Research Article  Open Access
Ayiguzhali Tuluhong, Weiqing Wang, Yongdong Li, Haiyun Wang, Lie Xu, "Research on Modelling and Stability Characteristics of Electric Traffic Energy System Based on ZVSDAB Converter", Journal of Electrical and Computer Engineering, vol. 2020, Article ID 5450628, 10 pages, 2020. https://doi.org/10.1155/2020/5450628
Research on Modelling and Stability Characteristics of Electric Traffic Energy System Based on ZVSDAB Converter
Abstract
We study and describe mostly used traditional simplified circuits for fullbridge Zero Voltage SwitchingDual Active Bridge (ZVSDAB) converter and deduce their mathematical model. On this basis, we propose a highfrequency (HF) mathematical model, which takes into account conduction loss and HF characteristics of the ZVSDAB converter model. We compare the static and dynamic stabilities of the traditional and the proposed HF mathematical model by simulation. Finally, the highfrequency planar transformer (HFPT) with good heat dissipation and the wide band gap (WBG) semiconductor SiC switches with fast switching speed are employed to build a 4.4 kw, 40 KHz experimental prototype to verify the effectiveness of the improved HF circuit of ZVSDAB converter. The results show that the proposed HF mathematical model is superior to the traditional one, and it fully considers the HF characteristics of the circuit and effectively improves the HF oscillation, DC bias, and waveform distortion of the ZVSDAB converter.
1. Introduction
Energy crisis and environmental pollution are two major social problems facing the world today, and vehicle exhaust, as traffic pollution, is one of the main culprits of environmental pollution [1]. With the development of electric transportation technology, traditional fuel transportation as an important way of nonrenewable energy consumption is gradually replaced by new energy transportation. Electric vehicles, multielectric aircraft, maglev highspeed trains, and vacuum highspeed trains, as representatives of new energy vehicles, do not rely on fossil fuels, but also have little environmental pollution. In the field of electrified transportation, more and more power electronic equipment and power supply system are being pursued to be miniaturized in size and light in weight. This trend has made new energy transportation power supply system, power electronic transformer (PET), which has become an important development direction of power electronic industry [2–4]. As one of the important parts of new energy transportation and the hub of the smart grid and the energy Internet, PET can improve the power density and reduce the volume and weight of power supply after high frequency (HF).
Compared with the same power level Sibased MOSFET, the wide band gap (WBG) semiconductor device, SiCbased MOSFET, has the advantages of fast switching speed and small on resistance, which will reduce the core volume, improve the working frequency of the transformer, reduce the system weight and volume, improve the energy density and system efficiency, and accelerate the HF development of PET. At present, the price of WBG semiconductor switches is decreasing every year, and it has begun to replace the market of Sibased switches. It is an inevitable trend to replace Sibased switches with WBG switches, such as SiC [5, 6]. In order to improve the efficiency of PET, the isolated DCDC converter with soft switches is generally used. The isolated DCDC converter can be divided into nonresonant dual active bridge (DAB) and resonant mode (LLC) converters. The performance comparison between DAB and LLC converters is shown in Table 1. In 1991, German scholar Rik W. Doncker put forward the concept of DAB, which can realize the controlled power transmission on both sides of the isolation transformer by phaseshifting control and then become one of the key core technologies of power electronic transformer [7].

By the end of the twentieth century, Chinese researchers developed a 2 kw power supply independently, and it was used in the field of communication with the phaseshifting full bridge soft switching technology, the module efficiency was 93%, and the weight of the product with PWM technology was fully reduced by 40%. Because the phaseshifting full bridge ZVSDAB converter can complete the conversion of large and medium power at HF and has high efficiency, simple structure [8], and good dynamic characteristics, it has attracted great attention of scholars in the power supply field at home and abroad in recent years [9–12].
