# A Novel Excitation Approach for Power Transformer Simulation Based on Finite Element Analysis
## 5 Conclusions  
This paper uses the finite element method to simulate the core loss and magnetic flux distribution of the iron core in the transformer. The finite element analysis model includes the iron loss model, equation of external excitation, and model depth. The iron loss model can be divided into three components: hysteresis loss, eddy current loss, and excessive loss. The non-linear factors of magnetic material are considered by the iron loss model. The non-linear factors include the \(B\)-\(H\) curve, \(P\)-\(B\) curve, conductivity, mass density, thickness, and operating frequency. The excitation current of each phase is composed of the steady-state AC component and the transient DC component in the equivalent open circuit. The magnetic density deviation is caused by the transient DC component. Therefore, the equation of external excitation voltage added the slow start function, which can avoid the magnetic deviation. The double exponential of the slow start function is proposed. Compared with the conventional external excitation equation, the new external excitation equation can improve the accuracy of simulation results and reduce the simulation time. According to the experimental results and simulation results, the error of core loss is 0.056%, and the error of medium limb magnetic density is 3.33% under \(\gamma\) = 25. The simulation time is reduced by 6 times. Therefore, the finite element analysis model is verified by the experimental results and simulation results. Finally, it can accurately predict the local \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & \multirow{2}{*}{**Measured Value**} & \multicolumn{6}{c}{**Simulation Results Error**} \\ \cline{3-10}  & & **No Slow Start** & \(\beta\) =5 & \(\beta\) =5 & \(\gamma\)=25 & \(\gamma\)=50 & \(\gamma\)=75 & \(\gamma\)=100 \\ \hline S1 & 1.5782 T & 59.92\% & 19.11\% & 8.47\% & 7.92\% & 8.26\% & 9.11\% & 10.68\% \\ \hline S2 & 1.5843 T & 46.66\% & 18.53\% & 8.05\% & 7.51\% & 8.13\% & 8.68\% & 10.25\% \\ \hline S3 & 1.7072 T & 94.14\% & 13.29\% & 4.71\% & 5.28\% & 5.34\% & 5.40\% & 6.40\% \\ \hline S4 & 1.6983 T & 44.88\% & 13.99\% & 6.08\% & 5.67\% & 5.96\% & 6.14\% & 7.60\% \\ \hline S5 & 1.5571 T & 52.17\% & 20.80\% & 10.02\% & 9.29\% & 9.94\% & 10.67\% & 12.30\% \\ \hline S6 & 1.5263 T & 61.58\% & 23.42\% & 12.24\% & 11.66\% & 12.16\% & 12.91\% & 14.51\% \\ \hline S7 & 1.6167 T & 162.90\% & 11.65\% & 6.21\% & 8.90\% & 7.24\% & 7.57\% & 8.93\% \\ \hline S8 & 1.7058 T & 150.22\% & 6.99\% & 3.80\% & 4.24\% & 4.37\% & 4.46\% & 5.23\% \\ \hline S9 & 1.6957 T & 70.54\% & 15.30\% & 3.90\% & 3.55\% & 3.67\% & 3.73\% & 7.37\% \\ \hline S10 & 1.7088 T & 68.35\% & 14.41\% & 3.34\% & 2.60\% & 3.07\% & 2.82\% & 4.90\% \\ \hline S11 & 1.6746 T & 74.11\% & 14.64\% & 6.39\% & 6.06\% & 6.27\% & 6.56\% & 5.65\% \\ \hline S12 & 1.5928 T & 83.25\% & 20.48\% & 8.87\% & 8.33\% & 8.62\% & 9.52\% & 11.44\% \\ \hline S13 & 1.6756 T & 110.43\% & 5.28\% & 4.00\% & 4.47\% & 4.79\% & 4.99\% & 6.04\% \\ \hline S14 & 1.6884 T & 56.52\% & 15.69\% & 4.45\% & 3.33\% & 4.19\% & 4.02\% & 7.84\% \\ \hline S15 & 1.6595 T & 59.28\% & 15.43\% & 5.91\% & 5.48\% & 5.73\% & 6.31\% & 7.83\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental results of magnetic flux density under different test coils.