  Renewable energy resources and power electronics-interfaced loads introduce
fast dynamics in distribution networks. These dynamics cannot be regulated by
slow conventional solutions and require fast controllable energy resources such
as Battery Energy Storage Systems (BESSs). To compensate for the high costs
associated to BESSs, their energy and power management should be optimized. In
this paper, a convex iterative optimization approach is developed to find the
optimal active and reactive power setpoints of BESSs in active distribution
networks. The objective is to minimize the total cost of energy purchase from
the grid. Round-trip and life-time characteristics of BESSs are modelled
accurately and integrated into a relaxed and exact formulation of the AC power
flow, resulting into a Modified Augmented Relaxed Optimal Power Flow (MAROP)
problem. The feasibility and optimality of the solution under the grid security
limits and technical constraints of BESSs is proven analytically. A 32-bus IEEE
test benchmark is used to illustrate the performance of the developed approach
in comparison to the alternative approaches existing in the literature.