In this paper, a new SiC device is used, and the proportion of PET’s turnoff loss in the total loss of the system is very low, so it is more economical to choose DAB converter. In addition, the utility of high frequency planar transformer (HFPT) in ZVSDAB has also accelerated the HF development and volume miniaturization of the PET [13, 14]. However, there are some disadvantages in the application of WBG and HFPT in ZVSDAB, such as HF oscillation, HF loss, and DC bias, which make the system unstable, and it needs to be solved. The oscillation is caused by the parasitic parameters of ZVSDAB, such as parasitic inductance and capacitance of semiconductor devices, HFPT, as well as PCB at HF [15]. In view of this, in reference [15], scholars have analyzed that the HF parasitic capacitance of HFPT causes serious distortion of the light load current and voltage waveforms of the LLC converter and brings regulation issues for the converter. In essence, the parasitic capacitance of HFPT can be reduced, and the output waveform can be reached stable by improving the transformer structure. In [16], researchers eliminate the HF oscillation in ZVSDAB via optimizing dv/dt, so as to achieve system stability. In addition to these problems, HF also causes DC bias. In [17], the deviation between the transient current and the steadystate current caused by the DC bias is discussed, and the transient phaseshifting strategy is adopted to eliminate the transient DC bias.
Generally, in order to simplify the calculation, the theoretical and simulation analysis of the ZVSDAB converter is generally carried out. Although the simulation results are consistent with the experimental results, some errors still occur. In this paper, in order to avoid errors and fully reflect the HF characteristics of the ZVSDAB converter, we study nonmechanism models of the ZVSDAB converter and propose a HF mathematical model for the ZVSDAB converter, which fully considers turnon loss and HF characteristics of the ZVSDAB converter such as oscillation, parasitic capacitance, and inductance in the electrified transportation energy system. This structure is organized as follows: Section 2 introduces three simplified circuit topological models of the ZVSDAB converter briefly. In Section 3, their mathematical models are deduced, respectively. Then, on this basis, section IV analyzes and compares the static and dynamic stability characteristics of the traditional ZVSDAB converter model and the proposed HFZVSDAB converter model by simulation and experimental prototype in detail. Finally, Section VII concludes the paper.
2. ZVSDAB Converter Topology Equivalent Circuit
2.1. ZVSDAB Converter
The main circuit topology of the electric traffic energy system based on the traditional ZVSDAB converter is shown in Figure 1, where L1 and L2 represent the primary and secondary phaseshifting inductors (PSI), and V1, V2 correspond to the input and output DC voltages of the DAB, and U_{p} and U_{s} are the primary and secondary AC voltages of the HFPT. The switching frequency is 40 kHz, and the transformation ratio k is set to 3. D_{1}, D_{2}, …, D_{8}, and C_{1}, C_{2}, …, C_{8} are body diodes and resonant capacitors connected in parallel at both ends of 8 SiC MOSFETs (Q_{1}, Q_{2}, …, Q_{8}), respectively. After expanding the HFPT topology, the complete equivalent mechanism model can be obtained, where R_{p} and L_{p,} and R_{s} and L_{s} represent the resistance and leakage inductance of the primary and secondary windings of the HFPT respectively; R_{m} is the equivalent core loss resistance; L_{m} is for the equivalent core magnetizing inductance generated in the primary side; C_{1} and C_{2} refer to the primary and secondary intrawinding capacitance, and C_{12} is the primary and secondary interwinding capacitance; I_{p} and I_{s} are the primary and secondary currents of the HFPT.
For ZVSDAB converters, the switches are alternately connected in pairs and the upper and lower switches of the same bridge work in the mutual intermittent state. For a given power, the current of full bridge DAB converter is only 1/2 of that of half bridge DAB converter, and the output power of the full bridge DAB converter is twice that of the half bridge DAB converter under the same switch current and the same switch voltage. Therefore, full bridge DAB converter is usually used in the occasion of a high power supply. In addition, the full bridge DAB converter only needs one smoothing capacitor, while the half bridge converter needs two smoothing capacitors.
