### Project purpose

The project designs a new generation of emergency control systems for the U.S. power grid that integrates with existing automated and manual protection and operational processes while also allowing these processes to continue to operate. The new emergency controls include automated, real-time corrective controls to ensure voltage stability and small signal stability following a significant system disturbance. These automated corrective controls will take the system from a post-disturbance emergency state to a stable restored state so that the system operator may confidently resume normal, economically optimized operations. The emergency control actions are computed in real time, making them adaptive to the current system state and the imposed system disturbance.

### Technical approach

The controls to ensure voltage stability are computed using non-traditional optimal power flow (OPF) formulations that represent the physics of AC power flow in computationally efficient forms to enable fast computations and control. Some offline, pre-computation might be required to speed up the real-time implementation of the control computations. Calculating load shedding relative to the pre-contingency load level and using with the conservative assumption that the generators must come back within their long-term reactive power limits and maintain fixed voltage magnitudes at their terminals, the steady-state optimization algorithms can provide stabilizing control actions and accurate predictions of the post-contingency operating point. The accuracy of the prediction is verified by comparison with dynamic simulations that assume control action implementation at different points in time. The designed methods based on approximating the voltage stability region based on the analytic tools (fixed-point argument – convex restrictions), machine learning (convex polytope machines), and convex relaxations/approximations (severe contingency solver, IV formulation). They outperform more traditional under-voltage load shedding schemes which were used as a benchmark. Furthermore, the methods can provide control actions sufficiently fast to save the system from voltage collapse. We further adopt our methods to ensure small-signal stability of the system using frequency regulation, HVDC power injections, SVC reactive power injections, and load shedding as controls. On that way, we propose to use time-discretization above convex restrictions and machine learning methods (convex polytope machines, neural networks).

**Yury Maximov (PI)** is a computer scientist working on power systems, high-dimensional statistics, empirical process theory, machine learning and optimization methods behind them. Yury obtained his Ph.D. in Math from Moscow Institute of Physics and Technology in 2013. During his study, Yury spent several years in the industry as a software engineer and project manager working on industry-grade machine learning, information retrieval and business intelligence solutions. He joined LANL in October 2016 as a postdoc in T-4 and was converted to a scientist in T-5 in March~2018. At LANL he is a PI of the DOE AGM “Robust Real-Time Control, Monitoring, and Protection of Large-Scale Power Grids in Response to Extreme Events” and DOE GMLC “Emergency Monitoring and Control Through New Technologies and Analytics” project. He is an author of more than 20 peer reviewed publications including the top ML/statistical venues such as NIPS, ICML, JAIR, EJOS, IJCAI etc.

**Deepjoyti Deka** is a staff scientist at Los Alamos National Laboratory, where he was previously a postdoctoral research associate at the Center for Nonlinear Studies. His research interests include the design and analysis of power grid structure, operations and data security, and modeling and optimization in social and physical networks. At LANL, Dr. Deka serves as a co-principal investigator for DOE-GMLC project on machine learning in distribution systems and an LDRD project in cyber-physical security. Before joining the laboratory, he received the M.S. and Ph.D. degrees in Electrical Engineering from the University of Texas, Austin, TX, USA, in 2011 and 2015, respectively.

**Andreas Wächter **is a Professor in the Department of Industrial Engineering and Management Sciences at Northwestern University. He obtained his master's degree in Mathematics at the University of Cologne, Germany, in 1997, and this Ph.D. in Chemical Engineering at Carnegie Mellon University in 2002. Before joining Northwestern University in 2011, he was a Research Staff Member in the Department of Mathematical Sciences at IBM Research in Yorktown Heights, NY. His research interests include the design, analysis, implementation and application of numerical algorithms for nonlinear continuous and mixed-integer optimization. He is a recipient of the 2011 Wilkinson Prize for Numerical Software and the 2009 Informs Computing Society Prize for his work on the open-source optimization package Ipopt. He is currently spending a year at Los Alamos National Laboratory as the Ulam Fellow in the Center for Nonlinear Studies

**Sidhant Misra** is a staff scientist at Los Alamos National Laboratory. His recent work has focused on the design of learning algorithms for inferring the structure of graphical models from data, use of mixed-integer optimization in learning, and use of learning to enhance real-time optimization. Dr. Misra obtained his PhD from the Massachusetts Institute of Technology in Electrical Engineering and Computer Science in 2014.

