사각형입니다.

https://doi.org/10.6113/JPE.2018.18.1.137

ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718



Single Pulse-Width-Modulation Strategy for Dual-Active Bridge Converters


Byeng-Joo Byen*, Byong-Hwan Jeong**, and Gyu-Ha Choe


*,†Department of Electrical Engineering, Konkuk University, Seoul, Korea

**Hyosung Power & Industrial Systems R&D Center, Seoul, Korea



Abstract 

This paper describes a single pulse-width modulation control strategy using the Single Pulse-Width Modulation (SPWM) method with a soft-switching technique for a wide range of output voltages from a bidirectional Dual-Active Bridge (DAB) converter. This method selects two typical inductor current waveforms for soft-switching, and proposes a rule that makes it possible to achieve soft-switching without any compensation algorithm from the waveforms. In addition, both the step-up and step-down conditions are analyzed. This paper verifies that the leakage inductance is independent from the rule, which makes it easier to apply in DAB converters. An integrated algorithm, which includes step-up and step-down techniques, is proposed. The results of experiments conducted on a 50-kW prototype are presented. The system efficiency is experimentally verified to be from 85.6% to 97.5% over the entire range.


Key words: DC-DC converters, Dual-active bridge converter, Pulse-width modulation, Soft-switching


Manuscript received Apr. 7, 2017; accepted Aug. 29, 2017

Recommended for publication by Associate Editor Chun-An Cheng.

Corresponding Author: ghchoe@konkuk.ac.kr Tel: +82-2-450-3486, Fax: +82-2-447-9186, Konkuk University

*Dept. of Electrical Eng., Konkuk University, Korea

**Hyosung Power & Industrial Systems R&D Center, Korea



Ⅰ. INTRODUCTION

Recently, the DAB converter has received a lot of attention in terms of modulation techniques for achieving high efficiencies over a wide operating region. A scheme for applying proper modulation control is important because the efficiency of the converter is sensitive to the modulation technique. Almost all DAB converters use phase-shift modulation (PSM) since it can easily provide soft-switching and it is simple to apply. For these reasons, many published papers have proposed the use of this modulation scheme [13]-[19]. The authors of [13] presented an analysis of the circulating current in PSM and proposed a modified PSM technique to compensate this problem. Meanwhile, the authors of [14] proposed a new isolated three-port bidirectional DC–DC converter that can be connected to both a PV panel and a battery unit. They also proposed an optimized PSM for the converter. An optimal modulation method based on fundamental component analysis was proposed in [15]. Akagi et al. [16]-[18] applied a DAB converter based on PSM to an energy storage system, a medium-voltage PCS, and a battery-charging system. Silicon carbide (SiC) power devices have made it possible for a DAB converter to achieve high efficiencies [19]. However, this PSM has a critical disadvantage. This disadvantage is related to the voltage conversion ratio at the input and output terminals. When the voltage ratio is not 1, the PSM cannot provide soft-switching operation in the low-power region. In addition, a high circulating current exists in this system. Therefore, various methods to solve this problem have been presented in [20]-[29]. The authors of [20] proposed a system design for minimizing loss and a modulation technique to reduce the switching loss in the low-power region. Meanwhile, the authors of [21] applied a DAB converter in vehicular applications, and described a modulation method based on a system model for high efficiency. The authors of [22] and [23] presented conventional PWM analyses, and proposed composite strategies based on analyses of wide soft-switching. The authors of [24] and [25] proposed control strategies to make the current waveform triangular or trapezoidal. Although these methods can achieve high efficiencies, they are complex and difficult to implement. A control method based on a system model of a DAB was proposed in [26] and [27]. A reactive power minimizing strategy for conduction-loss reduction was proposed in [28] and [29]. From these techniques, a low conduction loss was acquired, but high efficiency could not be obtained.


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Fig. 1. Configuration of a DAB converter.


TABLE I  System Parameters

Parameters

Values

Vdc1

750 V

Vdc2

580–820 V

Rated power

50 kW

HF transformer turns ratio

1 : 1

Auxiliary inductance L

38 µH

Switching frequency fs

10 kHz

Switching period Ts

100 µs


The main reason for the above-mentioned PWM techniques is to get a high efficiency in a wide operating region. There are many inductor current waveforms depending on how the PWM technique is used. Therefore, it is very important to determine which inductor current waveform is used.

The authors of [22] presented a hybrid technique using both dual PWM and single PWM. Meanwhile, the authors of [31] proposed various modulation techniques for gaining the minimum current stress for a given operating power region. The authors of [32] applied a hybrid technique using both PSM and single PWM. These techniques can obtain high efficiency, but are complex and not easy to implement.

