Design, Modelling and Control for a MW-level Hydrogen Converter

Design, Modelling and Control for a MW-level Hydrogen Converter | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 8 March 2025 V1 Latest version Share on Design, Modelling and Control for a MW-level Hydrogen Converter Authors : Rui Zhou , Fei Xiao , Jilong Liu [email protected] , Yufan Li , and Shanxu Duan Authors Info & Affiliations https://doi.org/10.22541/au.174143165.51605496/v1 319 views 173 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Water electrolysis is considered one of the most promising methods for hydrogen production using renewable energy sources (RES). In megawatt (MW)-level hydrogen production systems, a MW-level hydrogen converter is essential for interfacing the medium-voltage DC bus (MVDCB) with the electrolyzer. This paper proposes a novel hydrogen converter that incorporates a combined Input Series Output Parallel (ISOP) configuration, which offers several advantages, including a simplified topology, high voltage ratio, high energy efficiency, low output current ripple, and enhanced reliability. The design of the proposed hydrogen converter emphasizes the optimization of the snubber circuit, which plays a critical role in ensuring safe operation. To guide the design process, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is employed. Furthermore, an accurate model of the proposed hydrogen converter is developed to facilitate controller design, enabling power balance among the modules of this combined topology. This step is crucial to maintaining the stable operation of the hydrogen converter. Finally, experimental results are presented to validate the effectiveness of the snubber circuit design and the control strategy for the proposed hydrogen converter. not-yet-known not-yet-known not-yet-known unknown Design, Modelling and Control for a MW-level Hydrogen Converter Rui Zhou a, b, Fei Xiao b, Jilong Liu b, *, Yufan Li b, Shanxu Duan a a State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan, China b National Key Laboratory of Electromagnetic Energy, Naval University of Engineering, Wuhan, China * Corresponding author, E-mail address: [email protected] . ABSTRACT Water electrolysis is considered one of the most promising methods for hydrogen production using renewable energy sources (RES). In megawatt (MW)-level hydrogen production systems, a MW-level hydrogen converter is essential for interfacing the medium-voltage DC bus (MVDCB) with the electrolyzer. This paper proposes a novel hydrogen converter that incorporates a combined Input Series Output Parallel (ISOP) configuration, which offers several advantages, including a simplified topology, high voltage ratio, high energy efficiency, low output current ripple, and enhanced reliability. The design of the proposed hydrogen converter emphasizes the optimization of the snubber circuit, which plays a critical role in ensuring safe operation. To guide the design process, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is employed. Furthermore, an accurate model of the proposed hydrogen converter is developed to facilitate controller design, enabling power balance among the modules of this combined topology. This step is crucial to maintaining the stable operation of the hydrogen converter. Finally, experimental results are presented to validate the effectiveness of the snubber circuit design and the control strategy for the proposed hydrogen converter. Keywords: DC/DC converter, Electrolyzer, NSGA-Ⅱ, ISOP, modelling 1 Introduction Over the past few decades, fossil fuels, including coal, petroleum, and natural gas, have played a pivotal role in sectors such as transportation, industry, and electricity generation. However, with ongoing socioeconomic development, fossil fuels face significant challenges. On one hand, the growing demand for energy has led to a rapid depletion of fossil fuel reserves. On the other hand, their continued use contributes to greenhouse gas emissions, which significantly exacerbate global warming [1]. As a result, the development of alternative energy solutions has become an urgent necessity. In this context, hydrogen has garnered increasing attention due to its potential for zero greenhouse gas emissions [2]. Moreover, hydrogen possesses several key advantages, including high energy density, superior energy conversion efficiency, long-term storage capabilities, and suitability for long-distance transportation [3-4]. Hydrogen production can be achieved through various methods, including fossil fuel reforming, biological processes, and water electrolysis [5]. Among these, water electrolysis powered by renewable energy sources (RES) is widely regarded as the most promising and sustainable approach. Notably, water electrolysis offers an effective solution to address the power