# A Novel Excitation Approach for Power Transformer Simulation Based on Finite Element Analysis
## 4 Experimental Results  
This chapter uses the simulation results from simulation software ANSYS Maxwell and the experimental results to verify the proposed finite element analysis model. First, the adjustable AC power supply is applied to the three-phase five-limb transformer. Secondly, the induced electromotive force is measured by the test coil. Finally, the magnetic flux density of the iron core is calculated according to [PERSON]'s law. The setting diagram of the three-phase five-limb transformer is shown in Figure 15, in which the test coils S1-S12 are single yokes and single limbs, and the test coils S13-S15 are all limbs. The external voltage is 213.33 V, and the operating frequency is 60 Hz. The turn number of the excitation coil is 46 turns, and the turn number of the test coil is 6 turns. The measured three-phase five-limb is shown in Figure 16.  
Figure 14: The simulation results of the magnetic flux density distribution under different external excitation functions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Core Loss** & **Hysteresis Loss** & **Eddy Current Loss** \\ \hline No Slow Start Condition & 2.4093 kW & 76.92\% & 23.08\% \\ \hline Convention Equation (\(\beta=50\)) & 2.0087 kW & 64.43\% & 35.57\% \\ Convention Equation (\(\beta=5\)) & 1.9563 kW & 62.75\% & 37.25\% \\ \hline Proposed Equation (\(\gamma=25\)) & 1.9479 kW & 62.30\% & 37.70\% \\ Proposed Equation (\(\gamma=50\)) & 1.9345 kW & 61.85\% & 38.15\% \\ Proposed Equation (\(\gamma=75\)) & 1.9773 kW & 62.48\% & 37.52\% \\ Proposed Equation (\(\gamma=100\)) & 2.0012 kW & 62.91\% & 37.09\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulation results of the core loss under different slow start functions. The experimental results of the magnetic flux density under different test coils are shown in Table 6. The magnetic flux density of medium limb S14 is 1.6884 T. Compared with the simulation results without a slow start, the error is 56.52%. Compared with the simulation results of the convention equation, when \(\beta=50\) and \(\beta=5\), the error is 15.69% and 4.45%, respectively. Compared with the simulation results of the proposed equation, when \(\gamma=25\), \(\gamma=50\), \(\gamma=75\), and \(\gamma=100\), the error is 3.33%, 4.19%, 4.02%, and 7.84%, respectively. The structure of the three-phase five-limb transformer is symmetrical. When the simulation result of the magnetic flux density is good in the middle limbs, the simulation results of other local limbs and yokes are better. Therefore, the middle limb of the simulation result is the best under the proposed equation \(\gamma=25\). When the proposed equation \(\gamma=25\), the interlimb S10 error is 2.6%, the outer limb S1 error is 7.92%, the internal yoke S3 error is 5.28%, and the outer yoke S2 error is 7.51%. According to the experimental results and simulation results, the magnetic flux density of the inner iron core is bigger than the magnetic flux density of the outer iron core. The experimental results of the core loss are shown in Table 7. The measured core loss is 1.949 kW. Compared with the simulation results without slow start, the error is 23.61%. Compared with the simulation results of the convention equation, when \(\beta=50\) and \(\beta=5\), the error is 0.28% and 6.12%, respectively. Compared with the simulation results of the proposed equation, when \(\gamma=25\), \(\gamma=50\), \(\gamma=75\), and \(\gamma=100\), the error is 0.056%, 0.743%, 1.452%, and 2.678%, respectively. Comparing the conventional equation under \(\beta=5\), the accuracy of simulation results is improved and simulation time is shortened by 6 times in the proposed equation with \(\gamma=25\). If the simulation time is less than 0.1 s, the accuracy of core loss is increased by 31 times. The finite element model of the simulation is verified by Tables 6 and 7. It is verified that the slow start function and parameter are important for the accuracy of the simulation results. The simulation results have not considered the harmonics.