*4.1. E*ffi*ciency Assessment*

According to the presented ratings of the DAB units, the primary group utilizes power modules that are rated at 40 kW while the secondary group utilizes power modules that are rated at 10 kW. Accordingly, to realize the total desired power, relying only on the secondary group would result in a total number of 20 modules. However, relying on the primary group would result in a total number of five modules. Therefore, it can be said that the primary group results in a lower number of modules but has a limitation in terms of the switching frequency, while the secondary group results in a higher number of modules but with higher switching capability. On the other hand, applying the presented concept would result in a total number of eight modules. Table 3 presents a comparison between the three concepts in terms of the number of employed modules as well as power, voltage, and current ratings.

**Table 3.** System parameters for conventional and hybrid multimodule DC-DC converters.


The converter efficiency can be presented as in (50):

$$
\eta = \frac{P\_{\text{int}} - P\_{\text{f}}}{P\_{\text{in}}} \tag{50}
$$

where, *Pt* represents the total losses in the employed converter. The semiconductor devices' losses include two types; conduction and switching losses. It is worth mentioning that the following analysis is carried out considering MOSFETs for low power modules and IGBTs for high power modules. The semiconductor conduction losses of the primary and secondary sides can be obtained using the RMS switch currents *IS*1,*RMS* and *IS*2,*RMS*, respectively with the primary and secondary drain-to-source resistances *RDS*1 and *RDS*2 in case of using MOSFETs. The RMS switch currents can be found from the RMS inductor current as follows [42]:

$$\begin{array}{c} I\_{S1,RMS} = \frac{I\_{L,RMS}}{\sqrt{2}}\\ I\_{S2,RMS} = n \frac{I\_{L,RMS}^{I}}{\sqrt{2}} \end{array} \tag{51}$$

The conduction losses of the primary and secondary sides power switches can be represented as:

$$\begin{aligned} P\_{S1,Conl.} &= 4(I\_{S1,RMS})^2 R\_{DS1} \\ P\_{S2,Conl.} &= 4(I\_{S2,RMS})^2 R\_{DS2} \end{aligned} \tag{52}$$

In case of using IGBTs, the conduction losses can be obtained using the collector-to-emitter voltage *VCE*(*<sup>S</sup>a<sup>t</sup>*), average IGBT current *IIGBT* and the duty cycle *D*. The conduction losses of the primary and secondary IGBTs can be represented as follows:

$$\begin{array}{l}P\_{\text{S1,Cond.}} = 4V\_{\text{CE(Sat)}}I\_{\text{IGBT1}}D\\P\_{\text{S2,Cond.}} = 4V\_{\text{CE(Sat)}}I\_{\text{IGBT2}}D\end{array} \tag{53}$$

The modulation schemes derived and presented in [29] allow the DAB power converter to operate under ZVS throughout the entire period. Hence the switching losses of the employed power devices can be neglected, assuming that the converter is operating under ZVS [42–45].

The aforementioned power losses are the conduction losses of only one DAB unit. However, the presented converter has a hybrid modular structure, meaning that Equations (52) and (53) are modified according to the configuration of the proposed multimodule converter to include the primary and secondary groups consisting of *L* and *M* isolated modules, respectively. Therefore, Equations (52) and (53) are modified to include the conduction losses in the IGBTs and MOSFETs for multiple numbers of DAB units, as shown in (54) and (55). The primary-side conduction losses of the hybrid multimodule converter include the conduction losses in the IGBTs and the conduction losses in the MOSFETs for *L* and *M* modules, respectively, and can be represented as follows:

$$P\_{S1,Cond.} = 4LV\_{CE(Sat)}I\_{IGBT1}D + 4M(I\_{S1,RMS})^2R\_{DS1} \tag{54}$$

where, *IS*1,*RMS* = *ILM*,*RMS* √ 2.

Similarly, the secondary-side conduction losses can be represented as follows:

$$P\_{S2,Cand.} = 4LV\_{CE(Sat)}I\_{IGHT2}D + 4M(I\_{S2,RMS})^2R\_{DS2} \tag{55}$$

where, *IS*2,*RMS* = *nILM*,*RMS* √ 2.

