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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The high variability of renewable energy is a major obstacle toward its increased penetration. Energy storage can help reduce the power imbalance due to the mismatch between the available renewable power and the load. How much can storage reduce this power imbalance? How much storage is needed to achieve this reduction? This paper presents a simple analytic model that leads to some answers to these questions. Considering the multitimescale grid operation, we formulate the power imbalance problem for each timescale as an infinite horizon stochastic control problem and show that a greedy policy minimizes the average magnitude of the residual power imbalance. Observing from the wind power data that in shorter timescales the power imbalance can be modeled as an iid zero-mean Laplace distributed process, we obtain closed form expressions for the minimum cost and the stationary distribution of the stored power. We show that most of the reduction in the power imbalance can be achieved with relatively small storage capacity. In longer timescales, the correlation in the power imbalance cannot be ignored. As such, we relax the iid assumption to a weakly dependent stationary process and quantify the limit on the minimum cost for arbitrarily large storage capacity. We formulate the optimal placement, sizing and control of storage devices in a power network to minimize generation costs with the intent of load shifting. We assume deterministic demand, a linearized DC approximated power flow model and a fixed available storage budget. Our main result proves that when the generation costs are convex and nondecreasing, there always exists an optimal storage capacity allocation that places zero storage at generation-only buses that connect to the rest of the network via single links. This holds regardless of the demand profiles, generation capacities, line-flow limits and characteristics of the storage technologies. Through a counterexample, we illustrate that this result is not generally true for generation buses with multiple connections. For specific network topologies, we also characterize the dependence of the optimal generation cost on the available storage budget, generation capacities and flow constraints. 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. Phase balancing is essential to safe power system operation. We consider a substation connected to multiple phases, each with single-phase loads, generation, and energy storage. A representative of the substation operates the system and aims to minimize the cost of all phases and to balance loads among phases. We first consider ideal energy storage with lossless charging and discharging, and propose both centralized and distributed real-time algorithms taking into account system uncertainty. The proposed algorithm does not require any system statistics and asymptotically achieves the minimum system cost with large energy storage. We then extend the algorithm to accommodate more realistic non-ideal energy storage that has imperfect charging and discharging. The performance of the proposed algorithm is evaluated through extensive simulation and compared with that of a benchmark greedy algorithm. Simulation shows that our algorithm leads to strong performance over a wide range of storage characteristics.