## 5 Simulation and Analysis
### Analysis of Intra-Day Optimization Results  
In the intra-day rolling optimization stage, three methods are used for comparative analysis. Method 1: the proposed MPC method considers intra-day operating capacity balance. Method 2: the traditional open-loop rolling optimization method also considers intra-day operating capacity balance [12]. Method 3: the proposed MPC method without considering intra-day operating capacity balance [16]. Figures 11 and 12 show the intra-day variations of active power and reactive power and capacity ratio for VPSSHs and BES units under Method 1 every 15 min. We observed from the figure, VPSSH1, VPSSH2 and BES1 can well ensure the daily operating capacity balance during the intra-day period, while the capacity of BES2 at the end of the day is slightly lower than the initial value, primarily due to significant active power fluctuations from wind and fewer controllable resources on that branch. Figure 13 shows the intra-day reactive power of wind and PV under Method 1. The reactive power of wind exhibits significant fluctuations, while the reactive power of PV is relatively small. This is mainly because wind active power fluctuates throughout the 24 h period, affecting the limits of wind reactive power and the reactive power demand on the branch. In contrast, PV active power fluctuates minimally during the night, almost reaching zero, leading to relatively stable reactive power ability. Figure 14 presents the intra-day reactive power of two SVG under Method 1. We observed that SVG1 experiences frequent fluctuations, while SVG2 exhibits larger amplitude variations. From Figures 11-14, the intra-day optimization stage uses the model predictive control algorithm proposed in this paper, as in Method 1. The distribution network is optimized and dispatched every 15 min, with adjustments made to the day-ahead results, allowing the distribution network operation to adapt to the fluctuations of renewable energy. Figure 10: The optimization results of VPSSH operation conditions considering or not considering generating/pumping phase modulation conditions at the day-ahead stage: (**a**) VPSSH1 operation condition; (**b**) VPSSH2 operation condition. Figure 15 illustrates the capacity tracking performance of VPSSH and BES under three different methods compared to the day-ahead optimization results. From Figure 15a-d, we observed that Method 1 provides the best capacity tracking performance, ensuring daily operating capacity balance as much as possible. Method 2, on the other hand, shows poorer capacity tracking compared to Method 1, with noticeable discrepancies between the end of the day and the initial value. This is because Method 1 employs the MPC algorithm, which considers the system's future state, allowing devices to act in advance and providing feedback to reduce system error. Method 2 only considers current optimization, resulting in inferior tracking performance. Method 3 does not consider daily operating capacity balance, so it does not track the day-ahead optimization results but aims to optimize system economics and safety as much as possible but cannot guarantee the long-term operation  
Figure 11: Intra-day variations of active power and reactive power and capacity ratio for VPSSHs every 15 min under Method 1. Figure 12: Intra-day variations of active power and reactive power and capacity ratio for BESs every 15 min under Method 1. Figure 13: Intra-day reactive power of wind and PV under Method 1.  
of energy storage. Table 2 gives the specific imbalance value of the VPSSH and the BES capacity ratio at the end of the day under different methods. It can be seen that the method proposed in this paper can more effectively ensure the capacity balance of energy storage. Figure 16 compares the active power variations of GT under Method 1 and Method 2 throughout the day.