## 3 Materials and Methods
### Parametric Analysis
In Figure 4, the green rectangles show the vertical magnetic shunts placed on the tank walls. Figure 4 illustrates the complete set of objects included in the model. These objects comprise a transformer core, windings, magnetic shunts, and a tank. Figure 5 shows the variation in tank loss with time during the 2-millisecond simulation period with vertical magnetic shunts only on the short side wall of the tank and only on the long front walls. The tank loss values obtained were utilized as the basis for comparison. In the 2 ms analysis, the average tank loss values were 812.30 W and 699.70 W with vertical magnetic shunts only on the short side wall and only on the long front walls of the power transformer, respectively. Figure 6 illustrates the variables defined for the dimensions of the horizontal magnetic shunts in the parametric analysis. These variables are defined separately for the short side wall and the long front walls of the transformer tank. \(\Delta\)x = the width of the magnetic shunt on the short side wall of the transformer tank (mm); \(\Delta\)y = the height of the magnetic shunt on the short side wall of the transformer tank (mm); \(\Delta\)z = the width of the magnetic shunts on the long front walls of the transformer tank (mm); \(\Delta\)w = the height of the magnetic shunts on the long front walls of the transformer tank (mm);\(\Delta\)d = the distance between the magnetic shunts on the long front walls of the transformer tank (mm). The vertical magnetic shunts employed by the transformer manufacturer on the tank wall have a thickness of 15 mm. In order to facilitate an accurate comparison between horizontal and vertical magnetic shunts, the thickness of the magnetic shunts was taken as 15 mm for the horizontal shunts. After the variables were defined, parametric analyses were performed for three different situations involving magnetic shunts placed horizontally on the tank wall. Since finite element simulation is time-consuming, it was deemed sufficient to perform parametric analyses for only 2 milliseconds. In Case 1: While there was no magnetic shunt on the long front walls of the tank, the loss values in the magnetic shunts of different sizes to be placed on the short side wall were investigated. Size-dependent tank loss values were obtained by changing the \(\Delta\)y size by 400 mm at each step from 400 mm to 2800 mm for three different shunts with \(\Delta\)x sizes of 500 mm, 600 mm, and 700 mm. In Case 2: While there was no magnetic shunt on the short side wall of the tank and \(\Delta\)z was constant on the long front walls of the tank, the losses that occurred when magnetic shunts of different sizes were used were analyzed. The size-dependent tank loss values were obtained by keeping \(\Delta\)z = 3760 mm constant and increasing the \(\Delta\)w parameter of the horizontal shunts by 100 mm in each step from \(\Delta\)d = 300 mm to 900 mm for 300, 350, and 400. Figure 4: Three-dimensional model of a transformer with (a) vertical magnetic shunts only on the short side wall and (b) vertical magnetic shunts only on the long front walls. Figure 5: Time variation in transformer tank loss with (a) vertical magnetic shunts only on short side walls and (b) vertical magnetic shunts only on long front walls. In Case 3: While there was no magnetic shunt on the short side wall of the tank, the size-dependent tank loss values were obtained for the horizontal magnetic shunt with dimensions of \(\Delta\)w = 400 mm and \(\Delta\)d = 600 mm on the long front walls of the tank. The \(\Delta\)z value was increased by 300 mm in each step from 2100 mm to 3900 mm. In Case 4: Tank losses were obtained as a function of the magnetic shunt thickness by using the optimum horizontal magnetic shunt dimensions. The magnetic shunt thickness was increased by 5 mm in each step from 5 mm to 35 mm.