Existing scheduling models for Internet data center (IDC) commonly have two key shortcomings: insufficient consideration of the voltage fluctuations in distribution networks and the impact of IDC storage data constraints on the spatiotemporal transfer of the workloads. An optimized operation method for flexible distribution networks was proposed considering the flexible IDC scheduling. Uncertainty scenarios for renewable generation and load demand were generated using Monte Carlo simulation and the K-means clustering algorithm. Differentiated scheduling strategy was established to distinguish between sensitive and tolerant loads. An IDC power consumption model along with a data storage constraint model were constructed. A robust optimization model was established with the objective of minimizing both distribution network operating costs and IDC electricity purchasing costs. The dynamic regulation capability of soft open point (SOP) and voltage fluctuation constraints were also incorporated into the model. Simulation results demonstrated that the proposed method significantly enhanced voltage quality, markedly increased the renewable energy accommodation rate, and reduced the electricity procurement cost for IDC by collaboratively optimizing the spatiotemporal load shifting of IDC workload along with the power regulation and reactive power support capabilities of SOP. It also validated the impact of storage capacity constraints on the efficiency of spatiotemporal workload shifting.