  This paper proposes a new convex model predictive control strategy for
dynamic optimal power flow between battery energy storage systems distributed
in an AC microgrid. The proposed control strategy uses a new problem
formulation, based on a linear d-q reference frame voltage-current model and
linearised power flow approximations. This allows the optimal power flows to be
solved as a convex optimisation problem, for which fast and robust solvers
exist. The proposed method does not assume real and reactive power flows are
decoupled, allowing line losses, voltage constraints and converter current
constraints to be addressed. In addition, non-linear variations in the charge
and discharge efficiencies of lithium ion batteries are analysed and included
in the control strategy. Real-time digital simulations were carried out for an
islanded microgrid based on the IEEE 13 bus prototypical feeder, with
distributed battery energy storage systems and intermittent photovoltaic
generation. It is shown that the proposed control strategy approaches the
performance of a strategy based on non-convex optimisation, while reducing the
required computation time by a factor of 1000, making it suitable for a
real-time model predictive control implementation.
