Minimum resonant capacitor design of high‐power LLC resonant converter for comprehensive efficiency improvement in battery charging application
2018; Institution of Engineering and Technology; Volume: 11; Issue: 11 Linguagem: Inglês
10.1049/iet-pel.2017.0649
ISSN1755-4543
AutoresZhenxing Zhao, Qianming Xu, Yuxing Dai, An Luo,
Tópico(s)Multilevel Inverters and Converters
ResumoIET Power ElectronicsVolume 11, Issue 11 p. 1866-1874 Research ArticleFree Access Minimum resonant capacitor design of high-power LLC resonant converter for comprehensive efficiency improvement in battery charging application Zhenxing Zhao, Zhenxing Zhao College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorQianming Xu, Corresponding Author Qianming Xu hnuxqm@foxmail.com orcid.org/0000-0002-6188-2508 College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorYuxing Dai, Yuxing Dai College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorAn Luo, An Luo College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this author Zhenxing Zhao, Zhenxing Zhao College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorQianming Xu, Corresponding Author Qianming Xu hnuxqm@foxmail.com orcid.org/0000-0002-6188-2508 College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorYuxing Dai, Yuxing Dai College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this authorAn Luo, An Luo College of Electrical and Information Engineering, Hunan University, Changsha, Hunan Province, People's Republic of ChinaSearch for more papers by this author First published: 07 August 2018 https://doi.org/10.1049/iet-pel.2017.0649Citations: 14AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Here, a minimum resonant capacitor design approach is proposed for the insulated-gate bipolar transistor (IGBT)-based high-power LLC resonant converter to improve its comprehensive efficiency in the electric vehicle (EV) battery charging application. The mathematical model of LLC resonant converter is established by using the first harmonic approximation (FHA) method. Then, the switching losses of IGBT-based high-power LLC resonant converter are analysed. Also, the relationship between predominant turn-off losses and turn-off current of power device IGBT is derived. To improve the comprehensive efficiency, the minimum resonant capacitor is proposed to reduce the turn-off losses, avoiding complex control or auxiliary circuit. Finally, the proposed approach is verified by a 2 kW LLC resonant converter prototype with 690 V DC input voltage and 75–150 V DC output voltage. Experimental results show the comprehensive efficiency of the prototype is up to 93.7%. 1 Introduction With the development of electric vehicle (EV), the battery technology has made great progress. EVs with large mileage and fast charging speed are required in market applications, so the EV battery chargers should have high output power and high efficiency. As shown in Fig. 1a, the high-power battery charger includes an electromagnetic interference (EMI) filter, an AC/DC converter with power factor correction (PFC) function, and an isolated DC/DC converter. Generally, AC/DC converter uses a boost topology with the high DC voltage and the following DC/DC converter charges for the battery. Commonly used pulse width modulation (PWM) converters have large voltage and current stresses, high switching losses, as well as high EMI level. LLC resonant converter operates in the pulse frequency modulation mode, so zero-voltage switching (ZVS) operation of full controlled switches and zero-current switching (ZCS) operation of the secondary rectifier diodes can be both achieved over wide range of load. Moreover, the output filters of LLC resonant converters have only capacitive components, and there is no filter inductance in the conventional PWM converter. Hence, with the advantages of high efficiency and low EMI, LLC resonant converters have been widely applied in the field of battery chargers [1-5]. Fig. 1Open in figure viewerPowerPoint High-power EVs battery charger and its charging profile (a) Typical structure of the high-power EVs battery charger, (b) Simplified four-step charging profile of lead–acid battery The standard process curve for the battery charging is shown in Fig. 1b [6, 7]. It can be divided into constant current (CC) stage and constant voltage (CV) stage. The energy stored in the battery is mostly charged in these two stages, while the output voltage and output current of battery charger change in a larger range [8]. In addition, as shown in Fig. 1b, the output power of charger is much lower at the beginning and the end of charging process. Under the light-load condition, the operating frequency of LLC resonant converter is considerably higher than the resonance frequency and the output power can be adjusted by changing the operating frequency [9]. However, the converter will operate in the