fluctuations, intermittency, and uncertainties associated with RES while enhancing their overall energy utilization efficiency [6-7]. This approach also mitigates issues such as wind curtailment and photovoltaic energy wastage. In a water electrolysis system integrated with RES, the electrolyzer is a crucial component responsible for converting electrical energy into chemical energy to produce hydrogen. Additionally, the hydrogen converter plays a vital role in interfacing the DC bus with the electrolyzer, thereby determining its operating point. In recent years, advancements in electrolyzer technology have enabled MW-level hydrogen production systems to become a viable solution [8]. However, these systems impose stringent requirements on hydrogen converters, including a high voltage conversion ratio-necessitated by the tens-of-kilovolts medium-voltage DC bus (MVDCB) voltage-low output current ripple, high energy efficiency, high current density, and enhanced reliability [9-10]. Recently, there has been a growing interest in DC/DC hydrogen converters for electrolyzer applications. Broadly, these converters can be categorized into two main types: isolated and non-isolated topologies [11-14]. Given the high voltage level of the medium-voltage DC bus (MVDCB) and the megawatt (MW)-scale power requirements of electrolyzers, this study focuses on isolated DC/DC converters due to their high insulation capability, which is essential for meeting safety standards. Initially, half-bridge and full-bridge isolated DC/DC converter topologies were proposed for hydrogen production [15-17]. While these topologies offer advantages such as high energy efficiency, simplified control, and a high voltage conversion ratio, they cannot be directly interfaced with the MVDCB, making them unsuitable candidates for MW-level hydrogen conversion systems. To address the requirements of the MVDCB and the need for high output current, research has been conducted on single-stage converters employing an input-series output-parallel (ISOP) structure. Specifically, hydrogen generator systems utilizing dual active bridge (DAB) or LCLCL modules have been investigated for MVDCB applications [18-19]. However, these configurations struggle to accommodate MVDCB fluctuations in off-grid hydrogen production systems. Consequently, two-stage converters with ISOP structures have gained increasing attention [20-21], yet they often fail to provide adequate output current regulation to meet electrolyzer operational requirements. To overcome these challenges, this paper proposes a novel two-stage DC/DC converter topology that integrates half-bridge switched-capacitor (SC) submodules in series with phase-shift full-bridge (PSFB) converters operating in parallel at the output stage. This design aims to achieve high voltage conversion ratio, high efficiency, and enhanced stability for MW-level hydrogen production systems. In the design of the proposed hydrogen converter, particular emphasis is placed on the optimization of the snubber circuit. Previous studies have systematically investigated the causes of spike voltages in rectifier diodes, identifying parasitic capacitances as the primary contributing factor [22-23]. However, these studies did not propose specific solutions to mitigate spike voltages. Additionally, while some works briefly discussed spike voltage phenomena, they lacked a comprehensive analysis of the complete switching interval [24]. To address this issue, the RCD snubber circuit was introduced to suppress spike voltages [25]. However, due to the conflicting relationship between spike voltage suppression and power loss, an optimal design methodology for the snubber circuit was not established, making it challenging to achieve simultaneous optimization of both objectives [26-28]. Accordingly, the main purpose of this work is to propose a novel topology for the DC/DC converter connected to the MVDCB, designed to meet the high requirements of the hydrogen converter. Furthermore, the operational principle of the snubber circuit and the optimization process of the design based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) are presented to ensure a balanced trade-off between voltage suppression and power loss minimization. In addition, another important aspect treated in this work is the controller design strategy using the accurate modeling framework to realize the low output current ripple. The remainder of this paper is organized as follows. Section II presents the proposed topology and the modulation strategy for the MW-level hydrogen converter. Section III outlines the parameter optimization design of the snubber circuit. In Section IV, the modeling and control strategies of the converter are discussed. Section V provides the experimental verification results. Finally, the concluding remarks are presented in