# Multi-Source Data Fusion-Based Grid-Level Load Forecasting
## 2 Materials and Methods
### Comprehensive Evaluation Index System  
The foundation of our weighted fusion approach is a hierarchical evaluation index system that quantifies the reliability and significance of provincial forecasts. This system employs a three-level structure with three primary indicators: forecast reliability, provincial load impact on the main grid, and provincial forecasting complexity. Figure 1 illustrates the steps for constructing this evaluation system.  
The primary purpose of constructing this evaluation index system is to quantitatively assess the reliability of load forecasting results from different provinces, providing a basis for determining weights in forecast fusion. The three-level structure is detailed in Table 1.  
\begin{table}
\begin{tabular}{c c c} \hline
**Primary Indicators** & **Secondary Indicators** & **Tertiary Indicators** \\ \hline Forecast Reliability & Historical Forecast Performance & Day-ahead Forecast Accuracy, Real-time Forecast Accuracy \\ Forecast Reliability & Forecasting System Stability & System Update Frequency, Forecast Result \\ Continuity, Abnormal Forecast Proportion & Continuity, Abnormal Forecast Proportion \\ Data Quality Level & Data Completeness Rate, Data Timeliness, Data Consistency \\ \hline Provincial Load Impact & Load Scale Proportion & Maximum Load Proportion, Average Load Proportion, Peak Load Contribution Rate \\ Regulation Capability & Peak Regulation Capacity Ratio, Renewable Energy Installation Ratio, Demand Response Capability \\ \hline  & Load Fluctuation Characteristics & Daily Load Fluctuation Rate, Weekly Load Fluctuation Rate, Seasonal Fluctuation Intensity \\ Forecasting Complexity & External Factor Sensitivity & Temperature Sensitivity, Humidity Sensitivity, Holiday Sensitivity \\ Electricity Consumption Structure Complexity & Industrial Electricity Proportion, Number of Key Users, User Type Diversity \\ \hline \end{tabular}
\end{table}
Table 1: Load forecasting evaluation index system.  
Figure 1: Steps for constructing an evaluation indicator system.  
Key metrics within this system include the following:  
1. Data Completeness Rate (DCR):  
\[DCR_{t}=\frac{N_{valid}}{N_{total}}\times 100\% \tag{1}\]  
where \(N_{valid}\) is determined by multiple validation functions including basic validity, anomaly detection, time alignment, and rate change checks:  
\[Valid(x)=Valid_{basic}(x)\wedge Valid_{anomaly}(x)\wedge Valid_{time}(x) \wedge Valid_{rate}(x) \tag{2}\]  
2. Data Timeliness (DT):  
\[DT_{t}=\max(0,1-\frac{\Delta t}{\tau}) \tag{3}\]  
where \(\Delta t\) is the actual data delay time, and \(\tau\) is the maximum allowable delay threshold.  
3. Data Consistency (DC):  
\[DC=DC_{format}\times DC_{logic} \tag{4}\]  
where format consistency and logical consistency are assessed separately:  
\[DC_{format}=1-\frac{N_{format}+N_{structure}+N_{sampling}}{N_{total}} \tag{5}\]  
\[DC_{logic}=\frac{1}{n}\sum_{i=1}^{n}\exp(-\frac{|x_{i}-\mu_{i}|}{\sigma_{i}}) \tag{6}\]  
The entropy weight method is used to calculate indicator weights and aggregate them hierarchically. For the \(k\)-th secondary indicator with \(m_{k}\) tertiary indicators and \(n\) evaluation objects (provinces), the calculation process is as follows:  
1. Standardize tertiary indicators:  
\[y_{ij}=\frac{x_{ij}-\min_{i}x_{ij}}{\max_{i}x_{ij}-\min_{i}x_{ij}} \tag{7}\]  
2. Calculate entropy value for each tertiary indicator:  
\[e_{j}=-\frac{1}{\ln n}\sum_{i=1}^{n}p_{ij}\ln p_{ij} \tag{8}\]  
where  
\[p_{ij}=\frac{y_{ij}}{\sum_{i=1}^{n}y_{ij}} \tag{9}\]  
3. Calculate tertiary indicator weights:  
\[w_{j}=\frac{1-e_{j}}{\sum_{j=1}^{n_{k}}(1-e_{j})} \tag{10}\]  
4. Calculate secondary indicator scores:  
\[S_{i,k}=\sum_{j=1}^{m_{k}}w_{j}y_{ij} \tag{11}\]5. Apply entropy method to secondary indicators to obtain primary indicator scores:  
\[S_{i}=\sum_{k=1}^{K}w_{k}S_{i,k} \tag{12}\]