# Optimized Multiport DC/DC Converter for Vehicle Drivetrains: Topology and Design Optimization
## 5 Optimization Results Assessment
\begin{table}
\begin{tabular}{c l l c c c c c c} \hline \hline \multirow{2}{*}{**Notation \& Description**} & \multicolumn{4}{c}{**Battery Port**} & \multicolumn{4}{c}{**SC Port**} \\ \cline{3-8}  & & **Conventional** & **Optimized** & \(\Delta_{\text{BAT}}\) & **Conventional** & **Optimized** & \(\Delta_{\text{SC}}\) \\ \hline \(L\) & Inductance & \(\mu\)H & 166 & 177 & - & 148 & 150 & - \\ \hline \(n\) & Number of turns for & turns & 19 & 17 & - & 18 & 15 & - \\ \hline \(g\) & Air gap for & mm & 0 & 0.55 & - & 0 & 0.55 & - \\ \(W_{\text{Liat}}\) & Weight of inductors for & kg & 3.41 & 2.73 & **20\%** & 3.17 & 2.61 & **17.6\%** \\ \hline \(W_{\text{Isola}}\) & Power losses of & & & & & & & \\ converter at full load & kW & 1.41 & 1.36 & **3.5\%** & 0.74 & 0.72 & **2.02\%** \\ \(Q\) (\(Q\)) & & & & & & & & \\ converter at low load & kW & 0.55 & 0.51 & **7.2\%** & 0.39 & 0.38 & **2.56\%** \\ \(Q\) (\(Q\)) & & & & & & & \\ \hline \(\Delta\lambda_{\text{Is}}\) & Maximum input & A & 15 & 9.32 & **38\%** & 16.67 & 11 & **34\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison between the conventional and optimized design for Battery and SC ports. Since the input current ripple and converter losses are highly dependent on the inductance value, it is important to ensure that the real inductor can obtain value as close as possible to that of theoretical inductance. To fulfill this purpose, the commercial COMSOL Multiphysics software is employed to compute the model of the inductor based on Finite Element Method. Figure 8 illustrates the inductor design in SOLIDWORKS that is imported to the COMSOL software. The material name of the core is METGLAS Alloy 2605 SA1 that has high saturation flux density (1.56T) and a low loss resulting from micro-thin Metglas ribbon (25 \(\upmu\)m). To ease the computation time, the fitting technique is also used to find the inductance value in a function of air-gaps and number of turns. To do so, 16 inductance values are generated from COMSOL Multiphysics with air-gap range from 0-1.2 mm and number of turns from 10-22 turns. Using Matlab fitting function, a 2 nd-order polynomial surface can be found as Equation (28). \[\mathrm{L}(\mathrm{N}_{t},\mathrm{g}) = 12.36\times\mathrm{N}_{t}-123.3\times\mathrm{g}+0.36\times \mathrm{N}_{t}{}^{2}-12.22\times\mathrm{N}_{t}\times\mathrm{g}+122.3\times \mathrm{g}^{2}-4.7 \tag{28}\]  
where \(L\) is inductance (\(\upmu\)H); \(g\) is airgap (mm). The impact of air gap and number of turns is simulated by FEM. The result is fitted by 2-degree polynomial function, mentioned as above. Figure 9 illustrates the impact of air-gap and the number of turns on the inductance value. Figure 8: (**a**) SOLIDWORKS inductor design, (**b**) Magnetic flux distribution and current distribution of inductor in the COMSOL Multiphysics (Version 5.3a, COMSOL, Inc., Burlington, MA, USA, 2018). Figure 7: Weight of an inductor in function of number of turns. To calculate the reduction of losses, the SiC-based semiconductor switch (2 MBI150U2A-060) is used and switching frequency is kept as 60 kHz. The power losses of converters at full load 30 kW are reduced by 3.5% and 2.02% for battery port and SC port, respectively. More reduction of total loss, 7.2% and 2.56% for battery and SC port respectively, can be seen at low load 5 kW. The losses distribution at full load is shown in detail in Figure 10.  
The maximum input current ripple current, which is considered as a third objective function is also reduced by 38% and 34% for battery and SC converter ports, respectively. All diminution values that are shown in Table 4 validate the optimization methodology based on a multi-objective genetic algorithm and Average Ranking technique. Figure 10: Losses distribution comparison at full load 30 kW. Figure 9: Inductance value in function of air-gap and number of turns.