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This article investigates the current sharing and voltage regulation problem of a DC microgrid by a distributed supervisory control method. In the existing secondary control methods, current sharing feedback control loop and voltage regulation feedback control loop are linearly integrated to shift the droop equation. However, the linear combination of two loops may easily offset the control effect of each other, as the control dimension is less than the objective dimension. This fact motivates us to design a distributed supervisory secondary control (DSSC) scheme to achieve a more flexible configuring of each converter. The DSSC consists of two candidate controllers and a supervisor. The two controllers refer to current sharing configuring and DC bus voltage regulation respectively, and the supervisor is to orchestrate the switching between candidate controllers based on the system environment of DC microgrid. Under the proposed DSSC, each converter selects to configure the current sharing or regulates the DC bus voltage according to its need. Theoretical stability analysis is rigorously conducted. Finally, both simulation and experiment results are presented to demonstrate the effectiveness of DSSC. [ABSTRACT FROM AUTHOR]