## 5 Example Analysis
### Analysis of the Simulation Results
#### 5.2.7 Weight Sensitivity Analysis of the Objective Function of the Upper Distribution Network  
In the upper distribution-network level, the weights \(B=(0.5393,0.2974,0.1633)\) of multi-objective functions transformed into a single-objective function were obtained by expert experience in Section 3.1.3. To verify the influence on the operation state of the distribution network comprising the micro energy grid when the weight was changed, the sensitivity method was used to analyze the relevant problem. The relevant principle was shown in Reference [44]. The relationship equations between changes in weight, the weight sensitivity criteria, and the weight stable interval are shown in Formula (28). The conclusion is shown in Table 7.  
\[\left\{ \begin{array}{l}G_{\min}=B+\Delta M_{\min}\\ G_{\max}=B+\Delta M_{\max}\\ J=\Delta M_{\max}-\Delta M_{\min}\end{array} \right., \tag{28}\]  
where \(B\) is the weight factor of the independent variable in the upper distribution-network level; \(G_{\min}\) and \(G_{\max}\) are the minimum and maximum weight sensitivity criteria; \(\Delta M_{\min}\) and \(\Delta M_{\max}\) are the minimum and maximum changes in weight; and \(J\) is the weight stable interval. According to the data of the weight stable interval in Table 7, the weight stable interval of total system cost was less than the weight stable interval of the network's active power loss, which was less than the weight stable interval of the standard deviation of the voltage deviation. Relative to the system, the weight sensitivity of total system cost was greater than the weight sensitivity of network's active power loss, which was greater than the weight sensitivity of the standard deviation of the \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Cost of the Distribution Network (Does**} & \multicolumn{3}{c}{**Cost of the Micro**} & \multicolumn{3}{c}{**Total System Cost/RMB**} \\  & **Not Contain Micro Energy Grid/RMB** & & **Energy Grid/RMB** & & **Total System Cost/RMB** \\ \cline{2-7}  & **Winter** & **Summer** & **Winter** & **Summer** & **Winter** & **Summer** \\ \hline PSO algorithm & 1,126,004,317 & 39,809,957 & 94,318,029 & 3,292,247 & 1,220,322,346 & 43,102,204 \\ \hline IWO algorithm & 750,401,055 & 39,040,023 & 71,295,926 & 3,273,691 & 821,696,981 & 42,313,714 \\ \hline GWO algorithm & 741,777,648 & 38,852,914 & 68,603,822 & 3,266,733 & 810,381,470 & 42,134,740 \\ \hline GWO-EPD algorithm & 740,359,725 & 38,717,692 & 65,104,632 & 3,253,778 & 805,464,357 & 41,971,470 \\ \hline Improved GWO algorithm & 419,218,459 & 37,523,714 & 56,072,998 & 3,141,208 & 475,291,457 & 40,664,922 \\ \hline \end{tabular}
\end{table} 
Table 6: Daily cost of the distribution network comprising the micro energy grid using five algorithms—the particle swarm optimization (PSO) algorithm, the invasive weed optimization (IWO) algorithm, the grey wolf optimization (GWO) algorithm, the improved GWO algorithm, and the GWO/evolutionary population dynamics (GWO-EPD) algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Weight of Total System Cost**} & \multicolumn{3}{c}{**Weight of Network’s**} & \multicolumn{3}{c}{**Standard Deviation of**} \\  & & & **Active Power Loss** & & **the Voltage Deviation** \\ \cline{2-7}  & **Minimum** & **Maximum** & **Minimum** & **Maximum** & **Minimum** & **Maximum** \\ \hline Changes in weight & \(-\)0.1922 & 0.0463 & \(-\)0.0928 & 0.3266 & \(-\)0.0793 & 0.5894 \\ \hline Weight sensitivity criterion & 0.3471 & 0.5856 & 0.2046 & 0.624 & 0.084 & 0.753 \\ \hline Weight stable interval & \multicolumn{3}{c}{0.2385} & \multicolumn{3}{c}{0.4194} & \multicolumn{3}{c}{0.6687} \\ \hline \end{tabular}
\end{table} 
Table 7: Weight sensitivity analysis in the objective function of the upper distribution network. voltage deviation. For the high-sensitivity weight, the objective function value was easily changed by a subtle change in the independent variable of the corresponding objective function.