2.2. Equivalent Circuit of the ZVSDAB Converter
For the convenience of calculation, the model of ZVSDAB converter, as shown in Figure 1, is usually simplified into the circuit shown in Figure 2, where two controllable voltage sources V1 and V2 are connected with an inductor L. the voltage difference between the inductor is adjusted by controlling phaseshifting angle and duty cycle of the two voltage sources, so as to control the inductor current i_{L}, and then control the current and power of the ZVSDAB converter.
In an ideal case, all losses are ignored in the traditional ZVSDAB converter, and the DClink capacitors and two full bridges on both sides can be equivalent to two threelevel voltage sources, and the HFPT equivalent to a leakage inductance [18, 19], which acts as a power transfer component. The most commonly employed modulation algorithm of ZVSDAB converter is SPS control, so the equivalent threelevel voltage sources degrade to twolevel square wave voltage sources with duty cycle of 50%.
However, the traditional equivalent circuit cannot fully reflect HF characteristics of the ZVSDAB converter since it ignores many factors, that is, HF loss, HF oscillation, HF transmission, and so on. In view of this, scholars have studied and proposed different simplified circuits. Figure 3 is a simplified ZVSDAB circuit considering the conduction loss of converter researched by ETH scholar Florian Krismer. The HF loss model of ZVSDAB can be established through mathematical model, but the HF oscillation characteristics of ZVSDAB cannot be reflected accurately. Based on the circuit in Figure 3, this paper studies the simplified circuit of the ZVSDAB converter, which is shown in Figure 4, composed of lumped inductance, equivalent capacitance, and lumped resistance, and deduces the mathematical model of inductance current, that is demonstrated in formula (10). This proposed mathematical model fully embodies the HF characteristics of the ZVSDAB converter, and the results are closer to the real model.
3. Mathematical Model of the ZVSDAB Converter
There are some state of the art modulation schemes for ZVSDAB converters [20]. However, SPS control is a commonly used phaseshifting control strategy for ZVSDAB converters because of its simplicity. And its two Hbridge inner phaseshifting values are 0.5, so power transmission is controlled only via changing the outer phase shift. Under steadystate conditions, the primary and secondary side voltage and current waveforms are shown in Figure 5. It can be seen that the voltage and current values will repeat at each half cycle, as shown in the following formula:
The mathematical models of Figures 2–4 can be derived, respectively, according to Figure 5 and the above formula. In all expressions, and are two square waves with a duty cycle of 50%, and phaseshifting angle (0, 1), is the voltage converted from the secondary side to the primary side, L is the sum of the primary and secondary phaseshift inductance and leakage inductance.
3.1. Mathematical Model of the Traditional Simplified ZVSDAB Converter
The following formula can be deduced from Figure 2:
Then, the steadystate current of traditional ZVSDAB converter within one switching cycle Ts is as follows:
According to equation (1), the power transmission characteristics of ZVSDAB converter under SPS control mode are as follows:
3.2. Mathematical Model of the Improved ZVSDAB Converter considering Conduction Loss
The following formula can be deduced according to Figure 3:
The steadystate current of ZVSDAB converter considering conduction loss in one switching cycle Ts is as follows:where ,`
3.3. Mathematical Model of the Improved HF ZVSDAB Converter
From Figure 4, we can get the following formula:
The steadystate current of ZVSDAB converter considering HF loss and oscillation in one switching cycle Ts is as follows:where , and
4. Simulation and Experimental Verification of the ZVSDAB Converter
The model parameters used in the simulation and experimental analysis of the ZVSDAB model are tabulated in Table 2.

