resonant DC-DC converter for energy-efficient fuel cell electric vehicles with reduced battery dependency – Nature

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Scientific Reports volume 16, Article number: 28588 (2026) Cite this article
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The fuel cell electric vehicles (FCEVs) with a lower battery dependency have a big problem in terms of the stability of voltage, high dynamic response and low torque ripple under different load conditions. To overcome these challenges, this paper presents a Tunicate Swarm Algorithm and Teaching–Learning-Based Optimization (TSA-TLBO) optimized hybrid Proportional-Integral-Derivative (PID) and Fractional-Order PID (PID-FOPID) control strategy to enhance the regulation of a PEMFC-based powertrain. This proposed controller operates at the converter and motor drive stage and it is coupled with an Elongation Factor 2 (EF₂) resonant DC-DC converter to increase voltage stabilization and power conversion efficiency. The hybrid optimization approach effectively tunes controller parameters to minimize speed and current tracking errors under dynamic operating conditions. Simulation results demonstrate that the proposed system achieves a maximum efficiency of 90.7% with an output power of 187 W. The harmonic analysis was performed at the three-phase inverter output supplying the PMSM. The measured voltage total harmonic distortion (THD) and current THD are 0.21% and 1.78%, respectively. The results also show enhanced dynamic performance and reduced torque fluctuations compared to conventional control methods. These results prove that the proposed solution enhances considerably control performance and allows working with FCEVs that have less auxiliary energy storage efficiently.
The world has heavily relied on fossil fuels like coal, natural gas and oil as the main sources of energy over the past few decades¹. Even though these non-renewable energy sources have the potential to provide massive energy provision, they have caused a lot of problems in the environment, such as greenhouse gases, air pollution, and global warming². Additionally, due to their limited nature of their supply and the growing environmental issues, the adoption of clean and sustainable energy sources has been hastened³. In this regard, renewable energy technologies have proved to be a useful option in terms of power generation as well as transportation use⁴. FC technology has acquired a lot of interest among them, especially in the EV industry, because it operates at a high efficiency and is environmental friendly⁵. FCs process hydrogen to electrical energy and the process is electrochemical, without combustion, and is more efficient than traditional ICEs^6,7. This makes FCVs a promising alternative for next-generation transportation systems.
Zhou, J. et al.⁸ report various types of FCs, including alkaline, molten carbonate, phosphoric acid, microbial FCs, solid oxide, and direct methanol FCs. Though all these possess their own distinct features and applications, for EVs, especially PEMFC seems to be a most viable alternative⁹. Adding to this point,¹⁰ lists out the significant features of PEMFC as their robustness, compactness, ability to operate at lower pressures and temperatures, start swiftly, provide high energy density with noiseless operation. Thus,¹¹ suggests this cell as an ideal choice for electric cars where efficient and responsive power sources are vital to suit the on-and-off driving nature in urban environments. All these developments convey the shift in energy ecosystem towards sustainable and environmentally friendly nature, with the help of hybrid energy sources and technological advancements¹².
A common limitation that comes along with the EVs is their additional weight owing to the presence of larger battery packs, which is necessary for storing and delivering the electricity¹³. This extra weight caused by the battery pack presence may also have an impact on the vehicle handling and its performance¹⁴. Another major concern is the time taken for charging an EV which is much higher than the time taken for refuelling a conventional gas or diesel-based vehicles¹⁵. In a traditional method of EV charging, full charge can be achieved after several hours of waiting time. This is direct contradictory to the case of conventional filling of a gas tank associated with quick stops¹⁶. Also, as against ICE vehicles, even the more affordable EV designs have only a limited driving range¹⁷. This restriction may lead to creation of a ‘range anxiety’, where the drivers will have the doubt on reaching the destination with the available power¹⁸.
These challenges can be addressed using FC-based automobiles that are powered with hydrogen gas¹⁹. Usually, in a FC automotive system, any of the following three motors will be preferred for power: BLDC Motors, SRM and PMSM. BLDC Motors, the commonly employed motors suffer from overheating problems and torque vibrations at higher speeds. The SRM Motors, though robust, cannot provide precise control for FCVs. Comparatively, PMSM Motor have high efficiency and power density²⁰. Thus, advanced methodologies are required to improve the performance of the control system.
Although FCEVs have positive performance, various technical issues continue to constrain the performance, especially when the battery dependency is lower. FC systems are extremely responsive to load changes in the small auxiliary energy storage system creating voltage variability, higher torque ripple and poorer motor drive dynamic performance. Conventional control approaches, such as classical PID controllers, often fail to provide adequate robustness under nonlinear and time-varying operating conditions associated with FC systems. Despite the recent literature on advanced control techniques, there is still a gap in the literature about constructive hybrid control solutions that could achieve high dynamic response, higher voltage regulation, and lower torque ripple in FCV applications. Also, little focus has been on the coordinated combination of optimized controllers with resonant converter structures, including the EF₂ converter, to condition power better. Thus, there is an identified gap in research in order to design a regime of optimum and dynamic methods of control that can guarantee stable power supply and proper monitoring of load demand, uphold voltage and enhance the overall performance of the system in PEMFC EV with less reliance on batteries.
The EM and control functions of the proposed system need to be differentiated. The EM layer calculates the amount of power required due to driving conditions and assigns how much must be contributed by the FC and auxiliary energy storage system. By comparison, the hybrid PID-FOPID controller function at control level and thus provides proper regulation of voltage and response to dynamic changes through tracking of the reference signals. Therefore, the proposed controller is not considered a standalone EM system but an optimized control strategy that enhances the effectiveness of the overall EM framework.
The proposed research does not introduce a high-level EM strategy. Instead, it focuses on the control layer that accurately tracks the reference signals generated by an external EM system. The proposed hybrid PID-FOPID controller is implemented at the converter and motor drive control level to enhance voltage regulation, dynamic response, and system stability under varying operating conditions. Therefore, the primary objective of this work is to improve the control performance of the power conversion and motor drive system, thereby supporting the overall EM framework of PEMFC-based EVs.
The proposed work does not claim novelty in the individual components, namely the EF₂ resonant DC-DC converter, TSA, TLBO, PID controller, or FOPID controller. Instead, the novelty lies in the hybrid TSA-TLBO optimization of a hybrid PID-FOPID controller integrated with the EF₂ resonant converter for PEMFC-based EVs with reduced battery dependency, resulting in improved voltage regulation, dynamic response, converter stability, and reduced torque ripple.
The main contributions of this work are summarized as follows:
Development of a hybrid PID-FOPID control strategy for enhanced regulation of the EF₂ resonant DC-DC converter and PMSM drive.
Development of a hybrid TSA-TLBO optimization framework for optimal tuning of the hybrid PID-FOPID controller parameters by combining the global exploration capability of TSA with the efficient parameter refinement capability of TLBO.
Integration of the optimized hybrid PID-FOPID controller with the EF₂ resonant converter to improve voltage regulation, dynamic response, and converter stability under varying operating conditions.
Reduction of torque ripple and improvement of transient performance compared with conventional PID and FOPID control strategies.
Support for efficient PEMFC operation with reduced auxiliary battery dependency through improved converter regulation and dynamic power delivery, thereby enhancing the overall performance of the FCEV powertrain.
Therefore, the originality of the proposed work lies in the hybrid optimization-based controller design and its application to EF₂ resonant converter control for PEMFC-based EVs, rather than in the individual converter topology or optimization algorithms themselves.
The structure of the paperwork is as follows: Recent research works happening in the selected domain are presented in Sect. “Recent research work: a brief review“. The converter configuration used for renewable energies and EVs are explicated in Sect. “Configuration of the proposed PEMFC EV with reduced battery dependency“. Section “Proposed TSA-TLBO approach based gain parameter tuning” delves into the details of the proposed system, where their results are discussed in Sect. “Results and discussion“. Overall work is concluded in Sect. “Conclusion“.
