## 3 Case Study
Furthermore, neither bus presents any suspiciously far-out values (outliers) of the voltage that might require a deeper analysis. Table 6 shows the statistical details with the calculated values of the quartiles. These statistical indicators confirm reaching the objective, regarded as constant as possible voltage level in the electric network, in an optimal variation range, such that the power losses have the lowest values if the proposed coordinated control methodology is applied. In the following, the scenario with the integration of the wind farms in the network (named \(S1\)) has been analyzed. Three cases have been considered to investigate the optimal operation of the network. * Case 1: Wind Farm 1 (connected at the bus 6) is ON, and Wind Farm 2 (connected at the bus 8) is OFF;
* Case 2: Wind Farm 1 (connected at the bus 6) is OFF, and Wind Farm 2 (connected at the bus 8) is ON;
* Case 3: Both wind farms are ON. The obtained results are compared with the base scenario \(S0\), when both wind farms were OFF, to quantify the benefits on the operation of the network with the wind power  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Statistical Parameters**}} & \multicolumn{6}{c}{**without Coordinated Control of the OLTCs**} & \multicolumn{6}{c}{**with Coordinated Control of the OLTCs**} \\ \cline{2-13}  & **Bus2** & **Bus3** & **Bus4** & **Bus6** & **Bus7** & **Bus8** & **Bus10** & **Bus2** & **Bus3** & **Bus4** & **Bus6** & **Bus7** & **Bus8** & **Bus10** \\ \hline \multirow{4}{*}{**Quartiles**} & **Q0** & 1.088 & 1.078 & 1.076 & 1.075 & 1.058 & 1.044 & 1.044 & 1.036 & 1.031 & 1.031 & 1.032 & 1.027 & 1.027 & 1.023 \\  &  
sources integrated, overlapping the coordinated control of the OLTCs. The details of the analysis for each case are presented in the following. Figure 11 presents the hourly values of the objective function (1), without (solid line) and with (square dots and blue bars) coordinated control of the OLTCs in the analyzed network, and the power savings (red bars) in the three analyzed cases. The power flow was calculated using the Newton-Raphson method. Table 7 presents the numerical values of the objective function (1), without (\(F^{\ast}_{Loss}\)) and with (\(F^{\ast\ast}_{Loss}\)) coordinated control of the OLTCs in the analyzed network, the power savings (\(\Delta F_{Loss}\)) in absolute and percent units, and tap positions resulting from the optimization process in the three analyzed cases. The hourly power saving corresponding to each case has been calculated via Formula (31). The energy-savings in the three cases exceed 30%, having the minimum values recorded at hour 19 (31.33%, Case 1, 31.54%, Case 2, and 35.34%, Case 3) and the maximum values recorded at hour 2 (45.79%, Case 1, 46,67%, Case 2, and 50%, Case 3). The means in the three cases are 37.51%, 37.92%, and 41.58%, respectively. The total energy-savings in the analyzed period are 36.82%, 37.42%, and 41.27% of the total energy losses (30.88, 30.30, and 24.52 \(MWh\), respectively) recorded when the coordinated control of the OLTCs is not used. Figure 12 presents the tap positions of each transformer depending on the analyzed case. Thus, the transformers have the changers at different taps in the three time intervals ((1-7,8-21), and (22-24)) and analyzed cases. Transformer \(T_{(1,2)}\) has the tap changer at positions (8-10) in the first time interval, (9-12) in the second time interval, and (8,9) in the third time interval. Transformer \(T_{(5,6)}\) has the tap changer at positions (6-8) in the first interval, (8-10) in the second time interval, and (7,8) in the third time interval. The transformer \(T_{(8,9)}\) has the tap changer at the same positions, (7-9) in the first and third intervals, and (7-10) in the second time interval.