5.1.2. Constraints

The design constraints include temperature rise Δ*T*max, leakage inductance error *e*Lmax, and the spatial size *H*max, *W*max, *D*max.

$$\text{s.t.} \begin{cases} \Delta T < \Delta T\_{\text{max}} \\ H < H\_{\text{max}} \\ W < W\_{\text{max}} \\ D < D\_{\text{max}} \\ \left| \frac{L\_{\text{v}} - L\_{\text{v}t}}{L\_{\text{v}t}} \right| < \varepsilon\_{L,\text{max}} \end{cases} \tag{48}$$

where Δ*T* is the temperature increase; *H*, *W*, and *D* are spatial sizes; and *L*σ<sup>t</sup> is the target leakage inductance.

#### 5.1.3. Objectives

In general, efficiency and power density are the main parameters for evaluating the design results.

$$\begin{cases} f\_1(\mathbf{x}) = \max \eta(\mathbf{x}) = \max \left( \frac{P\_{\text{out}}}{P\_{\text{out}} + P\_{\text{fv}} + P\_{\text{Cu}}} \right) \\ f\_2(\mathbf{x}) = \max \, P\_d(\mathbf{x}) = \max \left( \frac{P\_{\text{out}}}{P} \right) \end{cases} \tag{49}$$

where *η* is efficiency, *P*out is the output power, *P*Fe is the core loss, *P*Cu is the winding loss, *V* is the volume of MFT (ignoring structural components and terminals).

The design procedures of inductor-integrated MFT are shown in Figure 19. The brute force grid search method, which is extremely robust, is adopted on the premise that the calculation time is acceptable. According to the free parameters of the design input, a design space is constructed, which contains all possible designs. Designs in the space are calculated, and the results are saved. According to the constraints, the qualified designs are obtained. The Pareto front is solved according to the optimization objectives, and the designer can determine the final design according to the front.

**Figure 19.** Design procedures of the CW ELII MFT.

*5.2. Design Results and Comparative Analysis*

The 4 kHz, 200 kW, 200 μH inductor-integrated MFT for a DAB converter is taken as an example of optimal design, and the main parameters and constraints are shown in Table 1.

**Table 1.** Parameters and constraints.


The optimal designs of the CW LII MFT and the CW ELII MFT are carried out, respectively. The CW LII MFT is also combined air–water cooling, the difference is that the CW LII structure has no additional core, and the target leakage inductance is achieved by adjusting the width of the main insulation layer. The SW LII structure and the SW ELII structure are not discussed in this paper due to the inevitable external leakage flux.

Figure 20 shows the comparison of qualified designs of the two integration structures. The designs with the maximum power density in the CW LII and the CW ELII qualified solutions are shown in Table 2, and only the transformer body and internal cooling plates are considered in the power density specification. The CW ELII design has a lower core

loss, but the eddy current of the water-cooling plate makes the efficiency of the CW ELII solution 0.09% lower than that of the CW LII solution. The volume power density of the CW LII solution is 2.24 kW/dm3, and that of the CW ELII solution is 5.16 kW/dm3, which is about 130% higher. Meanwhile, the weight power density of the CW ELII solution is only 9.9% higher than that of the CW LII solution, indicating that the main advantage of the CW ELII structure is the more compact structure. Considering the core material and wire material, the unit cost of the CW ELII design is 7.7% lower than that of the CW LII design.

**Figure 20.** Comparison of CW LII and CW ELII qualified designs. (**a**) CW LII qualified designs; (**b**) CW ELII qualified designs.


**Table 2.** Comparison of CW LII and CW ELII solutions.

In order to make a more comprehensive comparison of the two structures, the optimal designs for different leakage inductance values are carried out. It should be noted that other design inputs remain unchanged among the designs. The comparison of the Pareto fronts is shown in Figure 21. As shown in Figure 21a, when the leakage inductance is 10% p.u. (40 μH), the Pareto fronts of the CW LII solutions and the CW ELII solutions are very close. However, with the increase of leakage inductance, the power density of CW LII decreases continuously, while the CW ELII has not changed significantly.

**Figure 21.** Pareto fronts of CW LII and CW ELII solutions with different leakage inductances. (**a**–**h**) leakage inductance: 10% p.u. to 80% p.u. (40 μH to 320 μH).

Based on Figure 21, the CW LII and CW ELII solutions with the highest power density in each group are selected for comparison, as shown in Figure 22. As shown in Figure 22a, the power density of the CW LII solution decreases with larger leakage inductance, and the maximum power density is 6.2 kW/dm<sup>3</sup> at 10% p.u. (40 μH). The CW ELII solution achieves the maximum power density of 5.8 kW/dm3 at 20% p.u. (80 μH). When the leakage inductance per unit value exceeds 20% (p.u.), the CW ELII solution can achieve a higher power density than the CW LII solution. It becomes more evident as the leakage inductance increases. As shown in Figure 22b, as the leakage inductance increases, the efficiency of the two solutions is gradually reduced. When the leakage inductance per unit value is greater than 40% (p.u.), the CW ELII solution has advantages.

