Hybrid multimodule DC–DC converters accelerated by wide bandgap devices for electric vehicle systems

In response to the growing demand for fast-charging electric vehicles (EVs), this study presents a novel hybrid multimodule DC–DC converter based on the dual-active bridge (DAB) topology. The converter comprises eight modules divided into two groups: four Insulated-Gate Bipolar Transistor (IGBT) modules and four Metal–Semiconductor Field-Effect Transistor (MESFET) modules. The former handles high power with a low switching frequency, while the latter caters to lower power with a high switching frequency. This configuration leverages the strengths of both types of semiconductors, enhancing the converter’s power efficiency and density. To investigate the converter’s performance, a small-signal model is developed, alongside a control strategy to ensure uniform power sharing among the modules. The model is evaluated through simulation using MATLAB, which confirms the uniformity of the charging current provided to EV batteries. The results show an impressive power efficiency of 99.25% and a power density of 10.99 kW/L, achieved through the utilization of fast-switching MESFETs and the DAB topology. This research suggests that the hybrid multimodule DC–DC converter is a promising solution for fast-charging EVs, providing high efficiency, power density, and switching speed. Future studies could explore the incorporation of advanced wide bandgap devices to handle even larger power fractions.

• Hybrid multimodule DC-DC converter The design and implementation of a hybrid multimodule DC-DC converter integrating both IGBTs and MESFETs, with the dual-active bridge topology forming the backbone of the system.• Improved charging efficiency and power density The innovative hybrid design leverages the strengths of both IGBTs and MESFETs, enabling us to achieve a remarkable power efficiency of 99.25% and a power density of 10.99 kW/L, a significant improvement compared to existing models.• Enhanced control strategies Our research introduces advanced control strategies to ensure uniform power sharing among modules, contributing to the optimization of charging systems.• Experimental validation We provide experimental validation of our proposed converter using MATLAB simulations, confirming the effectiveness of the hybrid design in delivering fast, efficient charging for EVs.• Addressing the power limitations of WBG materials By overcoming the power limitations of WBG materials, our research expands the applicability of these materials in EV charging systems, opening up new possibilities for faster, more efficient charging solutions.
"Related Work" Section provides a comprehensive review of related studies that have explored wide bandgap (WBG) materials for their application in power converters for electric vehicles.The performance analysis of various semiconductor materials and WBG devices concerning Fault is undertaken within this section."Wide Bandgap Device Structure and Performance Evaluation" Section of this article covers the research methodology, presenting a small signal model that serves as a foundational tool for the investigation.The results, discussion, and conclusions derived from the research are outlined at the end of the article, offering insights into the effectiveness and potential limitations of the proposed hybrid multimodule DC-DC converter.Tables 1 and 2 are included, defining the symbolic representations of key parameters and providing a list of acronyms, respectively, to facilitate the reader's understanding and interpretation of the study's findings.

