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

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.

References:

[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.