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Renewable energy resources, such as wind and solar power, are rapidly becoming generation technologies of significance in the United States and around the world. However, because of their intermittency and inter-temporal variations, the integration of renewable energy resources is usually very challenging. Some of the previously proposed solutions, such as the use of energy storage units and fast-responding generators, are costly and may not be desirable in practice. Instead, in this paper, we argue that due to the workload flexibility in the Internet and Cloud Computing data centers they can offer a unique opportunity to tackle the challenges in integrating renewable energy resources. Moreover, by running data centers with behindthe-meter renewable generators, we can significantly reduce not only data centers' energy cost but also their Carbon Footprint. To achieve these objectives, we propose to optimally distribute the workload among geographically dispersed data centers such that we can benefit from the location diversity of different types of available renewable energy resources. The quality-of-service is guaranteed by real-time monitoring of the queue lengths and effectively stabilizing short queue lengths in each data center. Our simulation results, based on various experimental data, show that the proposed design can significantly reduce data centers' cost of electricity while maintaining quality-of-service.

Abstract-In this paper, we show that an uncertain departure time significantly changes the analysis in optimizing the charging schedule of electric vehicles. We also obtain a closed-form solution for the stochastic optimization problem that is formulated to schedule charging of electric vehicles with uncertain departure times in presence of hourly time-of-use pricing tariffs.Keywords: Electric vehicles, uncertain departure time, timeshiftable loads, stochastic optimization, closed-form solution. I. BACKGROUNDAssume that time is divided into T time slots. Consider an electric vehicle (EV) charging station with multiple charging outlets, c.f. [1], [2]. At each charging outlet, let α ≥ 1 denote the time slot at which an electric vehicle plugs in to the charging outlet. Also let e denote the total energy needed to charge the electric vehicle. In this section, we assume that the driver indicates her departure time β ≤ T . As an example, if a Chevrolet Volt with a depleted battery plugs in to the charging outlet at 10:00 AM and the driver indicates that she will depart at 2:00 PM and she expects a fully charged battery, then we have α = 10, β = 14, and e = 16 kWh. Let x[t] denote the scheduled energy usage for charging at time slot t. To finish charging before the departure time β, it is required that(1)Let µ[t] denote the price of electricity at time slot t. The cost to finish charging is. If all parameters are known, then the cost is minimized if we choose x[τ ] = e, where τ = arg min α≤t≤β µ[t]; and we set x[t] = 0 for t = τ . Here, τ is the time slot between α and β with the lowest price. Note that, the above analysis works at each charging outlet, regardless of the number of charging outlets at the charging station. An exception is when the charging station is very large and thus price-maker, as we point out in Section IV. II. ANALYSIS UNDER UNCERTAIN DEADLINENext, assume that the deadline β is not known. Once an EV plugs in, its target charge level e and start time α are identified. However, the charging station may not know when the EV will depart. Nevertheless, the charging station needs to operate in a way that it minimizes the cost of electricity.The system setup is as follows. At the beginning of each time slot t ≥ α, if the user indicates that the EV will departThe authors are with the Department of Electrical Engineering, University of California, Riverside, CA, USA, e-mail: {hamed, ghamkhari}@ee.ucr.edu. This work was supported by NSF grants ECCS 1253516, ECCS 1307756, and CNS 1319798. The corresponding author is H. Mohsenian-Rad.at the end of the current time slot, then we must setbecause we must assure finishing charging before the user's departure as required by (1). Otherwise, i.e., if the user does not indicate that it will depart at the end of the current time slot t, then the charging station faces the uncertainty that the EV may depart at any of the future time slots t + 1, . . . , T . At each time slot t ≥ α, let π k|t P r{β = k | β > t} denote the conditional probability that the user will depa...

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