Related work
Z. John Shen and his team thoroughly elaborated on the current advancements and development of power semiconductor devices, emphasizing their significance in hybrid, electric, and fuel cell vehicles 19 .Furthermore, with the emergence of wide bandgap (WBG) semiconductor technologies, the usage of WBG-based devices like MOSFETs and IGBTs has gained traction in the electrified transportation sector, as highlighted by the research of Ajay Moray and others 20 .Specifically, WBG devices find critical applications in AC electric drives, particularly in high-speed and low-inductance motors.Moreover, these devices are proving instrumental in achieving www.nature.com/scientificreports/operational feasibility in areas characterized by high temperatures, ensuring optimal performance in various scenarios, including high-speed and megawatt-level motors.The inherent capabilities of WBG devices, such as their ability to function at high junction temperatures, have led to their integration into integrated motor devices, further expanding their utility 21 .
EVs can be changed either by contactless approach or by direct contact.Inductive Power Transfer (IPT), a contactless charging approach, has several advantages and disadvantages.Capacitive Power Transfer (CPT) is an alternative method for transferring power wirelessly.Research scholars and scientists discuss Many aspects of CPT 22 .The authors described the quantified study of the usage of fast-switching low-losses Wide band gap devices over traditional Silicon devices in the DC/DC converters' switching.The fast switching of Silicon Carbide and Gallium Nitride semiconductors decreases switching power losses.A great improvement of 2.2% in switching efficiency is made possible by using the GaN E-HEMT cascade.About 2% improvement in switching efficiency is attained by SiC trench ACCUFET.In all conditions for the tested normal load, the efficiency gap between GaN and SiC switches is constant (about the range of 0.6-0.7%) 23.In electric vehicles, DC-DC power converters are replaced with DC-DC battery chargers and traction drives.Recent lateral GaN devices are not appropriate for these two power electronic modules.Some researchers have presented the two-phase DC-DC, where one phase is a GaN-based transistor while another phase is a SiC-based MOSFET 24 .A design of a 15,000W DC/DC converter along with LLC topology as SiC devices to decrease the power loss with high efficiency 25 .They showed that their  www.nature.com/scientificreports/proposed converter was 98.4%, which is 3% higher than the conventional converter.An increment of 27.6% takes place in the power density of proposed converters, whereas volume decreased by 21.9% compared to conventional converters.In this research paper, for level-2 integrated on-board chargers, the contrast of isolation converters based on SiC, Si, and GaN switching devices is presented.Operating constraints and design trade-offs are also explained 26 .In the field of electric vehicles, researchers have reviewed the benefits, framework, and challenges of V2G technology.They summarized major optimization techniques to attain various V2G objectives while satisfying constraints 27 .For low-voltage micro-generators, conventional two-stage power converters, along with bridge rectifiers, are not practicable and are inefficient 28 .They presented an efficient AC/DC power converter that prevents bridge rectification at a higher efficiency, which directly converts low AC input voltage to the desired high DC output voltage.In another research, authors reported that WBG of GaN provides more efficient chargers and converters, which makes electric vehicles efficient and environmentally friendly.They also reported discrete GaN depletion mode HEMT with V Br of 200 V and high isolation resistance of 2.89 × 1010 Ohms/sq and a mobility of 1600 cm 2 /V sec for 48 V DC-DC power converters employed in EVs 29 .The authors presented ways to make an electric vehicle charging system that is highly efficient.The photovoltaic EV charging design is becoming complex due to the various features included in the scheme.Photovoltaic EV charging design requires high-power-density storage, high-performance power switches, quick charging, and dynamic response with increased power quality.SiC and GaN semiconductor switches have fast switching ability due to the less power losses.These switches can operate at high-frequency operation because the size of the converter is decreased 30 .EV-related trends and global charging standards are summarized in 31 .Different integrated onboard charger (OBC) techniques, i.e., system integration with EVs' auxiliary power modules and wireless charging systems, are explained.During wireless charging of electric vehicles, ultra-wideband communication is implemented for the exchange of information.The authors in 32 explained the usage of ultra-wideband devices to control signaling in wireless power transfer for EVs.They also highlighted the potential uses of WBG devices in AC motor drives.To notice the full potential of WBG devices in motor derives, the converter design considerations, technical challenges, and the design trade-off are explained 33 .To deal with the low power rating of GAN, the authors presented two solutions in their research work: two-phase GaN-SiC-based and single-phase paralleled GaN.An instantaneous power loss analysis method is introduced to analyze the contributors of power loss.By implementing the instantaneous method on CAD Spice simulation samples, they demonstrated the paralleled GaN converter's superiority, i.e., in terms of efficiency 34 .Luca Concari et al. analyzed the performance of a 3-phase converter architecture with decreased common mode voltage that could be implemented in electric motor drives.They worked on three important parameters: efficiency, reliability, and common mode voltage.The reliability analysis was performed using the Coffin-Mason model, which showed that higher efficiency is provided by SiC devices 35 .For future devices, the power conversion topologies that are the most appropriate are explained.Power conversion topologies are current light two-medium HEV/EVs and two-level three-phase topology.Multiphase technologies have been applied in high-power applications.A control scheme is introduced to focus the main attention on the module's practical design aspects, which are the layout of the modules and direct bonded copper (DBC) routing with optimum we band-based die parallelization and placement 36 .