This paper presents a modulation control strategy using the single-PWM (SPWM) method with a soft-switching technique for a wide range of output voltages. The advantage of this method is that it can apply two inductor current waveforms without changing PWM rule. Thus, it can obtain a high efficiency while minimizing switching losses and reducing conduction loss more than the traditional PSM. A detailed analysis is presented by comparing the conducting current and soft-switching regions of the SPWM to verify its performance. Lastly, this paper derives a modulation strategy with SPWM for easy implementation. Results of experiments conducted on a 50-kW DAB converter are presented.



Ⅱ. SYSTEM CONFIGURATION

Fig. 1 illustrates a DAB converter for dc distribution applications. As can be seen in this figure, the converter consists of two full-bridge converters coupled with a high frequency (HF) transformer. The DAB converter has three control parameters α, β and ϕ. Here, α and β represents half of the zero-voltage intervals at the primary and secondary sides, respectively. The phase difference between the primary and secondary voltages is written as ϕ. Note that the three parameters are completely utilized with pulse-width based modulation strategies. Meanwhile, only the phase difference ϕ is employed for the PSM strategies. In many DAB applications, PWM methods are employed for reducing the conduction and switching losses over a wide operating range. However, this is more complicated than the PSM strategies. Since the switching loss can also be significantly mitigated depending on the modulation strategies, it is important to choose an appropriate modulation technique that considers the operation region and the application area of the DAB converter [19].

The system parameters of the DAB converter are given in Table I. The input voltage is fixed at 750V while the output voltage ranges from 580V to 820V. Here the nominal output voltage is 750V. As a result, that the turns ratio of the transformer is set to 1:1. The rated operating power is 50kW. The auxiliary inductance is set to 38 µH and the switching frequency is selected as 10kHz. The inductance is considered as the peak inductor current at the maximum operating power, and the peak inductor current is calculated from the SPWM modelling equation.



Ⅲ. PSM METHOD FOR DAB CONVERTERS

Fig. 2 depicts both the primary and secondary voltages as well as the inductor current of the HF transformer operating under the PSM. With the PSM, the direction of the power flow is mainly determined by the phase difference ϕ between the primary and secondary voltages of the HF transformer.


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Fig. 2. Waveforms of a DAB converter with PSM.


By referring Figs. 1 and 2, when the phase difference ϕ is positive, so that the primary voltage vpri leads the secondary voltage vsec, electrical power is transferred from the primary side to the secondary side. On the other hand, a negative phase difference induces power flowing from the secondary to the primary sides. In Fig. 2, Ip0 represents the magnitude of the inductor current iL when the polarity of vpri is changed from a negative value to a positive value. Similarly, I denotes the current value when vsec changes its polarity from a negative value to a positive value. Here, Ip0 and I can be written as follows [23]:

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where Vpri, L, ωsw and g represent the dc voltage of the primary side, the total inductance referred to the primary side, the switching angular frequency, and the voltage conversion ratio between the primary and the secondary sides with a 1:1 turns ratio of the HF transformer, respectively.

From (1) and (2), the zero voltage switching (ZVS) condition is derived as:

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It should be noted that (3) and (4) are the ZVS conditions for g ≤ 1 and g > 1.

Since the inductor current is symmetrical in a half cycle, the root-mean-square (RMS) value of iL can be easily calculated using (5):

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Fig. 3 compares the RMS values of iL under different operating conditions. In this figure, the RMS value at 750V, where the unity voltage conversion ratio is achieved, is the minimum among other conditions. This is due to the fact that the freewheeling current is minimized with a unity voltage conversion ratio. When approaching a low output power, the RMS values of the other voltage conditions are significantly increased. This means that more conduction loss is induced, and the system efficiency is reduced with a non-unity voltage conversion ratio. From this analysis, it is concluded that achieving a high efficiency with PSM over a wide output voltage range is a major challenge, and that the so-called PWM method should be introduced to optimize system efficiency.


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Fig. 3. Comparison of the inductor RMS currents for different Vdc2.



Ⅳ. PROPOSED SPWM STRATEGY

In the proposed SPWM strategy, the duty cycle of only a single active bridge is adjusted while that of another bridge is fixed. Here, three control parameters are defined as shown in Figs. 1, 4 and 6, and only two parameters α and ϕ or β and ϕ are utilized at one time. The biggest advantages of this method are that the ZVS range of the DAB converter can be considerably expanded and the circulating current can be reduced, so that low conduction and switching losses are achieved [22], [23].


