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.