**Marc Vuffray** is a staff scientist at Los Alamos National Laboratory. He received his M.Sc. in physics in 2008, and his Ph.D. in computer and communication sciences in 2014. His current work focuses on the development of new methods to control and optimize energy networks under uncertainties and machine learning technique for network reconstruction. In particular he developed risk-aware optimization methods with provable guarantees for safe economic dispatch and resource utilization for natural gas networks and he designed and analysed a genuine class of graphical-model reconstruction algorithms that are efficient both with respect to computational and sample complexity.

**Lab+1 (PNNL):** Yuri Makarov (co-PI), Mallikarjuna Vallem

**Additional contributors:** Scott Backhaus (NIST, Boulder), Michael Chertkov (University of Arizona), Dongchan Lee (MIT), Line Roald (University of Arizona), Konstantin Turitsyn (MIT).

#### Publications

- D. Lee, H. D. Nguyen, K. Dvijotham, K. Turitsyn.
*"Convex Restriction of Power Flow Feasibility Setы. IEEE Trans. on Control of Network Systems, 2019"* - K. Dvijotham, H. Nguyen, K. Turitsyn,
*"Solvability regions of affinely parameterized quadratic equations, IEEE Cont. Sys. Letters ( V.2, Iss. 1, 2018 )"* - H. Nguyen, K. Dvijotham, K. Turitsyn.
*"Construction of Convex Inner Approximations of Optimal Power Flow Feasibility Sets. IEEE Trans Power Systems, v 34 iss. 1, 2019"* - Y. Suhyoun, H. Nguyen, and K. Turitsyn.
*"Simple certificate of solvability of power flow equations for distribution systems, IEEE PES GM, 2015"* - S. Misra, L. Roald, M. Vuffray, M. Chertkov.
*"Fast and Robust Determination of Power System Emergency Control Actions, IREP, 2017"* - L. Roald, S. Misra, T. Krause and G. Andersson,
*"Corrective Control to Handle Forecast Uncertainty: A Chance Constrained Optimal Power Flow, IEEE Trans on Power Systems, March 2017"* - Lee, D., Turitsyn, K., Molzahn, D. K. & Roald, L.,
*"Feasible Path Optimal Power Flow using Convex Restrictions, in preparation (in review). Arxiv: 1906:09483"* - Owen, A.B., Maximov, Y. and Chertkov, M., 2019.
*"Importance sampling the union of rare events with an application to power systems analysis."*Electronic Journal of Statistics, 13(1), pp.231-254. - D. Lee, L. Aolaritei, L. Vu and K. Turitsyn.
*“Robustness against Disturbances in Power Systems under Frequency Constraints,”*In IEEE Transactions on Control of Network Systems, 2018. - D. Lee, Y. Maximov, K. Turitsyn.
*"Distributed Frequency Control with Transient Stability Constraint from Convex Polytope Machines (in preparation)"* - Lee, D., Roald, L., Molzahn, D. & Turitsyn, K.
*“Robust AC Optimal Power Flow under Power Injection Uncertainty”*, in preparation (in preparation) - Vallem M.R., B. Vyakaranam, J.T. Holzer, N.A. Samaan, Y.V. Makarov, R. Diao, and Q. Huang, et al. 2017.
*"Hybrid Cascading Outage Analysis of Extreme Events with Optimized Corrective Actions."*In 19th International Conference on Intelligent Systems Application to Power Systems (ISAP 2017), September 17-20, 2017, San Antonio, Texas - Vallem M.R., B. Vyakaranam, R. Tipireddy, J.T. Holzer, Y.V. Makarov, and N.A. Samaan. 2018.
*"Stochastic correlation analysis to rank the impact of intermittent wind generation on unreliability margins of power systems."*In IEEE International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2018), June 24-28, 2018, Boise, ID, 1-6 - Artem Mikhalev, Alexander Emchinov, Samuel Chevalier, Yury Maximov, Petr Vorobev
*"A Bayesian Framework for Power System Components Identification."*IEEE PES General Meeting, 2020. - Nikolay Stulov, Dejan J Sobajic, Yury Maximov, Deepjyoti Deka, Michael Chertkov.
*"Learning a Generator Model from Terminal Bus Data."*Power Systems Computation Conference 2020. - Pena-Ordieres, Alejandra, et al.
*"DC Optimal Power Flow with Joint Chance Constraints."*arXiv preprint arXiv:1911.12439 (2019). - Dongchan Lee, Konstantin Turitsyn, Daniel K. Molzahn and Line A. Roald,
*"Robust AC Optimal Power Flow with Convex Restriction,"*arXiv:2005.04835 - Dongchan Lee, Konstantin Turitsyn, Daniel K. Molzahn and Line A. Roald,
*"Feasible Path Identification in Optimal Power Flow with Sequential Convex Restriction,"*IEEE Transactions on Power Systems, arXiv:1906.09483 - Pena-Ordieres, Alejandra, et al.
*"DC Optimal Power Flow with Joint Chance Constraints."*arXiv preprint arXiv:1911.12439 (2019).

