Stochastic AC Optimal Power Flow: A Data-Driven Approach

There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow ({AC-}OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly scalable data-driven algorithm for stochastic AC-OPF that has extremely low sample requirement. The novelty behind the algorithm's performance involves an iterative scenario design approach that merges information regarding constraint violations in the system with data-driven sparse regression. Compared to conventional methods with random scenario sampling, our approach is able to provide feasible operating points for realistic systems with much lower sample requirements. Furthermore, multiple sub-tasks in our approach can be easily paralleled and based on historical data to enhance its performance and application. We demonstrate the computational improvements of our approach through simulations on different test cases in the IEEE PES PGLib-OPF benchmark library.

[1]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[2]  Sidhant Misra,et al.  Statistical Learning for DC Optimal Power Flow , 2018, 2018 Power Systems Computation Conference (PSCC).

[3]  Russell Bent,et al.  Security-Constrained Design of Isolated Multi-Energy Microgrids , 2018, IEEE Transactions on Power Systems.

[4]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

[5]  Xu Andy Sun,et al.  The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem , 2018, IEEE Transactions on Power Systems.

[6]  Line A. Roald,et al.  Towards an AC Optimal Power Flow Algorithm with Robust Feasibility Guarantees , 2018, 2018 Power Systems Computation Conference (PSCC).

[7]  John Lygeros,et al.  On the Road Between Robust Optimization and the Scenario Approach for Chance Constrained Optimization Problems , 2014, IEEE Transactions on Automatic Control.

[8]  Renke Huang,et al.  The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms , 2019, ArXiv.

[9]  Qing-Guo Wang,et al.  Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty , 2013, IEEE Transactions on Automatic Control.

[10]  N. Growe-Kuska,et al.  Scenario reduction and scenario tree construction for power management problems , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[11]  Veit Hagenmeyer,et al.  Chance-Constrained AC Optimal Power Flow: A Polynomial Chaos Approach , 2019, IEEE Transactions on Power Systems.

[12]  Göran Andersson,et al.  Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms , 2017, IEEE Transactions on Power Systems.

[13]  Michael Chertkov,et al.  Structure Learning in Power Distribution Networks , 2015, IEEE Transactions on Control of Network Systems.

[14]  Michael Chertkov,et al.  Chance-Constrained Optimal Power Flow: Risk-Aware Network Control under Uncertainty , 2012, SIAM Rev..

[15]  John Lygeros,et al.  A Probabilistic Framework for Reserve Scheduling and ${\rm N}-1$ Security Assessment of Systems With High Wind Power Penetration , 2013, IEEE Transactions on Power Systems.

[16]  Gabriela Hug,et al.  Convex Relaxations of Chance Constrained AC Optimal Power Flow , 2017, 2018 IEEE Power & Energy Society General Meeting (PESGM).

[17]  Michael Chertkov,et al.  Optimal Power Flow with Weighted chance constraints and general policies for generation control , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[18]  Kyri Baker,et al.  Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables , 2017, IEEE Transactions on Power Systems.

[19]  Deepjyoti Deka,et al.  Learning for DC-OPF: Classifying active sets using neural nets , 2019, 2019 IEEE Milan PowerTech.

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

[21]  Jitka Dupacová,et al.  Scenario reduction in stochastic programming , 2003, Math. Program..

[22]  Goran Andersson,et al.  Analytical reformulation of security constrained optimal power flow with probabilistic constraints , 2013, 2013 IEEE Grenoble Conference.