With the increasing proportion of renewable energy sources such as photovoltaic and wind energy in flexible distribution network, the intermittent output of renewable energy generation has a negative impact on the power system. Meanwhile, due to the differences in hardware parameters and working status of each energy storage unit during actual operation, it can lead to differences in SOC of different units, which in turn affects the subsequent operation of the battery energy storage system. This paper proposes a SOC balance control strategy based on fuzzy theory to address the SOC imbalance in multi-port power electronic transformer (PET) with battery energy storage system. Also, a corresponding DC voltage balance control strategy is designed to balance the DC voltage when different phases output different power. By designing an adaptive fuzzy control strategy, different discharging currents/droop coefficients are set for the battery energy storage units during discharging/charging, which balance the SOC of different units. Finally, a simulation model based on MATLAB/Simulink platform was used to validate the PET control strategy and SOC balance control strategy based on fuzzy theory proposed in this paper.