This paper proposes an advanced voltage source converter (VSC)-driven model for soft open points (SOPs) and battery energy storage systems (BESSs) to actively balance three-phase distribution networks. The proposed model addresses the phase imbalance caused by the increasing integration of renewable energy and distributed generation. Unlike traditional models, which mainly focus on AC capacity constraints, the proposed model explores the complexities of the DC-link. This allows for a thorough examination of the interactions between active and reactive power, as well as the voltage levels on both the AC and DC sides of VSCs. The relationship between pulse width modulation (PWM) control configurations and VSC power outputs is discussed, enhancing control on both sides of the converters. This improvement also facilitates better cross-phase power transfer through SOPs and enhances the overall balance among the three phases. In addition, the proposed model incorporates the cooperative functionality of VSC-driven BESSs to sustain the phase balance. To further optimize the load distribution, phase-specific dispatching (PSD) is introduced, allowing for the flexible allocation of individual loads to distinct phases. Together, these coordinated technical solutions constitute a systematic optimization strategy. An algorithm is developed to harmonize the VSC-driven modeling for SOPs and BESSs with PSD, thereby improving the computational efficiency in managing power flow and phase balance. The results show that the proposed model significantly reduces losses and enhances the phase balance.