(109e) Physics Informed Machine-Learning for Static Security Analysis of Optimal Power Flow Solutions

In power grid control centers, optimal power flow (OPF) problems are solved several times per day to find optimal setpoints given load demands. However, an even more challenging problem is to have the ability to quickly assess the security of the optimal operating points in the case of contingency events which can result in operating at insecure or suboptimal points. Static grid security analysis can be done through N-1 contingency enumeration, where each contingency event is simulated and the resulting OPF solution is checked for voltage and line flow violations. An operating point that has no voltage or line flow violations is N-1 secure, but this becomes intractable to solve online for large grids that have hundreds of contingencies and thousands of variables. Deep machine learning models have had success in predicting system security under contingency [1, 2] or functioning as a quick OPF solver [3], but operators are wary of these fully black-box models because they require a lot of reliable training data, they ignore well-established power-flow physics, and have no interpretability.

Physics-informed machine learning models have been shown to approximate complex, nonlinear functions while retaining physical generalizability in the areas of physics, differential equations, and systems engineering [4, 5]. In this work, deep neural networks with embedded physics have been trained to predict OPF solutions under contingency and the resulting system security. Various approaches are considered for the generation of balanced and realistic training data, using offline simulations of varying load profiles and rigorous optimization for all contingencies using power flow software package Egret [6]. Different techniques for developing the physics-embedded NN models will be presented, including an augmented loss term that considers Kirchoff’s Current Law at every node in the system, which allows for fewer training points and better performance outside of the training set. This framework is demonstrated on IEEE case studies of increasing size and complexity, and all solutions are compared to fully black-box approaches with respect to accuracy, training data requirements and complexity. Finally, integration of dimensionality reduction techniques with physics-informed NN training is presented for large case studies, which allows for maintaining model accuracy and tractability in the case of high-dimensional input spaces.

References:

1. Sunitha, R., R.S. Kumar, and A.T. Mathew, Online static security assessment module using artificial neural networks. IEEE transactions on power systems, 2013. 28(4): p. 4328-4335.
2. Donnot, B., et al., Fast Power system security analysis with Guided Dropout. arXiv preprint arXiv:1801.09870, 2018.
3. Hu, X., et al., Physics-Guided Deep Neural Networks for PowerFlow Analysis. arXiv preprint arXiv:2002.00097, 2020.
4. Raissi, M., P. Perdikaris, and G.E. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 2019. 378: p. 686-707.
5. Lutter, M., C. Ritter, and J. Peters, Deep lagrangian networks: Using physics as model prior for deep learning. arXiv preprint arXiv:1907.04490, 2019.
6. Knueven, B., et al., Egret v. 0.1 (beta). 2019: ; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Python.

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.