We consider using a battery storage system simultaneously for peak shaving and frequency regulation through a joint optimization framework which captures battery degradation, operational constraints and uncertainties in customer load and regulation signals. Under this framework, using real data we show the electricity bill of users can be reduced by up to 12%. Furthermore, we demonstrate that the saving from joint optimization is often larger than the sum of the optimal savings when the battery is used for the two individual applications. A simple threshold real-time algorithm is proposed and achieves this superlinear gain. Compared to prior works that focused on using battery storage systems for single applications, our results suggest that batteries can achieve much larger economic benefits than previously thought if they jointly provide multiple services.

We study the optimal control of battery energy storage under a general "pay-for-performance" setup such as providing frequency regulation and renewable integration. In these settings, batteries need to carefully balance the trade-off between following the instruction signals and their degradation costs in real-time. Existing battery control strategies either do not consider the uncertainty of future signals, or cannot accurately account for battery cycle aging mechanism during operation. In this work, we take a different approach to the optimal battery control problem. Instead of attacking the complexity of battery degradation function or the lack of future information one at a time, we address these two challenges together in a joint fashion. In particular, we present an electrochemically accurate and trackable battery degradation model called the rainflow cyclebased model. We prove the degradation cost is convex. Then we propose an online control policy with a simple threshold structure and show it achieve near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize the optimality gap and show it is independent to the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.

Battery participants in performance-based frequency regulation markets must consider the cost of battery aging in their operating strategies to maximize market profits. In this paper we solve this problem by proposing an optimal control policy and an optimal bidding policy based on realistic market settings and an accurate battery aging model. The proposed control policy has a threshold structure and achieves near-optimal performance with respect to an offline controller that has complete future information. The proposed bidding policy considers the optimal control policy to maximize market profits while satisfying the market performance requirement through a chance-constraint. It factors the value of performance and supports a trade-off between higher profits and a lower risk of violating performance requirements. We demonstrate the optimality of both policies using simulations. A case study based on the PJM regulation market shows that our approach is effective at maximizing operating profits. Index Terms-Battery energy storage, degradation, frequency regulation, power system economics NOMENCLATURE A. Parameters and Variables B Battery energy storage power rating in MW b t Battery dispatch power during t in MW b The set of all battery dispatch power b = {b t } C Regulation capacity in MW C Maximum regulation capacity E Battery energy storage capacity in MWh E, E Upper and lower energy limit for the battery energy storage in MWh E g t , E g t Upper and lower energy limit enforced by the control policy g during interval t in MWh e t Battery energy level during t in MWh e The set of all battery energy levels e = {e t } e max t , e min t Maximum and minimum energy level up to interval t in MWh g Control policy for the battery energy storage i Index of identified cycles j Index of regulation capacity bid segments J Number of total bid segments M Duration of one dispatch interval in hours R Battery cell replacement price in $/MWh r t Normalized regulation instruction during t r The set of all normalized regulation instructions r = {r t } The authors are with the

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