# Analysing and Computing the Impact of Geometric Asymmetric Coils on Transformer Stray Losses
## 4 Design Parameters and Loss Values  
### Estimation of Stray Losses with FEM and with the Proposed Model  
To compare the results obtained from the Finite Element Method (FEM) simulations with those derived from the proposed model, load tests were carried out on a 25 MVA power transformer operating at 115 kV-34.5 kV, with Delta-connection. The complementary values of the design and manufacturing parameters of the transformer are presented in Table 1. It should be noted that the losses per phase in the low voltage winding amounted to approximately 43.75 kW, while those in the high voltage winding were around 57 kW. Core losses were measured at approximately 21.7 kW, resulting in an overall transformer efficiency of approximately 98.5% at full load. From these measured loss values and considering efficiency, it was determined that the estimated additional losses would be approximately 35.6 kW. It is worth noting that this value of additional losses cannot be measured directly, much less separated between those attributed to the tank and those associated with the support structures. However, these losses can be estimated based on the total losses measured. Table 2 provides the losses obtained by electromagnetic simulations using finite element analysis for the tank walls and yoke beams.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Design Parameter** & **Value** \\ \hline Core window high (mm) & 1482 \\ LV—Margins (mm) & 89 \\ HV—Margins (mm) & 89 \\ Core Diameter (mm) & 552 \\ LV—HV Space (mm) & 51 \\ Tank Wall Thickness (mm) & 9.5 \\ Core-LV winding distance (mm) & 19 \\ Rw wall-HV winding distance (mm) & 381 \\ Fw wall-HV winding distance (mm) & 330 \\ LV width (mm) & 69.8 \\ LV height (mm) & 1219.2 \\ HV width (mm) & 123.8 \\ HV height (mm) & 960 \\ Volts/Turns & 23.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design and manufacturing parameters of 25 MVA transformer.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Losses** & **By FEM** & **1 Bd l by FEM** & **By (9 \& 2)** \\ \hline Lw, left side wall & 6455 W & 0.520 T & 6853 W \\ Rw right side wall & 6853 W & 0.528 T & 7262 W \\ Fw, front wall & 8322 W & 0.534 T & 7694 W \\ Bw, rear wall & 7694 W & 0.520 T & 7091 W \\ Bottom wall & 2517 W & 0.493 T & 2271 W \\ Top wall & 906 W & 0.420 T & 1063 W \\ Top yoke beams & 1252 W & 0.600 T & 1252 W \\ Bottom yoke beams & 1634 W & 0.680 T & 1634 W \\ \hline \hline \end{tabular}
\end{table}
Table 2: Stray or additional losses and \(\text{1B}_{\text{d}}\) estimation.  
The additional losses in the tank walls amounted to 32.23 kW and the losses in the yoke beams were calculated to be 1.84 kW, resulting in an estimated total additional loss of 34.0 kW using Equation (2). In contrast, finite element method (FEM) simulations yielded a total additional loss of 34.40 kW. The discrepancy between these values and those obtained by measurement is approximately 3.3% to 3.5%.  
The third column of Table 2 shows the effective values of the magnetic field density estimated by FEM, as illustrated by the characteristic curve on the walls in Figure 2b. In particular, employing both FEM and the proposed model (Equation (9)) allows detailed quantification of losses in each tank wall and facilitates the determination of losses in the metallic elements that support the core, such as the yoke beams. The introduction of magnetic shunts is seen in the reduction of losses. The obtained values have been summarised in Table 3. According to FEM estimates, the total additional losses with magnetic shunts are 19.70 kW, while the proposed model (Equation (9)) indicates the losses of 19.0 kW, which means a notable loss reduction of approximately 42%.