## 3 Reactive Power Optimization in Distribution Network Based on EWOSM
### Specific Steps of EWOSM  
The proposed EWOSM contains two procedures. Firstly, typical scenarios partitioning and load distribution matching method is used and select out \(N_{e}\) alternative schemes from historical database. Secondly, select the optimal scheme from alternatives with the entropy weight method, and the specific steps are expressed as follows.  
Step 1: Based on the power load at the time to be optimized, calculate the power flow with \(N_{e}\) alternatives respectively and the results of power flow must be checked according to Equations (5)-(9) to ensure the constraints are satisfied. If the constraints are not met, the corresponding alternative control scheme should be removed. Besides, three indexes containing the network loss, the node voltage offset and the minimum module-eigenvalue of the Jacobian matrix are used to evaluate the control effect of each alternative, and the three indexes are presented by \(y_{1},y_{2}\) and \(y_{3}\).  
Step 2: This is a multi-attribute decision-making problem with 3 evaluation indexes and \(N_{e}\) alternatives, and the evaluation index matrix is formed as expressed in Equation (12).  
\[Y=\left[\begin{array}{cccc}y_{11}&y_{12}&\cdots&y_{1N_{e}}\\ y_{21}&y_{22}&\cdots&y_{2N_{e}}\\ y_{31}&y_{32}&\cdots&y_{3N_{e}}\end{array}\right] \tag{18}\]  
Step 3: As the smaller the value of the network loss and the node voltage offset, the better the control effect of reactive power, standardize the two indexes according to Equation (13); conversely, the larger the minimum module-eigenvalue is, the more stable the system is, so standardize the index according to Equation (14). Then calculate the proportion \(p_{\bar{y}}\) that the evaluation index \(r_{\bar{y}}\) on the index \(i\) with Equation (15).  
Step 4: Calculate the entropy of each evaluation index and the corresponding entropy weight according to Equation (16) and Equation (17) respectively.  
Step 5: The objective weight \(w_{1}\), \(w_{2}\) and \(w_{3}\) of the three evaluation indexes are substituted into Equation (19) to calculate the total evaluation value of each alternative respectively. And the scheme that has the highest evaluation value is the optimal control plan.  
\[r_{j}=w_{1}r_{1j}+w_{2}r_{2j}+w_{3}r_{3j},\ j=1,\cdots,N_{e} \tag{19}\]  
In summary, the reactive power optimization process based on the entropy-weight method in distribution network is shown in Figure 4.  
As the proposed EWOSM is based on the analysis and comparison of a large number of historical reactive power optimization schemes, under the ideal condition, two assumptions are set up that the historical database is large enough to containing all the load distributions and the corresponding historical control scheme are optimized, so that the result of EWOSM should be the optimal scheme.  
Figure 4: Flow chart of reactive power optimization in distribution network based on entropy-weight method.  
But in practical engineering applications, the two assumptions are hardly to set up, so the result cannot be guaranteed the optimal scheme and it is more like a suboptimal feasible solution. Then, a hybrid method based on the combination of EWOSM and some existing methods, such as Genetic Algorithm (GA) method, neighborhood search method and Sequential Quadratic Programming (SQP) method, is proposed to ensure the optimality and practicability. For example, the neighborhood search algorithm can be used to find the global optimal solution in the neighborhood of the result of EWOSM; besides, the result of EWOSM also can be taken as an initial solution of the existing optimization algorithm to speed up the convergence and improve efficiency.