Various scenarios arise due to malicious cyber-attacks.Researchers are working comprehensively and providing recommendations to defend the effect of many data strategies on the power electronic hardware that is in an EV charger.Aritra Ghosh described the challenges faced due to the utilization of EVs in the transport sector for de-carbonization purposes.The main components of EVs are the storage systems and the charging station with efficient power electronics.The EV charging station is mainly given power from the grid station, but it can be replaced with solar energy.The battery of EVs is deficient in tailpipe emissions in contrast to other types of EVs.Therefore, EVs are thought to be true zero-emission vehicles 37 .Yuanjian Zhang et al., in their research work for EVs, designed an optimal control strategy in which IoVs are incorporated.As compared to the original strategy, the simulation result shows the greater performance of the novel optimal control technique for EVs 38 .Currently, there are many new developments aimed at making improvements in EVs and their parts.This plays a pivotal  39 .A research survey regarding various GaN devices-based DC-AC, AC-DC, and DC-DC converters along with their features has been conducted; methods for solving the issues of power modules, i.e., parasitic, thermal design, and layout other than that of the power converters are also provided in 40 .For evaluating the performance of wireless chargers, a figure of merit (FOM) is proposed for the mini scale 41 .Efren Fernandez et al., in contrast to the conventional Si devices, SiC-based switching devices have provided improvements in performance in various aspects, including high operating temperatures, lower power dissipation, and faster switching.SiC devices are used in the CSI topology, which is thought to be emerging.This work describes techniques to decrease total harmonic distortion (THD) output currents of current source inverter (CSI) topology by a V-I power converter based on SiC.In this method, the switching frequency and the phase-shift angle between the two carrier signals are adjusted.The efficiency is enhanced by changing the phase angle between the Pulse width modulation carriers of both the power converter switching modulators, i.e., V-I and CSI.Panbao Wang et al. presented in their research for high-speed SiC MOS-FETs, whereas a crosstalk suppression method is proposed.By this method, a crosstalk voltage is decreased by incrementing the gate to source capacitance and decreasing the wide band gap MESFETs' output characteristics.
In this regard, a better temperature-dependent analytical model is presented by S. Rehman et al.In this modeled data, improvement is made due to a comparative analysis of modeled and observed characteristics.To assess the Miller capacitance, the analytical expressions are developed for linear and saturation regions of operation 42 .An intelligent control method for DC fast charging stations is introduced in 43 , where a control strategy is presented to control the voltage fluctuations.The rises and drops of voltage are also challenging tasksin electric vehicles as they cause instability in modern power systems 44 .The power systems need a strong network like IoTs to manage the charging schedule of the latest V2G technology 45 .Multilevel converters have been introduced in the latest EV chargers because these converters can handle higher voltage values with lower THD 46,47 .On the other hand, cascade topology is also in debate for battery chargers of EVs as variation in SOC of the batteries is limiting the performance 48,49 .The property of DC-DC converters is that they can regulate the wide range of voltage for the on-boarding charging system 49 .The present study supports the beneficial results associated with multilevel converters in cascade topologies, as previously documented in the literature.Specifically, the suggested paradigm is influenced by a multimodule pattern described in reference 50 .This novel idea seeks to tackle the present obstacles related to ultra-fast electric vehicle (EV) chargers, with a particular focus on the simultaneous achievement of both high power and high switching capabilities [51][52][53] .The model stands out due to its utilization of a dual-group architecture of multimodule converters, with each converter specifically tailored to meet different operating needs 54 .The initial group is tasked with the duty of overseeing high power management, utilizing Insulated Gate Bipolar Transistors (IGBTs) as they have demonstrated their capacity to handle increased power levels effectively.In contrast, the second category, which focuses on demanding switching needs, incorporates switches made with Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) 55 .The design justification for this is based on the inherent benefits of MOSFETs, namely their superior switching speeds and reduced conduction losses 56 .The second group's use of wide bandgap (WBG) materials becomes crucial in response to the increasing need for ultra-fast charging in electric vehicles (EVs) 57,58 .Materials like silicon carbide (SiC) and gallium nitride (GaN), which are part of the wide bandgap (WBG) family, provide exceptional material features that allow for increased switching frequencies and reduced power consumption 59,60 .The deliberate distribution of converter duties guarantees a well-rounded strategy that combines the power-handling capacities of IGBTs with the switching efficiency of MOSFETs 61,62 .This technique effectively tackles the dual obstacles of high power and high switching.Although combining both groups has the potential to reach extremely high switching frequencies, it is important to recognize the intrinsic constraint of WBG devices-their inability to withstand high power levels 63 .Therefore, it is necessary to use a hybrid strategy that utilizes the advantages of both conventional and wide bandgap (WBG) devices in order to achieve an ideal equilibrium between power and switching needs 64,65 .
Expanding on the findings of reference 50 , the study emphasizes the existing lack of WBG devices and highlights the urgent requirement for their incorporation into EV fast-charging applications.In order to strengthen the theoretical basis of the suggested model, a comprehensive small-signal model for the converter is explained 66 .This model is crucial in developing a control approach that aims to achieve both the intended power-sharing dynamics and the overall stability and dependability of the charging system 67 .To summarize, the main benefit of multilevel converters, demonstrated by the suggested model, is their enhanced control capabilities due to a larger number of available switching states 68,69 .The hybrid design, which combines the most advantageous characteristics of conventional and wide bandgap (WBG) devices, has great potential for the development of high-speed electric vehicle (EV) chargers.This configuration effectively tackles the complex issues related to power and switching requirements in a comprehensive way 70 .The current revolution in WBG materials encourages fast switching where these devices are not capable of tackling high power.However, conventional converters have high power ratings but have a very slow switching speed as compared to WBG-based devices.Besides all these problems, the latest research is being strict on the fast charging of EVs.To compensate for these issues, we are developing a hybrid module multimodule-based converter that has a high-power rating with a high switching speed.The proposed model not only increased the power efficiency but also enhanced the power density with high switching as we used the WBG device MESFET in a multimodule converter.The topology we have adopted in the model is DAB, as it needs more attention, especially in grid-connected vehicles, as shown in Fig. 1. www.nature.com/scientificreports/

