# A Small-Sample Scenario Optimization Scheduling Method Based on Multidimensional Data Expansion
## 1 Introduction
Screening strategy: Retain stations with \(d\leq D_{\text{max}}\) as candidate source domains, with \(D_{\text{max}}\) set according to regional climate characteristics (e.g., \(D_{\text{max}}=50\) km for plains), or select the nearest n stations according to the number of stations. (2) Calculation of meteorological similarity  
The multi-kernel maximum mean discrepancy (MK-MMD) is employed to compute meteorological similarity. A temporal feature matrix is constructed for each candidate power station in the source domain \(X\in\mathbb{R}^{T\times F}\), where \(T\) denotes the time steps and \(F\) represents meteorological features such as irradiance, temperature, and wind speed. The source domain \(S=\left\{x_{i}^{s}\right\}_{i=1}^{n}\) and target domain \(T=\left\{x_{j}^{t}\right\}_{j=1}^{m}\) are defined, and MK-MMD quantifies their distribution discrepancy using multi-scale Gaussian kernels:  
\[\text{MK-MMD}^{2}(S,T)=\frac{1}{n^{2}}\sum_{i,j=1}^{n}K(x_{i}^{s},x_{j}^{s})+ \frac{1}{m^{2}}\sum_{i,j=1}^{m}K(x_{i}^{t},x_{j}^{t})-\frac{2}{nm}\sum_{i=1}^{ n}\sum_{j=1}^{m}K(x_{i}^{s},x_{j}^{t}) \tag{2}\]  
The multi-kernel function is defined as:  
\[K(x,y)=\sum_{k=1}^{K}\exp\left(-\frac{\parallel x-y\parallel^{2}}{2\sigma_{k} ^{2}}\right) \tag{3}\]  
where \(\sigma_{k}\) represents adaptive bandwidths. The similarity metric is computed by:  
\[\text{Similarity}=\frac{1}{1+\text{MK-MMD}} \tag{4}\]  
For station data comparison, a 24-h (1-day) cycle is adopted as the temporal unit. Daily similarity between each candidate station and the target station is calculated. PV output data are then converted proportionally based on date-matched similarity results. (3) PV Output Data Conversion:  
The historical daily power profiles \(P_{\text{CG}_{t}}\) from selected source domain PV stations are scaled according to the capacity ratio between the well-documented station capacity \(S_{\text{CG}}\) and the target distributed PV capacity \(S_{\text{DG}}\), yielding the reconstructed daily power curve \(P^{\prime}_{\text{DG}_{t}}\):  
\[P^{\prime}_{\text{DG}_{t}}=P_{\text{CG}_{t}}\frac{S_{\text{DG}}}{S_{\text{CG}}} \tag{5}\]  
For the filtered source domain PV stations \(S_{1}\), \(S_{2}\), \(\ldots\), \(S_{k}\), their output data \(P_{s}\) are temporally aligned with the target domain data \(P_{t}\) and concatenated:  
\[P_{\text{fused}}=\text{Concat}(P_{t},P_{s_{1}},P_{s_{2}},\ldots,P_{s_{k}}) \tag{6}\](4) Day Type Classification:  
To address the critical challenge of limited historical data in newly established energy systems, this study intelligently extracts and restructures load characteristics from existing weekday and weekend data. The original dataset is first partitioned into two distinct temporal categories:  
Let the original dataset be \(D\in\mathbb{R}^{p\times 24}\) containing \(p\) days of load profiles:  
* Weekday subset: \(D_{\text{weekday}}\in\mathbb{R}^{n\times 24}\) (comprising \(n\) days);
* Weekend subset: \(D_{\text{weekend}}\in\mathbb{R}^{m\times 24}\) (containing \(m\) days). where \(p=n+m\). (5) Same-Day Data Imputation:  
The periodic characteristics of the power load retained by the module are determined by the data type to ensure that the generated data conform to the actual power consumption pattern (such as the difference between the peak load on weekdays and weekends) and to avoid feature distortion caused by simple random generation. The uniform random sampling strategy is adopted to maintain the distribution characteristics of the original data while ensuring data diversity, so that the enhanced dataset can not only fully cover the decision-making space but also accurately reflect the uncertainty of power load demand, thereby significantly improving the generalization ability and robustness of the subsequent dispatching model.