The cophase traction power supply system (CTPSS) is a promising solution in the smart electrified railways to effectively eliminate the neutral section, improve regeneration braking energy (RBE) utilization and mitigate voltage unbalance (VU). It works by coordinating the power flow distribution (PFD) among the energy storage (ES), power flow controller, and traction transformer. However, the conventional dispatch considering VU mitigation may result in increasing extra operation costs and accelerating ES aging. Therefore, driven by the day-ahead forecasted information, a dynamic VU regulation strategy is proposed to draw up the VU compensation schedule (VU-CS), which can satisfy the probabilistic limitations of power quality standards. Consequently, a Copula-based VU dependence model is developed to transform the VU-CS into the PFD constraint set of CTPSS. Meanwhile, an ES degradation model is introduced to quantify the system operation cost within different scenarios. Taking the PFD as a VU regulation constraint, an economic dispatch scheme of CTPSS is established to obtain a minimum operation cost and maximum RBE utilization. Finally, case study tests verify the efficiency of the proposed approach. The results show that scheme can improve ES cycle life and decrease cost under the probabilistic limitations of VU.