4.1. Simulation Results of the ZVSDAB Converter
In this paper, we compare the stability of the HF mathematical model and the traditional mathematical model of the ZVSDAB converter through simulation and experiment. On the experimental setup, the WBG semiconductors generate parasitic inductance at HF, which leads to voltage spikes, and the HFPT generates parasitic capacitance at HF, which leads to current spikes. Moreover, the interaction between these parasitic inductance and capacitance distorts the voltage and current waveforms and leads to regulation issues and oscillations for the ZVSDAB converter [15]. However, there are no signs of these phenomena during the simulation, so the static stability of the ZVSDAB converter is analyzed in the simulation, and the dynamic stability is studied in the experiment. Figure 6 is the voltage and current simulation waveform of the ZVSDAB converter circuit model under SPS control condition, in which are the twolevel square waves with a duty cycle of 50%. Figure 7 is the simulation results of the ZVSDAB traditional simplified circuit, only considering leakage inductance and phaseshift inductance. It can be seen that there is obvious waveform distortion in the startup stage of the primary and secondary currents, and it takes longer to reach a steady state than the primary and secondary voltages. The common solution is to add startup control to the hardware, which results in the complexity of the control algorithm, the reduction of power density, and the increase of system cost. In this paper, formula (6) is derived from the high frequency simplified circuit of DAB without startup control, so that the primary and secondary currents can quickly attain a steady state.
Figure 8 shows the simulation waveform considering HF characteristics of the ZVSDAB converter, namely, the parasitic capacitance of HFPT and winding loss. It can be seen that the waveform of the primary and secondary currents are obviously improved. The above simulation results indicate that the HF simplified mathematical model of the ZVSDAB converter has better static stability than the traditional one.
4.2. Experimental Results of the ZVSDAB Converter
In order to verify that the dynamic performance of the improved HF mathematical model of the ZVSDAB converter is better than that of the traditional one, a 4.4kw, 40 khz ZVSDAB converter prototype based on SiC MOSFET has been constructed, and the experimental prototype is demonstrated in Figure 9. In which HFPT, transformation ratio is 3 : 1, with good thermal performance and small size, is adopted. During the experiment, the primary side of the converter is powered by adjustable DC power supply, and the primary voltage is adjusted to 33 V (rated voltage is 30 V); the secondary side is connected with adjustable resistance load, and the secondary voltage is adjusted to 9 V (rated voltage is 10 V). DSP (TMS320F28335) and CPLD (Altera Max II) are utilized as a controller.
Figures 10 and 11 are the results of the tests on the prototype, which is shown in Figure 9. And we can get four groups of data by measuring currents and voltages of port AB and port CD in the HFPT box, and then the waveforms of Figure 10 are obtained via MATLAB software using these data sets. Similarly, through measuring currents and voltages of port ab and port cd in the HFPT box, we can get another four groups of data, and then the waveforms of Figure 11 are obtained via MATLAB software using these data sets. Figure 10 is the experimental waveform corresponding to the traditional mathematical model only considering leakage inductance and phaseshift inductance of the ZVSDAB converter, in which the primary and secondary voltages oscillate violently at each switching point, and this caused waveform distortion. One of the reasons is that the DC bias makes the input and output current/voltage of the ZVSDAB converter have large ripples; another reason is that the parasitic inductance of WBG semiconductors resonates with the parasitic capacitance of transformer and PCB, which causes obvious voltage spike [14]. Therefore, this paper focuses on the HF characteristics of the ZVSDAB converter and deduces its HF mathematical model through adding resistance and capacitance to the circuit to suppress DC bias, thus reducing HF oscillation and waveform distortion of the circuit, stabilizing the input and output voltage waveforms. The experimental results are shown in Figure 11, we should take measures on the second reason, in order to eliminate the oscillation of the output waveform of the ZVSDAB converter completely. For example, first, we establish the simulation model of the ZVSDAB converter on the basis of the oscillation wave in the experiment and deduce its mathematical expression, then find out the solution. It can be seen from the two local enlarged drawings in Figures 10 and 11 that the distortion, fluctuation, and oscillation of the original and secondary voltage waveforms of the proposed HF mathematical model of ZVSDAB converter are much less than that of the traditional one, which further verifies the effectiveness of the proposed HF model of ZVSDAB converter.