Wide bandgap device structure and performance evaluation
Since SiC bulk wafer fabrication is highly advanced, SiC diodes are suitable for power applications as their manufacturing is based on a vertical structure.The drift area of SiC diodes is substantially thinner than that of Si PN diodes, and this is a reason for the high critical electric field strength of SiC.As a result, substantially less charge is held in the drift region, allowing for fast reverse recovery and high switching speeds.On the other hand, the GaN-on-GaN devices are considered the bulk native GaN substrates that are used to construct GaN power devices.Although the performance of these devices is very enticing, the price of free-standing GaN wafers is too high.Given the cost issues, the development of diodes based on GaN-on-SI wafers has recently been initiated.One of two fundamental configurations has been configured to create GaN-on-Si diodes 71 .The first is the vertical structure, as seen in Fig. 2, while Fig. 3 also shows the GaN-On-Si diodes in their Lateral Schottky configuration.In these latest PN junctions, a 2DEG is constructed at the heterojunction of the AlN and GaN layers.Due to the high electron mobility found in these types of materials, they can achieve high conductivity between the anode and the cathode.It has been observed from the performance analysis of SiC and GaN diodes that the SiC devices can withstand higher temperatures while GaN has the advantages of Low-Threshold Gate Voltage and a Higher rate of voltage changes.Therefore, it has fast switched in both on and off times.Johnson defined the relation for low-rating transistors where the power-frequency product is carried out.After that, the Baliga figure of merit has been introduced.The figure of merits has estimated the impact of material parameters.This modeling of the field distribution is usually done to calculate the intensity of the doping and the width depletion region which is desired to maintain the voltage 72 .
In this regard, the WBG diode performance can be observed by the ideal specific on resistance.It is the resistance per unit area of this layer of material required to support the voltage.This resistance defines the per unit area for the resistance of the specific layer to support the voltage 74 .Hence, the expression is given as: (1)  www.nature.com/scientificreports/where V is the breakdown voltage, and it indicates the conduction performance of the PN junction.Electron mobility, dielectric constant, and critical electric field denoted by ǫ, µ, and E f , respectively.Now, it comes to the transistor side, where MOSFET and JFETs are the common devices to carry the current only for the majority of careers.SiO2 is commonly considered a stable oxide of SiC to fabricate the SiC MOSFETs 73 .This fabrication is based on the development of the SiC wafer fabrication technology.To analyze the WBG transistor, there is a need for high reverse blocking voltage.The best suitable option to deal with this blocking voltage is SiC Lateral MOSFET structures, as shown in Fig. 4. It is especially well suited for monolithic integration with other circuits since the gate, drain, and source terminals of the device can be adjusted using the top surface.On the other hand, high voltage with high-power applications deals with SiC MOSFETs with a vertical design, as shown in Fig. 5. SiC MOSFET research is moving quite swiftly because the two devices' structures aren't all that dissimilar.The performance of the SiC MOSFET with vertical structure is extremely close to its theoretical limit.Affordable SiC MOSFETs are currently widely available.SiC MOSFETs from suppliers like Infineon, Wolfspeed, and ROHM are readily available off the shelf with voltage ratings ranging from 600 to 1700 V.As earlier mentioned in the section, the GaN-On-Si FET has received a lot of research and attention where the reason is the advancement of the wafer production technology.The structure of GaN-On-Si FET is shown in Fig. 6.The discussion is made about the Johnson figure of merit in 75 and Baliga figure of merit in 76 ; the minimum power losses can be written as: (2)  www.nature.com/scientificreports/Equation (1) covers only the PN junction, while Eq. ( 2) deals with Power JFETs.Here I DS is the conduction current of the device, and Vg is the gate voltage.Like the lateral GaN diode, as shown in Fig. 3, the lateral GaN FETs can carry a high electron mobility current using the 2DEGs.This typical device is HEMT, where the gateto-source bias voltage is zero, and the 2DEG is a normally-on depletion transistor.A cascade low-voltage Si-MOSFET can be applicable for a normally off-power device, but it is not suitable for EVs.A P-GaN layer placed between the gate and the AlGaN barrier can be used to create a genuine normally-off GaN E-HEMT despite the cascade shape, as shown in Fig. 6.The P-GaN layer can be depleted by properly planning the doping concentration and layer thickness 79 .As lateral GaN HEMT is not a junction structure, it has no avalanche effect for lateral GaN WBD.A high level of breakdown voltage can be problematic for a GaN device.In normal conditions, the GaN devices can deal with higher voltages, up to 650-1300 V.In EVs, there is a need to switch transistors with a high dielectric lifespan to create a high breakdown voltage in a substantial part.In this regard, GaN has been recognized as one of the potential materials and recently introduced a new structure of a normally-off vertical GaN-on-GaN Fin FET.This type of transistor based on GaN-on-si wafer is carried out where several advantages have been found as this type has series resistance provided by buffer layer as shown in Fig. 7. Like other FETs, a cross-sectional view of an operating MESFET, illustrating recessed gate technology, is illustrated in Fig. 8.Although power losses of FinFET are also dependent on the resistance R DS same as in Eq. (1) for the PN junc- tion.Here, this can be calculated: On the other hand, the power losses in HEMT can be calculated by Eq. ( 4) as given: The losses remain dependent on the same parameter as Eqs.( 3) and ( 4) as the = V DS /I D , but the duty cycle can change its effects on it.When the duty cycle is changed, the V-I characteristics are also changed, and where the relation of I D and V DS can be calculated as: gm f and gm f are used for the forward transconductance and output transconductance, respectively.V GS is the gate to source voltage where m, n, d, e are the parameters used for output characteristics to solve the nonlinear equation as given in 41 .In IGBTs, the calculation for the power losses becomes: Same as FETs, the V DS replaced by V CE , the collector-emitter voltages when IGBT is in the saturation region, whereas I o is the output current.Although the FET devices are normally considered for RF application here, we have required the high-power application as an electric vehicle.RF performance of FETs relies mainly upon the device's intrinsic parameters.Parameter extraction techniques play a crucial role in determining the accuracy of the predicted intrinsic parameters.For accurate small-signal modeling, a suitable capacitor model is needed.Such a model could help the design engineer to assess the reliability of the device under changing conditions.This is shown by making an exhaustive review of relevant literature based on the internal parameters that SiC/ GaN-based devices can operate at higher drain-to-source voltages and can reasonably mitigate self-heating effects compared to second-generation devices such as GaAs.Self-heating effects are directly proportional to the power handled by the device.Under high bias, the characteristics of the device could degrade, and a simple model, either analytical or numerical, may not be accurate enough to predict the device's performance.So, to get a better understanding and wide applicability, there is a need to develop a model for SiC/GaN MESFETs that incorporates self-heating effects.
Moreover, a detailed overview of FETs (MESFETs and HEMTs) is given in this section.Device performance with different aspects is reported.The performance of a FET depends upon the material used for its fabrication.It has been observed that devices fabricated using SiC and GaN have superior performance, both in DC and RF domains, compared to GaAs MESFETs.SiC MESFETs have excellent heat conduction in high-power applications and show maximum stability in performance 42 .By using work done by different researchers, it is shown that SiC MESFETs have great potential to be used in harsh environments.In this regard, multimodule converters have recently been introduced and are expected to be a viable option for the UFC charger as these provide high voltage and high power [81][82][83][84] .Low-power modules are the reason for increasing system complexity, overall cost, and conduction losses.On the other hand, the lower number of power modules can also raise the issue of limiting the switching frequency, less power density, and increasing weight and size as well.In the next section, we introduce the multimodule converters that have capabilities to handle high frequency, high-power, high-power density, low conduction losses, and fast charging for vehicles [84][85][86][87][88] .
After performance analysis, choosing a Wide Bandgap Device for Electric Vehicle systems is a hot talk in today's fast-switching converters.The power converters should be highly efficient and provide a high-power ( 5) www.nature.com/scientificreports/density.Ultimately, they reduce the size and weight as well.By developing a model with only conventional converters (IGBTs), we cannot meet the latest trend of high switching, as Table 3 shows.The WBG materials have the ability to switch fast, have high power efficiency and density, and have low switching losses.These materials can take a limited power fraction from the grid; that's why a Hybrid topology is introduced in the next section.

