## 3 Materials and Methods
### Parametric Analysis  
To perform a parametric analysis, it is necessary to create a transformer model in a FEM software program, assign the material, determine the solver type, assign the mesh, determine the boundary conditions, create the excitation, and determine the analysis time. A parametric analysis flow chart is shown in Figure 3. This study was carried out using a parametric analysis built into ANSYS. After defining the dimensions of the magnetic shunts in the model setup section of the ANSYS Electronics Desktop 2021 R1 software program, a parametric analysis was set up by defining the change intervals of the dimensions of the magnetic shunts as parametric variables in the Optimetrics tab in the Project Manager. The tank loss was obtained graphically depending on the parametric change in the magnetic shunt dimensions. Figure 3: Flowchart of parametric analysis. Figure 2: Star–star-connected external excitation circuit. In Figure 3, the input data for the flowchart are defined as follows:  
* The transient regime is entered as the solution type. * In the three-dimensional parametric model, M5 steel was designated as the transformer core and magnetic shunt material, copper as the winding material, and ST-52 steel as the tank material. Magnetic shunts are composed of a series of silicon steel laminations. * In order to conduct a parametric analysis, the dimensions of the magnetic shunt are defined as variables, and the symbols \(\Delta\)x, \(\Delta\)y, \(\Delta\)z, \(\Delta\)w, and \(\Delta\)d are defined as inputs. * As this is a three-dimensional analysis, the boundary conditions have not been defined. * In terms of excitation, the number of low-voltage windings is defined as 190, the number of high-voltage windings is 755, and the number of tap voltage windings is defined as 264 inputs. * In the context of parametric analysis, the designated analysis time is defined as two milliseconds of input. * The maximum mesh length is entered for each object. The maximum permissible length of the mesh for the transformer tank is 150 mm. The ANSYS Electronics Desktop 2021 R1 FEM software was used to perform numerical simulations. Analyses were carried out in the transient solver. Three-dimensional tetrahedral FEM meshes were used to simulate the transformer. It was defined by assigning the winding number of low-voltage, high-voltage, and tap windings to the excitation section. The ANSYS program automatically meshes all objects in the model prior to the commencement of the analysis process. Modifications to the mesh process can be made within the program. The mesh size is contingent upon the geometry of the simulation. The utilization of mesh operations comprising an excess of requisite elements prolongs the analysis and, in certain instances, results in the analysis being terminated, contingent upon the computer's processor and memory. The performance of the mesh process with a smaller number of elements than is necessary has an adverse impact on the sensitivity of the analysis. In light of these considerations, the maximum permissible mesh length was determined. For the horizontal magnetic shunt transformer tank, the maximum mesh length was 150 mm, and the total mesh number was 39,815. Since a 3D simulation was performed, defining boundaries was unnecessary. The largest object (region) boundary vector potential was considered zero. The results were convergent when the difference between the two iteration results was less than 1%. The circuit shown in Figure 2 was drawn in the SchematicEditor of the FEM software program and simulated by sending it as an external circuit to Excitations created in Project Manager. First, 2-millisecond tank loss samples were taken when the vertical magnetic shunt transformer tank had magnetic shunts only on the short side wall and only on the long front walls. Using these tank loss samples as a reference, the position and size of the horizontal magnetic shunts were determined via parametric analysis.