Considerable research has been devoted to FC-based EVs, focusing on EM, power converter design, intelligent controller development, and optimization techniques. The following review summarizes the most relevant contributions in these areas.
According to Kannan, R & Sundharajan, V²¹, PEMFCs can be regarded as the most efficient and feasible renewable energy resources that can find greater role in automobile applications. Till now, the research focus was on confronting issues related to maximum power extraction from FCs, speed control; torque ripples generated in BLDC motors for a FC based EV systems. Attaining optimal energy efficiency by varying the gain control parameters in an existing MPPT technique is still a challenge in FCs. To overcome this issue, a novel technique namely UFENN-MPPT is introduced in this work. UFENN, a machine learning methodology, effectively optimized the parameters to extract maximum energy from the FCs. Further, an interleaved SEPIC converter is also introduced to minimize the power failure and to regulate the voltage output.
Wang, J. et al.²² have suggested a new EM technique for an FCs-based hybrid commercial vehicle. The introduced EM perspective depends on the double delay deep deterministic policy gradient and can be employed into this topological framework. The main aim of this methodology is to optimize the damage caused in FC, damage caused in Battery and usage of FC Hydrogen. To match the battery output power and FC output power, Supercapacitors were introduced, which has the capacity to expand the possibility of optimization for both the storage systems. This methodology is found to improve the efficiency of energy storage system and its lifespan, which is much better than that offered by Non-linear Programming Algorithm and Deep Deterministic Policy Gradient. This was possibly by reducing the battery damage, FC damage and hydrogen usage. Another notable feature of the newly introduced deep reinforcement learning based EM System is its ability to optimize several indicators simultaneously, thereby extending the active life of the power system.
Meshginqalam, A., & Bauman²³ supports for convex optimization where the complete vehicle loss computations are executed in real-time using two different innovative techniques. As per the first strategy called as integrated technique, the efficiency of the FC is iteratively employed into the speed control algorithm. With the second strategy, the speed problem is addressed at the beginning, before transforming into an EM system concern.
An EV integrated with solar panel and grid has been developed by Kavin K.S., & Karuvelam P.S.²⁴ like an electric train structure. Further, a novel interleaved SEPIC converter is introduced to compensate for the low duty cycle operation. This converter is responsible for producing stepped up DC voltage with minimal switching losses. The output of the converter is connected to the grid using Single Phase Inverter and to the BLDC motor fed electric train using Three Phase Inverters. The switching operation of Inverters are controlled using a PI Controller. Thus, the available solar energy is completely utilized without wasting, by sending the output of PV panel to the electric train and grid, the whole day. During nighttime, the EV is powered by the grid with suitable converter arrangement. Thus, a single converter configuration functioning on dual source has been realized.
For EVs using dual inverters with dual electric drive systems, Pathmanathan et al.²⁵ suggests incorporating FCs as one of the sources, where the other source is the conventional EV battery system. For each component of EV driving cycle like retractable brakes, suitable power sharing algorithm have been employed. This algorithm ensures that one form of energy flow occurs from FC and the unnecessary shutdown of FC is minimized with controlled energy flow. Also, this algorithm takes cares of injecting the required reactive current and power transfer to FC, whenever transients occur due to sudden mechanical power reduction. Thus, with the introduced algorithm, the rapid mechanical power transitions are properly handled while upholding the slowly varying power reference of FC.
Silva et al.²⁶ have presented a comprehensive algorithm made of interactive Adaptive Weight GA and multi objective evolutionary algorithm for optimizing the distribution of energy and the schematic of FC-EV Battery-Ultracapacitor HESS. The focus of this introduced method is minimizing the usage of hydrogen fuel and the size of the HESS, while enhancing the battery span, vehicle’s driving span and accumulation of FCs. The power requirement is divided among the HESS, FCs, ultracapacitor pack and the traditional battery, using fuzzy based EM strategy.
Another hybrid arrangement for EM of a FC EV system powered with battery is suggested by Saravanan, R et al.²⁷. The hybrid technique introduced is referred to as JSO-RSA method, a combination of JSO and RSA. The main objective of this JSO-RSA method is to adjust the dynamic power factor, control the state of the machine and its functioning mode and minimize the proportional usage. Another notable feature identified in this research work is the optimization of battery charging with lessened amount of hydrogen.
Tehrani et al. ²⁸ have provided a thorough review of AI application in PESs and its usage throughout the system life cycle, which encompass design, control, optimization, and maintenance. The model of the work represents PESs as multidimensional systems of large-scale interconnections based on energy sources, converters, controllers, sensors, and loads where AI methods were introduced to solve multidimensional problems. It introduces a lifecycle-oriented framework that systematically categorizes AI-driven methods for design automation and intelligent converter control, while also structuring existing studies based on validation approaches.
Tehrani et al.²⁹ have illustrated a thorough overview of AI use in maintenance and forecasting stages of PESs in the lifecycle perspective introduced in Part I. It is centered on AI-based methods of health monitoring, fault and anomaly detection, and RUL prediction of power electronic items and converters. The work also addresses advanced applications such as soft-fault detection in complex system-of-systems environments (e.g., aircraft wiring networks). Moreover, it introduces AI-based forecasting methods of determining influential PES parameters, such as performance, thermal performance, component durability, load requirement, and energy output. The survey provides a structured overview of AI methodologies for enabling predictive and autonomous maintenance in next-generation PES.
Sankar et al.³⁰ introduced a hybrid Modified Boost-Cuk converter based on PV for battery-less EV traction systems, combined with a PMSM drive, with PSO-ANFIS optimizing the DC-link control and the SVPWM based VSI ensuring smooth operation of the motor, efficient power conversion and better utilization of energy.
Bodkhe et al.³¹ have presented a hybrid EM strategy in battery-free FC vehicles by using GOA-HGCNN to optimize the control of the DC-DC converter and predictive learning for voltage stability, reducing system cost, improving hydrogen utilization and making the system work efficiently without any auxiliary energy storage.
A self-learning robust control method of DC to DC buck converters has been shown by Gangula et al.³² to combine a simple single-hidden-layer neural network into a backstepping model to estimate and compensate load variations and disturbances to achieve asymptotic stability and better voltage tracking and current regulation behavior.
Mishra et al.³³ have presented a cost-effective HSAPF for harmonic and reactive power compensation. The system comprises of a RECKF for estimation of reference currents, IFGO optimized SAFPIDC for tuning the controller parameters and SMC to generate switching pulses for the VSC.
Nanda et al. ³⁴ have suggested a HSAPF for harmonic mitigation and reactive power compensation. The approach uses a KF to estimate the reference current, an AFPIDC optimized by the TLBO algorithm and SMC to generate the VSC switching pulses.
Mishra et al.³⁵ have presented a novel SHAF for Reactive power and Harmonic Compensation. The method is based on reference current estimation by KF, tuning of the T2FFOPIDC by hPSOFA, and performance improvement of the filter by source-side current-based compensation.
Mishra et al.³⁶ have suggested an HSAPF for Reactive power and harmonic compensation. An hSCATLBO is used to tune an IT2FPID controller to control the filter under nonlinear loading conditions.
The recent studies confirm the successful application of hybrid metaheuristic optimization algorithms to tune the intelligent controllers for the power electronic applications, especially in PQ enhancement. However, these studies primarily focus on harmonic mitigation and PQ applications rather than PEMFC-based EV power conversion. The present work applies a hybrid TSA-TLBO optimization strategy to tune a hybrid PID-FOPID controller for an EF₂ resonant DC-DC converter in a PEMFC-based EV, thereby extending hybrid optimization techniques to a different application domain with distinct control objectives.