Research methodology
In the previous section, we have chosen a MESFET for the Converters, and it is also decided that there is a need for a multimodule converter for the above to obtain the above-mentioned advantages.Some of the research is being conducted on the multimodule pattern, but a concept provided by 50 is based on two different groups of multimodule converters.The concept is that the first group has a low switching frequency with a very high fraction of the total power.The second group is based on wide bandgap material which has a high switching frequency with a lower fraction of power.Both groups of wideband devices can provide ultra-high switching frequency, but these are not able to handle high power as the charging of the vehicle systems is required.In 50 , the first group is based on IGBTs, and the Second group is based on switches of MOSFETs where the wideband gap was not introduced.We have proposed the same type of hybrid group, but the first one is based on IGBTs (for high power fraction), and the second group consists of a wide bandgap device, MESFET (for high switching frequency), as shown in Fig. 9.The work presented in this paper includes a generalized small-signal model for the presented converter as well as the control strategy required to achieve uniform power-sharing between the employed modules.Besides, a power loss evaluation has been conducted to compare the proposed converter with the other two options.To verify the presented concept, the number of modules needed to achieve the required ratings is calculated for both conventional multimodule DC-DC converters and hybrid multimodule DC-DC converters.In addition, the power loss analysis of the hybrid multimodule converter is provided.
We have adopted a DAB topology where Module-1 to Module-4 are identical, and IGBTs are used for switching as high-power fractions, as shown in Fig. 10a [89][90][91] .On the other hand, Modules 5-8 are also identical, but these have used the wideband gap device MESFET to deal with high switching, as shown in Fig. 10b.
So, the first group is responsible for dealing with high power and low frequency, whereas the second group caters to low power with high frequency.We are assuming that in our proposed model, the power to be delivered to the 440 V battery is 500 kW.As per Fig. 1, the voltage of the grid is assumed to be 11 kV.In this regard, the first group deals with a high portion of the power, that is, 85% of the total power, 500 kW, which becomes 425 kW.Similarly, the second group deals with the lower portion of power, which is 15% of total power, which becomes 75 kW.The switching frequencies are proposed to be 10 kHz and 200 kHz for the first and second groups, respectively.So, the voltage injected from the grid to the first group is 17/20 of 11 kV, which is 9.35 kV, and the second group takes a voltage of 3/20 of 11 kV, which is 1.65 kV.The charging current required for a battery is 600 A; the first group is responsible for 17/20 of 600 A, which is 510 A, and the second group can provide 3/20 of 600 A, which is 90A.The fractions 17/20 and 3/20 are denoted by K1 and K2, respectively.As there are different current and voltage ratings, there is a need for equal input voltage sharing (IVS) and equal output current sharing (OCS).Hence, the voltages of the first module have been reduced to V inA /17, and the current has reduced to I inA /17 .The terms V inA , V inB , I inA , I inB are used for the voltages and currents of the first and second groups, respectively.These specifications are modeled in a small signal model, as shown in Fig. 11.
The small signal is presented in Table 4 defines the formulation of the small signal analysis of the hybrid 8-module converter 92,93 .The design is interlinked with "Related Work" Section, where the wideband gap materials' performances are evaluated, where it is formulated that there would be a change of internal resistance after changing the switching frequency.As we are proposing a hybrid multimodule converter that can affect the input voltage and current by changing the duty cycle to provide a uniform charging current to the batteries of the vehicles.The issues raised are that these changings can affect the inductance and capacitance of the materials 94,95 .
To keep the uniform charging current, we formulated the transfer function for different terms 50 .First, the relation of the duty cycle with the output voltage for the module of the first group has been formulated.The transfer function for the output voltage of modules changes in the duty cycle for the second group, A. where L A and C A are the equivalent inductance and capacitance of modules of group-A.R DA is a change in the internal resistance due to the duty cycle due to switching frequency.Similarly, the transfer function for the output voltage of modules changed in the duty cycle for the second group, B.
where L B and C B are the equivalent inductance and capacitance of modules of the group B R DB is the change in the internal resistance due to the duty cycle and switching frequency.K defines the fraction that reduces the (8) www.nature.com/scientificreports/power for the modules of Group-B.So, the transfer function for the impedance for the modules of Group-A and Group-B can be calculated in ( 10) and (11).
where V oA and I oA are output voltages and current of the group-A.Similarly, V oB and I oB are output voltages and currents of the group-B.
D f1 and D f2 are the difference in power rating from actual power for Group-A and Group-B respectively.
To evaluate the efficiency of our proposed hybrid modules converter, we must calculate the power losses in both Groups of modules as per the ratings of Table 5 [96][97][98] .In "Wide Bandgap Device Structure and Performance Evaluation" Section, the power losses of IGBTs and MESFETs are estimated in Eqs. ( 5) and (7).Here, we have four modules in each group.Therefore, the multiplying factor 4 is multiplied, and cumulative power losses in both groups of modules are calculated as: PA losses are losses by IGBTs converters relying on the wide bandgap material and PB losses are losses by wide bandgap converter relaying on the MESFETs converter.System Parameters used in our proposed model are the data sheets of IKW25N120T2 (IGBT) and NES1823P-100 Datasheet (GaAs MESFET), then the power losses in PA lo es and PB losses are found 11.5 kW and 1.5 kW, respectively.On the other hand, our proposed model, which hybrid modules of both types of converters, found 3.5 kW .Then the efficiency can be calculated in 99 ; we modi- fied it accordingly as: www.nature.com/scientificreports/Then, efficiencies we found from Eq. ( 16) are 98%, 99.4%, and 99.25% for the, PandB losses and our proposed model, respectively.
The analysis of the outpower vs power efficiency curves is shown in Fig. 12.The power density can be found after getting the power efficiencies and power losses.The power density is defined as the ratio of the out power and the total volume contained by switching circuits, transformer core/windings, and cooling chips.Then the equation becomes: www.nature.com/scientificreports/ The total volume of the equipment used in the complete modules is estimated in 99 , which we considered the same for our calculations.The power density in the group of the PA losses is a little higher which contains 13.5 kW/L because of the conventional IGBTs group of modules.On the other hand, the power density in the group PB losses is small and contains 11.75 kW/L because of the conventional IGBT group of modules.In our proposed model, the power density is estimated to be 10.99 kW/L.www.nature.com/scientificreports/ The modules of both groups are not identical; therefore, there is a need for a control strategy that can handle the issue of mismatching among electrical parameters.It can provide thermal stress on the devices and cause uniformity among the power-sharing of the modules.A control strategy is presented for the converters, which are connected in series on the input side and parallel on the output side.So, the input series and output parallel topology is proposed by providing cross feedback output sharing configuration as shown in Fig. 13.For even power distribution in this case; the combination input series output parallels converter is connected to the cross feedback current sharing unit.Table 3 has a list of the design specifications that are meted out by our proposed controller.The OCS controller, shown in Fig. 13, comprises one outside output current loop and eight inner current loops.The primary multimodule group receives four of the eight inner loops, while the secondary multimodule group receives the four remaining inner loops.The primary focus of this paper is providing fast charging, and this current control strategy is based on but charging and negative pulse charging.The fractions 17/20 and 3/20 are denoted by K 1 andK 2 respectively.As there are different current and voltage ratings, there is a need for equal input voltage sharing (IVS) and equal output current sharing (OCS).Hence, the voltages of the first module have been reduced to V inA /17, and the current has reduced to I inA /17 .The terms V inA , V inB , I inA , I inB are used for the voltages and current of the first and second groups, respectively, while these specifications are modeled in a small signal model, as shown in Fig. 11.As the switching frequency of Group-B modules is 200Kz  therefore, we need a fast-charging time with a lower temperature.The proposed control strategy first controls the output current profile based on reflex charging with the help of output current.In the current output profile, the charging rate should not be increased because it causes overcharging, and ultimately, it decreases the life of the battery.These output currents behave as an outer current loop and inner current loops, as shown in Fig. 13. the same mechanism is adapted further as the feedback current of the first module is its output current, and the same pattern is applied to modules 2-3.Similarly, the feedback current of the third module is its output current, as shown in Fig. 13 (second group of modules).In steady-state conditions, all feedback currents should face the common reference (w.r.t output current loop) with zero static error.
As mentioned earlier, the first group delivers high power and low frequency, whereas the second group caters to low power with high frequency.We are testing our simulation on the 440 V battery with an input power of 500 kW where the grid voltages are 11 kV.The first group extracts a high portion of the power, 85% of the total power, 500 kW, which is 425 kW.The second group deals with the lower portion of power, which is 15% of total power, which is 75 kW.The switching frequencies are proposed to be 10 kHz and 200 kHz for the first and second groups, respectively.So, the injected voltage from the grid to the first group is 17/20 of 11 kV, which is 9.35 kV, and the second group takes a voltage of 3/20 of 11 kV, which is 1.65 kV.So, the topology is based on the input series and output parallel, and the current in each module remains at the same current of 45.45 A, as shown in the Fig. 14 which ensures our ratting given in Table 3.On the other hand, the total output Current for the proposed hybrid 8-module DC-DC Converter, which is 600 A, is also tested with reference current and ensures uniformity, as shown in Fig. 15.The charging current required for the battery is 600 A, where the first group is responsible for 17/20 of 600 A, which is 510 A, and the second group can provide 3/20 of 600 A, which is 90 A. These 510 A and 90 A current for group A and Group B are further divided by four as each group contains four modules.So, per module, currents are 127.5A and 22.5 A for group A and Group B, respectively in Fig. 16.To   www.nature.com/scientificreports/ensure the input voltages are different in both modules, we also examined the input voltages, as shown in Fig. 17.
As mentioned earlier, we are testing our simulation on the 440 V battery, as shown in Fig. 18.We formulated the power-sharing concept in Table 2 and further modeled it in Eqs.8-13, while the change in duty cycle has a major effect on power sharing among both modules.To keep this importance, we have examined the powersharing analysis of both modules with variation in duty cycles in Fig. 19.The Duty cycle changes from 0.45 to 0.85 between power share of 106.25 Kw and 18.75 Kw.As earlier discussed, two different modules of low frequency ( 10 kHz ) with high power and high frequency (200 kHz) with low power are considered.The analysis frequency and power are shown in Figs.20 and 21 for Group-A of IGBTs Modules and Group-B of MESFETs Modules, respectively.Figure 22 highlights our contribution as compared to other works.In 28 , the work is old-fashioned as it uses a 2 kHz switching frequency.In 100 , WBG material was used and got 99.3% efficiency at a low scale and low switching frequency of 27 kHz.The model presented in 50 has good power efficiency and density with a 100 kHz switching frequency.On the other hand, our proposed model has good power efficiency, high power density, and an ultra-high switching frequency of 200 kHz.The reason for this high switching is the development of MESFET switches in the second group of modules, and this makes our model efficient for others, as shown in Fig. 22.

