In order to avoid exceeding the multiplicity limit and system over-modulation after applying the equalization control

the inter-phase and intra-phase equalization coefficients are usually chosen conservatively

which leads to slow the state-of-charge (SOC) equalization. In this paper

the mathematical relationships between four factors (namely

power factor angle

phase current amplitude

battery cluster voltage and SOC distribution) and the modulation ratio margin and charging/discharging current boundaries after applying intra-phase equalization and inter-phase equalization are derived

respectively. The optimal intra-phase SOC and inter-phase SOC equalization coefficients are solved

respectively

and the intra-phase and inter-phase SOC equalization capabilities of the topology are utilized to the fullest extent possible and can be adjusted adaptively with the change of system operating conditions. Furthermore

the coupling constraints on the equalization capabilities of the intra-phase and inter-phase topologies are considered

and the adaptive decoupling control of inter-phase and intra-phase SOC equalization is proposed. The SOC equalization of all cell clusters in the system is achieved with the fastest convergence speed

and at the same time

it can ensure that the system is not over-modulated and the cells are operated within the safety boundary. The correctness of the theoretical analysis and the effectiveness of the control strategy are verified by the 10 kV/5 MW/5 MWh simulation model.