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.
Energy storage plays a major role in many aspects of the smart grid, and, consequently, there is a extensive literature on their analysis. The electrical grid requires that power generation and demand load are continuously balanced. This becomes more involved with time-variable renewable energy sources and storage systems absorbing the variations from such sources. Smart grid approaches that take the perspective of a utility operator are concerned with placement, sizing, and control of energy storage systems with the goal to optimally balance power @cite_4 @cite_24 @cite_25 , reduce power generation costs @cite_32 , or operational costs @cite_5 . Works in this area are frequently formulated as optimal control or optimization problems, with the objective to devise distributed algorithms that achieve a desired operating point.
@cite_4 @cite_32 @cite_24 @cite_5 @cite_25
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Electric energy storage devices are prime candidates for demand load management in the smart power grid. In this work, we address the optimal energy storage control problem from the side of the utility operator. The operator controller receives power demand requests with different power requirements and durations that are activated immediately. The controller has access to one energy storage device of finite capacity. The objective is to devise an energy storage control policy that minimizes long-term average grid operational cost. The cost is a convex function of instantaneous power demand that is satisfied from the grid, and it reflects the fact that each additional unit of power needed to serve demands is more expensive as the demand load increases. For the online dynamic control problem, we derive a threshold-based control policy that attempts to maintain balanced power consumption from the grid at all times, in the presence of continual generation and completion of demands. The policy adaptively performs charging or discharging of the storage device. The former increases power consumption from the grid and the latter satisfies part of the grid demand from the stored energy. We prove that the policy is asymptotically optimal as the storage capacity becomes large, and we numerically show that it performs very well even for finite capacity. The off-line problem over a finite time horizon that assumes a priori known power consumption to be satisfied at all times, is formulated and solved with Dynamic Programming. Finally, we show that the model, approach and structure of the optimal policy can be extended to also account for a renewable source that feeds the storage device. For the efficient operation of the smart grid, it is important that there is an instant by instant matching between the electricity supply and the power consumption. Electrical power storage provides a viable solution to managing power supply and electrical loads as well as unexpected imbalances. Electricity suppliers could deploy electricity storage facilities at various levels of the smart grid system: generation, transmission, substations and residential level. Storage would significantly address the power quality and reliability problems through peak shaving and frequency control. It also reduces the need for huge infrastructural expenditures by making them more efficient. At the residential level, smart storage together with dynamic pricing in the deregulated electricity markets presents the electricity suppliers with a strategy to achieve grid stability. In this paper, we consider a smart grid environment with a high penetration of households' storage batteries. By using an appropriate electricity price structure, the electricity supplier influences households' electricity consumption. On the other hand, the households aim to minimize their electricity bills by capitalizing on price fluctuation to schedule their electrical appliances and coordinate the charging and discharging of their batteries. The electricity supplier has a dynamic power limit for each hour that must not be exceeded by the hourly aggregate load of the households. Further, we assume that in supplying electrical power, the households' electrical devices are given priority over their storage devices. The policy is such that batteries will be charged by the residual power after the appliances loads have been satisfied. The households have to compete for the residual electricity so as to maximize the state of charge of their batteries. We have therefore modeled this system as a non-cooperative Nash equilibrium game where the households are considered as selfish but rational players whose objectives are to optimize their individual utilities. There is growing interest in the use of grid-level storage to smooth variations in supply that are likely to arise with an increased use of wind and solar energy. Energy arbitrage, the process of buying, storing, and selling electricity to exploit variations in electricity spot prices, is becoming an important way of paying for expensive investments into grid-level storage. Independent system operators such as the New York Independent System Operator NYISO require that battery storage operators place bids into an hour-ahead market although settlements may occur in increments as small as five minutes, which is considered near "real-time". The operator has to place these bids without knowing the energy level in the battery at the beginning of the hour and simultaneously accounting for the value of leftover energy at the end of the hour. The problem is formulated as a dynamic program. We describe and employ a convergent approximate dynamic programming ADP algorithm that exploits monotonicity of the value function to find a revenue-generating bidding policy; using optimal benchmarks, we empirically show the computational benefits of the algorithm. Furthermore, we propose a distribution-free variant of the ADP algorithm that does not require any knowledge of the distribution of the price process and makes no assumptions regarding a specific real-time price model. We demonstrate that a policy trained on historical real-time price data from the NYISO using this distribution-free approach is indeed effective. Renewable energy sources have a huge potential to reduce greenhouse gas emissions and decrease the dependence on fossil fuels in the energy sector. However, the energy output of these sources is variable and raises concerns regarding the electric grid reliability. Therefore, the deployment of energy storage would play a key role in enabling the integration of these sources in the electric grid. This paper proposes methods for determining the optimal operation and sizing of energy storage systems. The main purpose of the operation strategy is to maximize the revenues of the renewable farm. The sizing model, on the other hand, has a purpose to minimize the cost of the hybrid system while meeting the service requirement. Both methods were formulated as non-linear programming optimization models. To verify the effectiveness of these methods; case studies have been presented. Finally, this paper proposes an economical analysis to determine the cost added by the storage to each KWh of stored energy.