Controlling multiple batteries on a radial line

This paper studies the problem of optimizing the performance of multiple batteries located in a radial distribution line under the network constraints. A centralized controlling unit minimizes the charge/discharge costs of the batteries by coordinating the operation modes of the batteries on the line as well as their current input/output. The considered optimization problem is formulated as a mixed-integer-linear-program (MILP) in which the batteries´ currents are limited by voltage drop constraints, current rating constraints, battery capacity constraints and charge/discharge coordination constraints. The latter constraint is proposed to ensure that all batteries simultaneously operate in only one of the operation modes, i.e. charge or discharge, to avoid the undesirable situation wherein a subset of the batteries charge the rest of batteries. Our numerical results show that the proposed MILP effectively manages the operation of the batteries while satisfying the distribution network constraints.