In the scheduling of source network load storage in the distribution network, the dual uncertainty of meteorology and load has complex temporal dependence characteristics. If the martingale difference sequence correlation between the two is ignored, it can easily lead to conservative mismatch and interface instability risks in scheduling decisions, resulting in voltage exceeding limits. Therefore, this study proposes a robust optimization scheduling method for source network load storage considering both meteorological and load uncertainties. Firstly, a first-order autoregressive time series correlation model for meteorological forecast errors and a box interval model for load fluctuations are constructed, and a net load coupling mechanism considering dual uncertainties is established to form a joint uncertainty model that is closer to actual extreme scenarios; then, a multidimensional box shaped uncertain set with adjustable conservatism is used to characterize the fluctuation domain of net load, and the goal is to minimize the total cost of system power purchase, energy storage aging and interruptible load compensation. Taking into account constraints such as power balance, voltage safety, energy storage state of charge and interruptible load, a robust optimization scheduling model is constructed. The main problem and sub problems are iteratively solved through the column and constraint generation algorithm. Finally, design a real-time collaborative response framework for adaptive charging and discharging of energy storage and flexible adjustment of interruptible loads to address residual deviations in actual operation. The simulation results show that this method maintains the voltage of all nodes in the safe range of 0.94~1.06 per unit (p.u.) under the worst-case uncertainty scenario, and the safety margin remains positive, verifying the superiority of this method in improving the safety of the distribution network.