Although recent optimization-based and intelligent controller design methods have demonstrated improved control accuracy and dynamic performance, many are associated with increased computational complexity or have been developed primarily for PQ enhancement and converter control rather than PEMFC-based EV power conversion. Furthermore, most existing PEMFC-EV studies rely on conventional DC-DC converter topologies or hybrid energy storage architectures with relatively large battery capacities. To overcome these constraints, the suggested system combines a hybrid TSA-TLBO optimized PID-FOPID controller with a high-gain EF2 resonant DC-DC converter to improve voltage regulation, lower switching losses, improve dynamic response, and lessen reliance on high-capacity auxiliary battery storage. Table 1 presents a comparison of existing optimization and control methods for PEMFC-based EV applications.
The literature reviewed indicates significant progress in the development of PEMFC-based EV systems and their EM and control strategies. Nevertheless, several limitations remain in the existing approaches. In²¹, the research focuses on maximizing power extraction from PEMFCs using an optimized MPPT technique. Although the proposed approach improves energy utilization, it primarily addresses the FC side and does not comprehensively consider motor drive performance, torque ripple reduction, or overall vehicle dynamics. The approach described in²² presents an EM strategy based on deep reinforcement learning that integrates supercapacitor and battery storage devices. The dependence on hybrid energy storage raises system complexity, cost, and weight even as it improves system efficiency and component lifetime. In²³, convex optimization is employed to minimize vehicle energy losses; however, the computational burden may limit its practical implementation under rapidly changing driving conditions. The work in²⁴ presents a dual-source EV system using a high-gain interleaved SEPIC converter for PV-grid integration, but it does not address PEMFC dynamics or advanced intelligent controller optimization. The power-sharing strategy introduced in²⁵ effectively coordinates FC and battery power; however, it remains dependent on battery-assisted operation. Similarly, the hybrid EM approach in²⁶ improves system performance through multi-objective optimization but increases computational complexity and does not explicitly address converter-level dynamic performance. The hybrid JSO-RSA optimization strategy in²⁷ enhances battery charging and hydrogen utilization, yet it continues to rely on conventional converter architectures and battery-assisted designs. Recent developments have also demonstrated the growing application of AI and hybrid optimization techniques in power electronic systems. The comprehensive surveys presented in²⁸ and²⁹ summarize AI-based approaches for power electronic system design, intelligent control, predictive maintenance, and forecasting, highlighting the increasing importance of intelligent optimization in modern converter systems. In³⁰, a PSO-ANFIS-based controller is applied to a modified Boost-Cuk converter for battery-free EV traction, while³¹ suggests a GOA-HGCNN-based hybrid EM strategy for battery-free FCVs. Furthermore, Gangula et al.³² developed a self-learning neural network-based robust controller for DC-DC buck converters to improve voltage regulation under load disturbances. Hybrid metaheuristic optimization techniques have also been successfully applied to intelligent controller tuning for power electronic systems. Mishra et al.³³ employed IFGO to optimize a fuzzy-PID controller, Nanda et al.³⁴ utilized TLBO for adaptive fuzzy-PID tuning, Mishra et al.³⁵ presented an hPSOFA-optimized Type-2 FOPID controller, and Mishra et al.³⁶ introduced an hSCA-TLBO optimized IT2FPID controller. Although these methods demonstrate the effectiveness of hybrid optimization algorithms for controller tuning, they are primarily developed for PQ enhancement and active power filter applications rather than PEMFC-based EV power conversion. These research gaps motivate the present work, which integrates a high-gain EF₂ resonant DC-DC converter with a hybrid TSA-TLBO optimized hierarchical PID-FOPID controller to achieve improved voltage regulation, enhanced dynamic response, reduced torque ripple, reduced switching losses, and reduced dependence on high-capacity auxiliary battery storage in PEMFC-based EV applications.
FCVs when employed with large numbers of fuel stacks, can make the whole system to be expensive. Hence, as an alternate, this research work suggests use of FCVs locally powered by Hydrogen gas (H₂). This combination provides a good alternative to ICEs, by exhibiting higher efficiency. This could be possible as the tailpipe emissions are eliminated and only the water and heat are produced as outputs, adding to the environmental benefits. Thus, the feasibility of adopting the proposed hydrogen powered FCVs, their advantages in terms of reduced environmental impacts and operational costs³⁷ are showcased in this research work. To facilitate this work, two controllers namely PID and FOPID are also utilized, using which the torque ripple and speed of the PMSM motor can be controlled. To determine the best operating settings of the PID and FOPID controllers, hybrid TSA-TLBO algorithm is employed. This way of optimal fine-tuning helps in effectively controlling the vehicle torque and speed. As against the conventional system, the proposed method reduces the overall cost and size of the FC stack. Further, a steady voltage level to the PMSM fed drive is maintained under all the operating conditions with reduced dependence on high-capacity battery storage while maintaining stable operation. Introduction of EF₂ resonant converter to power the FCV helps in minimizing the fluctuations in the motor torque and enables the system to perform better under all scenarios, even under conditions of limited auxiliary energy storage. The overall configuration of the proposed FC EV system is illustrated in Fig. 1.
Schematic diagram of the proposed FCEV powertrain incorporating EF₂ resonant converter and PID-FOPID control strategy.
It is important to clarify that the proposed architecture does not assume a completely battery-free operation, but rather a system with reduced battery dependency supported by a minimal auxiliary energy storage element (e.g., a small battery or supercapacitor). This auxiliary unit is responsible for handling short-duration transient power demands, regenerative braking energy, and sudden load variations, which cannot be instantaneously supplied by the FC due to its slower dynamic response. Meanwhile, the FC operates as the primary energy source under steady-state conditions. The proposed hybrid PID-FOPID control strategy, together with the EF₂ resonant converter, ensures fast voltage regulation and mitigates transient fluctuations, thereby reducing the stress and size requirements of the auxiliary storage system instead of eliminating it entirely.
Although PEMFC-based EVs reduce reliance on large-capacity batteries, the inclusion of an auxiliary energy storage system remains essential. The dynamic response of the FC system is slow, and the battery’s transient response characteristics are important to meet transient load requirements, regenerative braking and battery system performance. This means that PEMFC EVs are usually configured as hybrid systems, with a fuel cell as the main energy source and the battery as a secondary energy buffer. However, the presence of a battery introduces additional weight, which is often considered a limitation. PEMFC EVs require much smaller battery capacity than conventional BEVs. For instance, while a typical BEV may require a battery pack in the range of 40–100 kWh (resulting in substantial weight), a PEMFC EV generally employs a much smaller battery (typically 1–10 kWh), thereby considerably reducing battery-related mass. Although the FC stack and hydrogen storage system add weight, the overall system benefits from improved energy density and faster refueling capability. Table 2 presents a comparison between BEV and PEMFC EV architectures, highlighting differences in battery size and associated weight.
This comparison indicates that, although PEMFC EVs include additional components such as the FC stack and hydrogen storage system, the significant reduction in battery capacity leads to a lower battery-related weight contribution compared to BEVs. Therefore, the overall impact of battery weight is effectively mitigated in PEMFC EV architectures. In the proposed EM framework, this limitation is further addressed by optimally coordinating the power sharing between the FC and the battery. The strategy reduces the peak load stress, thus lowering the required battery capacity, and efficiently manages transient conditions. As a result, the overall system achieves improved performance while limiting the impact of battery weight.
In the first step of FC EV modelling, the power necessary for different driving conditions must be calculated. From Eq. (1), it is clear that the performance of the vehicle relies on vehicle parameters like aerodynamic factors, acceleration, gravity forces and pitching.
where (V) represents velocity, (M) indicates vehicle mass, (A) represents acceleration, (rho) denotes air density, (C_{D}) indicates drag coefficient, (P_{AUXILIARY}) refers to auxillary power, (A_{J}) represents frontal area, (C_{RR}) refers to rolling resistance coefficient, (alpha) portrays slope, (P_{DEMAND}) denotes demanded power and (eta_{DRIVERTRAIN}) indicates drive train efficiency.
