(657f) Two-Stage Robust Optimization for Alternating Current Optimal Power Flows with Renewables Uncertainty

Over two thirds of the United States power demand is satisfied through one of the eight power grids controlled by an Independent System Operator (ISO) [1]. At the heart of managing power grids lies the alternating current optimal power flow problem (ACOPF), a nonlinear program aimed at ascertaining the most economical generation dispatch subject to physical and engineering constraints arising from network analysis of power grid infrastructures.

Renewable energy generation (REG) in electrical grids is expected to increase over the next few decades in response to economic and environmental driving forces [2, 3]. However, the successful integration of intermittent renewable energy sources into electrical grids requires accommodation of the high variability and limited predictability of REG at high levels of renewables penetration [4, 5]. Power grid management software therefore requires extensions of deterministic ACOPF models to formulations subject to the uncertainty in power generation intrinsic to REG. Renewables generation uncertainty in OPF problems has recently been addressed through stochastic optimization, chance-constrained, and robust optimization modeling extensions and solution algorithms [4–7].

In this work, we apply the recently developed two-stage nonlinear robust optimization algorithm PyROS [8] to the ACOPF under renewables generation uncertainty. In particular, we extend the deterministic ACOPF to a two-stage formulation similar to that of [4], wherein the day-ahead generation dispatch is determined in the first stage, and the real-time generation dispatch and bus voltages are determined in the second stage, subject to uncertainty in the renewable active power generation capacities. Subsequently, we obtain with the PyROS solver a day-ahead generation dispatch for which there exists a feasible real-time adjustment under any realization of renewable generation active power capacities from a predefined uncertainty set. We apply our modeling framework to a library of two-stage ACOPF model instances derived from benchmark instances in the Power Grid Library (PGLIb) [9], and obtain robust solutions for a hierarchy of uncertainty sets to assess trends in the extent and price of robustness. Our results demonstrate the utility of the proposed two-stage modeling framework for increasingly robust power systems operation.

References

[1] Federal Energy Regulatory Commision. Electric Power Markets. Accessed August 9, 2021. 2021. URL: https://www.ferc.gov/electric-power-markets.

[2] Intergovernmental Panel on Climate Change. IPCC Special Report on Renewable Energy Sources and Climate Change Mitigation. Cambridge, United Kingdom and New York, NY, USA: Cambridge University Press, 2012.

[3]Stephen Nalley and Angelina LaRose. Annual Energy Outlook 2022. Washington D.C: United States Energy Information Administration, 2022. Accessed April 7, 2022. URL: https://www.eia.gov/todayinenergy/

[4] Raphael Louca and Eilyan Bitar. “Robust AC optimal power flow”. In: IEEE Transactions on Power Systems 34.3 (2018), pp. 1669–1681.

[5] Daniel K Molzahn and Line A Roald. “Towards an AC optimal power flow algorithm with robust feasibility guarantees”. In: 2018 Power Systems Computation Conference (PSCC). IEEE. 2018, pp. 1–7.

[6] Dongchan Lee et al. “Robust AC Optimal Power Flow with Robust Convex Restriction”. In: IEEE Transactions on Power Systems (2021).

[7] Olga Kuryatnikova, Bissan Ghaddar, and Daniel K Molzahn. “Adjustable Robust Two-Stage Polynomial Optimization with Application to AC Optimal Power Flow”. In: arXiv preprint arXiv:2104.03107 (2021).

[8] Natalie M Isenberg et al. “A generalized cutting-set approach for nonlinear robust optimization in process systems engineering”. In: AIChE Journal 67.5 (2021), e17175.

[9] Sogol Babaeinejadsarookolaee et al. “The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms”. In: arXiv preprint arXiv:908.02788 (2019).