A. Step-Down Operation with the Proposed SPWM

The step-down operation in this paper means that the secondary output voltage Vdc2 in Fig. 1 is less than the primary input voltage Vdc1. Define the duty cycles of the primary and the secondary bridges in the DAB converter as follows:

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Fig. 4 illustrates typical waveforms under the proposed SPWM operation. For step-down operation with the proposed method, α is adjusted so that the duty cycle of vpri varies while β has the value of zero. This means that dsec is fixed at 0.5 with a no zero voltage interval in vsec. This is a rather different operating scheme when compared to traditional PSM, where both vpri and vsec have 0.5 of a duty cycle. Another control parameter in the proposed SPWM is the phase difference ϕ between vpri and vsec. In addition, ϕf is defined as the phase difference between the fundamentals of vpri and vsec, and following relationship is derived by referring to Fig. 4(a).


Fig. 4. Single PWM waveform for step-down operation.

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(a) ϕ ≥ 0.

 

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(b) ϕ < 0.


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Fig. 5. Inductor current variation depending on the control rules in the step-down operation (Vpri=750V, Vsec=650V).


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By transferring the zero output power, ϕf should be zero. Hence, (8) is simplified as (9).

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Since power is transferred from the primary side to the secondary side, the following conditions should be satisfied for ZVS operation of the primary switches:

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where Id1, Id2 and Id3 are defined as in Fig. 4(a), and derived as follows [26]:

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Unlike the PSM technique where ϕ≥0 is always fulfilled, the polarity of ϕ can be negative under a low power range with the proposed method as can be seen in Fig. 4(b). Again, (10) should be satisfied for ZVS operation, and the expression of Id3 is not changed even under the conditions in Fig. 4(b). However, Id1 and Id2 are changed as (14) and (15), respectively [26].

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Through the above equations, two control parameters, α and ϕ, are existent. If the number of control parameters can be reduced by 1, the controller design will be considerably simplified. In order to achieve this, two control rules are proposed to guarantee ZVS operation in this paper. First, the polarities of Id1 and Id2 should be opposite. Second, the relationship between them should be satisfied as below.


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For ϕ ≥ 0, by substituting (11) and (12) into (16), α and ϕ can be derived as follows:

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Similarly, the case of ϕ < 0 can be also derived. However, the α derived from this region has a non-calculated voltage conversion ratio. Therefore, in this paper, equations (17) and (18) are applied.

In practice, ZVS operation is not fully guaranteed near ϕ = 0, where the transition of the polarity change occurs, because of an insufficient inductor current. However, the magnitude of the inductor current is close to zero, and almost no switching loss is generated. Thus, the ZVS operation can be technically achieved for the entire operating range. In Fig. 5, the characteristic derived from the proposed control rules is shown.

From this characteristic, equation (16) is not a necessary condition for ZVS operation. However, it is a sufficient condition for reducing the number of control parameters.


B. Step-Up Operation with the Proposed SPWM

Fig. 6 shows vpri, vsec and iL for the step-up operation with the proposed method. Again, the input voltage Vdc1 is fixed, and the output voltage Vdc2 is controlled to be higher than Vdc1. This means that the direction of the power flow is from the primary side to the secondary side. Unlike the step-down operation, the duty cycle of the primary voltage is fixed at 0.5, and the secondary side duty cycle is changed. It should be noted that α is zero, and β is adjusted.


Fig. 6. Single PWM waveform for the step-up operation.

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(a) ϕβ.

 

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(b) ϕ < β.


The PSM technique always has a phase difference of ϕ≥0 in the operating region. However, in case of single-PWM, there is a region with a phase difference of ϕ<0 for the low power region because the PWM control is applied. For this reason, an additional analysis of this region is also needed [30]. As can be seen in Fig. 6(b), the figure represents the case of a phase difference of ϕ<0. Considering that the output power is zero by using the relation between β and ϕ, the following relation is obtained:

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As shown in Fig. 6(a), the soft-switching condition is obtained:

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where Iu1, Iu2 and Iu3 are defined as in Fig. 6(a), and derived as follows [26]:

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Similar to the step-down operation, the polarity of ϕ can be negative under a low power range with the proposed method as can be seen in Fig. 6(b). Again, (20) should be satisfied for ZVS operation, and the expression of Iu3 is not changed even under the condition in Fig. 6(b). However, Iu1 and Iu2 are changed as (24) and (25), respectively [26].

