## 2 The Method of Typical Scenarios Partitioning and Load Distribution Matching  
### Relationship between the Data Source and the Optimal Schemes in Reactive Power Optimization  
The database in distribution network has accumulated a large amount of historical data, which comes from different systems, such as SCADA (Supervisory Control and Data Acquisition), GIS (Geographic Information System) and EMS (Energy Management System). It also can be divided into operational monitoring data, marketing data, and management data according to the use of data. Besides, part of the data is well-structured, but more data is unstructured or semi-structured. Facing such a large amount of multi-source and heterogeneous data, it is necessary to consider how to select out the effective data and make fully use of it to solve reactive power optimization problem. Therefore, data fusion and data cleaning should be performed to make all the data well-structured firstly [33; 34]; then, the mathematic model of reactive power optimization is provided to analyze the relationship between the data source and the optimal schemes, which can guide us to find out the data that have a decisive effect on reactive power optimization. Reactive power optimization is a multi-objective programming problem, and generally the network loss, the node voltage offset and the minimum module-eigenvalue of the Jacobian matrix are chosen as the objective functions to evaluate the economy and security of the system. The minimum module-eigenvalue can measure the static voltage stability of the system; the smaller the value is, the more unstable the system is, and the value will decrease to 0 if the voltage collapse occurs. The formulas of the objective function are expressed as follows:  
\[\min f=w_{1}f_{1}+w_{2}f_{2}+w_{3}f_{3} \tag{1}\]  
\[f_{1}=\sum_{i,j=1}^{n}G_{ij}(V_{i}^{2}+V_{j}^{2}-2V_{i}V_{j}\cos\theta_{ij}) \tag{2}\]  
\[f_{2}=\sum_{i=1}^{n}\left(\frac{V_{i}-V_{i}^{B}}{\Delta V_{i}^{\max}}\right)^{2} \tag{3}\]  
\[f_{3}=\min(|eig(J)|) \tag{4}\]  
where \(f\) is the objective function; \(f_{1},f_{2}\) and \(f_{3}\) are respectively the network loss, the node voltage offset and the minimum module-eigenvalue; \(w_{1}\), \(w_{2}\) and \(w_{3}\) are the corresponding weight of \(f_{1},f_{2}\) and \(f_{3}\), and \(w_{1}+w_{2}+w_{3}=1\); \(V_{i}\) and \(V_{j}\) are the voltage amplitude of node \(i\) and node \(j\); \(G_{ij}\) and \(\theta_{ij}\) are respectively the conductance and voltage phase angle difference between node \(i\) and node \(j\), and particularly \(i\
eq j\); \(n\) is the number of nodes in the system; \(V_{i}^{B}\) is the ideal voltage amplitude of node \(i\), whose value is usually 1.0 (p.u. ); \(\Delta V_{i}^{\max}\) is the maximum allowable voltage offset of node \(i\), which is generally \(\pm 7\%\) in the distribution network; \(J\) is the Jacobian matrix while the power flow is converged; and \(eig\) (\(J\)) is the eigenvalue of matrix \(J\). The constraint of the reactive power optimization model contains power balance constraints, voltage constraints and control variables constraints. The power balance constraints are as follows:  
\[P_{Gi}-P_{Li}-V_{i}\sum_{j=1}^{n}V_{j}\big{(}G_{ij}\cos\theta_{ij}+B_{ij}\sin \theta_{ij}\big{)}=0 \tag{5}\]  
\[Q_{Gi}-Q_{Li}-V_{i}\sum_{j=1}^{n}V_{j}\big{(}G_{ij}\sin\theta_{ij}-B_{ij}\cos \theta_{ij}\big{)}=0 \tag{6}\]where \(P_{Gi}\) and \(Q_{Gi}\) represent the active and reactive power of node \(i\); \(P_{Li}\) and \(Q_{Li}\) represent the active and reactive load of node \(i\); \(B_{ij}\) represents the susceptance between node \(i\) and node \(j\).