## Case Study
### A Practical Distribution System with 173 Nodes
#### 4.1.4 The Entropy Weight Method of the 173 Nodes System  
Power flow is calculated in turn with the 59 alternatives based on the load at 17 o'clock, and the corresponding network loss, node voltage offset and minimum module-eigenvalue are shown in Figure 8, which are calculated according to Equations (2)-(4).  
\begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **The Typical Load Scenarios** & **The Number of Days** & **No.** & **The Typical Load Scenarios** & **The Number of Days** \\ \hline
1 & Weekday in Spring & 328 & 5 & Weekday in Autumn & 325 \\
2 & Weekend in Spring & 132 & 6 & Weekend in Autumn & 130 \\
3 & Weekday in Summer & 328 & 7 & Weekday in Winter & 323 \\
4 & Weekend in Summer & 132 & 8 & Weekend in Winter & 128 \\ \hline \end{tabular}
\end{table}
Table 3: The typical load scenarios information of the 173 nodes system.  
Figure 6: The load curve of the next day.  
As shown in Figure 8, there are some cases that the network loss or node voltage offset of the 59 alternatives is similar or the same. It is because that a part of the control schemes of the alternatives may be same or similar. The weights of the network loss, node voltage offset and minimum module-eigenvalue are 0.5402, 0.2106 and 0.2492 respectively, and the optimal scheme is the thirty-second alternative. The specific optimal scheme and results are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**High Load Level (at 17 \(\sigma\)/clock)**} & \multicolumn{3}{c}{**Middle Load Level (at 10 \(\sigma\)/clock)**} & \multicolumn{3}{c}{**Low Load Level (at 2 \(\sigma\)/clock)**} \\ \cline{3-10}  & & **GA** & **SQP** & **EWOSM** & **GA** & **SQP** & **EWOSM** & **GA** & **SQP** & **EWOSM** \\ \hline \multirow{9}{*}{Optimal schemes} & Qc1/kvar & 950 & 400 & 400 & 1000 & 300 & 350 & 950 & 250 & 200 \\  & Qc2/kvar & 1000 & 800 & 850 & 900 & 550 & 550 & 950 & 350 & 350 \\  & QoS/kvar & 600 & 800 & 850 & 800 & 700 & 650 & 450 & 550 & 500 \\  & Qc4/kvar & 900 & 550 & 550 & 450 & 450 & 400 & 500 & 350 & 300 \\  & QoS/kvar & 1050 & 950 & 1000 & 1150 & 800 & 800 & 600 & 600 & 600 \\  & QoS/kvar & 600 & 450 & 450 & 250 & 400 & 350 & 350 & 300 & 300 \\  & Qc7/kvar & 600 & 500 & 500 & 450 & 400 & 400 & 300 & 300 & 300 \\  & QoS/kvar & 500 & 500 & 500 & 450 & 450 & 450 & 350 & 350 & 300 \\  & QoS/kvar & 1200 & 800 & 800 & 700 & 650 & 600 & 450 & 500 & 500 \\  & Qc1/kvar & 1900 & 1150 & 1200 & 1150 & 950 & 950 & 650 & 700 & 700 \\  & Qc11/kvar & 650 & 1150 & 1150 & 850 & 950 & 900 & 850 & 700 & 700 \\  & Qc12/kvar & 1900 & 1500 & 1650 & 1450 & 1350 & 1300 & 900 & 1050 & 1000 \\  & Qc13/kvar & 800 & 750 & 800 & 550 & 650 & 650 & 450 & 500 & 450 \\  & TI & \(1+6\times 125\%\) & & \multicolumn{3}{c}{\(1+6\times 125\%\)} & \multicolumn{3}{c}{\(1+6\times 125\%\)} \\  & T2 & \multicolumn{3}{c}{\(1+6\times 125\%\)} & \multicolumn{3}{c}{\(1+6\times 125\%\)} \\ \hline Network loss/kW & 637.16 & 632.86 & 631.40 & 494.76 & 494.34 & 495.39 & 342.93 & 342.11 & 342.40 \\ Node voltage offset & 32.28 & 16.826 & 18.40 & 29.84 & 19.578 & 17.84 & 33.09 & 25.332 & 23.15 \\ Minimum module-eigenvalue & 0.0659 & 0.0056 & 0.00569 & 0.00590 & 0.00582 & 0.00581 & 0.00606 & 0.00601 & 0.00599 \\ Computation time/s & 44.663 & 13.64 & 4.37 & 44.29 & 10.143 & 4.846 & 39.2 & 11.497 & 3.925 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The results of reactive power optimization with two methods under different load levels.  
Figure 8: The evaluation indexes of alternatives: (**a**) the network loss; and (**b**) the node voltage offset; (**c**) the minimum module-eigenvalue.  
Figure 7: The result of load distribution matching at 17:00.