CCM with increasing turn-off losses. The reason is the secondary rectifier diodes lose the ZCS turn-off characteristic even the full controlled switches keep the ZVS turn-on characteristic, deteriorating the conversion efficiency [10]. In [9], a double-transformer-based LLC resonant converter is presented with a controlled bidirectional switch. With the heavy load, the two transformers operate in parallel to ensure the gain of the output voltage. As for the light load, only one transformer will be used by turning off the bidirectional switch to improve the light-load efficiency. However, an additional transformer and a bidirectional switch are required, resulting in the complex control system as well as increased cost. In [11], a large transformer magnetic inductance and the PWM control method under light-load condition are designed to decrease the switching frequency and improve the light-load efficiency. This will lose the high voltage gain ability and increase the EMI level. In [12, 13], the burst control is applied to converter with light-load, which increases the control complexity and the charging current perturbation, shortening the battery life. In [14], to reduce the switching losses under light-load condition, the PWM method is applied to regulate the output power. In [15], a step-gap transformer is proposed to reduce power losses of LLC resonant converter with light load. Overall, since the LLC resonant converter has excellent efficiency at rated load, above solutions are optimised for light-load conditions. In [9, 11, 15], the light-load efficiency is improved by reducing light-load conduction losses. In [12-14], the light-load efficiency is improved by reducing duty cycle. The loss distribution of LLC resonant converter is presented in [16]. At 20% load, the turn-off loss is ∼1.8 times the conduction loss, while the conduction loss is ∼2.5 times the turn-off loss at rated load. Moreover, the turn-off loss at 20% load is 1.5 times the turn-off loss at rated load. The charge time of large-capacity batteries for EVs is longer. As shown in Fig. 1b, the conduction loss is greater than the turn-off loss in the middle of the entire charging process, and the turn-off loss at both ends (light load) is greater than the conduction loss. Increasing the comprehensive efficiency of the entire charging process is more reasonable and meaningful than only considering peak efficiency or light-load efficiency, as shown in Fig. 1b (1)Compared with MOSFETs, insulated-gate bipolar transistors (IGBTs) have the advantage of smaller conduction losses in high-power applications, which can effectively reduce the conduction losses in the middle of the charging process. However, the tailing current of the IGBT results in a large turn-off loss, and the conventional resonant tank design is no longer applicable. Therefore, this paper proposes a resonant tank design approach characterised by minimum resonant capacitor to reduce the IGBT turn-off loss and improve the overall efficiency of charging process. The paper is organised as follows. Section 2 addresses the first harmonic approximation (FHA) of LLC resonant converter. Section 3 analyses the switching losses of IGBTs and rectifier diodes and the characteristics with varying load in the case of CCM. The relationship between the turn-off losses of switches and the turn-off current is shown in Section 4. The design in consideration of minimised resonant capacitor for resonant tank is proposed in Section 5. In Section 6, the overall system is designed and verified by a laboratory prototype. 2 FHA analysis of LLC resonant converter The typical half-bridge LLC resonant converter is shown in Fig. 2a, and the full-bridge rectifier is used in the secondary side. Vin is the output voltage of PFC module. Q1 and Q2 are power switch devices (IGBTs). D1 and D2 are fast-recovery bulk diodes of IGBTs. C1 and C2 are the absorption capacitors in parallel with the IGBTs. DO1–DO4 are secondary rectifier diodes and CO is the output filter capacitor. Fig. 2Open in figure viewerPowerPoint Structure diagram of half-bridge LLC resonant converter (a) Detail structure of LLC resonant converter, (b) Simplified equivalent circuit of LLC resonant tank Since the resonant tank usually operates near the resonance point, the harmonic contents of resonant current are quite low. Consequently, the simplified equivalent circuit can be accurately obtained by the use of the FHA method [6]. As shown in Fig. 2b, the resonant tank is composed of resonant capacitor Cr, resonant inductor Lr, and magnetic inductor Lm. According to the FHA model, the resonant tank has two resonant frequencies as below (2) (3)To facilitate the analysis, some important definitions are given as below (4)where RL is the equivalent load resistance, fs the converter switching frequency, and Np and Ns are the primary and secondary winding turns