## 3 Case Study
However, the number of turns for the tap changers is different for the three transformers in the analyzed cases to keep the voltage at the level of each bus within an optimal range corresponding to minimum power losses in the network, see Figure 13.  
A high number of turns is recorded in Case 2 (14 turns recorded for the transformer \(T_{(8,9)}\)) followed by Case 1 (10 turns recorded for transformer \(T_{(5,6)}\)) and Case 3 (11 turns recorded for transformer \(T_{(5,6)}\)). The number is higher in Cases 1 and 2 for all transformers than in scenario 50, where six turns are performed by transformers \(T_{(1,2)}\) and \(T_{(5,6)}\) and eight for transformer \(T_{(8,9)}\). Fewer turns are recorded in Case 3 for transformers \(T_{(1,2)}\) and  
Figure 11: The hourly values of the objective function (without and with coordinated control of the OLTCs) and the energy-savings, in the three cases of scenario 51: (a) Case 1; (b) Case 2; (c) Case 3. \(T_{(8,9)}\) (five and seven, respectively) and almost double-figure turns for transformer \(T_{(5,6)}\) to ensure a voltage level was in a narrow range. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Hour**} & \multicolumn{4}{c}{\(F^{\star}{}_{Loss}\)(MW)} & \multicolumn{4}{c}{\(F^{\star\star}{}_{Loss}\)(MW)} & \multicolumn{4}{c}{\(T_{(1,2)}\) (Tap * = 1  
Figure 14 shows the voltage variation at the 110 kV buses, without and with coordinated control of the OLTCs. Tables 13-14 from Appendix A present the hourly values of the voltage at each bus, without and with coordinated control of the OLTCs, in the three analyzed cases. The voltage at the buses has a variation between 1.1 (Bus 2) and 1.05 (Bus 10, Case 1). The highest values are recorded in the time intervals (1-7) and (22-24). The variation is reduced at 0.03 p.u., being very close at each bus, if the coordinated control of OLTCs is used. The exploratory analysis based on the voltage boxplots confirmed this statement. Figure 15 shows that the median voltage at the buses (drawn with a red line inside each box), when the coordinated control of the OLTCs is not used, and it has a multi-step decrease slightly attenuated for the four groups in the three analyzed cases compared to in scenario 50: _Group 1_ (Buses 2) between \(Q2\) = 1.091 and 1.092, _Group 2_ (Buses 3, 4, and 6) with \(Q2\) between 1.081 and 1.092, _Group 3_ (Bus 7) with \(Q2\) between 1.068 and 1.074, and _Group 4_ (Buses 8 and 10) with \(Q2\) between 1.053 and 1.061. Figure 14: The variation of the voltage at the 110 kV buses in the analyzed period (24 h) in the three analyzed cases of scenario 51. Figure 7:0 The number of turns for the tap changers of the three transformers in the three analyzed cases of scenario 51. This decrease is attenuated between groups from Case 1 to Case 3 (see Tables 8-10). At the same time, the median voltage from Groups 3 and 4 in Case 3 increases to 1.074 and 1.061, respectively. The interquartile ranges are reasonably similar in all cases, as seen by the lengths of the boxes (lower and upper sides of the box). The voltage distribution at all buses is positively skewed in all cases, being observable, the whisker and half-box are longer on the lower side of the median than on the upper side. Buses 2 and 6 present a few outliers of the voltage but, these values are very close to the quintile Q4, without being considered a problem. The obtained data are different when the coordinated control of the OLTCs is used, as can be  
The simulations run on a computer with an Intel Core i7 processor, 3.4 GHz, and 8 GB RAM, and the source code has been written in Matlab. The authors highlighted, in Paragraph 1.1, higher performances of classical algorithms from the mathematical programming compared to the meta-heuristic algorithms.