Systematic monitoring and accurate control of FC dynamics is necessary for effective EM in FCs. The equivalent circuit of the FC is depicted in Fig. 2, in which the voltage output is generated based on the imbalance between the voltage produced due to the chemical reaction and the reduction of voltage along their path ^38,39. The output voltage generated by the chemical reaction is influenced by various factors like FC type, oxygen pressure input, hydrogen pressure and operating temperature. Using Eq. (2), the generated voltage from chemical reaction can be determined.
where, (E_{NERNST}^{{}}) denotes nernst voltage, (alpha_{1}), (alpha_{2}), (alpha_{3}) refers to chemical reaction coefficients, (P_{H2}) represents hydrogen pressure, (P_{O2}) indicates oxygen pressure and (T_{ST}) portrays the FC’s operating temperature.
FC stack model.
The calculation of initial activation voltage using Eq. (3) necessitates computation of Eq. (4) that gives saturation concentration of oxygen gas. Adding to that, the values of activation capacitance and resistance are also required to be computed using Eq. (3). Post which, using Eqs. (5) and (6), the ultimate activation voltage can be determined.
where (V_{ACT}) denotes initial activation voltage, (xi) represents model fitting coefficient, (I_{FC}) depicts FC current and (C_{O2}) refers to the concentration of oxygen. The (C_{O2}) can be described using Eq. (4).
where, (p_{o2}) denotes oxygen pressure. The activation resistance, (R_{ACT}) can be described using below equation.
Activation capacitance ((C_{ACT})) is given by,
The superiority of EF₂ Resonant converters in delivering notable performance as against the conventional DC-DC converters makes them the optimal choice for WPT systems. With properly tuned quality factor, the resonant circuit will be capable of producing a significantly higher output voltage approximately about 10 times, with the lowest duty ratio of 0.5 and reduced impact on output current^3,40,41,42. Figure 3 demonstrates the EF₂ Resonant Converter circuit diagram consisting of stages like rectification, transformer coupling and inverter sections. The transformer shown in Fig. 3 is utilized as a high-frequency coupled energy transfer element rather than for galvanic isolation. Therefore, the primary and secondary reference nodes are intentionally connected, representing a common ground configuration consistent with the non-isolated EF₂ resonant converter topology⁴³. The proposed EF₂ resonant converter is implemented using a single-switch configuration. Hence, only switch S₁ is employed, and an additional switch (S₂) is not required. This simplifies the control structure while maintaining effective resonant operation.
Circuit diagram of class EF₂ resonant converter.
The voltage gain enhancement capability of the proposed EF₂ resonant DC-DC converter is achieved through the combined effect of resonant energy exchange and transformer action. In general, for any DC-DC converter, the power balance principle must be satisfied:
This implies that an increase in output voltage is typically accompanied by a corresponding adjustment in output current. Therefore, the statement of “gain boost without output current loss” is not strictly valid in an ideal sense and requires clarification.
In the proposed EF₂ resonant converter, the voltage gain can be expressed as:
where (n) represents the transformer turns ratio, (Q) is the quality factor of the resonant tank, and (f,left( w right)) denotes the frequency-dependent gain characteristic. At resonance, efficient energy exchange occurs between the inductive and capacitive elements, minimizing reactive power loss and reducing switching losses due to near ZVS operation.
The converter operates with high efficiency, and the majority of the input power is effectively transferred to the output. This leads to a condition where the output current does not experience significant degradation despite the increase in output voltage. The maximum efficiency of the converter in this study is approximately 90.7%, which shows that there is minimal power loss during the conversion process.
The selection of the EF₂ resonant converter in this study is motivated by its capability to achieve high voltage gain with reduced switching losses under low-duty-cycle operation, which is particularly suitable for FCEV applications with reduced battery dependency. Unlike conventional LLC resonant converters, which typically require operation near resonance and complex control strategies to maintain ZVS, the EF₂ converter provides a wider soft-switching range and maintains efficient operation even under varying load conditions. For instance, an LLC-based converter, such as the converter introduced in ⁴⁴ is very efficient and requires frequency control and complexity in the converter design to handle wide variations in input/output. The EF₂ topology inherently supports high step-up conversion with simpler control and reduced switching stress, making it more suitable for applications where the FC output voltage is relatively low and fluctuating. Moreover, the EF₂ converter allows fewer components and better power density because these measures are essential in compact EV powertrain design. Hence, the EF₂ resonant converter is chosen in this work since it is a balanced solution with high gain, less losses, and less complex implementation than traditional resonant topologies.
The proposed EF₂ resonant converter is being applied as a non-isolated topology which has its benefits as well as drawbacks to the FCEV. On an advantage perspective, non-isolated converters have less component count, lower conduction and switching losses, compact, and more efficient designs, so are appropriate in the low- to medium-power range, as well as in scaled prototype validation. These aspects are especially useful in this research as the emphasis here lies in the assessment of control performance and converter dynamics in the conditions of reduced battery dependency. Galvanic isolation is generally necessary in working FCEV systems to guarantee user safety, fault protection and EMC performance. In this respect, it can be considered that the use of non-isolated topology is a drawback in direct application to full-scale automotive systems. In response to this, it is possible to add on the proposed architecture, a high-frequency isolation stage, e.g. an isolated DC-DC converter, or transformer-based topology in future designs. Therefore, the non-isolated EF₂ converter used in this work should be interpreted as a simplified and efficient configuration for control validation and performance analysis, while its adaptation to real-world FCEV systems would require appropriate isolation mechanisms to meet safety and regulatory requirements.
The operation of converter can be considered as two different modes. Initially, S1 Switch is at off condition. Input current is provided to the L2-C2 and L3-C3 resonant tanks². Once the exchange of energy occurs among the two resonant tanks, the primary of the transformer will start experiencing voltage oscillations. The secondary side of the step-up transformer with 1:5 turns ratio, acquires the generated voltage. As a result, this secondary side voltage is rectified by the diode and used to supply power to the motor. This switch activation indicates the beginning of the second operation mode, where the inductor L1 starts charging. In this way of repeated actions, L2-C2 and L3-C3 resonant tanks involves in the exchange of energy, thereby replicating the operation of a DC-DC converter.
The proposed powertrain employs a three-phase VSI to convert the regulated DC-link voltage obtained from the EF₂ resonant DC-DC converter into AC supply for the PMSM. The inverter is configured as a conventional two-level, three-phase bridge consisting of six power semiconductor switches. These switches are operated using PWM to control the output voltage magnitude and frequency, enabling effective speed and torque regulation of the PMSM drive.
On the inverter side, the input voltage is represented as (left( {V_{in} } right)), output voltage as (left( {V_{Out} } right)), output power as (left( {kW} right)) and switching frequency as (left( {F_{s} } right)). The FC stack voltage available at the primary side of the coupling transformer can be increased up to 4 times, by properly tuning the resonant circuits. Further amplification can also be obtained by adjusting the transformer’s turns ratio⁴⁵.
The duty ratio (left( d right)) is assumed to be 0.5 and (Delta ,I_{Max} = 10,%) of the input current is taken as the maximum permissible ripple in the inductor current.
Here, the angular frequency can be computed by (omega_{s} = 2,pi ,F_{S})
Here, (I_{in}) indicates the input current whose value is 666.67 A.
The capacitance and their ratio value during maximum power transfer is
Let (f_{0} , = ,2f_{s}) and (omega_{o} , = ,2pi ,f_{0}), (f_{s}) denotes the resonant frequency.
Inside the FCV drive system, for a minimum of 10% fall in converter voltage, the power is drastically reduced by 20%, which may have a serious impact on the overall performance. Considering this issue, it is necessary to precisely model the dynamic behaviour of the converter and evaluate their operation stability, so as to achieve an enhanced performance. The proposed design of FCV incorporates all these aspects at every step.
