This paper investigates the power loss minimization problem of solar DC nanogrids that are designed to provide energy access to households in off-grid areas. We consider nano-grids with distributed battery storage energy systems and that are enabled by multi-port DC-DC converters. As the nano-grids are not connected to the national grid and have batteries and converters distributed in each household, addressing the power loss problem while ensuring supply-demand balance is a challenge. To address the challenge, we propose a novel quasi-consensus based distributed control approach. The proposed approach consists of two algorithms namely, incremental loss consensus algorithm and voltage consensus algorithm. The incremental loss consensus algorithm is proposed to optimally schedule the battery charge/discharge operation while ensuring that supply-demand balance and the battery constraints are satisfied. The voltage consensus algorithm is proposed to determine optimal distribution voltage set points which act as optimal control signals. Both algorithms are implemented in a distributed manner, where minimal information exchange between households is required to obtain the optimal control actions. Simulation results of a solar DC nano-grid with five interconnected households verify the effectiveness of the proposed approach at addressing the nano-grid power loss problem.