Conclusions and future research directions
This article presents a hybrid multimodule DC-DC converter based on DAB topology for EVs that are designed to increase power efficiency and power density.Eight modules from two different groups of semiconductor devices make it a hybrid concept, a multimodule DC-DC converter.The first group consists of four modules of IGBTs, which have a low switching frequency and a very high fraction of the total power.Similarly, the second group consists of four modules of MESFETs based on wide bandgap material, which has a high switching frequency with a lower fraction of power.Both groups of wideband devices can provide ultra-high switching frequencies, but these are not able to handle high power as the charging of the vehicle systems is required.The performance analysis of these semiconductor devices is done where the first group extracts a high portion of the power, which is 85% of the total power of 500 kW, and the second group extracts a lower portion of the power, which is 15% of the total power.The fast-charging phenomenon is achieved by providing switching frequencies of 10 kHz and 200 kHz for the first and second groups, respectively.WBG materials have the ability to switch fast, have high power efficiency, have high power density, and have low switching losses, but they can deal with high amounts of power.In this article, a generalized small-signal model is analyzed as a control strategy required to achieve uniform power sharing between the employed modules.An output current-sharing configuration ensures uniformity among individual modules where the current of the controller is compared and tested with a reference current.Simulation results on MATLAB show the confirmation of current uniformity and provide the charging current to the batteries of the EVS.The conduction losses of both groups are examined.We achieved a power efficiency of 99.25% and a power density of 10.99 kW/L, which is remarkable at 200 kHz fast switching.
The future work can be extended by adding more advanced WBG devices that can handle a larger fraction of the power.Future research directions include exploring advanced wide bandgap devices such as GaN and SiC for enhancing converter performance, efficiency, and power density 101 .Novel control strategies, possibly based on artificial intelligence or machine learning algorithms, could improve converter stability and reliability, particularly in dynamic load conditions.Additionally, system integration and optimization of the hybrid DC-DC converter within the EV charging infrastructure need attention, along with understanding scalability and application flexibility for different power levels and grid constraints 102 .Finally, a comprehensive techno-economic analysis should be conducted to evaluate the cost, performance, and environmental impact of the hybrid converter compared to conventional solutions, informing its commercial viability in the growing electric vehicle market 103 .

