## 3 Case Study  
A real 10-bus network, representing a zone of a real transmission and distribution system, has been used to verify the effectiveness of the proposed methodology. Figure 6 presents the topology of the system. The system has two voltage levels, ultra-high voltage (220 kV) and high voltage (110 kV). Buses 2, 3, 6, 7, 8, and 10 belong to the high voltage level (110 kV), and buses 1, 5, and 9 have an ultra-high voltage level (220 kV). On the other hand, buses 2, 3, 4, 5, 7, and 10 belong to the category of load buses, Buses 6 and 8 are generation buses, and Bus 1 represents the slack-bus. Two wind farms with an installed capacity of 50 MW are connected to Buses 6 and 8 through electric lines with short lengths. The three power transformers (\(T_{(1,2)}\), \(T_{(5,6)}\), and \(T_{(8,9)}\)) have the on-load tap changer (OLTC) so that the possibility to implement the proposed coordinated control methodology is accomplished. The power transformers have the following initial tap positions, tap 15 for \(T_{(1,2)}\), tap 10 for \(T_{(5,6)}\), and tap 8 for \(T_{(8,9)}\), which ensure a high voltage level at the 110 kV buses (between 1.05 and 1.1 pu.). The Supplementary File _Network Data_ contains the technical characteristics of the electric lines and power transformers. The analysis has been performed considering one day as the study period. The active and reactive power profiles requested by the loads and injected by the two wind farms in the analyzed day have been uploaded from the database of the SCADA master system. The Supplementary File _Power Profiles_ contains the profiles associated with each load bus and Wind Farm. The obtained results have been compared with a base scenario (S0) where both wind farms are OFF to quantify the benefits on the operation of the network with the wind power sources integrated, overlapping the coordinated control of the OLTCs. The results for the 220 kV buses are not presented in the case study because the voltage variation is very close during the analyzed period, and the coordinated control OLTCs operate at the level of the 110 kV buses. Figure 7 presents the hourly values of the objective function (1) obtained in the base scenario S0, without (solid line) and with (square dots and blue bars) coordinated control of the OLTCs in the analyzed network, the power savings are also shown (red bars). The power flow was calculated using the Newton-Raphson method. Table 5 presents the numerical values of the objective function (1) obtained in the base scenario S0, without (\(F^{*}\)Loss,h) and with (\(F^{*}\)Loss,h) coordinated control of the OLTCs  
Figure 6: The topology of the 10-bus test network. Figure 7: The hourly values of the objective function (without and with coordinated control of the OLTCs) and the energy-savings, base scenario S0. in the analyzed network, the power saving (\(\Delta F_{Loss}\)) in absolute and percent units and tap positions resulting from the optimization process. The hourly power savings have been calculated with the formula:  
\[\Delta F_{Loss,h}(MW)=F^{*}{}_{Loss,h}-F^{**}{}_{Loss,h};\quad\Delta F_{Loss,h}( \%)=\frac{F^{*}{}_{Loss,h}-F^{**}{}_{Loss,h}}{F^{*}{}_{Loss,h}}\cdot 100;\quad h =1,\dots,T_{H} \tag{31}\]  
where: \(\Delta F_{Loss,h}\) (\(MW\)) is the power saving calculated in \(MW\) at hour \(h\); \(\Delta F_{Loss,h}\) (\(\%\)) is the power saving calculated in percent at hour \(h\); \(F^{*}{}_{Loss,h}\) represents the power losses calculated without a coordinated control of the OLTCs at the hour \(h\); \(F^{**}{}_{Loss,h}\) represents the power losses calculated with coordinated control of the OLTCs at the hour \(h\). The energy-savings have values between 28.34% (recorded at hour 19) and 42.74% (recorded at hour 2), with a mean of 34.13%. The energy-saving in the analyzed period was 12.62 \(MWh\), representing 33.47% of the total energy losses (37.7 \(MWh\)) calculated without a coordinated control of the OLTCs.