of the transformer, respectively. The RMS value of the resonant current and the peak value of the magnetising current can be obtained as follows: [8] (5) (6)where Ts and Tr are the switching cycle and resonant cycle, respectively. Vo and Io denote the output voltage and output current, respectively. The DC voltage gain of LLC resonant converter can be expressed as (7)According to (7), the relationship between the DC voltage gain and the typical normalised frequency of LLC resonant converter under different load conditions can be obtained as shown in Fig. 3a. It can be divided into three regions. In region 1, there is , and the power switches operate at ZVS condition, but the secondary rectifier diodes lose the ZCS turn-off characteristic in the case of CCM. In region 2, there is , and the ZVS turn-on of the power switches as well as the ZCS turn-off of the secondary rectifier diodes can be obtained concurrently. In region 3, the ZVS turn-on feature of the power switches is unavailable, so the LLC resonant converter should avoid working in the region. In the application of battery charger, the frequency of the inflexion point, where CC charging mode turns into CV charging mode, is often chosen as the design resonance frequency of the resonant tank [17, 18]. Therefore, in Fig. 1a, the converter works in region 1 (in CCM) for quite a long time in the entire charging process. Fig. 3Open in figure viewerPowerPoint Operation analysis of LLC resonant converter in different frequency ranges (a) DC gain variation based on FHA model, (b) Primary currents and secondary currents in DCM, (c) Primary currents and secondary currents in resonant point, (d) Primary currents and secondary currents in CCM 3 Switching losses analysis of power devices in LLC resonant converter In general, LLC resonant converter can achieve ZVS turn-on. Hence, the switching losses are dominated by turn-off losses. In this section, the turn-off losses of IGBTs and rectifier diodes under different conditions will be analysed. Also, the turn-off current will be investigated with varying operating frequency and output load. In region 2 of Fig. 3a, Q1 and Q2 of the converter can realise ZVS turn-on, but the loss-free turn-off is not available. The turn-off current iLm-peak is small, so are the turn-off losses. Meanwhile, the secondary rectifier diodes DO1–DO4 can achieve ZCS turn-off, so high efficiency is prone to obtain in region 2. However, in region 1 of Fig. 3a, Q1 and Q2 can also operate with ZVS turn-on, but the turn-off current increases, resulting in larger turn-off losses. In addition, the secondary rectifier diodes DO1–DO4 lose ZCS turn-off feature and the reverse turn-off losses appear accordingly. Figs. 3b–d show the primary currents and the secondary rectifier diode currents in three different frequency ranges. From Figs. 3b and c, namely fr2≤ fs < fr1, it can be found that the turn-off currents of IGBT are the magnetising current iLm-peak, and the turn-off currents of secondary rectifier diodes are zero. However, in region 1 from Fig. 3d, namely fr1 < fs, the turn-off currents of IGBT meet ic-off >iLm, while the turn-off currents of secondary rectifier diodes can be expressed as below (8)Therefore, in region 1, the turn-off losses of power switches occupy a large proportion in the total losses. As mentioned above, in region 2, the highest efficiency of converter can be obtained when fs = fr1. It should be noted that the converter works in DCM when fr2 ≤ fs < fr1. The secondary winding is open-circuit during the period of diodes free-wheeling. As a result, the converter does not transfer energy to the secondary side. Therefore, the converter efficiency correspondingly decreases to a certain extent. However, compared to region 2, the converter has lower efficiency in region 1 since the switching losses will become larger with the increase in operating frequency and loads, which occurs in the initial charging stage. 4 Relationship between turn-off losses and turn-off current of power device In Section 3, it is found that the power losses of the LLC resonant converter are predominant turn-off losses. Specifically, the phenomenon is more obvious in region 1. This section will analyse the relationship between the turn-off losses and the currents flowing through the power devices during the turn-off time. The purpose is to provide the basis for efficiency optimisation. As illustrated in [19], the relationship between the power losses and the current of IGBT (MM40GTU120B) can be obtained. It can be seen that the conduction losses Eon and turn-off losses Eoff will decrease with decreasing collector current. With the collector current ic-off decreasing, the forward current IF of the freewheeling diodes in IGBT will be reduced. Further, the reverse recovery losses EREC of the freewheeling diodes can be also effectively reduced. When secondary rectifier