Figure 1 .
Figure 1.Presence of Bi-Directional DC/DC Converter in Power Grid Setup.
Power delivered to the first group of modules D A1 Change in duty cycle in the first module D V A1 Change in voltage by changing the duty cycle for the first module D I A1 Change in current by changing the duty cycle for the first module I AT The total current of the first module after a change in duty cycle P B Power was delivered to the second group of modules D B1 Change in duty cycle in the second module D V B1 Change in voltage by changing the duty cycle for the second module D I B1 Change in current by changing the duty cycle for the second module L A The equivalent inductance of modules of group A C A Equivalent capacitance of modules of group A L B The equivalent inductance of modules of group B C B Equivalent capacitance of modules of group B R DA Change in the internal resistance due to the duty cycle due to switching frequency in group A R DB Change in the internal resistance due to the duty cycle due to switching frequency in group B G vDA Transfer function for the output voltage of modules to change in the duty cycle for the second group-A G vDB Transfer function for the output voltage of modules to change in the duty cycle for the second group-B Z A The transfer function for the impedance for the modules of Group-A Z B The transfer function for the impedance for the modules of Group-B V oA Output voltages of the group-A I oA The output current of the group-A V oB Output voltages of the group-B I oB The output current of the group-B PA losses Power losses by IGBT converters relying on the wide bandgap material PB losses Power losses are caused by the wide bandgap converter relaying on the MESFETs converter ρ Power density Vol.:(0123456789) Scientific Reports | (2024) 14:4746 | https://doi.org/10.1038/s41598-024-55426-6 Vol.:(0123456789) Scientific Reports | (2024) 14:4746 | https://doi.org/10.1038/s41598-024-55426-6

