###### Abstract  
As the penetration of renewable energy increases, the distribution grid faces great challenges in integrating large amounts of distributed energy sources and dealing with their output uncertainty. To address this, a multi-time scale optimal dispatch method based on model predictive control is proposed, including a day-ahead stage and an intra-day rolling stage. In the day-ahead stage, to fully utilize the flexibility of variable speed pumped storage hydropower, the generating/pumping phase modulation condition is considered, not just generating or pumping. Day-ahead optimal dispatch is established with the objective of minimizing the operation economy and node voltage deviation of the distribution network. In the intra-day rolling stage, model predictive control with finite time domain rolling optimal dispatch is used to replace the traditional single-time section optimal dispatch, considering the forecast data of wind, photovoltaic (PV), and load within the finite time domain, so that can respond in advance to smooth the generator output. At the same time, the uncertainty problem of the distribution network is solved effectively by rolling optimization and feedback correction of model predictive control. In order to consider the daily operating capacity balance of energy storage in the intra-day stage, the capacity imbalance penalty is added to the intra-day rolling optimization objective function, so that the energy storage capacity tries to track the results of the day-ahead optimization, achieving the long-term development of energy storage. Simulation analysis proves the feasibility and effectiveness of the proposed method. The proposed method enhances the generation-load-storage coordinated dispatching ability, effectively improving the distribution network's capability to respond to fluctuations of renewable energy. flexibility and rapid response characteristics as a flexible adjustment resource [7]. Currently, there are studies on the optimal dispatch of PSH. Reference [8] proposes a day-ahead market structure based on the PSH model, which improves the utilization of PSH resources and the flexibility of the power system. Reference [9] uses the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm to study the economic emission dispatch problem of renewable energy and PSH, considering uncertainties and outages of renewable energy. Reference [10] introduces PSH in wind-fire-water systems to address wind fluctuations. Reference [11] studies an off-grid sustainable power generation system in rural areas composed of wind energy and PSH. The above research only considers the operation conditions of generating and pumping, ignoring the generating/pumping phase modulation condition of VPSSH, and has not fully utilized the function of phase modulation and voltage modulation of VPSSH. To address the difficulties in wind and PV forecast errors for the optimal dispatch of the distribution network since the wind and PV forecast accuracy increases with a decrease in the time scale, a multi-time scale optimal dispatch method was studied to reduce the impact of forecast error on the optimal dispatch. Reference [12] uses a multi-time scale dispatch model to realize reactive power and voltage control of wind farms. Reference [13] addresses the impact of different time scales load forecast error on optimal dispatch of a microgrid using two stages including day-ahead and intra-day. Reference [14] proposes an optimal dispatch scheme including day-ahead, intra-day, and real-time stages for wind-PV-electrochemical storage-PSH station. However, the above research used traditional multi-time scale optimal dispatch, which is an open-loop optimization that only considers a single time section. When the output of wind and PV fluctuates significantly, it can lead to substantial changes in other controllable power sources and difficulties in meeting generator ramp rates.