Section VI. 2 Proposed topology and modulation method not-yet-known not-yet-known not-yet-known unknown 2.1 Proposed topology As is shown in Fig. 1, a MW-level off-grid hydrogen production system based on the water electrolysis with the use of RES is presented, where the voltage of the MVDCB can reach tens of kilovolt. However, the voltage of the electrolyzer is only several hundreds volt. Consequently, there is a high conversion ratio between the MVDCB and the electrolyzer. Therefore, the electrical isolation is necessary for the hydrogen converter. On the other hand, the hydrogen converter serves to provide power for the electrolyzer, the controller of the converter aims to control the current flowing through the electrolyzes, the starting and stopping of the electrolyzer and the other operations. In this study, we focus on the design and the control of the hydrogen converter. Fig. 1 The MW-level off-grid hydrogen production system. For the above reasons, the structure diagram of the MW-level hydrogen converter proposed in the paper is shown in Fig. 2. To be specific, the system is composed of the two parts, the former sub-converter includes n half-bridge SC submodules, and each SC submodule is connected in series to share the medium voltage. In addition, the later includes n PSFB submodules, whose outputs are in parallel. In other words, to increase the input voltage and the power of the hydrogen converter, an ISOP structure and the modular design are adopted in the topology. In summary, the benefits of the topology are presented as follows. a. The proposed hydrogen converter is a step-down DC-DC converter connecting the MVDCB with the electrolyzer. In this case, the voltage of the MVDCB is ±10kV, and the power of the converter is 5MW with 26 modules. b. A large voltage transition range could be obtained with the use of the high-frequency transformer. More importantly, it provides the high frequency electrical isolation between the medium voltage source and the electrolyzer loads. c. The proposed hydrogen converter has great flexibility with changing the number of the modules without modifying the plant owing to its modularity. d. The proposed hydrogen converter has excellent fault-tolerant capability and reliability. A continuous driving pulse could be given in the inferior tube of the SC submodules when a short-circuit fault occurs in the modules. In Fig. 2, U M represents the input voltage, namely MVDCB. U E represents the output voltage, namely the voltage of electrolyzer. i M and i E are the input current and the current of the electrolyzer, respectively. u Mn is the medium voltage for the SC submodule, and u MS is the sum of the medium voltage for the SC submodules. u Cn is output voltage of SC submodule, which is also the input voltage of the PSFB converter. L rn and C bn are the resonant inductor including the leakage inductor of the transformer, the DC-blocking capacitor, respectively. Tn is an independent high-frequency transformer. R cn, C cn, and D cn are the resistor, capacitor, and the diode of the clamping circuit, respectively. Lfn and Cfn are the filter inductor, the filter capacitor of the low-pass filter circuit, respectively. Q hbn 1 and Q hbn 2 are the switches of nth SC submodule. Qn 1-Qn 4 are the primary-side switches, and D rn 1- D rn 4 are the rectifier diodes of the secondary-switches. Fig. 2 Proposed circuit topology of the MW-level hydrogen converter. 2.2 Modulation Method To effectively decrease the current fluctuation and the volume of the inductor L MV , a multi-level modulation strategy (MMS) is adopted in the modulation method of the SC submodules. To be specific, the switches Q hb n 1 and Q hb n 2 work alternatively. In this case, the duty ratio of the upper switch is d s , and the duty ratio of the inferior switch is 1- d s . However, the switching states of the switches in same location of the SC submodules is different. In other words, the carrier phase pulse width modulation (CPS-PWM) is adopted, where there is a phase-shift angle 2π/ n between the adjacent SC submodules, and n is the number of SC submodules. Moreover, switching frequency f s of the SC submodules are same. To illustrate the MMS modulation method, two submodules are adopted as an example in Fig. 3(a). In Fig. 3(a), the phase-shift angle of the adjacent SC submodules is π within n =2. Importantly, the voltage fluctuation frequency of the inductor L MV is twice times as large as the switching frequency f s . As a result, the current fluctuation is reduced obviously within the MMS. It is noteworthy that there would be no current fluctuation when the duty ratio of the upper switch is 1/2. Obviously, the volume of the inductor L MV and its power loss could be effectively decrease within the MMS. (a) (b) Fig. 3 The modulation method of the proposed hydrogen converter. (a) The