# Analysing and Computing the Impact of Geometric Asymmetric Coils on Transformer Stray Losses
## 3 Assessment and Model of the Stray Magnetic Field
### Impact of Winding Asymmetry  
The dimensions of the transformer windings, including height and width, play an important role in setting the magnitudes of \(\mid\)B\({}_{\mathrm{d}}\)\(\mid\) that reach the tank wall and other ferromagnetic structural elements. These dimensions, in turn, influence additional losses. Consequently, this study evaluates the effects of winding geometric asymmetry on the values of \(\mid\)B\({}_{\mathrm{d}}\)\(\mid\), examining the balance of the magnetic field intensity \(\mid\)H\(\mid\) that arises from the geometry of the windings. For the designers, it is evident that they will seek to centre the windings; however, it is not evident what effect would be caused to the \"magnetic centre\" by this geometric asymmetry of the windings, so this impact must be analysed and shown so that the designer can take precautions when they estimate the stray magnetic flux that reaches the tank walls and core clamps. In an ideal two-winding transformer, the magnetic field intensity \(\mid\)H\(\mid\) exhibits an isosceles trapezoidal characteristic, as shown in Figure 4. This ideal condition is achieved when the heights and thicknesses of both windings are equal (hs = hp and ws = wp), which is often observed in transformers with a 1:1 ratio. During the transformer design process, efforts are made to balance the ampereturns of both windings. However, due to geometric complexities, variations in conductor dimensions and manufacturing adjustments, winding heights and thicknesses may differ. This deviation results in a scalene trapezoidal feature in \(\mid\)H\(\mid\).  
The variation in \(\mid\)H\(\mid\) serves as a key parameter to determine the strength of the scattered magnetic field with \(\mid\)H\({}_{\mathrm{d}}\)\(\mid\) reaching the core walls and other components. To explore this effect, several cases were analysed to determine the corresponding values of \(\mid\)H\({}_{\mathrm{d}}\)\(\mid\) and \(\mid\)B\({}_{\mathrm{d}}\)\(\mid\) that impact the walls of the tank. The results of these analyses are presented in Figure 5, which provides a complete visual representation of the various scenarios considered in this study. Case 1 is the ideal design (hp = hs, wp = ws). The parameters of other cases are mentioned as follows: Case 2, (hp = 0.85-hs, wp = ws), Case 3 (hp = 0.85-hs, wp = 1.15-ws) and Case 4 (hp = 0.85-hs, wp = 1.30-ws).  
Figure 4: Ideal isosceles trapezoidal characterisation of \(\mid\)H\(\mid\) between the coils of a typical two-winding transformer. It can be seen that the field intensity is uniform and greater in the space between the windings. It shows a homogeneous and completely trapezoidal distribution (own authorship).  
These cases were considered in a very general way to visualise the impact of the geometric asymmetry of the windings. Analysing and addressing a very specific case could be the content of another work; an example of a specific case could be when tap changers are added. Taps with a wide voltage regulation range, sometimes outside the standards (NFPA-70, IEC-60364-1) \(\pm\) 5%, implies including more turns and having ampere-turns causes unbalances in the coil, which produces a magnetic unbalance between the coils and increases the stray magnetic field. Case 4 is a common scenario encountered in practical transformer design, where efforts are made to achieve a balance in winding dimensions. Despite these attempts, there is a disparity in both the heights and thicknesses of the windings. Regardless of the specific case, this variation in dimensions directly influences the magnitudes of \(\mid\)H\({}_{\text{d}}\mid\), \(\mid\)B\({}_{\text{d}}\mid\), consequently contributing to additional losses experienced in the tank walls.