<p>This paper proposes a novel distributed cooperative control strategy for state of health (SoH) equalization of battery energy storage system in DC microgrid (DC-MG). Firstly, a communication-free SoH online estimation method based on the semi-empirical degradation model is derived, and the method is generalized to the case of different rated capacities by introducing the concept of weighted Ampere-hour throughput. Secondly, a hierarchical control structure is established. In the primary control layer, the adaptive droop controller can achieve SoH convergence and significantly improve the convergence speed and accuracy by introducing a capacity normalization factor and convergence factors. In the secondary control layer, a single secondary control loop based on integrator regulation can achieve precise current allocation and bus voltage compensation, thus further achieving SoH dynamic equalization. In the communication layer, a sparse communication network is established, and a dynamic consensus algorithm is used to accurately and iteratively estimate the global average state variables. Then, the stability of the proposed strategy is demonstrated by small-signal analysis. Finally, the MATLAB/Simulink simulations and StarSim RCP/HIL experiments verify the excellent performance of the proposed strategy in achieving SoH equalization, precise current allocation, and bus voltage compensation.</p>