The PMSM is modeled in the synchronous rotating reference frame (dq-frame), which enables independent control of torque and flux components. Since PMSM modeling is well established in the literature^{46,47,48,49,50,51,52,53}, only the final governing equations required for control design are presented here.
The stator voltage equations in the dq reference frame are expressed as:
where d and q axis stator voltages are represented by (v_{d}),(v_{q}), d and q axis stator currents are represented by (i_{d}),(i_{q}), d and q axis inductances are referred to (l_{d}),(l_{q}), electrical speed of rotor or the resistance per phase of stator winding is depicted as (r_{s}) and finally, the differential operation in indicated as (d).
The electromagnetic torque is given by:
The mechanical dynamics of the motor are represented as:
Here, (P) denotes the number of poles, (t_{e}) refers electromagnetic torque, (t_{l}) represents the load torque, (D) indicates the damping coefficient, (s_{m}) represents the rotor mechanical power and (j) depicts the moment of inertia.
For maximum torque per ampere operation, the direct-axis current (i_{d})​ is set to zero, which simplifies the torque expression and improves efficiency. The abc-dq transformation and its inverse are standard and are used for implementing vector control of the PMSM. These transformations are not detailed here for brevity. Parameters of the proposed EF₂ resonant converter are listed in Table 3.
Among the various power control techniques available for PMSM drives, vector control provides superior dynamic performance because of its ability to decouple torque and flux control. To design the hybrid PID-FOPID controllers accurately, an appropriate machine model is required. These controllers are generally susceptible to external disturbances such as load variations and parameter fluctuations. Hence, optimal tuning of the controller parameters is necessary to achieve an effective operating range. In this regard, the proposed TSA-TLBO approach effectively compensates for these disturbances and provides fast dynamic response with reduced torque ripple under varying driving conditions. The reference torque is generated by the speed controller according to the error between the reference speed and the measured speed^{3,53,54,55,56,57,58}. The optimization process is performed prior to system operation, and the obtained optimal controller parameters are subsequently used during simulation. Therefore, the proposed method does not involve online adaptation but rather an offline optimized control strategy designed to perform effectively under varying operating conditions. Figure 4 illustrates the speed and current control architecture of the proposed hybrid PID-FOPID controller.
Speed and current control using PID/FOPID controller.
The change in torque is described as,
The total torque change can be obtained by integrating the Eq. (20),
Here, (domega_{m} = omega_{m}^{*} – omega_{m}) represents the error difference between the reference speed and the actual speed. Further, the torque equation can be reframed as below, by application of laplace transform.
As shown in Fig. 4, the proposed hybrid PID-FOPID controller adopts a hierarchical cascade control architecture. The outer control loop employs a conventional PID controller for speed regulation, where the speed error between the reference and actual motor speeds is processed to generate the reference q-axis current. The inner current control loops employ FOPID controllers for both the q-axis and d-axis currents, providing accurate current tracking and improved robustness against parameter variations and external disturbances. In this hierarchical cascade configuration, the PID controller performs speed regulation, while the FOPID controllers regulate the motor currents, thereby improving voltage regulation, dynamic response, and torque ripple performance under varying operating conditions.
To justify the selection of the proposed EF₂ resonant converter, a quantitative comparison with commonly used resonant converter topologies, namely LLC and SRC, is presented in Table 4. The comparison is based on key performance metrics including voltage gain capability, efficiency, switching characteristics, dynamic response, control complexity, load adaptability, and suitability for FCEV applications. As shown in Table 4, the proposed EF₂ converter provides a higher voltage gain than the LLC and SRC converters, thereby reducing the requirement for a high transformer turns ratio and enabling a more compact converter design. In addition, the EF₂ topology exhibits reduced switching losses within its designed operating range, resulting in improved voltage regulation and enhanced dynamic response under varying load conditions. Although LLC converters can achieve high conversion efficiency, they generally require complex frequency modulation control and their performance is more sensitive to load variations. Similarly, SRC converters exhibit comparatively limited voltage regulation capability and slower dynamic response under changing operating conditions.
The maximum efficiency of the proposed EF₂ converter is 90.7% at 187 W, which is the scaled simulation model that was developed to validate the proposed TSA-TLBO optimized PID-FOPID control strategy. The reported efficiency is that of operation under the operating conditions studied here, but primarily considering the objective of increasing voltage regulation, dynamic response and reducing torque ripple, not just optimizing the converter hardware to maximize its efficiency. Although the efficiency is lower than that reported for some optimized high-power resonant converter implementations, the proposed converter demonstrates superior voltage gain, stable operation, effective transient performance, and reduced battery dependency under the considered operating conditions. Therefore, the proposed EF₂ resonant converter, together with the TSA-TLBO optimized PID-FOPID controller, provides an effective trade-off between conversion efficiency, dynamic performance, implementation complexity, and suitability for PEMFC-based EV applications.
While there are many benefits to the EF2 resonant converter, including a high voltage gain, low switching losses and better voltage regulation in the specified operating range, there are some drawbacks. Like traditional class-E resonant converters, the ZVS condition is not guaranteed for the entire operating range and the converter efficiency can drop under light load operating conditions because of departures from the optimum resonant operating point. But, in most normal driving situations, EV propulsion systems are required to run under medium to high load conditions, where the EF2 converter can effectively operate resonantly. Further, the proposed TSA-TLBO optimized PID-FOPID controller enhances voltage regulation and dynamic response in the investigated operating range which makes the EF2 resonant converter appropriate for the considered application even though it has light-load limitation.
For optimally tuning of the control parameters of the hybrid PID–FOPID controller, this proposed work is based on TSA–TLBO method. The main aim of this optimization technique is to reduce the tracking errors of speed and current in order to enhance voltage regulation, dynamic response, converter stability and torque ripple performance of the EV powertrain with a PEMFC. The motivation behind the use of the hybrid TSA-TLBO optimization algorithm is that the two types of metaheuristic techniques are used for controller parameter tuning as complementary. TSA has demonstrated good global search ability, which can be used to select the regions of the search space with good exploration efficiency, and avoid the problem of early convergence to local optimum. Unlike that, TLBO can effectively carry out local exploitation and parameter refinement without using any algorithm-specific control parameters so that it can achieve better convergence to the optimum solution. The hybrid TSA-TLBO algorithm is able to adaptively balance the exploration and exploitation more effectively due to the complementary properties of both the TSA and TLBO algorithms. Thus, the hybrid PID-FOPID controller shows a better voltage regulation, dynamic response, less torque ripple, and better converter stability under the different operating conditions. The details of the proposed TSA-TLBO optimization algorithm are presented in the following subsection.
TSA is one of the bio-inspired metaheuristic optimization techniques, whose behavioural model is derived from the swarm behaviour of the tunicates. This particular swarm behaviour enables the tunicates to persist effectively even at the depth of the ocean. Tunicates generally own the notable ability of locating sources of food in the sea. Two of their exceptional characteristics are their capacity to behave in swarms while seeking the food in marine ocean and proficiency in propelling themselves as jet. While tracing out the best food source, they combine these two characteristics. In this work, TLBO is incorporated to effectively enhance the performance of TSA behaviour. These together are expected to enhance the behaviour of the FC EV system. As the name suggests, the TLBO approach concentrates on creating the impact that a teacher does on a student. This is also a nature-inspired and a population-based technique, which searches the set of solutions and produces global solution. The group or class of learners are referred to as “population” in this approach. The TLBO approach progresses as Teacher in the first phase and as Learner in the second phase. In the first phase namely Teacher, the learner receives the knowledge from the teacher and during the second phase called Learner, there will be dynamic exchanges between the learner and the instructor^{59,60,61,62,63}. The overall workflow of the proposed TSA-TLBO optimization algorithm for tuning the PID-FOPID controller parameters is illustrated in Fig. 5. The flowchart provides a clear representation of the initialization, optimization, and convergence processes involved in the proposed method.