The results of the experimental data analysis, as shown in Figure 12, show that the DC bias of the primary voltage in the traditional ZVSDAB model is the highest, and the total DC bias can be reduced by the improved ZVSDAB converter model, which further proves that the proposed HF mathematical model of ZVSDAB converter can improve the dynamic characteristics of the system.
5. Conclusions
This paper has fully considered the HF characteristics of the ZVSDAB converter. And we have presented mostly used traditional simplified circuits for full bridge ZVSDAB converter and deduce their mathematical model, respectively, in this paper. On this basis, we propose a HF mathematical model, which take conduction loss and HF characteristics of the ZVSDAB converter model into account. The stability of the HF circuit and traditional circuit of the ZVSDAB converter is compared in simulation and experiment. Since the simulation model cannot fully reflect the real model, and the switches as well as the transformer utilized in the simulation cannot fully reflect HF oscillation caused by the parasitic parameters which arise during the HF scenario. In the end the steadystate performance of the ZVSDAB converter is analyzed in the simulation, and the dynamic performance is studied in the experiment. It can be seen from the results of the simulation and experiment that the proposed HF mathematical model of ZVSDAB converter, compared with the traditional one, can effectively reduce the DC component in the circuit and avoid the DC bias of the transformer which leads to magnetic saturation. Moreover, it can decrease the output waveform distortion rate, improve the system stability, reduce the output waveform oscillation rate of the primary and secondary side voltage, and advance the dynamic performance of the electric traffic energy system.
After analyzing the results from simulation and experiment, we can draw the following conclusions:(1)The PSI of the ZVSDAB converter should be on both sides of the transformer so that the PSI can play the role of filtering and restrain the HF oscillation of ZVSDAB primary and secondary currents.(2)The HF oscillation of the ZVSDAB converter can be suppressed through adding absorption capacitance to the WBG switches, but there will be current overcharge issues, or inserting parallel resistance at Hbridge port to restrain dv/dt by resistance energy consumption, or build a simulation model of the ZVSDAB converter based on the oscillation wave in the experiment and deduce its mathematical expression to improve circuit topology or control algorithm, so as to reduce or eliminate the primary and secondary voltage oscillation of the ZVSDAB converter.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
All the authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The work was supported by the National Natural Science Foundation of China (Grant no. 51667020 and no. 61364010), the Outstanding Doctor Graduate Student Innovation Project of Xinjiang University (No. XJUBSCX2016018), and the Graduate Student Innovation Project of Xinjiang Uygur Autonomous Region (No. XJGRI2017025).
References
 Z.B. Ya, Life Cycle Assessment of Energy Use, Carbon Emissions and Cost Benefit of Electric Vehicle, Tsinghua University, Beijing, China, 2016.
 M.L. Fu, W.T. Fei, and D.K. Qi, “Research on wide voltage output vehicle power supply based on LLC topology,” Mechanical and Electrical Engineering, vol. 8, pp. 911–915, 2017. View at: Google Scholar
 L. Jing, Y.L. Qiang, and G. Qing, “An efficiency optimization method of dual active bridge DCDC converter based on loss model,” Journal of Electrical Technology, vol. 32, no. 14, pp. 66–76, 2017. View at: Google Scholar
 Y.J. xi, L.J. Qiang, and Z.J. Fu, “Voltage balance control of power electronic traction transformer based on double active bridge DCDC converter,” Journal of Electrical Technology, vol. 31, no. 1, pp. 119–127, 2016. View at: Google Scholar
 Z. Mariusz, K. Konstantin, R. Jacek, and B. Roman, “Design and evaluation of reduced selfcapacitance inductor in DC/DC converters with fastswitching SiC transistors,” IEEE Transactions on Power Electronics, vol. 29, no. 5, pp. 2492–2499, 2014. View at: Google Scholar
 X. Fei, Y.R. Yang, and H.Q. Alex, “A 98.3% efficient GaN isolated bidirectional DC–DC converter for DC microgrid energy storage system applications,” IEEE Transactions on Industrial Electronics, vol. 64, no. 11, pp. 9094–9103, 2017. View at: Google Scholar
 R. W. A. A. De Doncker, D. M. Divan, M. H. Kheraluwala, and M. H. Kheraluwala, “A threephase softswitched highpowerdensity DC/DC converter for highpower applications,” IEEE Transactions on Industry Applications, vol. 27, no. 1, pp. 63–73, 1991. View at: Publisher Site  Google Scholar
 C. Hong, Development of 15 kw Phase Shifted Full Bridge ZVS Charger, Southwest Jiaotong University, Chengdu, China, 2012.