diodes working in region 1, the ZCS turn-off function is unavailable, resulting in large reverse recovery losses. From Fig. 4, the reverse recovery losses are proportional to the reverse recovery charge Qrr (the grey region). is the reverse recovery time of the diode, and IRRM is the maximum reverse recovery current (9) Fig. 4Open in figure viewerPowerPoint Reverse recovery waveform of secondary rectifier diode Further, reverse recovery losses can be deduced as follows: (10)The curves in [20] show the relationship between and forward currents of secondary rectifier diode (MM60F060PC). In accordance with (8), the reverse recovery charge Qrr will decrease with the ic-off decreasing. In summary, the turn-off losses of the power device are related to the current magnitude during the turn-off time. Hence, the turn-off losses can be effectively reduced by diminishing the current when turning off the power switches. 5 Turn-off losses analysis and improved design with minimum Cr Based on the analysis results in Sections 3 and 4, it can be concluded that the light-load efficiency of LLC resonant converter can be greatly enhanced if the following two conditions are fulfilled. The one is the effectively reduced turn-off currents of the primary and secondary windings. The other is the deliberately shrunken frequency range of the resonant tank. Generally, the conventional resonant tank design focuses on the design of resonant inductor Lr at first and then the resonant capacitor Cr can be deduced via (2) [6-11]. To reduce the conduction losses, the key point of resonant tank design is to find out the optimal value of k, namely the ratio of magnetic inductance and resonant inductance [21, 22]. However, in the above-mentioned design, the turn-off losses of the converter under light-load condition are more possible to increase rather than decrease, since the frequency range will be enlarged with the big k in the application of wide output voltage [9], such as battery charger. In order to achieve the ZVS operation, the input-impedance of the resonant tank should be inductive. Hence, the proposed design scheme is to predetermine the value of the resonant capacitor Cr. In consideration of inductive input-impedance, the minimum value Cr is obtained in the case of the lowest frequency and full load. Subsequently, the other resonance parameters can be derived accordingly. According to (2), the proposed design method indicates the impact of characteristic impedance on the resonant tank current. 5.1 Simulation and analysis with minimum Cr In the case of Vin = 690 V, VO = 100 V, RO = 5 Ω, and fs = 32 kHz, simulation results of resonant capacitor voltage and resonant current with different resonant parameters are shown in Fig. 5. It can be seen that the turn-off current of resonant tank with larger Lr/Cr is smaller. Hence, turn-off losses can be decreased, including the reverse recovery losses of the diode. Besides, the turn-off current of secondary rectifier diode can be reduced as well according to (8). Therefore, the first condition is satiable. Fig. 5Open in figure viewerPowerPoint Simulation results of resonant capacitor voltage and resonant current with different resonant parameters (a) Cr = 0.33 μF, Lr = 98 μH, (b) Cr = 0.68 μF, Lr = 48 μH 5.2 Characteristic impedance analysis with minimum Cr As depicted in (4), the value of Q is related to Zr when the load is determined. The curves in Fig. 6a illustrate the relationship between Q and Zr. Obviously, under the same conditions of resonant frequency, load and transformer turn ratio, the larger Zr implies larger value of Q. Fig. 6Open in figure viewerPowerPoint Operation analysis of Zr and Q (a) Relationship curves between Zr and Q, (b) Frequency modulation range in region 1 with different Q Moreover, the impedance characteristic of battery is different from the passive load. In the initial stage of charging, the equivalent impedance of LLC resonant converter is small due to the low output voltage and large output current. However, the circumstance is just the opposite at the end of the charging process. Therefore, the change in impedance of battery load makes the value of Q increase at the beginning and decrease at the end. Comparison of frequency modulation range in region 1 with two different Q is shown in Fig. 6b. It can be seen that the larger the Q is, the smaller the frequency modulation range is. Therefore, this means the second condition is also satiable. 