(724b) Stochastic Model Predictive Control for Battery Systems

Authors: 
Zavala, V. M., University of Wisconsin-Madison
Kumar, R., University of Wisconsin-Madison
Battery storage systems are flexible assets that can be used to provide frequency regulation for ISOs and to modulate loads for energy-intensive facilities to aid utilities (e.g. buildings or manufacturing) [1]. This flexibility is becoming increasingly valuable as more intermittent renewable power is injected into the grid. In particular, ISOs have reported an increased demand for frequency regulation services to mitigate fast renewable power fluctuations and stranded power [2]. Battery storage systems can be used to mitigate these issues and can be strategically placed in the network to maximize system-wide flexibility. Various studies have shown the economic benefits of using stationary battery systems to provide frequency regulation to the grid and to save cost by reducing demand charges in buildings and microgrids (via load peak shaving) [3,4,5]. These studies assume perfect knowledge of markets and loads. In real-time settings, however, diverse uncertainties can hinder battery performance and revenue potential. While stochastic optimization models for these types of applications have also been recently explored [6], an important general limitation of these studies is that they do not evaluate the economic potential of stochastic formulations against deterministic counterparts. Moreover, as in general stochastic optimization applications, uncertainty modeling and scenario generation from operational data remains a challenge. This is particularly relevant in battery systems performing simultaneous frequency regulation and demand peak shaving, because load uncertainty limits the amount of frequency regulation revenue that can be obtained to the ISO and can induce large demand charges if regulation participation potential is overestimated.

In this work we propose a stochastic model predictive control (MPC) framework to determine optimal participation strategies for stationary battery systems in ISO frequency regulation markets while simultaneously mitigating demand charges from a local utility associated to a set of attached loads that need to be modulated. The proposed framework solves a two-stage stochastic program that maximizes the expected revenue over a receding horizon and considers uncertainty of the modulated load. We propose to use a Ledoit-Wolf covariance estimator [7] to generate load scenarios from limited historical data and to capture short- and long-term load correlations. We use the framework to study the flexibility and economic benefits provided by a 1 MW battery system attached to a load from a collection of buildings. We use the proposed framework to study the benefits of stochastic MPC policies compared to those obtained with deterministic MPC and perfect information MPC strategies. We also study the effect of the prediction horizon length and of peak demand carryover prices on the performance of the MPC policies.

Using real load data of a typical university campus and price data from PJM, we find that stochastic MPC can significantly outperform its deterministic counterpart and improves the value of the battery. Our simulations illustrate that stochastic MPC can mitigate large demand charges and better manage frequency regulation commitments. Notably, stochastic MPC can recover 88% of the ideal value of the battery obtained with operations under perfect information, while deterministic MPC can only recover 79%. Moreover, we show that stochastic MPC can be used to modulate revenue volatility and with this mitigate risk. We have also found that the length of the prediction horizon and scaling of the demand charge significantly affect economic performance.

References:

[1] A. Oudalov, D. Chartouni, C. Ohler, and G. Linhofer, “Value Analysis of Battery Energy Storage Applications in Power Systems,” in 2006 IEEE PES Power Systems Conference and Exposition, pp. 2206–2211, 2006.

[2] K. Kim, F. Yang, V. M. Zavala, and A. A. Chien, “Data Centers as Dispatchable Loads to Harness Stranded Power,” IEEE Transactions on Sustainable Energy, vol. 3029, no. c, pp. 1–1, 2016.

[3] A. Oudalov, R. Cherkaoui, and A. Beguin, “Sizing and optimal operation of battery energy storage system for peak shaving application,” in 2007 IEEE Lausanne POWERTECH, Proceedings, pp. 621–625, 2007. 
[4] Y. Wang, B. Wang, C. C. Chu, H. Pota, and R. Gadh, “Energy management for a commercial building microgrid with stationary and mobile battery storage,” Energy and Buildings, vol. 116, pp. 141–150, 2016.

[5] A. Lucas and S. Chondrogiannis, “Smart grid energy storage controller for frequency regulation and peak shaving, using a vanadium redox flow battery,” International Journal of Electrical Power and Energy Systems, vol. 80, pp. 26–36, 2016.

[6] J. Donadee and M. Ilic ́, “Stochastic Co-Optimization of Charging and Frequency Regulation by Electric Vehicles,” IEEE, 2012. 
[7] O. Ledoit and M. Wolf, “A well-conditioned estimator for large-dimensional covariance matrices,” Journal of Multivariate Analysis, vol. 88, no. 2, pp. 365–411, 2004.