efficiently embed NN models using the Pyomo environment (Hart 2017).

Disclaimer: Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the USDOE or the United States Government.

References:

M.B. Cain, R.P. Oneill, A. Castillo, 2012, History of Optimal Power Flow and Formulations, Federal Energy Regulatory Commision, p:1-36

Dias, Lisia, Atharv Bhosekar, and Mariathi Ierapetritou. "Adaptive Sampling Approaches for Surrogate- Based

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W.E. Hart, C.D. Laird, J.P. Watson, D.L. Woodruff, G.A. Hackebeil, B.L. Nicholson, J.D. Siirola, 2017, Pyomo – Optimization Modeling in Python. Second Edition. Vol. 67. Springer.

Metta, Nirupaplava, Rohit Ramachandran, and Marianthi Ierapetritou. "A novel adaptive sampling based methodology for feasible region identification of compute intensive models using artificial neural network." AIChE Journal 67.2 (2021): e17095

Venzke, D. Molzahn, S. Chatzivasileiadis, 2019, Efficient Creation of Datasets for Data-Driven Power System Applications, Electrical Engineering and Systems Science: Systems and Control, Under Review.

Venzke, D.T. Viola, J. Mermet-Guyennet, G.S. Misyris, S. Chatzivasileiadis, 2020, Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow to Mixed-Integer Linear Programs, Under Review.