## 5 Case Studies
### Simulation Results and Discussions  
The proposed multi-time-scale coordinated scheduling model is essentially a MILP optimization problem, and it is solved by the CPLEX tool developed by IBM(International Business Machines) Corporation as a high-performance mathematical programming solver [25]. Discussion on the day-ahead scheduling results  
The day-ahead scheduling results of the WPTBH are shown in Figure 4. In the time periods of 0:00-5:00 and 22:00-24:00, the hydro-pumped storage units and the batteries have charged electrical energy during off-peak load periods. In the peak load hours from 9:00 to 18:00, the hydro-pumped storage units and the batteries release electrical energy, which helps to maintain a stable active power output of thermal power units during the peak and off-peak hours. It can be clearly seen that the day-ahead scheduling plan has a good peak-shaving and valley-filling performance due to hydro-pumped storage units and batteries, and they can reduce the climbing-up or down frequency of thermal power units. Additionally, as demonstrated in Figure 4b,c, both the reservoir energy of the hydro-pumped storage station consisting of three units and the batteries at the beginning of the day are exactly the same as the energy reservoir at the end of the day. This means that the proposed model has guaranteed the continuous operation of hydro-pumped storage units and batteries on the next day. Figure 3: Actual and forecasted wind–photovoltaic power load demand in multi-time scales. Figure 4: Day-ahead power generation plan. Discussion on hour-level rolling corrective scheduling results  
The hour-level rolling corrective scheduling model is conducted for the next 3 h with an interval of 15 min. The corrected power outputs of hydro-pumped storage units and thermal power generators are shown in Figure 5.  
It can be seen that the deviation of 3 h ahead forecasted wind-photovoltaic power load with regard to the day-ahead forecasted wind-photovoltaic power load was well balanced in the hour-level rolling corrective schedule by hydro-pumped storage units. In specific, hydro-pumped storage units rapidly adjust the charging and discharging power to bear the fast-fluctuated wind-photovoltaic power load, while the thermal power units bear the slowly-changed load. The proposed hour-level rolling corrective scheduling model fully takes advantages of the fast power-regulation speed of the hydro-pumped storage units to reduce the ramping-up and down pressure of thermal power units. Discussion on the real-time corrective scheduling results  
In the real-time correction stage, the 15 min ahead forecasted wind-photovoltaic power load is used to correct the power outputs of thermal power units, hydro-pumped storage units and batteries. The corrective active power outputs of thermal power units, hydro-pumped storage units and batteries are presented in Figure 6. Both the hydro-pumped storage unit and the batteries can quickly adjust their active power outputs to alleviate the power output adjustment of thermal power units. The proposed real-time corrective scheduling model has fully explored the rapid power-adjustment capability of hydro-pumped storage unit and batteries to track the wind-photovoltaic power load fluctuation and thus well maintain system power balances in real-time. The power deviation percentage is defined as the error of the total active power output of a scheduling plan benchmarked with the actual wind-photovoltaic power load. From the power deviation percentage comparisons of three time scales shown in Figure 7, the power deviation percentage of the day-ahead scheduling plan is the largest. When the hour-level rolling corrective schedule is further conducted as the supplementary of the day-ahead scheduling, the power deviation percentage is greatly reduced but still with large fluctuations.