## 5 Simulation Results and Discussion
### Simulation Test for Strengthening the Weighting Coefficients of the First Scheduling Interval  
In the MPC decision process, only the current time decision values are determined, and the future (the remainder) decision values are discarded. Due to this difference in processing, we consider that the weights of the current time decision values should be greater than those of the future decision values. The simulation test validates our hypothesis. Although this idea is simple, it is an effective means of improving the optimal objective. For the sake of the simplicity of the simulation test, only the single-level MPC method was used to test this hypothesis. The test is described as follows:  
The first weighting coefficients were increased by a factor of five, and the rest remained unchanged. The expressions for the weighting coefficients are:  
\[w_{i}(t)= \begin{cases}2.5&t=1\\ 0.5&t=2\dots,24\end{cases} ,w_{2}(t)= \begin{cases}0.5&t=1\\ 0.1&t=2\dots,24\end{cases} ,W_{1}(t)= \begin{cases}5.0&t=1\\ 1.0&t=2\dots,24\end{cases}  \tag{32}\]  
The system was simulated for a 24 h period. The results of three sub-objectives are as follows:  
Figure 17 shows the comparison of \(p_{i}^{\text{\tiny{m}}}\) using the increased and original weights, respectively. In Figure 17, three power signals are shown: the plan of the grid \(p_{i}^{\text{\tiny{plan}}}\) (solid, gray), the enhanced weight \(p_{i}^{\text{\tiny{p}}^{\text{\tiny{m}}}}\) (no line-dot, black), and the original weight \(p_{i}^{\text{\tiny{p}}^{\text{\tiny{m}}}}\) (line, black). The enhanced weight \(p_{i}^{\text{\tiny{p}}^{\text{\tiny{m}}}}\) follows the plan of the grid completely, whereas, for the original weight \(p_{i}^{\text{\tiny{m}}}\), a slight error is observed. This result suggests that the method of increasing the weight could assist \(p_{i}^{\text{\tiny{m}}}\) in tracing the plan of the grid. Figure 18 shows the comparison result of \(p_{i}^{\text{\tiny{m}}}\) using the enhanced weight and the original weight, respectively. In Figure 18, four power signals are shown: the plan of the grid \(p_{i}^{\text{\tiny{plan}}}\) (solid-plus, red), the available wind power \(p_{i}^{\text{\tiny{wind}}}\) (dash, gray), the enhanced weight of wind curtailment \(p_{i}^{\text{\tiny{m}}}\) (solid, black), and the original weight of wind curtailment \(p_{i}^{\text{\tiny{m}}}\) (solid, gray). Note that there are two \(y\)-axes: the origin of the left \(y\)-axis is zero, and \(p_{i}^{\text{\tiny{plan}}}\), \(p_{i}^{\text{\tiny{wind}}}\), and the enhanced weight of wind curtailment \(p_{i}^{\text{\tiny{m}}}\) are correlated; Moreover, the origin of the right \(y\)-axis is \(-2\), and it is a correlation of the original weight of wind curtailment \(p_{i}^{\text{\tiny{m}}}\). The two y-axes are set to different scales and intercepts to prevent the overlap of the two \(p_{i}^{\text{\tiny{m}}}\). As the weight of first moment increases, the number of times \(p_{i}^{\text{\tiny{m}}}\) occurred and decreases from 17 to 12, and \(p_{i}^{\text{\tiny{m}}}\) decreases from 0.974 to 0.915 MWh. Comparing the two \(p_{i}^{\text{\tiny{m}}}\), we can  
Figure 16: Operating states of the fly wheel. **(a)** One day operating states of fly wheel; **(b)** Four days operating states of fly wheel. find the enhanced weight \(p_{t}^{\text{\tiny{uu}}}\) occurs for five fewer times, and the amount of the enhances weight decreased by 6%. To show the details of the reduction of \(p_{t}^{\text{\tiny{uu}}}\), the case of the minute 435 was tested again with the same data. For the original weight of \(p_{t}^{\text{\tiny{uu}}}\), reduction occurs at minute 435, while for the enhanced weight of \(p_{t}^{\text{\tiny{uu}}}\), it does not occur. The decision values obtained are listed in Table 5.  
Figure 17: Results of the first objective after increasing the weighting.