modulation method of SC submodules within different duty ratio. (b) The key working waveform of PSFB submodule n . Fig. 3(b) shows the key working waveform diagram of a PSFB submodule with the switching frequency f Ps . Among them, Q n is the PWM gate control signals sent to the IGBT, where there is a phase-shift angle between the leading-leg ang the lagging-leg. v ABn and v abn represent the midpoint voltage of the primary bridge arm, the midpoint voltage of the second bridge arm, respectively. i Drn represents the current through the rectifier diodes. v Dn 1 is the voltage of the rectifier diode D r n 1 . Moreover, to reduce the output current ripples, the CPS-PWM is also used, and there would also be a phase-shift angle π/ n between the PSFB submodules considering the frequency of the filtering inductors is twice as much as the switching frequency f Ps . not-yet-known not-yet-known not-yet-known unknown 3 Parameters optimization design of snubber circuit 3.1 Working principle of the snubber circuit For the time interval [0-t 1] in Fig. 3(b), the equivalent circuit referred to the primary side is presented in Fig. 4. Uin represents the input voltage of the PSFB converter. L rn is the sum of the leakage inductances. represents the junction capacitance of the rectifier diode D rn 1, whose voltage is referred to the primary side. In this time interval, the current through the filter inductor Lfn can be considered constant, and the filter inductor is replaced by a constant current source. Moreover, it should be noted that the snubber circuit does not participate in the resonance because the voltage of snubber capacitor is larger than that of the junction capacitance. Fig. 4 The equivalent circuit model in the time interval [0-t 1]. The equations describing the equivalent circuit in Fig. 4 can be given by In addition, the boundary condition in the time 0 is expressed as where K is the transformer ratio, is the output current of a PSFB submodule, and is the current ripple of the filter inductor. Therefore, with Eq. and, the voltage referred to the secondary side, the current flowing through the leakage inductor can be derived as where, . At the end of the time t 1, the voltage of the junction capacitance is equal to the minimum voltage of the snubber capacitor, which means . From Eq., the time t 1 can be calculated as Furthermore, the current flowing through the leakage inductor can be rewritten as, where . For the time interval [t 1-t 2] in Fig. 3(b), the snubber capacitor and the junction capacitance would participate in the resonance. Owing to, is satisfied. In this case, the equivalent circuit referred to the primary side is presented in Fig. 5. Fig. 5 The equivalent circuit model in the time interval [t 1- t 2]. The equations describing the circuit from Fig. 5 can be given by, the boundary conditions in the time t 1 are derived in Eq. (5) and. After mathematical manipulation of Eq. (6), the voltage of the snubber capacitor referred to the secondary side and the current flowing through the leakage inductor can be calculated as, where, and. At the end of the time t 2, the voltage of the snubber capacitor reaches its maximum value, which indicates that the resonant energy of the leakage inductor has been transferred into the snubber capacitor. As a result, the following equivalent relationship can be easily obtained., where . Solving the Eq., t 2 can be derived. In this case, the spike voltage of the snubber capacitor can be obtained with Eq. . As mentioned above, the charging energy of the snubber capacitor in the time interval [t 1-t 2] can be expressed by . From the time t 2, the snubber circuit would step into the discharging stage, and the diode D S is reverse biased. For the time interval [t 2-t 3] in Fig. 3(b), a new resonant circuit including the leakage inductor, the junction capacitance of the rectifier diode and the parasitic resistance of the resonant loop is operating. On the other hand, the snubber capacitor can be regarded as a voltage source, whose capacitance is much larger than that of the junction capacitance. Also, the output voltage of the rectifier bridge is, which can be regarded as a voltage source. Therefore, the equivalent circuit model in the time interval [t 2-t 3] referred to the secondary side is shown in Fig. 6. Fig. 6 The equivalent circuit model in the time interval [t 2-t 3]. In Fig. 6, represents the voltage of the snubber capacitor, and is acceptable for its very little changing. The discharging current of the snubber capacitor is derived as follows. . Furthermore, the discharging energy of the snubber capacitor in the time interval [t 2-t 3] can be given by, where can be easily calculated from Fig. 3(b). For the time interval [t 3-t 4] in Fig. 3(b), the secondary side of the transformer is in the short circuit status. There are