100 Figure 11 .
Figure 11.Small Signal Model Configuration of Proposed Hybrid Multimodule Converter.
A1 + D�V A1 ) Where D V A1 and D I A1 are the change in voltage and current by changing the duty cycle for the first module in the first group Ix 1 = I AT (D�I A1 + D�V A1 ) Where I AT is the Total current of the first module after a change in duty cycle I 1 = I AT (�D A1 ) V 2 = 17 vin 20PA (�D A2 ) Wher D A2 is a change of duty cycle by fraction 17/20 in the second module Vx 2 = 1 vin 20PA (D�I A2 + D�V A2 ) Where D V A2 and D I A2 are the change in voltage and current by changing the duty cycle for the second module in the first group Ix 2 = I AT (D�I A2 + D�V A2 ) I 2 = I AT (�D A2 ) V 3 = 17 vin 20PA (�D A3 ) Wher D A3 is a change of duty cycle by fraction 17/20 in the third module Vx 3 = 17 vin 20PA (D�I A3 + D�V A3 ) Where D V A3 and D I A3 are the change in voltage and current by changing the duty cycle for the third module in the first group Ix 3 = I AT (D�I A3 + D�V A3 ) I 3 = I AT (�D A3 ) V 4 = 17 vin 20PA (�D A4 ) Where D A4 is a change of duty cycle by fraction 17/20 in the fourth module Vx 4 = 17 vin 20PA (D�I 4 + D�V A4 ) Where D V A4 and D I A4 are the change in voltage and current by changing the duty cycle for the fourth module in the first group Ix 4 = I AT (D�I A4 + D�V A4 ) I 4 = I AT (�D A4 ) Second group modules V 5 = vin 85PB (�D B5 ) Where P B is the power delivered to the second group of modules, and D B5 is a change of duty cycle by fraction 1/85 in the fifth module Vx 5 = vin 85PA (D�I B5 + D�V B5 ) Where D V B5 and D I B5 are the change in voltage and current by changing the duty cycle for the fifth module in the second group Ix 5 = I BT (D�I B5 + D�V B5 ) Where I BT is the Total current of the sec- ond module after a change in duty cycle I 5 = I AT (�D B5 ) V 6 = vin 85PB (�D B6 ) Where D B6 is a change of duty cycle by fraction 1/85 in the sixth module Vx 6 = vin 85PA (D�I B6 + D�V B6 ) Where D V B6 and D I B6 are the change in voltage and current by changing the duty cycle for the sixth module in the second group Ix 6 = I BT (D�I B6 + D�V B6 ) I 6 = I AT (�D B6 ) V 7 = vin 85PB (�D B7 ) Where D B7 is a change of duty cycle by fraction 1/85 in the seventh module Vx 7 = vin 85PA (D�I B7 + D�V B7 ) Where D V B7 and D I B7 are the change in voltage and current by changing the duty cycle for the seventh module in the second group Ix 7 = I BT (D�I B7 + D�V B7 ) I 7 = I AT (�D B7 ) V 8 = vin 85PB (�D B8 ) Where D B8 is a change of duty cycle by fraction 1/85 in the eighth module Vx 8 = vin 85PA (D�I B8 + D�V B8 ) 8 arehere D V B8 and D I B8 are the change in voltage and current by changing the duty cycle for the eighth module in the second group Ix 8 = I BT (D�I B8 + D�V B8 ) I 8 = I AT (�D B8 )

Figure 13 .
Figure 13.Output current sharing configuration for the proposed hybrid multimodule DC-DC Converter.

Figure 14 .
Figure 14.Input Current for the proposed hybrid 8-module DC-DC Converter.

Figure 15 .
Figure 15.Total output Current for the proposed hybrid 8-module DC-DC Converter.

Figure 16 .
Figure 16.Output currents of both groups for the proposed hybrid 8-module DC-DC Converter.

Figure 17 .
Figure 17.Input Voltages of both groups for the proposed hybrid 8-module DC-DC Converter.

Figure 18 .
Figure 18.Output Voltages of Each Module/Each Group for the proposed hybrid 8-module DC-DC Converter.

Figure 19 .
Figure 19.Power sharing analysis of both modules with variation in duty cycles.

Table 3 .
Performance Analysis of WBG-based Devices.

Table 4 .
Small signal formulation of the proposed hybrid multimodule converter.Where P A is the power delivered to the first group of modules, and D A1 is a change of duty cycle by fraction 17/20 in the first module

Table 5 .
Rating of the parameters for both groups of modules.