Flowchart of proposed TSA-TLBO approach.
The gain parameters of the PID controllers namely ((k_{p} ,k_{i} ,k_{d} )), gain parameters of FOPID controller namely ((K_{p} ,K_{i} ,K_{d} ,lambda ,mu )) and maximum iteration count will be the input vectors to the TSA. The position of the search agent can be computed by,
where, gravity force is indicated as (vec{g}), advection of water flow in the ocean depth is represented as (vec{f}) and the random numbers are denoted as (r_{1}) , (r_{2}) , and (r_{3}).
The initialized parameter of the random generation is best described by,
Here, (delta) implies (k_{p} ,k_{i} ,k_{d}),(K_{p} ,K_{i} ,K_{d} ,lambda ,mu)
In this step, each search agent is evaluated by computing its fitness using the objective function. The TSA-TLBO algorithm optimizes the PID-FOPID controller parameters by minimizing a weighted Integral Time Absolute Error (ITAE)-based objective function considering both the speed and current tracking errors. The objective function is defined as
where (e_{s} left( t right)) and (e_{i} left( t right)) represent the speed and current tracking errors, respectively, while (w_{1}) and (w_{2}) denote their corresponding weighting factors. In this study, equal weighting factors (left( {w_{1} = w_{2} = 0.5} right)) are selected to provide balanced optimization of both tracking objectives.
The speed and current tracking errors are calculated as
where (omega_{m}^{*}), (omega_{m}) represents the reference speed and actual motor speed, while (I_{dref}^{*}) and (I_{d}) denotes reference and actual current.
To reduce the conflicts among the search agents, i.e. the tunicates, the position of new search agent is determined using the vector (mathop Elimits^{ to }).
In these expressions, the Gravity Force is represented as (mathop Elimits^{ to }) , the Water Transportation in the deep ocean is depicted as (mathop Plimits^{ to }) and the societal interaction forces among search agents is denoted as (mathop Dlimits^{ to }). The (v{}_{1},v{}_{2}) and (v{}_{3}) are the random variable numbers, which is bound to the range of [0,1]. The (mathop Dlimits^{ to }) vector can be calculated as follows:
where (O_{Min}) and (O_{Max} ,) respectively indicates the primary rate and secondary rate of social contact. These (O_{Min}) and (O_{Max} ,) indices have a value of 1 and 4.
The random numbers denoted as A₁ and A₂ can be considered to have a value between 0 and 1. This will help in improving the reliability of TLBO by providing a quick convergence to the optimal solution.
(J_{R}) is the teaching factor used to fine tune the mean values. It generally takes the value of 1 or 2. The choice of (J_{R}) is done randomly using Eq. (35).
During the search process, whenever conflict is faced among the neighbours, the search algorithm eliminates this conflict and advances towards the best neighbour’s direction.
where (,mathop {OJ}limits^{ to }) represents the distance of tunicate from the food source, (Y) depicts the most recent version, and (mathop {PN}limits^{ to }) indicates the optimal position of the food source. The tunicate’s location is illustrated by the vector together with R. The range of the random integer is [0, 1].
The search agent starts moving towards the food source direction, which is the ideal search direction.
where, (mathop {O_{0} (Y,{prime} ),}limits^{ to }) denotes the time the tunicate was visible in connect with the food source (mathop {PN}limits^{ to }).
The position of the brokers is regularly updated and maintained, so that the foremost two solutions owing to the swarm activity of the tunicate, can be replicated statistically. The following equation is used to characterize the swarm behaviour of the tunicate.
The search agents in space can modify their search positions based on the value of (mathop {O_{0} (Y,)}limits^{ to }). In line with the tunicate location, the ultimate location can be determined and is found to be either cylindrical or cone shaped. Some of the important aspects of the proposed TSA algorithm are listed below:
(a) The confrontations happening among the search agents are prevented by (,mathop {E,}limits^{ to }),(mathop Slimits^{ to }) and (mathop Plimits^{ to }), thus enabling the solutions to act unpredictably and confined to the particular search area (b) (,mathop {E,}limits^{ to }),(mathop Slimits^{ to }) and (mathop Plimits^{ to }) vectors can be varied to derive enhanced phases of exploration and exploitation (c) The TSA Algorithm’s collective behaviour is characterized by swarm activity of tunicate and its jet propulsion nature, within a specific search space.
Check out for the terminating condition. On reaching the maximum iteration count, end the procedure else direct the control to Step 4.
The TSA-TLBO algorithm is executed offline during the controller design stage to obtain the optimal PID-FOPID controller parameters. The optimization was carried out in MATLAB R2020a using a population size of 30 and a maximum of 100 iterations, requiring an average execution time of approximately 18.6 s on an Intel Core i7 (3.40 GHz) computer with 16 GB RAM. The optimization is carried out offline when designing the converter so there is no extra computation during the operation of the converter. The optimized controller gains remain fixed during operation, making the online computational complexity comparable to that of a conventional PID-FOPID controller. The controller parameters are optimized under representative operating conditions and tested under load disturbances, and the results indicate a stable voltage regulation and an acceptable dynamic performance across the range of operation under test conditions. These results confirm the robustness and practical applicability of the proposed control strategy for the operating conditions considered in this study.
The proposed TSA-TLBO algorithm is employed solely for offline controller parameter optimization and addresses low-level converter and motor control rather than a standalone EM strategy. Therefore, the optimization is executed only during the controller design stage, while the optimized PID-FOPID gains are used during real-time operation.
For validation of the proposed system, the TSA-TLBO algorithm is demonstrated using MATLAB Simulation Software and their results are compared with that of conventional methodologies. The PMSM drive used in this study is regulated by employing both the PID and FOPID controllers. And these controllers’ system parameters are being tuned by TSA-TLBO approach.
Figure 6 illustrates the switching pulse waveforms of S1 and S2 generated using the PID-FOPID controller. It can be observed that the switches are triggered in a controlled manner to achieve near ZVS, thereby reducing switching losses and minimizing voltage stress across the devices.
Switching pulse waveforms of S1 and S2 generated using PID-FOPID controller.
Figure 7 illustrates the switching waveforms of the EF₂ resonant converter for switches S₁ and S₂. The resonant tank current assists in discharging the switch capacitances prior to the turn-on instant, which allows the switches to operate under near ZVS conditions during the steady-state operating region. However, during certain transient intervals, the voltage across the switches does not reach exactly zero before switching due to variations in resonant current and load conditions. Nevertheless, the resonant behavior significantly reduces switching stress and switching losses compared with conventional hard-switching converters.
Switching waveforms illustrating the quasi ZVS behavior of the EF₂ resonant converter: (a) ZVS condition of switch S₁ (b) ZVS condition of switch S₂.
Figures 8 and 9 provide the dynamic response of the DC-link voltage across capacitors C₁ and C₂ and the load voltage of the EF₂ resonant DC-DC converter. Voltages increase quickly and the steady-state voltages of about 95.5 V across the capacitors and 190 V across the load are achieved in a very short period of 2–3 s. This enhanced transient behavior is obtained by suitable tuning of the controller parameters and choice of the components of the system to provide a rapid and stable voltage control. The outcomes validate that the proposed converter offers a high enough DC-link voltage accumulation, and it can be used in the operation of an inverter with high reliability in EVs.
Dynamic response of DC voltage across capacitors C1 and C2 of the EF₂ resonant DC-DC converter under fast transient conditions.
DC-link load voltage response of the EF₂ resonant DC-DC converter showing rapid voltage regulation suitable for inverter operation.
