Energy storage is a crucial component of the smart grid, since it provides the ability to buffer transient fluctuations of the energy supply from renewable sources. Even without a load, energy storage systems experience a reduction of the stored energy through self-discharge. In some storage technologies, the rate of self-discharge can exceed 50 of the stored energy per day. In this paper, we investigate the self-discharge phenomenon in energy storage using a queueing system model, which we refer to as leakage queue. When the average net charge is positive, we discover that the leakage queue operates in one of two regimes: a leakage-dominated regime and a capacity-dominated regime. We find that in the leakage-dominated regime, the stored energy stabilizes at a point that is below the storage capacity. Under suitable independence assumptions for energy supply and demand, the stored energy in this regime closely follows a normal distribution. We present two methods for computing probabilities of underflow and overflow at a leakage queue. The methods are validated in a numerical example where the energy supply resembles a wind energy source.
Electric system operators rely on regulation services to match the total system supply to the total system load in quasi real-time. The regulation contractual framework requires that a regulation unit declares its regulation parameters at the beginning of the contract, the operator guarantees that the regulation signals will be within the range of these parameters, and the regulation unit is rewarded proportionally to what it declares and what it supplies. We study how this service can be provided by a unit with a non-ideal storage. We consider two broad classes of storage technologies characterized by different state of charge evolution equations, namely batteries and flywheels. We first focus on a single contract, and obtain formulas for the upward and downward regulation parameters that a unit with either a battery or a flywheel should declare to the operator to maximize its reward. We then focus on a multiple contract setting and show how to analytically quantify the reward that such a unit could obtain in successive contracts. We quantify this reward using bounds and expectation, and compare our analytical results with those obtained from a dataset of real-world regulation signals. Finally, we provide engineering insights by comparing different storage technologies in terms of potential rewards for different contract durations and parameters. Although modern society is critically reliant on power grids, modern power grids are subject to unavoidable outages. The situation in developing countries is even worse, with frequent load shedding lasting several hours a day due to a large power supply-demand gap. A common solution for residences is, therefore, to back up grid power with local generation from a diesel generator (genset). To reduce carbon emissions, a hybrid battery-genset is preferable to a genset-only system. Designing such a hybrid system is complicated by the tradeoff between cost and carbon emission. Toward the analysis of such a hybrid system, we first compute the minimum battery size required for eliminating the use of a genset, while guaranteeing a target loss of power probability for an unreliable grid. We then compute the minimum required battery for a given genset and a target-allowable carbon footprint. Drawing on recent results, we model both problems as buffer sizing problems that can be addressed using stochastic network calculus. Specifically, a numerical study shows that, for a neighborhood of 100 homes, we are able to estimate the storage required for both the problems with a fairly small margin of error compared to the empirically computed optimal value. Energy storage - in the form of UPS units - in a datacenter has been primarily used to fail-over to diesel generators upon power outages. There has been recent interest in using these Energy Storage Devices (ESDs) for demand-response (DR) to either shift peak demand away from high tariff periods, or to shave demand allowing aggressive under-provisioning of the power infrastructure. All such prior work has only considered a single specific type of ESD (typically re-chargeable lead-acid batteries), and has only employed them at a single level of the power delivery network. Continuing technological advances have provided us a plethora of competitive ESD options ranging from ultra-capacitors, to different kinds of batteries, flywheels and even compressed air-based storage. These ESDs offer very different trade-offs between their power and energy costs, densities, lifetimes, and energy efficiency, among other factors, suggesting that employing hybrid combinations of these may allow more effective DR than with a single technology. Furthermore, ESDs can be placed at different, and possibly multiple, levels of the power delivery hierarchy with different associated trade-offs. To our knowledge, no prior work has studied the extensive design space involving multiple ESD technology provisioning and placement options. This paper intends to fill this critical void, by presenting a theoretical framework for capturing important characteristics of different ESD technologies, the trade-offs of placing them at different levels of the power hierarchy, and quantifying the resulting cost-benefit trade-offs as a function of workload properties. We consider the performance modeling and evaluation of network systems powered with renewable energy sources such as solar and wind energy. Such energy sources largely depend on environmental conditions, which