The widespread integration of distributed power sources affects the power flow distribution of the system. Reactive power optimization can maintain voltage stability and improve operational economy. To address the insufficient regulation capability of traditional reactive power devices, the introduction of a soft open point with self-energy storage （E-SOP） enhances the reactive power-voltage optimization performance of distribution networks. In the day-ahead stage, a long-term reactive power optimization model is developed to determine the scheduling strategies for on-load tap-changing transformers, switchable capacitors, and energy storage devices. In the day-to-day stage, a rolling optimization model based on short-term source-load forecasts is established to refine the day-ahead optimization results. The proposed multi-time scale reactive power optimization method for flexible distribution networks considers the modeling accuracy of E-SOP loss characteristics, achieving coordinated optimization of continuous and discrete reactive power resources while reducing operational costs and voltage deviations. Based on convex relaxation techniques, the aforementioned reactive power optimization model is transformed into a mixed-integer second-order cone programming problem, and an accelerated technique based on an induced objective function （IOF） is further introduced to enhance the computational efficiency of the reactive power optimization model. The IEEE 33-node system after retrofitting is used as an example for analysis, and the results verify the feasibility and effectiveness of the proposed method.