Figure 10 illustrates the dynamic variation of operating conditions in the PEMFC-based system. Figure 10(a) presents the temperature variation applied to the FC stack, where the temperature changes from 330 to 300 K at 3 s, and later increases to 360 K at 5 s. Such variations are added to test the strength of the converter control in various conditions of thermal operation. Figure 10(b) shows the DC-link power response under load variation using PID and FOPID control strategies. When the load demand decreases around 5 s, the DC-link power drops accordingly, and when the load increases near 8 s, the system rapidly adjusts to the new operating point. The results indicate that the proposed control approach maintains stable power regulation and improves the power extraction capability of the PEMFC system under varying load conditions.
Dynamic analysis of operating conditions in the PEMFC-based power system: (a) Temperature variation applied to the PEMFC stack (b) DC-link power response under load variation using PID and FOPID control strategies.
The time-based variation of DC Link Power and Temperature are presented in Fig. 10. It can be observed that comparing the power extracted with EF₂ Resonant DC-DC Converter and that using PID-FOPID controllers, the latter seems to exhibit maximum power extraction.
The three-phase VSI operating under PWM control generates balanced AC voltages to drive the PMSM traction motor. Figure 11 illustrates the inverter phase voltages for phases A, B, and C. The VSI produces approximately 188 V peak line voltage, ensuring stable AC supply for the motor drive. The three subplots represent the individual phase voltages, which are phase-shifted by 120°, confirming proper inverter operation and balanced three-phase output.
Three-phase output voltages of the VSI using PWM control (a) phase A, (b) phase B, and (c) phase C.
The three phase VSI using split inductor depicts an amount of 188 V line voltage, which is visible in Fig. 12. Thus, VSI helps in synchronizing with the PMSM control.
Analysis of line voltage of VSI system using PWM.
Figure 13 represents the motor’s stator current waveform. Here, SVPWM technique is used for controlling the three-phase PMSM’s stator current.
Analysis of stator current of motor.
Figure 14 Speed response of the PMSM drive system: (a) transient response illustrating startup dynamics and initial oscillations, and (b) zoomed steady-state response highlighting speed stability. The PMSM speed rises smoothly from 0 rpm to the reference value of approximately 940 rpm within about 10–15 s, exhibiting a moderate overshoot of around 5–8% (peak ≈ 980–1000 rpm) due to transient electromagnetic torque dynamics. The first oscillations shown in Fig. 14(a) can be explained by the interaction between converter switching behavior and motor control response at the start-up; these oscillations quickly disappear by the proposed control strategy. The steady-state performance, as shown in Fig. 14(b), confirms that the motor speed stabilizes around 940 rpm with a very small ripple of approximately ± 2–3 rpm, demonstrating effective regulation, system stability, and physically realistic dynamic behavior suitable for practical EV applications.
Speed response of the PMSM drive system: (a) transient response illustrating startup dynamics and initial oscillations, and (b) zoomed steady-state response highlighting speed stability.
 × 10^–3.
The torque response of the PMSM is shown in Fig. 15 for the proposed control strategy. During the initial startup phase, significant oscillations are observed, with torque varying approximately between -25 Nm and + 30 Nm due to transient interactions between the converter, inverter, and motor dynamics. These oscillations gradually decay as the system stabilizes. The torque converges to a steady-state value of approximately 15 Nm after 120 s. The zoomed-in view of the steady state region (150–200 s) shows stable operation with low ripple (± 0.2 Nm), indicating good damping of the transient effects and accurate torque control.
Torque response of the PMSM: (a) transient response showing initial oscillations due to startup dynamics, and (b) zoomed steady-state response (150–200 s).
Harmonic analysis was performed at the three-phase inverter output supplying the PMSM, and the corresponding FFT results are presented in Fig. 16(a) and (b). The measured voltage THD and current THD are 0.21% and 1.78%, respectively. These low THD values indicate good output PQ at the inverter output and confirm the suitability of the proposed control strategy for PMSM drive applications.
Analysis of THD of (a) Output voltage (b) Output current.
Figure 17 presents the comparative evaluation of voltage gain characteristics of different DC-DC converter topologies as a function of duty cycle (D). The comparison includes the proposed EF₂ resonant converter along with conventional topologies such as LLC resonant, LCC resonant, and boost converters. The duty cycle is varied within the normalized range of 0.1 to 0.9. The proposed EF₂ resonant converter has a higher voltage gain in the entire range of operation in comparison with the rest of the converter topologies. The proposed EF₂ resonant converter has a higher voltage gain in the entire range of operation in comparison with the rest of the converter topologies. The resonant operation and optimized design is credited to this stronger performance and the ability to transfer more energy and minimize switching losses. The findings support the efficiency of the proposed converter in obtaining high voltage gain in an operating environment with different conditions.
Comparative analysis of voltage gain versus duty cycle for different DC–DC converter topologies, including the proposed EF₂ resonant converter, LLC resonant converter, LCC resonant converter, and conventional boost converter.
Figure 18 compares the convergence characteristics of the standalone TSA, standalone TLBO, and the proposed TSA-TLBO optimization algorithms using the same objective function. The TSA algorithm exhibits slower convergence due to its stronger emphasis on global exploration, whereas TLBO achieves improved convergence through its teacher-learner updating mechanism. The proposed TSA-TLBO algorithm combines the exploration ability of TSA and the exploitation ability of TLBO, which converges faster and achieves the lowest objective function value in the specified iterations. The results show that the proposed hybrid algorithm can be used to tune the PID-FOPID controller parameters with higher optimization efficiency, faster convergence speed, and better solution quality.
Convergence comparison of TSA, TLBO, and the proposed TSA-TLBO optimization algorithm.
Table 5 shows a quantitative analysis of dynamic performance of conventional PID, FOPID and the proposed TSA-TLBO optimized PID-FOPID control strategy under the same operating conditions. The conventional PID controller has a settling time of about 2.5 s, an overshoot of 12%, and a steady state error of 0.05 which shows that it has a slow response and is less stable. The performance of the FOPID controller is better, with steady state error of 0.03, overshoot of 8% and settling time of 1.8 s. The proposed method achieves a significantly lower settling time of 1.2 s, minimal overshoot of 3%, and steady-state error of 0.01, demonstrating superior transient and steady-state performance. Furthermore, the efficiency is improved from 85% (PID) and 88% (FOPID) to 90.7% with the proposed approach. These results clearly confirm that the observed improvements are directly attributable to the proposed TSA-TLBO optimization strategy integrated with the EF₂ resonant converter.
To further clarify the contribution of the proposed optimization strategy, the hybrid TSA-TLBO algorithm combines the complementary strengths of TSA and TLBO. TSA performs effective global exploration of the controller parameter search space, reducing the possibility of premature convergence, while TLBO refines the obtained solutions through efficient local exploitation to improve convergence accuracy. Consequently, the optimally tuned hierarchical PID-FOPID controller achieves faster transient response, lower overshoot, reduced steady-state error, improved DC-link voltage regulation, and reduced torque ripple compared with individually tuned PID and FOPID controllers. These performance improvements are consistent with the quantitative results presented in Table 5 and demonstrate that the principal contribution of the proposed work lies in the effective integration of hybrid TSA-TLBO optimization with the hierarchical PID-FOPID control architecture for the EF₂ resonant converter.
During the 187 W load step, the transient power demand is initially supported by the DC-link capacitor together with the auxiliary battery while the PEMFC gradually reaches the required operating point because of its inherently slow electrochemical response. The DC-link capacitor provides immediate energy to maintain the DC-link voltage, whereas the auxiliary battery assists in supplying the transient power until the FC output stabilizes. As shown in Table 6, the proposed system employs a DC-link capacitance of 2200 µF. The maximum DC-link voltage dip is limited to 2.3%, and the voltage recovers to its nominal value within 16 ms, demonstrating that the proposed TSA-TLBO optimized PID-FOPID controller effectively regulates the converter output and maintains stable DC-link voltage regulation and satisfactory dynamic performance during transient loading conditions.
