text: abstract—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.
  index terms—battery energy storage, energy management,
  microgrid, model predictive control, optimal power flow,
  quadratic programming.