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In both equations (24) and (25), it is possible to find the two control parameters, β and ϕ. Reducing the number of control parameters to 1 helps simplify the controller design. In order to achieve this, two control rules are proposed to guarantee ZVS operation in this paper. First, the polarities of Iu1 and Iu2 should be opposite. Second, the relationship between them should be satisfied as below.

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For ϕβ, by substituting (21) and (22) into (26), β and ϕ can be derived as follows:

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Similarly, the case of ϕ < β can be also derived. However, the β obtained from this region cannot be applied to the whole voltage conversion ratio. Thus, this paper uses equations (27) and (28) for voltage control.

In practice, ZVS operation is not fully guaranteed near ϕ = β, where the transition of the polarity change is occurs, due to an insufficient inductor current. However, the magnitude of the inductor current is close to zero, and almost no switching loss is generated. Thus, the ZVS operation can be technically achieved for the entire operating range. In Fig. 7, the characteristic derived from the proposed control rules is shown.

Similar to the step-down operation, equation (26) can provide a wide ZVS operation, and a sufficiently simple controller design.


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Fig. 7. Inductor current variation depending on the control rules in the step-up operation (Vpri=750V, Vsec=820V).


C. Control Algorithm of the Proposed Rules

In the above-mentioned analysis of SPWM, the control rules were analysed. This section proposes a control algorithm.

Fig. 8 presents a modulation selection algorithm for the proposed modulation rules, which consist of a step-down operation and a step-up operation. As shown in Fig. 8, the modulation rule is distinguished by the voltage conversion ratio g. g ≤ 1 is the step-down operation, while g > 1 is the step-up operation. Firstly, ϕf and g are checked. Then, a proper modulation method is applied.


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Fig. 8. Flow chart of the proposed control algorithm.


According to the aforementioned analysis, Fig. 9 shows the control system structure of the DAB converter to implement the proposed control strategy. The voltage conversion ratio is used as a voltage reference Vref to avoid transient operation at the start-up stage. In addition, the proposed strategy requires the input voltage Vdc1.


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Fig. 9. Control system structure of the DAB converter with the proposed strategy.



Ⅴ. EXPERIMENTAL RESULTS

The performance of the proposed method is verified through experimental results in this section. Fig. 10 shows a 50-kW DAB converter prototype. It consists of two full-bridge converters, auxiliary inductors and a high frequency transformer. The switch is realized using FF450R12ME4 insulated-gate bipolar transistors (IGBTs) manufactured by Infineon Technologies. The cores of the transformer and the auxiliary inductor are built using nano-crystalline and high flux materials, respectively. The entire control algorithm is implemented with Texas Instruments’ 32 bit micro controller unit TMS320F28335. The same system parameters shown in Table I are utilized for the experiments.


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Fig. 10. Experimental setup.


Fig. 11 illustrates the primary and secondary voltages, the inductor currents, and the output voltages of the DAB converter under the step down operation with the proposed control strategy. Here, the input and output voltages are 750V and 580V, respectively. In order to verify the operation of the proposed method, the no-load, half-load, and full-load conditions have been tested.

In Fig. 11(a), the test result under the no-load condition is shown. It should be noted that the duty cycle of the primary side is adjusted by varying α, while the duty cycle of the secondary side is fixed at 0.5. In this condition, only a small amount of freewheeling current flows through the power stage. As can be seen in this figure, the output voltage is very well regulated as 580V, even under the no-load condition.

For the half-load condition in Fig. 11(b), the phase angle difference between vpri and vsec is slightly increased, while the shapes of both voltages are maintained. The peak of the inductor current increases slightly. Again, the output voltage is very well regulated.


Fig. 11. Experimental waveforms of a DAB converter under Vo = 580V: (a) Po = 0 kW; (b) Po = 25 kW; (c) Po = 50 kW.

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(a)

 

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(b)

 

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(c)


Experimental results of the full-load condition where Po = 50kW under 580V are shown in Fig. 11(c). When compared to Fig. 11(b), a larger phase difference is present. It should be noticed that the maximum load current is handled under this condition. The output voltage is well regulated, and no significant voltage or current spike has appeared. In addition, it can be seen that the inductor currents Id1, Id2 and Id3 satisfy equation (10) in all cases.