 S. Ling, L.W. Jun, L.Z. Qiang, and H. Jun, “Bilinear discretetime modeling and stability analysis of the digitally controlled dual active bridge converter,” IEEE Transactions on Power Electronics, vol. 32, no. 11, pp. 8787–8799, 2017. View at: Google Scholar
 Q. Hengsi and K.W. Jonathan, “Generalized average modeling of dual active bridge DC–DC converter,” IEEE Transactions on Power Electronics, vol. 27, no. 4, pp. 2078–2084, 2012. View at: Google Scholar
 W.S. En, Z.Z. Dong, L. Chi, and W. Kui, “Time domain analysis of reactive components and optimal modulation for isolated dual active bridge DC/DC converters,” IEEE Transactions on Power Electronics, vol. 34, no. 8, pp. 7143–7146, 2019. View at: Google Scholar
 S. Kai, L.Y. Jing, and W.H. Fei, “Variable temperature parameter modeling of silicon carbide MOSFET,” Chinese Journal of Electrical Engineering, vol. 33, no. 3, pp. 33–43, 2013. View at: Google Scholar
 G.Y. Shi, W.Y. Jie, X.D. Guo, and W. Wei, “A 1 MHz halfbridge resonant DC/DC converter based on GaN FETs and planar magnetics,” IEEE Transactions on Power Electronics, vol. 32, no. 4, pp. 2876–2891, 2017. View at: Google Scholar
 L. Bin, L. Qiang, and L.C. Fred, “Highfrequency PCB winding transformer with integrated inductors for a bidirectional resonant converter,” IEEE Transactions on Power Electronics, vol. 34, no. 7, pp. 6123–6135, 2019. View at: Google Scholar
 A.S. Mohammad, S. Navid, and O. Martin, “LLC converters with planar transformers: issues and mitigation,” IEEE Transactions on Power Electronics, vol. 32, no. 6, pp. 4524–4542, 2017. View at: Google Scholar
 C. Bin, X. Peng, and J.X. Hua, “Elimination of high frequency oscillation in dual active bridge converters by dv/dt optimization,” IEEE Access, vol. 7, pp. 55554–55564, 2019. View at: Google Scholar
 Z. Biao, S. Qiang, L.W. Hua, and Z.Y. Ming, “Transient DC bias and current impact effects of highfrequencyisolated bidirectional DC–DC converter in practice,” IEEE Transactions on Power Electronics, vol. 31, no. 4, pp. 3203–3216, 2016. View at: Google Scholar
 G.C. Yang, Research on Topology and Control of Power Electronic Transformer for Electric Traction, Tsinghua University, Beijing, China, 2015.
 S.S. Li and L.Z. Qiang, “Modeling and control method of threephase double active bridge DC converter,” Journal of Electrical Technology, pp. 1–13, 2019. View at: Google Scholar
 G.Z. Qiang, “Modulation scheme of dual active bridge converter for seamless transitions in multi working modes compromising ZVS and conduction loss,” IEEE Transactions on Industrial Electronics, vol. 67, no. 9, pp. 7399–7409, 2019. View at: Google Scholar
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Copyright © 2020 Ayiguzhali Tuluhong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.