While keeping other parameters unchanged, the rated current in the design input is changed to analyze the influence of the power on the design result. In all groups, the leakage inductance in per-unit is 50%. Figure 23 shows the comparison of the Pareto fronts of CW ELII MFT designs with different power requirements. As the power increases, it is easier to achieve higher power densities. A possible reason is that the insulation distance in the MFT is a fixed parameter under the same insulation requirement. A possible reason is that the insulation distance in the MFT is a fixed parameter under the same insulation requirement. With the increase of rated current (80 kW to 280 kW), the proportion of windings in the core window increases and the proportion of insulating space decreases, which makes the MFT power density increase. When the rated current is large enough (280 kW and 320 kW), the proportion of insulating space is small, and this effect is no longer obvious.

**Figure 22.** Comparison of solutions for different inductance requirements. (**a**) Max power density; (**b**) efficiencies.

## *5.3. Prototype and Experimental Verification*

According to the final design of the CW ELII MFT, a prototype was manufactured and tested in a 200 kW DAB converter, which is a module of a 2 MW MMC-BDC. The MFT prototype and the experimental platform are shown in Figure 24.

**Figure 24.** Experimental platform and the MFT prototype.

Figure 25 shows the waveforms of the no-load voltage and current under LV side excitation. The voltage was measured by Tek P5210A voltage probe (bandwidth 50 MHz), and the current was measured by Tek TCP303 + TCPA300 current probe (bandwidth 15 MHz). The no-load loss can be calculated by the no-load voltage and current.

Figure 26 shows the voltage and current waveforms under the load condition with an output power of 200 kW, in which the DC voltages is 1.6 kV/1 kV and the phase-shifting duty is 0.0875. The temperature rise experiment was carried out under this condition, where the inlet water temperature was 35.5 ◦C, the ambient temperature was 39 ◦C, and the average inlet wind speed was 1.0 m/s (measured by KIMO VT110). Figure 27 shows the MFT surface temperature distribution in thermal steady state. Contact sensors were placed on the core surface to monitor the core temperature. At the same time, to avoid the influence of internal wind on winding temperature measurement, the resistance method was used to measure the average winding temperature.

**Figure 26.** Voltage and current waveforms of the load condition.

**Figure 27.** Temperature distribution measured by the infrared thermal camera.

The experimental results are summarized as in Table 3. The experimental results of the inductance, no-load loss, and temperature increase are basically consistent with the calculated values, verifying the validity of the parameter models and the optimization design method.


**Table 3.** Experimental results.

#### **6. Conclusions**

The design and analysis of the inductor-integrated MFT is a challenging multi-physical problem. Facing the application requirements of the DAB converter, the research on the inductor-integrated MFT is carried out. The main conclusions are drawn as follows:

(1) By comparing different integration structures, the CW ELII structure is adopted. The operating mode of CW ELII MFT under typical DAB excitation is analyzed based on the magnetic circuit model, then obtaining the magnetic flux expressions at different phase-shifting duties. Aiming at the characteristics of the irregular cross-section of the main insulation layer and the non-uniform arrangement of conductor layers, the leakage inductance model is improved. The results show that the maximum error of the proposed model is 2.4%, and that of the classical model is 15.0% for the cases with the non-uniform arrangement of conductor layers.

(2) The thermal network model of air–water combined cooled CW ELII MFT is established. Based on the combination of classical models, the thermal resistance model for the winding air channel under forced convection is proposed, and the relative error with FEM results is less than 10%. The analysis shows that a higher average heat transfer coefficient can be obtained using a higher wind speed or a shorter channel.

(3) The 200 kW, 4 kHz, 200 μH MFT for DAB converter is chosen as an example, and the optimal design is carried out using two structures of CW LII and CW ELII. The volume power density of the CW ELII solution is about 130% higher than that of the CW LII solution with the similar efficiency and cost. The weight power density is 9.9% higher. A CW ELII MFT prototype was manufactured with the power density of 5.16 kW/dm3 and the efficiency of 99.30%. The prototype was tested in a 2 MW DC MMC-BDC prototype verifying the electrical and thermal performance.

(4) According to a more extensive comparison and analysis, the power density of the CW LII solution decreases with the increase of the leakage inductance. In contrast, the CW ELII solution achieves a max power density of 5.8 kW/dm3 when leakage inductance is 20% (p.u.). The CW ELII solution can achieve a higher power density when the per unit value of leakage inductance exceeds 20% (p.u.). Both structures achieve the highest efficiency when the leakage inductance is the smallest. The CW ELII solution has an efficiency advantage when the leakage inductance exceeds 40% (p.u.).

There are still some limitations in this work, which is also the direction of the future research. In this work, the operating frequency of the research object is relatively low. With the popularization of SiC devices, the operating frequency of MFT is also gradually increasing. Therefore, it is necessary to further develop research of the inductor-integrated MFT with higher operating frequency, focusing on the high-frequency winding loss and the fringing flux loss of the additional core. In this work, only the optimization design of the MFT body is carried out; however, parameters of the converter will significantly affect the MFT design. Therefore, it is necessary to further carry out the system-level optimal design of the converter. The modeling and design method of the CW ELII MFT presented in this paper lays a foundation for further research.

**Author Contributions:** Conceptualization, X.Z., R.W. and F.X.; Methodology, X.Z. and R.W.; Software, X.Z.; Validation, X.Z.; Writing—original draft preparation, X.Z., W.K. and B.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant no. 51907199.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

### **References**

