## 5 Results and Discussion
### Large-Scale Simulation Validation Experiments  
In order to test the performance of the Modified PSO and IUPSO algorithms in more complex scenarios, 400 scenarios were generated using equal probability random sampling based on the parameters of the cloud movement model. The simulation results are shown in Figure 14, and the difference in simulation data between the IUPSO and Modified PSO algorithms is illustrated in Figure 15.  
The purpose of the real-time scheduling optimization of the heliostat aiming strategy is to maximize the output power of the heliostat field under the premise of satisfying the heliostat field scheduling constraints, and thus, the fitness value function is proposed in Section 2.1.2. From Figures 14 and 15, for the heliostat, IUPSO achieve the real-time scheduling of the heliostat aiming strategy under dynamic cloud cover, satisfying the scheduling constraints of the heliostat aiming strategy. Compared with Modified PSO, the IUPSO adaptation value function is improved by 19%, and the \begin{table}
\begin{tabular}{l l} \hline \hline
**Metric** & **Equation** \\ \hline
**MAE** & \(MAE=\frac{1}{N}\sum\limits_{i=1}^{N}\left|Y_{i}-\hat{Y}_{i}\right|\) \\
**MSE** & \(MSE=\frac{1}{N}\sum\limits_{i=1}^{N}\left(Y_{i}-\hat{Y}_{i}\right)^{2}\) \\
**RMSE** & \(RMSE=\sqrt{\frac{1}{N}\sum\limits_{i=1}^{N}\left(Y_{i}-\hat{Y}_{i}\right)^{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance indexes [33]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Equivalent Velocities 5.0**} \\ \hline
**Algorithm** & **MSE** & **RMSE** & **MAE** &
\begin{tabular}{c} **Difference of Mean** \\ **Iteration Periods** \\ \end{tabular} \\ \hline
**IUPSO/Modified PSO** & 1923.9562 & 43.8629 & 14.5977 & 110 \\
**IUPSO/GA** & 8953.7463 & 94.6242 & 75.3990 & 110 \\
**IUPSO/BA** & 32,429.9280 & 180.0831 & 185.5373 & \textgreater{}130 \\
**IUPSO/WOA** & 4191.5491 & 64.7422 & 219.0136 & 10 \\
**IUPSO/RDA** & 8390.6510 & 91.6005 & 92.0474 & — \\ \hline \hline \multicolumn{5}{c}{**Equivalent Velocities 6.0**} \\ \hline
**IUPSO/Modified PSO** & 1351.7197 & 36.7657 & 31.8737 & 80 \\
**IUPSO/GA** & 7517.8218 & 86.7054 & 78.4167 & 70 \\
**IUPSO/BA** & 28,827.2781 & 169.7860 & 168.2572 & \textgreater{}130 \\
**IUPSO/WOA** & 3993.9796 & 36.1379 & 39.4935 & 60 \\
**IUPSO/RDA** & 6635.3528 & 81.4577 & 69.1545 & — \\ \hline \hline \multicolumn{5}{c}{**Equivalent Velocities 10.0**} \\ \hline
**IUPSO/Modified PSO** & 9724.3286 & 98.6120 & 93.7950 & \textgreater{}130 \\
**IUPSO/GA** & 22,535.1572 & 150.1171 & 145.2421 & \textgreater{}130 \\
**IUPSO/BA** & 37,189.3496 & 192.8454 & 190.0358 & \textgreater{}130 \\
**IUPSO/WOA** & 5710.2145 & 75.5660 & 60.3263 & 70 \\
**IUPSO/RDA** & 7077.4914 & 84.1278 & 76.5827 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Data comparison between seven algorithms. output power is improved by 16%. Modified PSO exhibits two performance degradations after 40-60 obscured heliostats compared to more than 90, indicating its limitations. On the other hand, IUPSO demonstrates better overall simulation robustness. However, specific dispersion points are observed after obscured heliostats exceed 160, highlighting its limitations under some real-time dynamic cloud shadow scenarios. Furthermore, dispersion points are along other axes, particularly noticeable in Figure 13(a). This dispersion is attributed to calculation errors arising from varying direct irradiation intensities on the heliostats positioned across different locations within the sector region. As a cloud moves closer to the sector region's center, the direct sunlight angle increases, resulting in a steeper heliostat solar irradiance gradient. When clouds traverse the central axis of the X-axis, passing through the sector's center, the neighboring heliostats experience significant variations in irradiation intensity. This can lead some heliostats to converge into local optima, resulting in the presence of dispersion points.