c  2013 IEEE THE FINAL VERSION OF THIS MANUSCRIPT APPEARED IN THE PROCEEDINGS OF THE IEEE ICC 2013, 9-13 JUNE 2013, BUDAPEST, HUNGARY. 1 Energy Storage Optimization Strategies for Smart Grids Claudio G. Codemo, Tomaso Erseghe, Andrea Zanella Abstract—The efficient management of the supply and demand in electricity networks is becoming a pivotal issue with important fallbacks both in the technological and financial domains. An interesting topic in this domain is the use of large batteries at the end users premises to reduce the average cost of energy supply, by storing energy when its cost is low and releasing it when the cost is high. In this paper, we wish to gain insights on the impact of some system model parameters, such as battery capacity, charge/discharge rate, power request process, and cost functions, on the cost saving that can be achieved by some selected energy storage algorithms. The study shows that the battery capacity has a direct and rather linear impact on cost reduction, while the effect of charge/discharge rates is less straightforward to predict. Furthermore, we show that, with piecewise, convex and non- decreasing cost functions, the optimal energy storage strategy has a threshold structure, where the number of thresholds depend on the shape of the cost function and the constraints of the battery. Index Terms—SmartGrid, Energy Storage, Optimization, Dynamic-Programming, Single-Threshold Algorithm I. I NTRODUCTION The Smart Grid is an attempt at modernizing the current existing electric grid by incorporating modern digital com- munication technologies to ensure efficient use of the electric energy and reduce the cost for energy supply. Smart Grids could exploit the fact that the cost of en- ergy production and delivery undergoes significant fluctuations during each day due to variations in demand and generator capacity. These fluctuations are traditionally hidden to the end users, who pay a fixed retail energy price. However, dynamic pricing creates an opportunity for users, such as households or data centers, to reduce energy costs by exploiting the price fluctuations [1]. Unfortunately, in practice, users’ power demands are not much reactive to changes in the energy prices [2]–[5]. A possible solution is to equip single users, or small groups organized in a micro-grid, with an energy storage device, e.g., a large battery, that can store energy when the price is low and release it when the price is high. This allows users to benefit from the energy price variations without having to adjust their consumption. There exists a significant amount of work on energy storage strategies in various contexts: among them, our starting points are [6] and [7]. In [6], the authors address the optimal energy storage control problem that is faced by a grid operator, whose controller has access to one energy storage device of finite This work is partially funded by the PRIN 2009 “Alter-Net” project. c  2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. storage capacity. The simple Single-Threshold (ST) policy proposed by the authors is proved to be be asymptotically optimal as the battery storage grows to infinity. However, it does not take into account realistic charge and discharge rates of the battery, nor a realistic power demand process, which is arbitrarily modeled as the state of a M/M/∞ queueing system. The problem of optimal control of the battery charge/discharge process to minimize the long-term average cost is investigated in [7] as a Markov Decision Process (MDP): under rather general assumptions, the optimal policy is shown to have a two-thresholds structure. Thresholds are numerically computed in some specific scenarios, using real-world power request traces from existing energy markets. The results of [7], however, have been obtained under the assumption that the energy cost function is always linear with respect to (wrt) power demand requests, a model that does not capture the more-than-linear increase of the cost to produce and delivery energy as the request grows. In this paper, we wish to shed some light on the effect that different model parameters may have on the performance of energy storage strategies. To this aim, we consider realistic power request traces, obtained from the high-detailed models proposed in [8]. For the energy storage device, i.e., the battery, we adopt a very simple and abstract model that, however, keeps into account the most important physical limitations of these devices, such as finite storage capacity, limited charge/discharge rates, power losses during charg- ing/discharging operations. Charge-retention and battery cost depreciation in time have also been considered in our study but are not included in this paper because their effect has turned out to be either negligible or not significant in our scenario. Concerning the energy cost function, we consider an always increasing, convex, piecewise linear cost function similar to that proposed in [6] that reflects the more than linear increase in the cost of producing and delivering each additional power unit. Nonetheless, to get insights on the relation between the shape of the cost function on the optimal energy storage strategy, we consider three cost functions that, while sharing the same piecewise convex structure, differ for the number and/or slope of linear segments. The study considers four different energy storage strate- gies, named A-posteriori Optimal Strategy (AOS), Dynamic Programming with Markovian requests (DPM), Dynamic Programming with Independent request (DPI), and Single- Threshold (ST) algorithm, respectively. We selected these strategies because they require progressively less prior infor- mation on the statistic of the user’s power requests but, on the other hand, offer progressively diminishing cost saving with respect to a reference system with no battery. Comparing