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(393c) Uncertainty Quantification and Stochastic Programming Strategies for Energy Market Participation

Dowling, A. W., University of Notre Dame
Gao, X., University of Notre Dame
Atkinson, S., University of Notre Dame
During the past few years, announcements of several utility-scale energy storage projects have made the headlines, promising to improve the grid reliability, ease renewable integration, curtail emissions, and reduce overall systems cost [1]. The financial soundness of these investments has yet to be proven because energy storage economics heavily depends on the surrounding electricity market dynamics, energy policies, and long-term performance (e.g., degradation, wear-and-tear).

A standard technique for economic assessment is to formulate market participation as an optimization problem and calculate the maximum possible revenue in hindsight, i.e., with perfect information [2]. Here physical limitations and market rules are modeled as constraints. Our recent analysis of California market data revealed over 60% of revenue opportunities come from the fastest market layers (i.e., real-time market, ancillary services) for batteries, concentrated solar thermal power, and industrial systems [3-5]. The finding that energy arbitrage in the day-ahead market is the least profitable participation strategy is consistent with other studies [2,6,7].

An important limitation of these studies is the assumption of perfect information, while in reality, market participants must bid under price and weather uncertainties [8,9]. We develop an integrated approach for uncertainty quantification and stochastic optimization of energy systems biding into complex energy markets. First, Gaussian Process (GP) statistical models [10] are trained using historical data and used to generate probabilistic forecasts for market prices. These forecasts are input parameters for a two-stage stochastic model predictive control framework to compute optimal market participation policies. Preliminary benchmarks indicate the proposed approach, implemented in a receding horizon framework, is capable of capturing over 90% of theoretical market revenues, compared to only 75% with simple backcasting. We also explore different strategies to integrate probabilistic forecasts including sampling and Smolyak quadrature rules (sparse grids) [11-13]. Finally, we discuss how the proposed framework enables comparison of different energy storage technologies based on the ability to cope with exogenous (market, weather, etc.) uncertainty.


[1] Cardwell and Krauss (2017). A Big Test for Big Batteries. New York Times. https://www.nytimes.com/2017/01/14/business/energy-environment/california-big-batteries-as-power-plants.html

[2] Walawalkar, Apt, and Mancini (2007). Economics of electric energy storage for energy arbitrage and regulation in New York. Energy Policy 4, pg. 2558-2568.

[3] Dowling, Kumar, Zavala (2016). A Multi-Scale Optimization Framework for Electricity Market Participation. Applied Energy 190, pg. 147-164.

[4] Dowling, Zheng, and Zavala (2018). A decomposition algorithm for simultaneous scheduling and control of CSP systems. AIChE Journal, in press.

[5] Dowling and Zavala (2017). Economic opportunities for industrial systems from frequency regulation markets. Computers & Chemical Engineering, in press.

[6] Fares and Webber (2014). A flexible model for economic operational management of grid battery energy storage. Energy 78, pg. 768-776.

[7] Lizarraga-Garcia, Ghobeity, Totten, and Mitsos (2013). Optimal operation of a solar-thermal power plant with energy storage and electricity buy-back from grid. Energy 5, pg. 61-70.

[8] Dominguez, Baringo, and Conejo (2012). Optimal offering strategies for a concentrating solar power plant. Applied Energy 98, pg. 316-325.

[9] Kumar, Wenzel, Ellis, ElBsat, Drees, and Zavala (2018). A Stochastic Model Predictive Control Framework for Stationary Battery Systems. IEEE Transactions on Power Systems, in press.

[10] Bishop (2006). Pattern Recognition and Machine Learning. Springer.

[11] Chen, Mehrotra, and Papp (2015). Scenario generation for stochastic optimization problems via the sparse grid method. Computational Optimization and Applications 62, pg. 669-692.

[12] Laínez-Aguirre, Mockus, and Reklaitis (2015). A stochastic programming approach for the Bayesian experimental design of nonlinear systems. Computers & Chemical Engineering 72, pg 312–324.

[13] Renteria, Cao, Dowling, and Zavala (2017). Optimal PID controller tuning using stochastic programming techniques, AIChE Journal, in press.