5.3 Soft-switching of IGBT IGBT has the advantages of high-voltage level and low conduction voltage drop, so it is superior to MOSFET in the high-power converter. As previously analysed, the turn-off losses of power devices are optimised. However, the turn-off time of IGBT is longer so the turn-off losses are greater than that of MOSFET. It is detrimental to IGBT since the turn-off process of the LLC resonant converter is a lossy hard-switching. Besides, during the turn-off period of IGBT, due to the parasitic inductance, the larger di/dt between the collector and the emitter of IGBT may trigger high-voltage spike. Commonly used method is to set the snubber capacitor between the collector and the emitter of the IGBT. In [23], the snubber capacitor can reduce the turn-off losses to 64% of the hard-switching turn-off losses. When the snubber capacitor added, the EMI can be effectively inhibited as well as the voltage spike. Generally, the snubber capacitor should ensure VCE is less than or equal to the input DC bus voltage when the IGBT turn-off time is over. Therefore, the snubber capacitor is calculated as follows: (11)where ic-off is the collector current when IGBT is turned off, the turn-off time, and the input voltage. It should be noted that the large capacitance CCE will lead to the large resonance current, resulting in the increscent primary loop current and conduction losses. Therefore, the value of capacitance CCE should be minimised under the premise of the soft-switching of IGBT. From (11), it can be seen that to reduce the value of CCE, IGBT with smaller turn-off time should be chosen and the value of ic-off should be minimised as well. 5.4 Conduction losses analysis In [24], the relationship between the resonant current, magnetising current and the output power, operating frequency in the resonant tank is analysed. It can be found that the magnetising current iLM is slightly affected by the output power, and it is inversely proportional to the operating frequency. Meanwhile, the resonant current ir is proportional to the output power when the operating frequency is greater than the resonant frequency. When the operating frequency is less, the resonant current is also affected by the operating frequency. As the frequency decreases, the resonant current will increase first and then decrease slowly after reaching the peak point. It is concluded that the resonant tank current is inversely proportional to the characteristic impedance. Hence, the proposed minimisation design of the resonant capacitor does not increase the resonant tank current. However, a higher magnetising current is required to achieve the charge and discharge of the CCE, which results in an increase in conduction losses. 5.4.1 Conduction losses of active elements Compared with MOSFET, the conduction voltage drop of IGBT is much smaller. For comparison, IGBT MM40GTU120B (40 A/1200 V) and MOSFET IXFN36N100 (36 A/1000 V) with similar parameters are selected to compare the output characteristic curves at 25°C, as shown in [19, 25]. It can be seen that the conduction voltage drop VCE of the IGBT (∼1.625 V) is much smaller than the conduction voltage drop VDS (∼4.2 V) of the MSOFET under the same resonant tank current condition (20 A). The conduction losses of the IGBT are ∼38.7% of those of the MOSFET, offsetting the slightly increased conduction losses of power switches caused by the enlarged magnetising current. 5.4.2 Conduction losses of passive components Under the same output voltage and output current conditions, the conduction losses of the secondary rectifier diode and the losses of the transformer core are modestly unchanged [16]. According to the conduction losses model in [26], other passive components, resonant capacitors, resonant inductors, output filter capacitors etc. can be represented by equivalent resistance, and these resistance values are all relatively small, so the loss of this part can be considered as modestly unchanged. In addition, the on-resistance of the transformer primary winding is relatively small, the slightly increased power conduction losses within the transformer caused by the magnetising current can be ignored by optimising the transformer design. 5.5 Benefits and restrictions To sum up, the benefits of the proposed design approach are as follows. The currents and of IGBT and secondary rectifier diode during the turn-off time are effectively reduced, so the turn-off losses of power devices can be lowered. Thereby, the efficiency of the LLC resonant converter with light load can be promoted in region 1. The frequency range of the LLC resonant converter is shrunken in region 1, so the operating frequency of the converter is closer to the resonant frequency. It is beneficial to further reduce the switch losses and improve the efficiency. It is worth to note that the proposed design approach has several restrictions. The turn-off time of IGBT is longer, and the converter frequency is generally not too high. Therefore, this approach is more suitable for the high-power power supply, which is not very sensitive to the volume. Minimisation design of the resonant capacitor Cr is conducive to reducing the turn-off losses of IGBT and diode, but this will lead to the increased voltage stress of the resonant capacitor Cr, as shown