 To evaluate the losses associated with the hybrid ISOP DC-DC converter and compare it with conventional multimodule DC-DC converter relying on the secondary group and conventional multimodule relying on the primary group, Equations (52)–(55) are used to calculate the conduction losses associated with the semiconductor devices. It is assumed that the turns ratio of the employed transformers is 1 : 1 and that the duty cycle is 0.5 with an RMS inductor current of 25 A for each module, where each converter is rated at 200 kW. The number of *L* and *M* modules is specified in Table 3 for the three converters. In the provided assessment, the device parameters of a SiC MOSFET CMF20120D with a drain-to-source resistance of 80 m Ω and the device parameters of an IGBT IKW25N120T2 with a collector-to-emitter voltage of 1.7 V are considered. Considering only the conduction losses of the switching devices in the three multimodule converters, the following can be observed. Conventional multimodule DC-DC converter relying on the secondary group and conventional multimodule DC-DC converter relying on the primary group would results in losses of 5.1 kW (i.e., e fficiency of 97.5%) and 680 W (i.e., e fficiency of 99.6%), respectively. However, conduction losses in the hybrid multimodule DC-DC converter are found to be 1.6 kW ((i.e., e fficiency of 99.2%). Figure 7 presents the e fficiency loss curve with respect to power loading for the three converter systems.

**Figure 7.** Hybrid Efficiency loss curve with respect to power loading.

## *4.2. Power Density Assessment*

This subsection presents a rough estimation of the power density for the three converters presented in Table 3. The power density can be evaluated in terms of power losses and the volume of the converter components, as defined in (56). The total volume of the converter can be represented by summing up the volume of the utilized power switches, heat sinks, the transformer's winding, and the transformer's core as defined in (57) [46]:

$$
\rho = \frac{P\_{\text{int}} - P\_{\text{f}}}{Volume} \tag{56}
$$

$$Vol\_t = Vol\_{sw} + Vol\_{HS} + Vol\_{Corr} + Vol\_{Winding} \tag{57}$$

The volume of the overall converters is evaluated, considering the study provided in [47,48]. In which it is assumed that the converter components contribute with the same percentage as presented in [48]. Based on the study provided in [47,48], the volume contribution for the converter components is presented in Figures 8 and 9 considering hard switching and soft switching operation, respectively. It can be observed from Figure 8 that the volume of the heat sinks in the primary group multimodule DC-DC converter is almost the same as the volume of the heat sinks in the secondary group multimodule DC-DC converter. However, the volume of the transformer is higher in the primary group multimodule DC-DC converter due to the lower switching frequency. Accordingly, considering the losses for the three converters presented earlier, the power density of the conventional multimodule DC-DC converter relying on the secondary group is 12.2 kW/L, while the power density of the conventional multimodule DC-DC converter relying on the primary group is 9.9 kW/L. On the other hand, the power density in the hybrid multimodule DC-DC converter is found to be 10.3 kW/L.

**Figure 9.** Converter components volume contribution in liters considering soft-switching operation.

#### **5. Power-Sharing in the Eight-Module Hybrid ISOP Fast Charger DC-DC Converter**

Since modules in practical applications are not identical, any mismatch in the parameter values can cause unequal power distribution among the modules. Consequently, the voltage of modules is unbalanced, which may cause heavy loading or thermal overstress [39]. Accordingly, a control scheme that ensures uniform power-sharing among the modules is required to achieve reliable operation for the hybrid ISIP-OSOP DC-DC converter.

Since the presented converter is connected in series and parallel at the input and output sides, respectively, a control scheme that ensures IVS and OCS is required. A control strategy for equal power-sharing among the modules is addressed for the eight-module hybrid ISOP DC-DC converter. In other words, a cross-feedback OCS (CFOCS) for ISOP has been presented in [49] to ensure both equal IVS and OCS. The OCS is achieved among the modules and automatically ensuring IVS without the need for an IVS control loop. The presented control strategy in [49] has a fault-tolerant feature even when introducing a mismatch in the module's parameters. In addition, the output voltage regulation for the converter is simplified. The concept of this control strategy is based on applying the feedback control to be the summation of all the other current control loops instead of applying its own current feedback control loop.

In this paper, the CFOCS is applied to the presented hybrid ISOP converter to ensure uniform power-sharing where the system parameters are shown in Table 4. The OCS control, shown in Figure 10, consists of one outer output current loop and eight inner current loops where four are dedicated to the primary multimodule group, and the other four inner loops are dedicated to the secondary multimodule group. The control scheme, shown in Figure 10, for the eight-module hybrid ISOP converter is current-controlled considering a reflex charging technique that is termed as burp charging or negative pulse charging. The control scheme, presented in Figure 10, is tested with reference current relying on the burp charging algorithm to the output current reference signal. The charging cycle starts with a positive sequence from 0.2 s to 0.6 s. After that, a rest period for 0.1 s is applied, then a short discharge sequence for 0.1 s.


**Figure 10.** OCS control scheme for the proposed hybrid ISOP DC-DC converter.
