Sizing energy storage systems in DC networks: A general methodology based upon power losses minimization

In this paper, an analytical approach that deals with the optimal sizing of energy storage systems in direct current networks is proposed. In modern power systems, the widespread use of power electronics, storage devices, and automation is driving power engineers to focus on the use of direct current networks. This new focus requires specific tools for the optimal planning and operation of these networks in order to increase energy efficiency and reduce operating costs. This paper is focused on the improvements in the efficiencies of direct current networks, which are characterized by the presence of loads, units for the generation of renewable power, and storage devices. Based on the calculus of variations, an original matrix formulation which starts with the nodal representation of the direct current network is proposed. Two attractive closed-form solutions are presented for minimizing power losses, i.e., (1) a solution based on the approximation of considering the voltage constant at all the network's busses and (2) a solution based on the linear approximation of the load flow. In both cases, the goal is to minimize losses over a given time horizon (e.g., the daily cycle). The formulation of the problem allows an analytical solution to be obtained that represents a suitable tool for the purpose of designing storage. In addition, the proposed approach can be applied and extended to the optimal sizing of storage systems. The proposed sizing procedure, which uses an analytical approach, is formulated in a general manner that can be used for various storage technologies. The results of numerical applications clearly have demonstrated both the feasibility and accuracy of the methodology to be used in the proposed design. We also propose an interesting parametric study in order to determine the optimal technology and the optimal size of the storage device.