in Fig. 5b. 5.6 Design flow Next, the flow of the proposed design approach will be described in detail. In region 1, regardless of the value of Q, the impedance of the resonant tank is always inductive. However, in region 2, the greater the value of Q is, the more likely the impedance of the resonant tank becomes capacitive. According to (7), the maximum value of Q in region 2 can be obtained as (12)where Gmax is the gain maximum and fn-min the normalised minimum frequency. According to (3) and (4), the minimum resonant capacitor can be obtained (13)where RL-min is the minimum load resistance. The selected resonant capacitor value should be greater than the calculated value in (13). Once Cr is determined, the resonant inductance can be obtained by (2) (14)Magnetic inductance Lm must be selected to achieve ZVS under no-load conditions [6] (15)where tdead is the dead time and CHB the equivalent input capacitance of the resonant tank. In practical application, CHB can be approximated to two times of CCE. Meanwhile, the magnetic inductance Lm should fulfil the maximum gain at the lowest switching frequency [6] (16)Then, the smaller one among Lm(ZVS) and Lm(maxG) is chosen. In order to ensure the resonant tank operates in the inductive mode, the inductance value should meet the following equation (17)In CCM mode, the magnetic inductance Lm does not participate in the resonance of the converter. With the frequency increasing, the capacitive reactance decreases while the inductive reactance increases. The turn-off current of IGBT can be estimated by (18), and then the parallel capacitance can be determined by (11) (18)On the whole, the parameter design process of the resonant tank is summarised as shown in Fig. 7. Fig. 7Open in figure viewerPowerPoint Design flow of the proposed design approach 6 Experimental results According to the described design scheme, a test prototype with the output power rated at 2 kW is established. The DC output voltage is from 75 to 150 V and the maximum output current is 20 A. The measurement schematic for experimental set-up is shown in Fig. 2a. The fore snapshot of the experimental prototype is shown in Fig. 8a. Table 1 shows the system parameters of the prototype. The charging object is the 96 V/40 AH battery array. The compared resonant tank has the parameters of Cr = 0.68 μF, Lr = 48 μH, and Lm = 240 μH. Besides, the IGBT does not include the snubber capacitor. Table 1. Design specification of the converter Specification Value rated power 2 kW input voltage 690 VDC output voltage 75–150 VDC output current 0–20 A IGBT MM40GTU120B ultra-fast diode MM60F060PC D.T. duration 2 μs first res. freq. 28 kHz second res. freq. 13.9 kHz T. turn ratio 2.2 snubber cap 1 nF Cr 0.33 μF Lr 98 μH Lm 500 μH Fig. 8Open in figure viewerPowerPoint Experimental prototype and results (a) Experimental prototype, (b) DCM mode when Vo = 120 V and Po = 1.8 kW: Ch.1 – resonant capacitor voltage (200 V/div, 10 μs/div), Ch.2 – collector–emitter voltage of Q2 (100 V/div, 10 μs/div), Ch.3 – resonant current (15 A/div, 10 μs/div), Ch.4 – diode current of D1 (20 A/div, 10 μs/div), (c) Full-resonant mode when Vo = 100 V and Po = 2.0 kW. Ch.1 – resonant capacitor voltage (200 V/div, 10 μs/div), Ch.2 – collector emitter voltage of Q2 (100 V/div, 10 μs/div), Ch.3 – resonant current (20 A/div, 10 μs/div), Ch.4 – diode current of D1 (20 A/div, 10 μs/div), (d) CCM mode when Vo = 90 V and Po = 900 W: Ch.1 –resonant capacitor voltage (200 V/div, 5 μs/div), Ch.2 – collector emitter voltage of Q2 (100 V/div, 5 μs/div), Ch.3 – resonant current (10 A/div, 5 μs/div), Ch.4 – diode current of D1 (10 A/div, 5 μs/div) Figs. 8b and c show the experimental waveforms of the LLC resonant converter operating in region 2. It can be found the turn-off current of IGBT is equal to the magnetising current, and secondary rectifier diode realise ZCS turn-off, which are consistent with the previous analysis. Fig. 8d shows the experimental waveforms of the LLC resonant converter operating in region 1. It is observed that the turn-off current of IGBT is larger than the magnetising current, and the ZCS turn-off is unavailable for the secondary rectifier diode. The contrastive experimental results with and without snubber capacitor of the LLC resonant converter in CCM mode is illustrated in Figs. 9a and b when Vo = 90 V and Po = 1.2 kW. It can be seen that the snubber capacitor connected in parallel with IGBT can effectively reduce the interference spike generated by the IGBT turn-off action. Fig. 9Open in figure viewerPowerPoint Contrastive experimental results (a) IGBT without snubber capacitor in CCM mode when Vo = 90 V and Po = 1.2 kW, (b) IGBT with 1 nF snubber capacitor in CCM mode when Vo = 90 V and Po = 1.2 kW. Ch.1 – resonant capacitor voltage (200 V/div, 5 μs /div), Ch.2 – magnetising current (10 A/div, 5 μs/div), Ch.3 – resonant current (10 