  Stand-alone direct current (DC) microgrids may belong to different owners and
adopt various control strategies. This brings great challenge to its optimal
operation due to the difficulty of implementing a unified control. This paper
addresses the distributed optimal control of DC microgrids, which intends to
break the restriction of diversity to some extent. Firstly, we formulate the
optimal power flow (OPF) problem of stand-alone DC microgrids as an exact
second order cone program (SOCP) and prove the uniqueness of the optimal
solution. Then a dynamic solving algorithm based on primal-dual decomposition
method is proposed, the convergence of which is proved theoretically as well as
the optimality of its equilibrium point. It should be stressed that the
algorithm can provide control commands for the three types of microgrids: (i)
power control, (ii) voltage control and (iii) droop control. This implies that
each microgrid does not need to change its original control strategy in
practice, which is less influenced by the diversity of microgrids. Moreover,
the control commands for power controlled and voltage controlled microgrids
satisfy generation limits and voltage limits in both transient process and
steady state. Finally, a six-microgrid DC system based on the microgrid
benchmark is adopted to validate the effectiveness and plug-n-play property of
our designs.