#### Panel Presentation: Emergency control analysis, IEEE ISGT 2019

- Line Roald. Fast Decision-Making for Emergency Control: Using Steady-State Optimization to Detect and Mitigate Imminent Voltage Collapse
- Yury Maximov. Emergency Control and Monitoring through New Technologies and Analytics:

Mathematical Tools - Vallem. Emergency control analysis using Dynamic Contingency Analysis Tool (DCAT)

#### Other talks:

- Vallem. Workshop presentation: Dynamic Contingency Analysis Tool (DCAT) – A Framework for Analysis of Extreme Events in Power Systems, LANL 2017 Grid Science Winter School & Conference, Santa Fe, NM
- Lee.
*“Convex Restriction of Power Flow Feasibility Sets,”*INFORMS Annual Meeting, Phoenix, AZ, November 2018. - Lee.
*“Convex Restriction of Power Flow Feasibility Sets,”*23rd International Symposium on Mathematical Programming (ISMP), Bordeaux, France, July 2018. - Maximov. Statistical Learning for Power Flow Feasibility, January, 2017. Santa Fe Grid Science School, Santa Fe, NM
- Maximov. Statistical Learning with Proxies for Power Flow Feasibility, March 2017. Workshop on Optimization and Inference for Physical Flows on Networks, Banff, Canada
- Lee.
*“Convex Polytope Machine Approach for Transient Stability Assessment,”*23rd International Symposium on Mathematical Programming (ISMP), Bordeaux, France, July 2018.

#### 2019

In 2019 we have investigated the small-signal stability problem. In our study, we adapt our

methods to ensure small-signal stability of the system using frequency regulation, HVDC power injections, SVC reactive power injections, and load shedding as controls. On that way, we propose to use time-discretization above convex restrictions and machine learning methods (convex polytope machines, neural networks). According to our results, machine learning methods (convex polytope machines, neural networks) significantly outperform existing analytical tools. On another hand, even a conservative analytic approximation allows to reduce sample/time complexity of machine learning methods and make them applicable in practice. We also designed novel robust algorithms for the voltage stability optimal controls and optimal power flow problem behind them. Finally, we in 2020 we have extended our algorithms for small-signal and voltage stability to for a range of possible uncertainty realizations and demonstrate their efficiency. Our team member Prof. Andreas Wachter was awarded the second prize at the DOE Grid Optimization Competition.

#### 2018

In 2018 the team designed and tested with Dynamic Contingency Analysis Tool (DCAT) novel algorithms for voltage stability based on convex restrictions, convex relaxations, and machine learning methods. In our experiments, we figured out that the performance of novel methods is better than the one for the state-of-the-art algorithms. Based on these results, we have submitted two technical reports to DOE (“Demonstration of Emergency Control Methods for Voltage Stability”, “Road Map for Emergency Control of Electric Power Systems”), more than five peer reviewed publications, and several contributed talks.