# A Small-Sample Scenario Optimization Scheduling Method Based on Multidimensional Data Expansion
## 5 Case Studies
### Analysis of Data Expansion Effectiveness  
Figure 8a presents a heat map showing the total annual output of photovoltaic power, which shows that solar power has a clear time-varying character, varying within a day and between days. Its output is concentrated in the daytime, especially between 9:00 A.M. and 5:00 P.M., with peaks around noon. In addition, the intensity and pattern of the output vary considerably from day to day, reflecting the effects of seasonal changes and weather conditions. This strong time variation means that the small amount of PV output data from newly built integrated energy systems cannot cover the diversity of the operating \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Prediction Error**} & \multicolumn{2}{c}{**Without Data Expansion**} & \multicolumn{3}{c}{**With Data Expansion**} & \multicolumn{3}{c}{**Oversampling**} \\ \cline{2-10}  & **Trans.** & **Sum.** & **Win.** & **Trans.** & **Sum.** & **Win.** & **Trans.** & **Sum.** & **Win.** \\ \hline RMSE (kW) & 17.35 & 20.42 & 20.13 & 12.92 & 13.47 & 18.26 & 12.06 & 10.34 & 17.16 \\ \hline MAE (kW) & 9.05 & 11.47 & 9.88 & 7.82 & 6.74 & 8.74 & 6.06 & 4.97 & 8.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prediction errors in different seasons. Figure 7: Comparison of PV power prediction results by different methods in different seasons. (**a**) Summer PV power prediction results. (**b**) Winter PV power prediction results. (**c**) Transitional season PV power prediction results. (**d**) Error comparison of each method (MAE). scenarios, especially those rare but critical situations (e.g., cloudy days in the winter or peak hours in the summer). This lack of diversity results in an inability to provide sufficient state space coverage for downstream tasks such as PV output prediction or reinforcement learning-based scheduling. Therefore, it is necessary to supplement the limited data with spatial correlation-based sample transfer and meteorological similarity metrics to construct a more representative and comprehensive training dataset, ensuring the learned models are highly stable and applicable to a wider range of real-world situations. The kernel density estimation (KDE) curves before and after the expansion of the PV data are shown in Figure 8b. The probability density distribution pattern of the data is demonstrated. The figure shows that the distribution of a small amount of data differs from that of the complete data, in which there is a significant difference between the blue curve (original data and original one-month data) and the orange curve (year-round distribution). The original data distribution is wider, the main peak is lower, and the tail is longer, indicating that, when only a small amount of data are used, the characteristics of the distribution deviate significantly from the year-round data and cannot represent the overall characteristics of the year. It also shows that the data expansion method can better restore the missing data, in which the green curve (after expansion) and the orange curve (year-round distribution) are highly overlapped. The locations of the main peak and the distribution pattern are almost the same. This indicates that the data expansion method can effectively restore the missing year-round data distribution characteristics, making the sample distribution closer to the real year-round situation. This provides a more reliable database for subsequent modeling and reinforcement learning. The oversampling method proposed in this paper is mainly used to improve the accuracy of PV prediction. We have effectively proved the effectiveness of oversampling through the ablation experiments in Section 4.3 of the paper. Compared to the prediction method without oversampling, this method can improve the accuracy to a certain extent. When combined with time-of-day tariffs and electricity load demand, the expanded PV output data can provide a richer and more diverse state action space for reinforcement learning.