# Analysing and Computing the Impact of Geometric Asymmetric Coils on Transformer Stray Losses  
[PERSON]  
1 Departamento Ingenieria Electrica, Universidad de Guanajuato, Guanajuato 36885, CP, Mexico; [EMAIL_ADDRESS]
2 Departamento de Energia, Universidad Autonoma Metropolitana, Mexico City 02120, CP, Mexico; [EMAIL_ADDRESS] (J.C.O.-G)
3 Ingenieria Electrica y Electronica, Universidad Nacional Autonoma de Mexico, FES Aragon, Mexico City 57171, CP, Mexico; [EMAIL_ADDRESS]
* [2]Correspondence: [EMAIL_ADDRESS]  
[3]  
transformer manufacturers continue to use the empirical analytical formulas from this literature or from their experience in their current practices. Calculating stray losses requires an understanding of the stray magnetic field. To address this problem, efficient methods have emerged to quickly and approximately estimate the equivalent leakage reluctance, in particular by using the Reluctance Network Modelling (RNM) method [12, 13]. The adoption of numerical methods, such as the Finite Element Method (FEM), has greatly facilitated the evaluation of the stray magnetic field and its associated additional losses. These methods make the simulation of stray magnetic fields in two- and three-dimensional scenarios more accessible and less complex. However, it is imperative to note that the utilisation of such methods comes at the expense of high computational requirements during the transformer design stage. These considerations are essential to effectively reduce stray losses and prevent hot spots. Furthermore, the application of the Finite Element Method (FEM) has allowed us to examine the impact of additional factors, such as geomagnetically induced currents, that contribute to increased stray losses in the transformer tank [14]. Minimising stray losses in transformers represents an important competitive advantage in the industry. Consequently, there has been an increase in research dedicated to identifying the optimal location of magnetic shunts, with the objective of decreasing stray losses within the transformer tank [15, 16]. The research is also focused on finding the optimal geometry of the magnetic shunt [17]. The orientation of the shunt also plays an important role in reducing losses, which is why works such as [18] clearly and conclusively confirm the effectiveness of orienting the shunt horizontally. In [19] non-magnetic stainless steel, an insert was utilized to reduce the stray losses in a significant way in 80% of the region of the Tertiary Voltage Bushings of the transformer. The effect of magnetic shunts on shell-type transformers' characteristics was recently analysed and determined. This helped in determining the magnetic flux density distributions, and the points with high values in the shell-type core and movable shunt sub-areas [20]. Despite the important technical literature on this topic, in the design stage there are still some technical doubts about how the stray magnetic field is affected when there are different widths and heights of the windings. In the design, it is common and very normal for the thicknesses of the windings to be different and the height of the high voltage winding to be similar to the height of the low voltage winding, but most of the time it is not possible to achieve this, so this work contributes to the analysis and quantification of the effect of these differences in dimensions in the windings on the stray magnetic flux that reaches the tank. Therefore, it helps to have an overview of its magnetic field density, which assists in controlling additional losses. In this work, the characterisation of the magnetic field that reaches the tank walls was added along with a quick-to-apply model to approximately estimate the stray magnetic field from the coil to the limits of the tank walls and the impact of reducing stray losses by placing magnetic shunts and using a shell-type configuration transformer.