## 5 Case Studies
### Comparison of different scheduling schemes  
In order to further illustrate the superiority of the proposed multi-time-scale coordinated scheduling model, two different scheduling models are compared as follows.  
Scheme A: The proposed multi-time-scale active power coordinated scheduling model based on MPC for wind-photovoltaic-thermal power generator, hydro-pumped storage, and battery units.  
Scheme B: The multi-time-scale active coordinated scheduling model based on the single time-section correction instead of MPC-based multiple time-section correction in the real-time corrective scheduling stage.  
Scheme C: MPC-based multi-time-scale active power coordination scheduling for thermal generators, namely the scheme C considers only thermal power generators to balance wind-photovoltaic power fluctuations.  
The load ratio of a transmission line is defined as the percentage of actual apparent power flow of the transmission line over its rated power capacity. Figure 8 shows the load ratio of all transmission lines in scheme A and B. As shown in Figure 8a-c, the load ratios of lines 1, 3, and 9 in scheme B are larger than 1 during the periods of 7:00-8:00, 10:00-11:00, and 20:00-21:00, which indicates that transmission lines 1, 3, and 9 are overloaded and the static security of the power networks is threatened. However, the load ratio of all transmission lines in scheme A is maintained within a range fully less than 1, and thus the proposed scheme A could well maintain the network static security. At the same time, the fluctuation of load ratio amplitude of all transmission lines in scheme B is larger than that of scheme A. This is because the here proposed scheme A uses an MPC-based real-time correction strategy to consider the wind-photovoltaic power and load prediction for a time period in advance, and thus can timely sense the load demand changing trend in the coming time period compared with scheme B only for a single-time section. Therefore, scheme A can properly adjust the active power output of thermal power generators, hydro-pumped storage units, and battery units in advance to avoid the large fluctuations of transmission lines' power flow.  
Figure 8: Cont.  
Figure 8: _Cont._  
The comparison of scheme A with scheme C (Figures 9-11) clearly demonstrates that the active power outputs of thermal units in scheme A are relatively smooth and their fluctuation magnitudes are small for all the three time-scale scheduling methods. That is because the proposed scheme A has the capability of energy shifting with the help of energy storage devices, such as the hydro-pumped storage units and batteries, the subject of this paper, which greatly reduces the ramp-up/down pressure of thermal power units. Furthermore, as shown in Table 2, the daily power generation cost of scheme A is $746,480 ($ is for United States dollar.), which is 18% smaller than the $908,400 cost of scheme C, this mean that the proposed scheme A could greatly improve the operation economics of the combined system.  
Figure 8: Load ratio (line apparent power flow over rated capacity) of nine transmission lines in scheme A and B.  
Figure 9: Thermal generator power outputs in the day-ahead scheduling of schemes A and C.  
Figure 11: Thermal generator power outputs after applying real-time scheduling of schemes A and C.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Scheme No.** & **Power Generation Costs (S)** \\ \hline A & 746,480 \\ C & 908,400 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Power generation operating costs of schemes A and C.  
Figure 10: Thermal generator power outputs after applying the hour-level rolling correction scheduling of schemes A and C.