Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications

This paper presents for the first time, to our knowledge, a framework for verifying neural network behavior in power system applications. Up to this moment, neural networks have been applied in power systems as a black box; this has presented a major barrier for their adoption in practice. Developing a rigorous framework based on mixed-integer linear programming, our methods can determine the range of inputs that neural networks classify as safe or unsafe, and are able to systematically identify adversarial examples. Such methods have the potential to build the missing trust of power system operators on neural networks, and unlock a series of new applications in power systems. This paper presents the framework, methods to assess and improve neural network robustness in power systems, and addresses concerns related to scalability and accuracy. We demonstrate our methods on the IEEE 9-bus, 14-bus, and 162-bus systems, treating both N-1 security and small-signal stability.

[1]  Louis Wehenkel,et al.  Using Machine Learning to Enable Probabilistic Reliability Assessment in Operation Planning , 2018, 2018 Power Systems Computation Conference (PSCC).

[2]  Suyog Gupta,et al.  To prune, or not to prune: exploring the efficacy of pruning for model compression , 2017, ICLR.

[3]  Douglas Kline,et al.  Revisiting squared-error and cross-entropy functions for training neural network classifiers , 2005, Neural Computing & Applications.

[4]  Louis Wehenkel,et al.  Recent Developments in Machine Learning for Energy Systems Reliability Management , 2020, Proceedings of the IEEE.

[5]  Yoshua Bengio,et al.  Understanding the difficulty of training deep feedforward neural networks , 2010, AISTATS.

[6]  Deepjyoti Deka,et al.  Is Machine Learning in Power Systems Vulnerable? , 2018, 2018 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm).

[7]  Francesco Croce,et al.  Provable robustness against all adversarial $l_p$-perturbations for $p\geq 1$ , 2019, ICLR.

[8]  O. Alsaç,et al.  DC Power Flow Revisited , 2009, IEEE Transactions on Power Systems.

[9]  Goran Strbac,et al.  A Deep Learning-Based Feature Extraction Framework for System Security Assessment , 2019, IEEE Transactions on Smart Grid.

[10]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[11]  Robert Eriksson,et al.  Efficient Database Generation for Data-Driven Security Assessment of Power Systems , 2018, IEEE Transactions on Power Systems.

[12]  M. Ferris,et al.  The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms , 2019, ArXiv.

[13]  J. Ramos,et al.  State-of-the-art, challenges, and future trends in security constrained optimal power flow , 2011 .

[14]  M. B. Cain,et al.  History of Optimal Power Flow and Formulations , 2012 .

[15]  David Fridovich-Keil,et al.  Toward Distributed Energy Services: Decentralizing Optimal Power Flow With Machine Learning , 2018, IEEE Transactions on Smart Grid.

[16]  Xueping Gu,et al.  Neural-Network Security-Boundary Constrained Optimal Power Flow , 2011, IEEE Transactions on Power Systems.

[17]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[18]  Ananthram Swami,et al.  The Limitations of Deep Learning in Adversarial Settings , 2015, 2016 IEEE European Symposium on Security and Privacy (EuroS&P).

[19]  R. Sunitha,et al.  Online Static Security Assessment Module Using Artificial Neural Networks , 2013, IEEE Transactions on Power Systems.

[20]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[21]  Louis Wehenkel,et al.  Advanced optimization methods for power systems , 2014, 2014 Power Systems Computation Conference.

[22]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[23]  Yan Du,et al.  Achieving 100x Acceleration for N-1 Contingency Screening With Uncertain Scenarios Using Deep Convolutional Neural Network , 2019, IEEE Transactions on Power Systems.

[24]  Cho-Jui Hsieh,et al.  Efficient Neural Network Robustness Certification with General Activation Functions , 2018, NeurIPS.

[25]  Russell Bent,et al.  Optimization-Based Bound Tightening Using a Strengthened QC-Relaxation of the Optimal Power Flow Problem , 2018, 2023 62nd IEEE Conference on Decision and Control (CDC).

[26]  Jonathon Shlens,et al.  Explaining and Harnessing Adversarial Examples , 2014, ICLR.

[27]  Mevludin Glavic,et al.  (Deep) Reinforcement learning for electric power system control and related problems: A short review and perspectives , 2019, Annu. Rev. Control..

[28]  Fangxing Li,et al.  From AlphaGo to Power System AI: What Engineers Can Learn from Solving the Most Complex Board Game , 2018, IEEE Power and Energy Magazine.

[29]  Yoshua Bengio,et al.  Deep Sparse Rectifier Neural Networks , 2011, AISTATS.

[30]  Aleksander Madry,et al.  Towards Deep Learning Models Resistant to Adversarial Attacks , 2017, ICLR.

[31]  Min Wu,et al.  A Game-Based Approximate Verification of Deep Neural Networks with Provable Guarantees , 2018, Theor. Comput. Sci..

[32]  Matthias Hein,et al.  Provable robustness against all adversarial lp-perturbations for p≥1 , 2019, ICLR.

[33]  Pushmeet Kohli,et al.  A Dual Approach to Scalable Verification of Deep Networks , 2018, UAI.

[34]  Florian Thams,et al.  Deep Learning for Power System Security Assessment , 2019, 2019 IEEE Milan PowerTech.

[35]  Isabelle Guyon,et al.  Introducing machine learning for power system operation support , 2017, ArXiv.

[36]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

[37]  Shie Mannor,et al.  Chance-Constrained Outage Scheduling Using a Machine Learning Proxy , 2018, IEEE Transactions on Power Systems.

[38]  Dmitry Shchetinin,et al.  Efficient Bound Tightening Techniques for Convex Relaxations of AC Optimal Power Flow , 2019, IEEE Transactions on Power Systems.

[39]  Louis Wehenkel,et al.  Automatic Learning Techniques in Power Systems , 1997 .

[40]  Aleksander Madry,et al.  Training for Faster Adversarial Robustness Verification via Inducing ReLU Stability , 2018, ICLR.

[41]  Daniel K. Molzahn,et al.  Efficient Creation of Datasets for Data-Driven Power System Applications , 2019, ArXiv.

[42]  Robert Eriksson,et al.  Data-Driven Security-Constrained OPF , 2017 .

[43]  Gabriela Hug,et al.  Data-Driven Local Control Design for Active Distribution Grids Using Off-Line Optimal Power Flow and Machine Learning Techniques , 2019, IEEE Transactions on Smart Grid.

[44]  Russ Tedrake,et al.  Evaluating Robustness of Neural Networks with Mixed Integer Programming , 2017, ICLR.

[45]  Isabelle Guyon,et al.  Fast Power system security analysis with Guided Dropout , 2018, ESANN.

[46]  Federico Milano,et al.  Power System Modelling and Scripting , 2010 .