# A Three-Port Power Electronic Transformer Based on Magnetic Integration
## 6 Economic Benefits Analysis
### Magnetic Volume Comparison  
For magnetic volume comparison shown in Table 2, the arm inductors and transformers volume are the main considerations. The parameters of integrated transformer of the proposed PET are selected as same as simulation value in Table 1, where the turn ratio \(n=3.2\), magnetizing inductance \(L_{\text{m}}=20\) mH, and leakage inductance \(L_{\text{$\sigma$}}=158.2\)\(\mu\)H. The total arm inductors (\(L_{\text{arm}}=2.4\) mH) of the MMC + distributed DABs PET is equal to the equivalent arm inductors of the proposed PET, which is formed by magnetizing inductance and leakage inductance in parallel [\(2\)\(L_{\text{arm}}=(4n^{2}\)\(L_{\text{$\sigma$}}\times L_{\text{m}})/(4n^{2}\)\(L_{\text{$\sigma$}}+L_{\text{m}})\)]. The volume of transformer or inductor can be obtained from their area product \(A_{\text{P}}\), calculating by \(V_{\text{magn}}=K_{\text{vol}}\) (\(A_{\text{P}}\))\({}^{0.75}\)[17]. The area product of a transformer is proportional to the total apparent power of all windings, while the area product of inductor (\(L\)) is proportional to the maximum energy storage \(W=\frac{1}{2}L^{2}\) peak, where \(I_{\text{peak}}\) is the peak value of inductor current. Thus, the area product of the transformer with \(K\) (\(K\geq 2\)) windings can be obtained by (13) [14], and the area product of inductor can be expressed as (14) [17]. \[A_{\text{P-Tr}}=\frac{\sum_{j=1}^{K}P_{j}}{K_{t}K_{W}I_{\text{rms}}B_{\text{ max}}f}\times 10^{4}(\text{cm}^{4}) \tag{13}\]  
Figure 11: Dynamic experimental results: (a) power transfer between the MVAC and MVDC port; (b) power transfer between the LVDC and MVDC port. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Parameters**} & & & & \\ \(K_{\text{vol}}=\)17.9, \(K_{t}=4\), \(K_{\text{W}}=0.4\), \(J_{\text{rms}}=50\)A, \(B_{\text{max}}=1\)T, \(f_{\text{m}}=2\) kHz, \(n=30\)) & & & \\ \hline Transformers volume & 10.64 m\({}^{3}\) & 1.46 m\({}^{3}\) & 0.93 m\({}^{3}\) & 1.02 m\({}^{3}\) \\ Arm inductors volume & 0.99 m\({}^{3}\) & 1.94 m\({}^{3}\) & 1.94 m\({}^{3}\) & \\ Total magnetic volume & 11.63 m\({}^{3}\) & 3.40 m\({}^{3}\) & 2.87 m\({}^{3}\) & 1.02 m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Magnetic volume comparison of proposed PET with existing typical PETs. \[A_{\rm P\_L}=\frac{2W}{K_{\rm W}J_{\rm rms}B_{\rm max}}\times 10^{4}({\rm cm}^{4}) \tag{14}\]  
where \(P_{\rm j}\) is the processed power of \(j\)th winding, \(K_{\rm f}\) is the waveform factor, \(K_{\rm W}\) is the core window utilization factor, \(J_{\rm rms}\) is the rms current density of the winding, \(B_{\rm max}\) is the maximum magnetic flux density, and \(f\) is the working frequency of transformer. \(K_{\rm vol}\) is the core structure factor, which reflects the relationship between volume and area product, and it can be obtained from datasheet of magnetic core manufacturer. For the MMC + distributed DABs PET, \(6N\) transformers are used and each one process a total power of \([2P_{\rm LVDC}/(6N)]\). So, the total volume of \(6\)\(N\) transformers can be calculated by  
\[V_{\rm 6N\times Tr}=6N\times K_{\rm vol}\left(\frac{2P_{\rm LVDC}/(6N)}{K_{ \rm K}K_{\rm W}J_{\rm rms}B_{\rm max}f_{\rm m}}\times 10^{4}\right)^{0.75}({\rm cm }^{3}) \tag{15}\]  
In contrast, for the proposed PET, there are only three integrated transformers. In each transformer, as shown in Figure 12, each split primary winding process a power of \((u_{\rm mx\_rms}i_{\rm P\_rms})\), while the secondary winding power is \(P_{\rm LVDC}/3\), thus the total power of all windings of the integrated transformer is \((2u_{\rm mx\_rms}i_{\rm P\_rms}+P_{\rm LVDC}/3)\).