A/div, 5 μs/div), Ch.4 – diode current of D1 (10 A/div, 5 μs/div), (c) Proposed design converter fs = 29.8 kHz in CCM mode when Vo = 100 V and Io = 15 A, (d) Contrastive design converter fs = 31.2 kHz in CCM mode when Vo = 100 V and Io = 15 A. Ch.1 – magnetising current (5 A/div, 10 μs/div), Ch.2 – diode current of D1 (15 A/div, 10 μs/div), Ch.3 – resonant capacitor voltage (200 V/div, 10 μs/div), Ch.4 – resonant current (15 A/div, 10 μs/div) Figs. 9c and d show contrastive experimental results of the proposed design and contrastive design converters in CCM mode when Vo = 100 V and Io = 15 A. In the same condition of load and gain, and the operating frequency of the proposed resonant tank is 29.8 kHz, that of the conventional resonant tank is 31.2 kHz. Apparently, the proposed converter is closer to the resonant frequency 28 kHz. Moreover, turn-off currents of both resonant current and diode current of the proposed design approach are much lower than those in contrastive design approach. Fig. 10a shows the output voltage and current waveforms of the proposed design converter with battery load when Vo = 100 V, Io = 15 A. It can be seen the ripples of the output voltage and current are 0.8 V (0.82%) and 500 mA (3.3%), respectively. Fig. 10Open in figure viewerPowerPoint Experimental during entire charging process (a) Output voltage and current ripples. Ch.1 – output voltage (2 V/div, 10 μs/div), Ch.2 – output current (500 mA/div, 10 μs/div), (b) Efficiency comparison of the proposed design scheme and conventional design scheme for IGBT-based LLC resonant converter, (c) Efficiency comparison of the proposed design scheme for IGBT-based LLC resonant converter and conventional design scheme for MOSFET-based LLC resonant converter The representative and conventional design method in [6] is used for efficiency comparison. According to [6], the resonant inductance and resonant capacitance can be obtained as Cr = 0.68 μF and Lr = 48 μH. Meanwhile, the parameters calculated by the proposed design method are Cr = 0.33 μF and Lr = 98 μH. Figs. 10b and c demonstrate the experimental efficiency comparison of the proposed design scheme and conventional design scheme [6] for IGBT-based LLC resonant converter. From Fig. 10b, the light-load efficiency is significantly improved with the maximum difference of 6%. Moreover, the comprehensive efficiency of the design scheme is 93.7%, significantly higher than that of conventional scheme 92.3%. From Fig. 10c, the comprehensive efficiency of the proposed design scheme for IGBT-based LLC resonant converter is higher than that of conventional MOSFET-based LLC resonant converter 93%. It can be concluded the comprehensive efficiency of the charging process has been obviously improved by using the proposed design method. It is worth mentioning that, for large-capacity battery, the output power of the charger is often large in the initial charging stage and relatively small at the end of charging, namely the CV charging stage. Hence, the experimental results show that the proposed scheme could significantly improve the efficiency of the charger operating in CCM at the beginning of charging, which is of importance to improve the comprehensive efficiency of the entire charging process. 7 Conclusion In this paper, a minimum resonant capacitor design scheme is proposed to reduce the power losses of IGBT-based LLC resonant converter, further to enhance the comprehensive efficiency of the entire charging process. The proposed design scheme can decrease the power losses by two means. The one is the effectively reduced turn-off currents of power switches in CCM, as a result of reduced turn-off losses. The other is the deliberately shrunken frequency modulation range of the resonant tank in CCM, resulting in the further decreased switching losses. Moreover, the turn-off losses of IGBT and EMI level can be inhibited by adding the parallel snubber capacitor with IGBT. The proposed design scheme avoids the complex control or auxiliary circuit. Experimental results validate that the losses of LLC resonant converter can be effectively reduced and the comprehensive efficiency is up to 93.7%. 8 Acknowledgments This work was supported by the National Key Research and Development Program of China under Grant Number 2016YFB0601302, Science and Technology Major Programs of Hunan Province, China under Grant Number 2016GK1002 and Postdoctoral Innovative Talent Support Program of China under Grant Number BX201700311. 9 References 1Deng J., Mi C.C., and Ma R. et al.: 'Design of LLC resonant converters based on operation-mode analysis for level two PHEV battery chargers', IEEE/ASME Trans. Mech., 2015, 20, (4), pp. 1595– 1606 2Deng J., Li S., and Hu S. et al.: 'Design Methodology of LLC Resonant Converters for Electric Vehicle Battery Chargers', IEEE Trans. Veh. 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