1949-3053 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSG.2016.2602480, IEEE Transactions on Smart Grid 1 Optimal allocation of energy storage systems for voltage control in LV distribution networks Antonio Giannitrapani, Member, IEEE, Simone Paoletti, Member, IEEE, Antonio Vicino, Fellow, IEEE, Donato Zarrilli Abstract—This paper addresses the problem of finding the optimal configuration (number, locations and sizes) of energy storage systems (ESS) in a radial low voltage distribution network with the aim of preventing over- and undervoltages. A heuristic strategy based on voltage sensitivity analysis is proposed to select the most effective locations in the network where to install a given number of ESS, while circumventing the combinatorial nature of the problem. For fixed ESS locations, the multi- period optimal power flow framework is adopted to formulate the sizing problem, for whose solution convex relaxations based on semidefinite programming are exploited. Uncertainties in the storage sizing decision problem due to stochastic generation and demand, are accounted for by carrying out the optimal sizing over different realizations of the demand and generation profiles, and then taking a worst-case approach to select the ESS sizes. The final choice of the most suitable ESS configuration is done by minimizing a total cost, which takes into account the number of storage devices, their total installed capacity and average network losses. The proposed algorithm is extensively tested on 200 randomly generated radial networks, and successfully applied to a real Italian low voltage network and a modified version of the IEEE 34-bus test feeder. Index Terms—Energy storage systems, siting and sizing, volt- age sensitivity matrix, multi-period optimal power flow. I. I NTRODUCTION P ROBLEMS of voltage quality are becoming more and more important in low voltage (LV) distribution networks. Among these, maintaining voltage between specified limits, as required by typical quality of supply standards, is one of the main issues faced by distribution system operators (DSO). This is mostly due to the growing penetration of low carbon technologies, such as distributed generation (DG), electric vehicles and heat pumps, causing modifications of typical power flows in distribution networks. Since peaks of load demand and DG are typically not aligned in time, over- and undervoltage conditions may regularly show up. In order to mitigate these problems, several actions can be taken. Grid reinforcement is a possible solution, but in a rapidly evolving scenario as the one distribution networks are now witnessing, deferral of investments in infrastructures could be advisable, and solutions both cheaper and faster to be implemented, should be looked for. In this respect, real and reactive power control of DG, and control of on-load tap changers (OLTC) at secondary substations, are valid alternative solutions proposed in the literature [1]. However, these solutions cannot be always The authors are with the Dipartimento di Ingegneria dell’Informazione e Scienze Matematiche, Universit` a degli Studi di Siena, Siena 53100, Italy (e-mail: giannitrapani@dii.unisi.it; paoletti@dii.unisi.it; vicino@dii.unisi.it; zarrilli@dii.unisi.it). put into practice. On the one hand, depending on both technical and regulatory issues, the DSO might not have control on distributed generators. On the other hand, OLTC control is impracticable when secondary substations are not automated, as is the case in most electricity systems worldwide. In addition, this type of control might have the serious drawback to transmit large disturbances to the medium voltage (MV) network. Very recently, the use of energy storage systems (ESS) has been investigated to tackle over- and undervoltages [2], [3], [4]. The idea is that an energy storage should play the role of a load in case of overvoltage, and of a generator in case of undervoltage. Pros of the use of ESS are that voltage problems are solved locally, thus limiting the impact on the MV network, and no curtailment of renewables is required. These advantages add to the well-known general benefits that the use of energy storage brings to the different players (see [5], [6] for general surveys). Optimal ESS siting and sizing have been addressed in the literature for both transmission and distribution networks, and from the point of view of different power system stakeholders (see, e.g, [7], [8], [9], [10] and references therein). A quite general approach is to formulate the problem in an optimal power flow (OPF) framework, where storage locations and sizes are considered as optimization variables, and a cost function (including, e.g., generation costs, storage installation costs, network losses, etc.) is optimized, subject to power flow constraints and storage dynamics. Since integer variables (used to decide ESS locations) and non-convex power flow constraints make the OPF problems NP-hard, different ap- proaches have been devised to approximate the exact problems and alleviate the computational burden. Linearization via DC approximation is adopted when dealing with transmission networks, where the assumptions underlying DC OPF are typically valid [11], [12], [13], [14]. In [7], the computationally demanding unit commitment (UC) problem over one year to determine optimal storage locations and parameters, is tackled by solving a UC problem for each day of the year separately. When the full AC OPF is considered, as is common for distribution networks, appropriate convex relaxations are often exploited. The second-order cone programming OPF approach of [15] is considered in [16], while convex relaxations based on semidefinite programming (SDP) are used in [17], [18], [19]. Alternating direction method of multipliers is proposed in [4] to break down the original problem into a distributed parallel convex optimization. In [16], [19] convex relaxations are embedded in a mixed integer formulation of the placement problem.