two reasons for this case, first, the PWM gate control signal sent to Q 2 is turned off, while the PWM gate control signal sent to Q 3 is turned on. Therefore, the two sides of the transformer are in the short circuit status. Moreover, the duty ratio loss of the secondary side is the other reason for the short circuit status. The equivalent circuit model corresponding to this time interval is presented in Fig. 7. Fig. 7 The equivalent circuit model in the time interval [t 3-t 4]. The equation describing the circuit in Fig. 7 can be obtained as follows. . Similarly, the discharging energy of the snubber capacitor in the time interval [t 3-t 4] can be calculated as, where . As mentioned above, energy conservation law of the snubber capacitor in the half of the switching period, the following equivalent relationship is easily obtained, where the snubber resistor RS can be derived. . Based on this, the power loss of the snubber resistor in the discharging stage can also be calculated as . 3.2 Optimization design of the snubber circuit Based on the working principle of the snubber circuit proposed above, the spike voltage of the snubber capacitor U Cmax and the power loss of the snubber resistor P s can be obtained with Eq., Eq., respectively, if the capacitance of the snubber capacitor C s and its minimum voltage are regarded as the two independent variates. On the one hand, spike voltage U Cmax plays an important role in the safe operation of the rectifier diodes. On the other hand, the power loss P s is considerable with numerous modules, which has influence on the efficiency of the hydrogen converter. Therefore, from the viewpoint of the optimization design of the snubber circuit, there are two optimization targets, spike voltage U Cmax and the power loss P s , which are the smaller the better. Furthermore, three-dimensional diagrams of the spike voltage U Cmax and the power loss P s varying with the snubber capacitor C s and its minimum voltage are respectively presented in Fig. 8. (a) (b) Fig. 8 Three-dimensional diagram of the spike voltage U Cmax and power loss P s varying with the snubber capacitor C s and its minimum voltage, respectively. (a) Spike voltage U Cmax varying with the snubber capacitor C s and its minimum voltage . (b) Power loss P s varying with the snubber capacitor C s and its minimum voltage . From Fig. 8, it’s clear that the spike voltage U Cmax decreases with the increase of the snubber capacitor C s and the decrease of the minimum voltage, while the power loss P s is quite opposite. In other words, there is a conflict between the two optimization targets. Specifically, if the spike voltage U Cmax is a constant, many data sets including the snubber capacitor C s and its minimum voltage could be obtained, like the Line 1 or Line 2 in Fig. 8(a). However, it’s a difficult work to get the smallest power loss P s among the data sets. Therefore, the minimization of the spike voltage U Cmax and the power loss P s is treated as a multi-objective optimization problem to resolve the conflict between the two optimization targets. Based on the above analysis, the non-dominated sort genetic algorithm-Ⅱ (NSGA-Ⅱ) based on the elite strategy is employed to optimize the snubber capacitor and the snubber resistor to minimize the spike voltage U Cmax and the power loss P s for its good performance in solving the multi-objective optimal problems. The detailed implementation is presented as follows. (1) Initialization Let the population size be 100, the iteration times is 200, the range of the snubber capacitor C s is [0.6, 4], and the range of its minimum voltage is [951, 1100]. The crossover ratio is 0.9, instead, the mutation ratio is 0.1. Moreover, the initial population can be obtained as follows for its diversity. , where i =1, 2 represents the two different independent variables, and is a random variable from 0 to 1. (2) Fast nondomination sorting and Crowding distance calculation The chromosomes of offspring groups and parents are sorted with the fast non-dominated solution, where the population is layered sorted to different ranks determined by their own objective value. Besides, the crowding distance of i th individual is presented as follows. , where is the objective function value. (3) Selection, crossover and mutation First, the selection is operated based on the individuals, who has larger front number and the larger crowding distance with the same Pareto front number. Second, the crossover is the core of the population evolution. Similar with the biological evolution, the filial generations can be generated by swapping a gene segment among the parental generations. A simulated binary crossover is employed to generate the filial generations as follows [28]. , where and are the filial generations, and are the parental generations, is a random variable. Third, the