# Optimized Multiport DC/DC Converter for Vehicle Drivetrains: Topology and Design Optimization
## 5 Optimization Results Assessment  
To validate the proposed optimization framework, the optimized design and a conventional design are needed to satisfy the same specification as summarized in Table 1.  
In the proposed optimization design, the upper bound and lower bound of design variables are defined in advance, as shown in Table 2. To be more detailed, the setting of NSGA-II parameters is shown in Table 3.  
After executing the NSGA-II optimizer for the problem in Equation (21), the Pareto optimal solutions are sketched in Figure 6. The final optimal solution found by AR method shows that the optimal number of phases is three and optimal switching frequency is 60 kHz. The optimal core is AMCC50 from Metglas(r)Inc, a subsidiary of Hitachi Metals America, Ltd, Conway, SC, USA. For the sake of a fair comparison, the switching frequency and number of phases, both found from the proposed methodology, are kept unchanged to design inductors in the conventional design that are based on well-established equations of a boost converter. The inductance value of conventional design, as shown in Equation (25), should be sufficient to ensure the predefined input current ripple under the worst case (minimum input voltage \(V_{in\_min}\)). \[L_{conv}=\frac{V_{in\_min}\times(1-D_{max})\times D_{max}}{f_{sw}\times I_{o\_ min}} \tag{25}\]  
The selected core is AMCC50 with cross-section area \(A_{C}=400\) mm\({}^{2}\), the maximum flux density \(B_{max}=1.2\) T. Without air gap, number of turns in the conventional design can be calculated by Equation (26). \[n_{conv}=\frac{L_{init}\times I_{L\_peak}}{A_{C}\times B} \tag{26}\]  
The conventional and optimal design of inductors for battery and SC port are shown in Table 4. As can be seen, the inductance values increase from 166 \(\mu\)H (conventional design) to 177 \(\mu\)H (optimized design) for battery port, and from 148 \(\mu\)H (conventional design) to 150 \(\mu\)H (optimized design) for SC port even though the number of turns for both are reduced. The number of turns are reduced from 19 turns (conventional design) to 17 turns (optimized design) for the battery port, and from 18 turns (conventional design) to 15 turns (optimized design) for the SC port. It is understandable since the air-gaps 0.55 mm are added into the optimized inductor designs for two ports. As the results, the values of three objective functions are decreased considerably. As shown before in Equation (12), the weight of the inductor consists of the weight of core, the weight of coil that is dependent on the length of wire, and the weight of the bobbin. The weight of AMCC50 core is 586 g and the weight of bobbin is 14 g. The Litz wire used for the wire of inductors is rectangular HF-LITZ WIRE covered with Polyester PET tape from Von Roll Isola France SA, Belfort, France, which has 0.2 kg/meter, 2600 strands, and the diameter of each strand is 0.1 mm. According to Equation (10), the length of wire for inductor coil can be calculated. Afterward, the weight of an inductor can be determined in a function of number of turns. For fast calculation, the relation between the weight of an inductor and the number of turns can be assumed as a 2 nd-order polynomial curve that can be derived by using the fitting-curve function in Matlab as shown in Equation (27). Figure 7 illustrates the relation described in Equation (27). As can see from Table 4, the total weight of inductors is reduced by 20% and 17.6% for the battery port and the SC port, respectively. \[W_{ind}(\text{N})=0.43\times N^{2}+19\times N+596.8 \tag{27}\]