In the present work, the term “reduced battery dependency” refers to reducing the reliance on the auxiliary battery for transient power support through improved voltage regulation and dynamic power delivery provided by the EF₂ resonant converter together with the TSA-TLBO optimized PID-FOPID controller. The primary objective of this study is to improve converter and motor drive control performance rather than to perform battery energy storage sizing. Therefore, the present work does not quantify the reduction in battery capacity (kWh) relative to a baseline configuration. Instead, the proposed approach demonstrates that improved converter regulation and faster dynamic response reduce the requirement for frequent auxiliary battery support under the simulated operating conditions.
A detailed validation scheme is included to ensure that the proposed control strategy is reliable and robust. The performance of the method is assessed by detailed simulation studies carried out under different operating conditions. The system is shown to be robust to such changes in load and operating parameters by performing a sensitivity analysis. The stability of the control strategy is guaranteed by optimal tuning of the controller parameters with the TSA-TLBO algorithm that is used to obtain a minimum oscillation and bounded system response under changing conditions. The system parameters, such as the gains of the controller, switching frequency and converter components are determined according to standard design rules and optimized for better dynamic response. Although experimental or hardware-in-the-loop validation is not included in the present study, it is considered as a future extension to further validate the practical applicability of the proposed system.
Although the proposed system is validated through MATLAB simulations, practical implementation of the EF₂ resonant converter and the hybrid PID-FOPID control strategy involves several hardware-level challenges that must be carefully addressed. The converter implementation aspect of the EF₂ resonant converter is the difficulty of designing the inductors and capacitors to maintain resonance at varying loads. The resonant frequency and overall system performance is subject to component tolerances, parasitic resistances and non-ideal switching characteristics. In addition, achieving consistent ZVS in hardware is more challenging due to switching delays and device non-linearities. The implementation of the hybrid PID-FOPID controller also introduces computational complexity. Real-time realization of fractional-order controllers requires approximation techniques such as Oustaloup filters, which increase memory usage and processing requirements. Therefore, the selection of an appropriate digital controller platform (such as DSP or FPGA) is critical to ensure stable and fast control execution. Thermal management is another important consideration. Switching frequencies and resonant operation can result in higher switching and conduction losses in semiconductor devices, requiring proper heat dissipation mechanisms to ensure the device’s reliable operation, including heat sinks or active cooling systems. Another important issue in high-frequency converters is electromagnetic interference (EMI). The fast switching transitions and resonant currents can introduce conducted and radiated EMI, which must be mitigated using proper shielding, filtering, and PCB layout techniques to comply with automotive standards. Despite these challenges, the proposed approach is particularly beneficial for low-to-medium power FCEV applications, scaled laboratory prototypes, and research-oriented powertrain validation platforms, where improved voltage regulation, reduced torque ripple, and enhanced efficiency are critical. The lower reliance on high capacity battery storage enables the system to be used for applications where weight and cost are critical to satisfactory dynamic performance. Future work will focus on hardware prototyping and experimental validation to further verify the feasibility and robustness of the proposed system under practical operating conditions.
This study presented a TSA-TLBO optimized hybrid PID-FOPID control approach to achieve better control performance of an EV powertrain using a PEMFC while reducing the reliance on batteries. The proposed approach enhances voltage regulation and dynamic response at the converter and motor drive levels. Simulation results indicate a maximum efficiency of 90.7% at an output power of 187 W. Additionally, harmonic analysis performed at the three-phase inverter output supplying the PMSM indicates voltage and current THD values of 0.21% and 1.78%, respectively, demonstrating improved PQ of the inverter output. Compared to conventional methods, the proposed strategy achieves better stability and reduced torque fluctuations under varying operating conditions. The reported output power level of 187 W corresponds to a scaled prototype model developed for validating the proposed control strategy and converter performance. This power level does not represent a full-scale FCEV, which typically operates in the kilowatt range. The proposed control framework is scalable and can be extended to higher power applications with appropriate system design modifications. Overall, the results confirm that the proposed method effectively enhances control performance and supports efficient operation of FC-based EV systems. The reduced battery dependency reported in this work refers to reduced reliance on the auxiliary battery for transient power support through improved converter regulation and dynamic response, rather than a quantified reduction in battery capacity.
Although the proposed TSA-TLBO optimized hybrid PID-FOPID control strategy integrated with the EF₂ resonant converter demonstrates improved performance in terms of voltage regulation, dynamic response, converter stability, and efficiency, the validation presented in this work is limited to MATLAB/Simulink-based simulations under representative transient operating conditions and load disturbances. The proposed study focuses on the design and optimization of the converter and motor drive control strategy rather than complete vehicle-level EM. Consequently, validation under standard EV driving cycles such as UDDS, NEDC, and WLTC has not been included, as it requires an integrated vehicle dynamics and EM model. In addition, the present work does not include experimental or hardware-in-the-loop validation. Future work will therefore focus on experimental verification, hardware implementation, and comprehensive evaluation under standard driving cycles to further demonstrate the practical applicability and robustness of the proposed control strategy for PEMFC-based EV applications.
The data that support the findings of this study are available on request from the corresponding author.
Fuel cell electric vehicles
Power electronic systems
Tunicate swarm algorithm
Remaining useful life
Teaching–learning-based optimization
Particle swarm optimization
Proportional-integral-derivative
Adaptive neuro-fuzzy inference system
Fractional-order proportional-integral-derivative
Space vector pulse width modulation
Elongation factor 2
Voltage source inverter
Total harmonic distortion
Hybrid graph convolutional neural network
Power quality
Gazelle optimization algorithm
Internal combustion engines
Hybrid shunt active power filter
Fuel cell vehicles
Robust extended complex Kalman filter
Fuel cells
Improved football game optimization
Proton exchange membrane fuel Cell
Sliding mode control
Electric vehicles
Voltage source converter
Switched reluctance motor
Kalman filter
Brushless direct current motor
Adaptive fuzzy PID controller
Permanent magnet synchronous motor
Shunt hybrid active filter
Maximum power point tracking
Hybrid particle swarm optimization-firefly algorithm
Unified firefly ersatz neural network
Type-2 fuzzy FOPID controller
Energy Management
Hybrid sine cosine algorithm-TLBO
Proportional-integral
Interval type-2 fuzzy PID
Single-ended primary inductor converter
Wireless power transfer
Photovoltaic
Zero-voltage switching
Hybrid energy storage systems
Electromagnetic compatibility
Jellyfish search optimizer
Pulse width modulation
Reptile search algorithm
Series resonant converter
Artificial intelligence
Electromagnetic interference
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Department of Electronics and Instrumentation Engineering, SRM Valliammai Engineering College, Chennai, India
Joe Marshell Manuel Raj
Department of Electrical and Electronics Engineering, Chaitanya Bharathi Institute of Technology, Proddatur, Andhra Pradesh, India
Mahesh Kumar Reddy Vennapusa
Department of Electrical and Electronics Engineering, Sri Krishna College of Engineering and Technology, Coimbatore, India
Sivaranjani Subramani
Department of Electrical and Electronics Engineering, Sri Eshwar College of Engineering, Coimbatore, India
Gunapriya Devarajan
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M.J – Conceptualization; Methodology; Writing V.M.K – Formal Analysis; Investigation; Reviewing S.S – Resources; Validation D.G – Supervision; Simulation.
Correspondence to Joe Marshell Manuel Raj.
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Manuel Raj, J., Vennapusa, M.K., Subramani, S. et al. Hybrid TSA-TLBO optimization of an EF₂ resonant DC-DC converter for energy-efficient fuel cell electric vehicles with reduced battery dependency. Sci Rep 16, 28588 (2026). https://doi.org/10.1038/s41598-026-69653-6
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Received: 08 January 2026
Accepted: 28 August 2026
Published: 14 September 2026
Version of record: 14 September 2026
DOI: https://doi.org/10.1038/s41598-026-69653-6
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