main purpose of the mutation is to increase the diversity of solutions, which can effectively prevent the population evolution from falling into a local optimum. Furthermore, the polynomial mutation operation is given by , where is a random variable from 0 to 1 and is the cross index, a nonnegative real number. Moreover, it needs to be indicated that the new parameters generated by the crossover or mutation are constrained by the set boundary. (4) Elite retention The main aim of the elite retention is to preserve the better candidate solutions from the parental generations to the filial generations. Specifically, the new generations can be obtained by combining the parental generations with the filial generations. Then, the new parental generations are got based on the calculations of the nondomination sorting and the crowding distance. Fig. 9 The Pareto front of the NSGA-Ⅱ. Fig. 10 Flowchart of the optimal design of the snubber circuit based on the NSGA-Ⅱ. Based on the above optimization process, the Pareto optimal solutions obtained is shown in Fig. 9. Differently from the single-objective optimization algorithm, the NSGA-Ⅱ gives a set of the Pareto optimal solutions as the optimal solution set instead of an absolute optimal solution, where all solutions are mutually non-dominant. Since the two optimal objectives, the spike voltage and the power loss have equal importance, a trade-off parameter in Fig. 11 can be selected as a guidance of the snubber circuit design, where the snubber capacitor and the snubber resistor are calculated as 3μF, 1kΩ, respectively. Furthermore, the flowchart of the specific optimization process of the snubber circuit based on NSGA-Ⅱ is presented in Fig. 10. 4 Control strategies The design of the control strategies is a crucial step to ensure the stable operation of the hydrogen converter. Firstly, the hydrogen flow rate is sensitive to the current density through the electrolyzer. Secondly, the MVDCB voltage variation is inevitable because the system is disconnected with the power grid. Therefore, it’s important for the controller to regulate the current through the electrolyzer to its reference despite the operation point variation of the MVDCB. Thirdly, the interleaving technology is introduced to enhance the power level of the electrolyzer. For this reason, the controller should ensure the current sharing between the different modules. 4.1 Converter modeling Fig. 11 Equivalent circuit of the SC submodules Fig. 11 shows the equivalent circuit of the SC submodules. The voltage U M represents voltage of MVDCB. The inductor L MV is physically modelled as the inductance L MV , whose parasitic resistance connected in series is R L . The resistor R eqn represents the equivalent loads of the converter. The current i dn represents the current fluctuation of the load. Moreover, the current flowing through the inductor L MV is i M . represents the voltage of the capacitors C in n , whose current is regarded as i SM n . Note that the Q hb i 2 is controlled in the control of the SC submodules, and the duty is represented by . From Fig. 11, the mathematical model without the phase-shift angle can be given by , Therefore, the average state space model can be given by , where the input variables are defined as, and the state variables are defined as . Based on the average state space model in Eq. (22), the following transfer function matrix can be obtained. . . (23) To verify the correctness of the modelling method of SC modules, we take N =2 as an example. From Eq. (23), the transfer function from the duty to the current of the inductor L MV is derived by , where U C , I MV , D M represent the steady-state values. Additionally, the transfer function from the duty to the voltage of the capacitor C in n is also given by To demonstrate the effectiveness of the modelling method, the comparisons between the bode graph with the frequency sweep function in the Simulink and the bode graph of the transfer functions derived in Eq. (24) and (25) drawn by MATLAB software are shown in Fig. 12. The system parameters are given in Tab. 1. Tab. 1 Simulation parameters. Input voltage, U M 1600V Output current, I E 800A Inductor, L MV 3mH Parasitic resistor, R L 0.1Ω Equivalent resistor, R eqn 4.6Ω Capacitor, C in 420μF×6 Steady-state current value, I MV 271.6A Steady-state duty, D m 0.2 Steady-state voltage, U C 1000V DC-blocking capacitor, C b 500μF Leakage inductance, L r 53μH Transformer capacity, S T 320kVA Transformer ratio, K 1.25:1 Filtering inductor, L f 260μH Filtering capacitor, C f 420μF×2 Equivalent load 0.68Ω Switching frequency of SC submodules 1kHz Switching frequency of PSFB submodules 2kHz not-yet-known not-yet-known not-yet-known unknown (a) (b) Fig. 12 The comparisons between the simulation model and the calculated model. (a) Transfer function . (b) Transfer function . As it can be observed in Fig. 12, the frequency ranges are from 10Hz to 500Hz, which is half of the switching frequency. It’s clear that the amplitude-frequency curves and the phase-frequency curves obtained by the mathematical models and frequency sweep function in the Simulink are almost overlapped, which can prove the accuracy of the mathematical model. In addition, the state-average model of the PSFB converter is given as, where and R represents the equivalent resistance of the electrolyzer. Therefore, the transfer function from the duty to the current of the filtering inductor is easily derived by . In recent years, many research works have been carried out about the modelling of the PSFB converter [29]. Therefore, the correctness verification of the Eq. (27) is omitted due to the length of the content. The focus is concentrated on the controller design as follows. 4.2 Controller design The mathematical models and transfer functions of the converter have been obtained as mentioned above. Obviously, it would be unstable without the controller. Hence, the controller design is carried out to ensure the closed loop system stable in the subsection. The control strategies are presented in Fig. 14. Fig. 13 The diagram of the proposed control strategies. In Fig. 13, the control objective of the SC submodules is to realize the voltage balance of the SC submodules and dynamic performance of the control. Specifically, the voltage outer loop controller takes the difference value between the sampled average voltage and the set reference value to its PI controller, whose output value is the reference value of the inductor L MV to improve the dynamic performance of the control. Furthermore, the output of the current inner loop is the common duty of the half-bridge. In addition, the output of the average voltage loop is to modify the common duty based on the realization of the voltage balance. As for the control of the PSFB, the current control is employed to realize the power control of the electrolyzer, where the average current loop is used to ensure the current balance between the PSFB submodules. Note that the following rules are followed during the progress of designing the controller. a. Bandwidth: B ≥ f s (switch frequency). b. Type of the system: 1. c. Gain margin: m g ≥ 8dB. d. Phase margin: m g ≥ 45°. Furthermore, the bode graph of the open-loop transfer function, and without and with the PI controllers are presented in Fig. 14, respectively. (a) (b) (c) Fig. 14 The bode graph of the open-loop transfer functions without and with the PI controller. (a) Transfer function . (b) Transfer function . (c) Transfer function . From Fig. 14, it can be observed that the control requirements are satisfied to obtain the different values of K p and K i . 5 Experimental verifications To verify the effectiveness of the theoretical analysis of the snubber circuit and the control strategies, the following experiments have been performed. The experimental test bench with two modules set up for this work is shown in Fig. 15, whose power reaches 420kW. The experimental parameters are listed as Tab. 2. Tab. 2 Experimental parameters IGBT FF600R17ME4 Rectifier diode and snubber diode DD300HF170T1WH Input voltage, U M 1600V Output current, I E 800A Inductor, L MV 3mH Capacitor, C in 420μF×6 DC-blocking capacitor, C b 500μF Leakage inductance, L r 53μH Transformer capacity, S T 320kVA Transformer ratio, K 1.25:1 Filtering inductor, L f 260μH Filtering capacitor, C f 420μF×2 Equivalent load 0.68Ω Switching frequency of SC submodules 1kHz Switching frequency of PSFB submodules 2kHz Fig. 15 Develop experimental test bench with two modules of the hydrogen converter 5.1 Verification of the analysis of the snubber circuit To prove the correctness of the theoretical analysis of the snubber circuit, two cases with different snubber circuit parameters have been carried out. For simplicity, it is achieved by comparing the numerical results of the spike voltage with its experimental results, which is presented in Tab. 3, and the experimental results are shown in Fig. 16. (a) (b) (c) Fig. 16 The experimental results with different snubber circuit parameters. (a) C s = 3μF, R s =833.3Ω. (b) C s = 3μF, R s =1153.8Ω. (c) C s = 3μF, R s =5.0kΩ. Tab. 3 The comparison between the numerical results and the experimental results with different snubber circuit parameters. not-yet-known not-yet-known not-yet-known unknown Rs Cs UCmax Rs Cs UCmax Case 1 3μF 1083.4V 3μF 1096.0V 1.15% Case 2 3μF 1150.7V 3μF 1118.0V 2.92% Case 3 4μF 1391.9V 3μF 1357.0V 2.65% The spike voltage of three different cases with the different snubber circuit parameters are compared between the theoretical results and the experimental results in Tab. 3. It’s clear that the errors between the theoretical values and the experimental values of the spike voltage do not exceed 3%, which shows the effectiveness and the reliability of the analysis method. In addition, the errors mainly come from the parameters errors of the snubber resistors and the capacitors. 