# A Small-Sample Scenario Optimization Scheduling Method Based on Multidimensional Data Expansion
## 1 Introduction
A Small-Sample Data Expansion Method Based on Spatiotemporal Meteorological Synergistic Enhancement  
The optimized scheduling of newly built Integrated Energy Systems (IESs) faces the challenge of data scarcity in small-sample scenarios, particularly when renewable energy output is highly uncertain. Traditional data enhancement methods (e.g., interpolation and generative adversarial networks) are prone to overfitting or pattern collapse when the sample size is too small. Since closely spaced PV power plants in the same region tend to have similar meteorological factors, the output of PV equipment with similar capacities, efficiencies, etc. exhibits a high degree of similarity. Therefore, when historical data for a new PV power plant are lacking, they can be expanded by utilizing the historical data of similar PV power plants. Although the power load also has a certain degree of uncertainty, its overall distribution characteristics are more stable, making it appropriate to use dynamic data enhancement methods for data expansion. Therefore, this paper proposes a small-sample data expansion method based on Spatiotemporal Meteorological Augmentation (STMA), which replaces the target distributed photovoltaic (PV) daily power curves based on meteorological similarity by surrounding PV daily power curves with multiple stations with measured power. The electricity load data employ a dynamic enhancement strategy based on day type division, which fully considers the differences in load patterns between weekdays and weekends. A uniform random sampling method generates synthetic data that conform to the real distribution characteristics, thereby constructing an enhanced dataset applicable to the target area. The data expansion is divided into PV output data expansion and electricity load data expansion. The complete data expansion method flow is shown in Figure 1 and contains the following core steps:  
1. Spatial correlation screening: Selecting neighboring PV plants based on geographic distance. 2. Meteorological similarity calculation: Quantify the difference in the distribution of meteorological features between the source and target domains using the multi-kernel maximum mean difference (MK-MMD) method. 3. Data conversion and fusion: Retain the source PV plant data with the highest similarity, convert the source PV plant data to the target PV plant according to the capacity ratio, and obtain complete PV output data. 4. Day Type Classification: Classify the electricity load data according to day type. 5. Same-day data filling: Fill in the missing historical load data by random sampling according to the same day type and time. 6. Data Merging: Merge the generated PV output and load data with the existing data, aligning them with time to obtain a more comprehensive historical electricity consumption dataset. The basic idea of missing power data reconstruction for information at all-black sites is to utilize the surrounding PV daily power curve multi-field stations with measured power to replace the target distributed PV daily power curve based on meteorological similarity. The specific process is as follows:  
(1) Spatial correlation screening  
The closer the spatial distance of the PV power stations decreases, the stronger the correlation between the meteorological conditions and the power pattern. Therefore, the PV power stations with stronger correlation are first screened by spatial correlation. Define the coordinates of target area power plants as (\(lat_{t}\), \(lon_{t}\)), the coordinates of candidate source  
Figure 1: Framework diagram of the STMA-based small-sample data augmentation approach. domain power plants as (\(lat_{s}\), \(lont_{s}\)), and [PERSON]'s formula calculates the geographic distance \(d\):  
\[d=2R\text{arcsin}\Bigg{(}\sqrt{\sin^{2}\biggl{(}\frac{\Delta lat}{2}\biggr{)}+ \cos(lat_{t})\cos(lat_{s})\sin^{2}\biggl{(}\frac{\Delta lon}{2}\biggr{)}}\Bigg{)} \tag{1}\]  
where R = 6371 km is the radius of the Earth, \(\Delta lat=lat_{t}-lat_{s}\), \(\Delta lon=lon_{t}-lon_{s}\).