## 3 Reactive Power Optimization in Distribution Network Based on EWOSM  
### Introduction to Multi-Attribute Decision Making Problem Based on Entropy Weight Method  
While selecting the optimal control scheme from alternatives, several reactive power optimization evaluation indexes should be considered comprehensively, including the network loss, voltage offset, power factor and so on. Therefore, it is a multi-attribute decision making problem, which is also called multiple objective decision making with finite alternatives. It is a decision making problem that select the optimal scheme from alternatives or schedule the alternatives ranking with the consideration of multiple attributes. Entropy weight method based on information entropy can solve the problem. The objective weights of multiple attribute indexes are determined by information entropy calculated from alternatives, and then the best scheme is selected out.  
The concept of entropy is derived from thermodynamics and it is a physical quantity that reflecting the directivity of natural thermal processes in initially. Then information entropy is put forward with the development of related research, which opens up a new way for quantitative decision method. In information theory, the amount and quality of information obtained in decision-making is an important factor to determine the accuracy and reliability of final decision. Exactly, entropy is a good measure for useful information provided by data.  
In the multi-attribute decision making problem with \(M\) evaluation indexes and \(N\) alternatives, the evaluation index matrix is expressed as follows:  
Figure 3: Flow chart of load distribution matching.  
\[Y=\left[\begin{array}{cccc}y_{11}&y_{12}&\cdots&y_{1N}\\ y_{21}&y_{22}&\cdots&y_{2N}\\ \vdots&\vdots&\cdots&\vdots\\ y_{M1}&y_{M2}&\cdots&y_{MN}\end{array}\right] \tag{12}\]  
where \(y_{ij}\) is the value of the \(i\)-th evaluation index at the \(j\)-th alternative.  
Matrix \(R=\{r_{ij}\}\) is got with the standardized of matrix \(Y\). The greater the value of the element in matrix \(R\) is, the better the evaluation effect is, so all evaluation indexes should be standardized according to this regulation. For the evaluation index that smaller value has better evaluation effect should be standardized with Equation (13), and conversely with Equation (14).  
\[r_{ij}=\frac{\max\limits_{j}\{y_{ij}\}-y_{ij}}{\max\limits_{j}\{y_{ij}\}-\min \limits_{j}\{y_{ij}\}} \tag{13}\]  
\[r_{ij}=\frac{y_{ij}-\min\limits_{j}\{y_{ij}\}}{\max\limits_{j}\{y_{ij}\}-\min \limits_{j}\{y_{ij}\}} \tag{14}\]  
where \(\max\limits_{j}\{y_{ij}\}\) and \(\min\limits_{j}\{y_{ij}\}\) are respectively the maximum and minimum value of the \(i\)-th row in matrix \(Y\). The maximum value of the elements in matrix \(R\) is \(1\) and minimum is \(0\), that is, \(0\leq r_{ij}\leq 1\), where \(i=1,\ldots,M;j=1,\ldots,N\).  
Calculate the proportion \(p_{ij}\) that evaluation index \(r_{ij}\) on the \(i\)-th index according to Equation (15), where \(r_{ij}\) is the \(i\)-th evaluation index of the \(j\)-th alternative.  
\[p_{ij}=r_{ij}\Bigg{/}\sum\limits_{j=1}^{N}r_{ij} \tag{15}\]  
And the entropy of the \(i\)-th evaluation index is expressed as follows [35]:  
\[H_{i}=-k\sum\limits_{j=1}^{N}p_{ij}\ln p_{ij} \tag{16}\]  
where \(p_{ij}\times\ln p_{ij}=0\) if \(p_{ij}=0\); and \(k=1/\ln N\) in order to make it meet the constrain that \(0\leq H_{i}\leq 1\).  
Entropy is a measure of uncertainty, and the smaller the entropy value is, the more effective the information corresponding to the evaluation index is. Therefore, the entropy weight \(w_{i}\) of the \(i\)-th index is shown as follows:  
\[w_{i}=\frac{1-H_{i}}{M-\sum\limits_{i=1}^{M}H_{i}} \tag{17}\]  
After the entropy weight of each evaluation index is determined, the multi-attribute decision making is transformed into a single attribute decision making problem; and then the optimal scheme can be selected from the alternatives.