5.2 Verification of the control strategies The effective design of the control strategies is necessary to ensure the stability of the converter and regulate the operation point of the electrolyzer. Based on the above developed experimental test bench, the steady-state operation of the hydrogen converter has been performed based on the previous control strategies. The experimental results are presented as follows. (a) (b) (c) (d) (e) (f) Fig. 17 Experimental waveforms of the hydrogen converter with N =2 under the control strategies. (a) Current waveforms of the inductor L MV . (b) Voltage waveforms of the capacitor C in . (c) Current waveforms of the transformers at the primary side. (d) Current waveforms of the filtering inductors. (e) Current waveforms of the total output. (f) Current waveforms of the alternating component in the total output. To confirm the proposed control strategies, experimental tests have been carried out. Fig. 17 shows the experimental waveforms of the hydrogen converter acquired during the steady-state operation. Specifically, it shows the current waveforms of the inductor L MV in Fig. 17(a), and the pulsation frequency of the inductor current is twice as that of the switch frequency of the SC submodules, which indicates the CPS-PWM can effectively decrease the current fluctuation of the inductor. From Fig. 17(b)-(d), the voltages and currents of the two modules are equal, which reflects a well voltage and power balance among the two modules under the control strategies. Additionally, the waveforms of the total output current are presented in Fig. 17(d). it’s clear that the output current ripple ratio is less than 1% within the MMS. To improve the efficiency of the hydrogen converter, the zero-voltage soft switching (ZVS) technology has been also employed except for the optimization design of the snubber circuit. Fig. 18 shows the waveforms of the drive signal and the voltage of a IGBT on the lagging-leg. It’s clear that the ZVS technology is realized. In this case, the ZVS technology of the leading-leg is also easily obtained. Furthermore, the measured efficiency of the experimental prototype is presented in Fig. 19 employing the power analyzer LMG671. Fig. 18 Experimental waveforms of the drive signal U GE and the IGBT voltage U CE on the lagging-leg. Fig. 19 The efficiency of the hydrogen converter for different output power. 6 Conclusions The hydrogen converter plays a critical role in hydrogen production systems by enabling efficient energy transfer from the medium-voltage DC bus (MVDCB) to the electrolyzer. This paper presents a novel MW-level hydrogen converter topology that offers a high conversion ratio, enhanced reliability, and superior efficiency, making it well-suited for MW-level green hydrogen production applications. The design of the proposed hydrogen converter, including the optimization of snubber circuit parameters, is conducted using the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), providing a systematic approach to snubber circuit design. Additionally, advanced control strategies are developed to ensure voltage and power balance among the converter modules, based on an accurate modeling framework. Experimental results validate the effectiveness of the optimized snubber circuit design and demonstrate the excellent control performance of the proposed hydrogen converter. Acknowledgements This work was supported by the National Natural Science Foundation of China under Grant (52177202). References [1] Yue M, Lambert H, Pahon E, et al. 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Keywords dc/dc converter electrolyzer isop modelling nsga-ⅱ Authors Affiliations Rui Zhou Huazhong University of Science and Technology State Key Laboratory of Advanced Electromagnetic Technology View all articles by this author Fei Xiao Naval University of Engineering School of Electrical Engineering View all articles by this author Jilong Liu [email protected] Naval University of Engineering School of Electrical Engineering View all articles by this author Yufan Li Naval University of Engineering School of Electrical Engineering View all articles by this author Shanxu Duan Huazhong University of Science and Technology State Key Laboratory of Advanced Electromagnetic Technology View all articles by this author Metrics & Citations Metrics Article Usage 319 views 173 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Rui Zhou, Fei Xiao, Jilong Liu, et al. Design, Modelling and Control for a MW-level Hydrogen Converter. Authorea . 08 March 2025. 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