are hard to predict accurately. As such, it may only make sense to require the network systems to support a soft quality of service (QoS) guarantee, i.e., to guarantee a service requirement with a certain high probability. In this paper, we intend to build a solid mathematical foundation to help better understand the stochastic energy constraint and the inherent correlation between QoS and the uncertain energy supply. We utilize a calculus approach to model the cumulative amount of charged energy and the cumulative amount of consumed energy. We derive upper and lower bounds on the remaining energy level based on a stochastic energy charging rate and a stochastic energy discharging rate. By building the bridge between energy consumption and task execution (i.e., service), we study the QoS guarantee under the constraint of uncertain energy sources. We further show how performance bounds can be improved if some strong assumptions can be made. We consider an electricity consumer equipped with a perfect battery, who needs to satisfy a non-elastic load, subject to external control signals. The control imposes a time-varying upper-bound on the instantaneous energy consumption (this is called "Demand-Response via quantity"). The consumer defines a charging schedule for the battery. We say that a schedule is feasible if it successfully absorbs the effects of service reduction and achieves the satisfiability of the load (making use of the battery). Our contribution is twofold. (1) We provide explicit necessary and sufficient conditions for the load, the control, and the battery, which ensure the existence of a feasible battery charging schedule. Furthermore, we show that whenever a feasible schedule exists, we can explicitly define an online (causal) feasible schedule. (2) For a given arrival curve characterizing the load and a given service curve characterizing the control, we compute a sufficient battery size that ensures existence of an online feasible schedule. For an arrival curve determined from a real measured trace, we numerically characterize the sufficient battery size for various types of service curves. The wide range of performance characteristics of storage technologies motivates the use of a hybrid energy storage system (HESS) that combines the best features of multiple technologies. However, HESS design is complex, in that it involves the choice of storage technologies, the sizing of each storage element, and deciding when to charge and discharge each underlying storage element ( operating strategy ). We formulate the problem of jointly optimizing the sizing and the operating strategy of an HESS that can be used for a large class of applications and storage technologies. Instead of a single set of storage element sizes, our approach determines the Pareto-optimal frontier of the sizes of the storage elements along with the corresponding optimal operating strategy. Thus, as long as the performance objective of a storage application (such as an off-grid microgrid) can be expressed as a linear combination of the underlying storage sizes, the optimal vector of storage sizes falls somewhere on this frontier. We present two case studies to illustrate our approach, demonstrating that a single storage technology is sometimes inadequate to meet application requirements, unlike an HESS designed using our approach. We also find simple, near-optimal, and practical operating strategies for these case studies, which allows us to gain several new engineering insights.  Renewable energy such as solar and wind generation will constitute an important part of the future grid. As the availability of renewable sources may not match the load, energy storage is essential for grid stability. In this paper we investigate the feasibility of integrating solar photovoltaic (PV) panels and wind turbines into the grid by also accounting for energy storage. To deal with the fluctuation in both the power supply and demand, we extend and apply stochastic network calculus to analyze the power supply reliability with various renewable energy configurations. To illustrate the validity of the model, we conduct a case study for the integration of renewable energy sources into the power system of an island off the coast of Southern California. In particular, we asses the power supply reliability in terms of the average Fraction of Time that energy is Not-Served (FTNS).  In an isolated power grid or a micro-grid with a small carbon footprint, the penetration of renewable energy is usually high. In such power grids, energy storage is important to guarantee an uninterrupted and stable power supply for end users. Different types of energy storage have different characteristics, including their round-trip efficiency, power and energy rating, self-discharge, and investment and maintenance costs. In addition, the load characteristics and availability of different types of renewable energy sources vary in different geographic regions and at different times of year. Therefore joint capacity optimization for multiple types of energy storage and generation is important when designing this type of power systems. In this paper, we formulate a cost minimization problem for storage and generation planning, considering both the initial investment cost and operational maintenance cost, and propose a distributed optimization framework to overcome the difficulty brought about by the large size of the optimization problem. The results will help in making decisions on energy storage and generation capacity planning in future decentralized power grids with high renewable penetrations. 