The increasing flexibility of active distribution systems (ADSs) coupled with the high penetration of renewable distributed generators (RDGs) leads to the increase of the complexity. It is of practical significance to achieve the largest amount of RDG penetration in ADSs and maintain the optimal operation. This study establishes an alternating current (AC)/direct current (DC) hybrid ADS model that considers the dynamic thermal rating, soft open point, and distribution network reconfiguration (DNR). Moreover, it transforms the optimal dispatching into a second-order cone programming problem. Considering the different control time scales of dispatchable resources, the following two-stage dispatching framework is proposed. ① The day-ahead dispatch uses hourly input data with the goal of minimizing the grid loss and RDG dropout. It obtains the optimal 24-hour schedule to determine the dispatching plans for DNR and the energy storage system. ② The intraday dispatch uses 15 min of input data for 1-hour rolling-plan dispatch but only executes the first 15 min of dispatching. To eliminate error between the actual operation and dispatching plan, the first 15 min is divided into three 5-min step-by-step executions. The goal of each step is to trace the tie-line power of the intraday rolling-plan dispatch to the greatest extent at the minimum cost. The measured data are used as feedback input for the rolling-plan dispatch after each step is executed. A case study shows that the comprehensive cooperative ADS model can release the line capacity, reduce losses, and improve the penetration rate of RDGs. Further, the two-stage dispatching framework can handle source-load fluctuations and enhance system stability.