Figs. 12(a), (b) and (c) show operating waveforms of the DAB converter where g=1 with the proposed modulation strategy. Unlike the cases in Fig. 11, both the primary and secondary duty cycles are 0.5, and only the phase difference between the two voltages contributes to the power transfer. Note that the resultant modulation is fairly close to the conventional PSM. In addition, it can be seen that Id2 is almost equalled to Id3. This result can be derived from equations (11) and (12) at α=0. Through Figs. 12(a), (b), and (c), it is confirmed that a larger phase difference occurs when increasing the load. Neither a significant voltage or current spike nor a ringing is detected. The soft-switching condition equation (10) is achieved in the whole range.


Fig. 12. Experimental waveforms of a DAB converter under Vo = 750V: (a) Po = 0 kW; (b) Po = 25 kW; (c) Po = 50 kW.

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(a)

 

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(c)


Experimental results for the step-up operation with the proposed algorithm are shown in Fig. 13. The output voltage is 820V while the input is set to 750V. Compared with the step-down operation, the duty ratio of the primary side is fixed at 0.5, while the duty ratio of the secondary side is changed as 그림입니다.
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Fig. 13. Experimental waveforms of a DAB converter under Vo = 820V: (a) Po = 0 kW; (b) Po = 25 kW; (c) Po = 50 kW.

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(c)


Through the presented experimental results, it can be seen that the voltage and current waveforms are very well matched with the analyses done in earlier sections.

Fig. 14 shows the total efficiency of the DAB converter with the proposed strategy under the various output voltage conditions. In Fig. 14, less efficiency is monitored with a larger voltage conversion ratio under low power operation. However, the efficiency remains almost the same for the rated power regardless of the voltage conversion ratio.


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Fig. 14. Experimentally measured efficiency.


Efficiency comparisons between PSM and the proposed method are shown in Fig. 15. Overall, the proposed method remarkably increases the total efficiency under the low to medium power ranges regardless of the voltage conversion ratios. It can be seen that the proposed method shows a much better efficiency than the traditional PSM in the entire operating range. Overall, the proposed efficiency is far less affected by voltage conversion ratio g than the traditional PSM.


Fig. 15. Efficiency comparison between PSM and the proposed strategy: (a) 750V/580V; (b) 750V/600V; (c) 750V/650V; (d) 750V/700V; (e) 750V/750V; (f) 750V/800V; (g) 750V/820V.

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(a)

 

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(b)

 

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(g)



Ⅵ. CONCLUSIONS

This paper presented an analysis and experimental verification of the proposed control strategy using SPWM over a wide voltage range. The purposes of this method were to provide soft-switching in the whole operating range by choosing SPWM patterns, and to reduce conduction loss by the PWM technique at low loads. The performance of the proposed strategy was verified using a 50-kW DAB converter. The system efficiency was increased from 85.6% to 97.5%. In addition, the strategy can be used to optimize the DAB system design.



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Byeng-Joo Byen was born in Seoul, Korea. He received his B.S. and M.S. degrees from Konkuk University, Seoul, Korea, in 2011 and 2013, respectively, where he is presently working towards his Ph.D. degree in Power Electronics. His current research interests include electric vehicle chargers, PWM control, DC grids, bidirectional DC-DC converters and single phase inverter control methods.


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Byung-Hwan Jeong received his B.S. degree from Kyungsung University, Pusan, Korea, in 2001; and his M.S. and Ph.D. degrees from Konkuk University, Seoul, Korea, in 2003 and 2007, respectively, all in Electrical Engineering. From 2006 to 2008, he was a Senior Researcher at the Energy Conversion Laboratory of KESRI (Korea Electrical Engineering and Science Research Institute), Seoul, Korea. From 2008 to 2011, he was a Senior Research Engineer at the Mechatronics Group of Samsung Thales Co., Ltd., Yongin, Korea. Since 2011, he has been working as a Chief Researcher in the DC Grid Team of the Power/Industrial Systems R&D Center of Hyosung Co., Anyang, Korea. His current research interests include the power electronic control of e-Powertrain systems, photovoltaic/battery power electronic systems, and low and medium voltage dc power transmission systems.


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Gyu-Ha Choe was born in Pusan, Korea. He received his B.S., M.S. and Ph.D. degrees from Seoul National University, Seoul, Korea, in 1978, 1980 and 1986, respectively. Since 1980, he has been with the Department of Electrical Engineering, Konkuk University, Seoul, Korea, where he is presently a Professor and the Director of the Energy Electronics Research Center. From 1987 to 1988, he was a Post-Doctoral Fellow in the Department of Electrical Engineering, Oregon State University, Corvallis, OR, USA; and from 1998 to 1999, he was a Visiting Scholar in the Department of Electrical Engineering, Virginia Tech, Blacksburg, VA, USA. From 1997 to 1998, he was the Dean of Academic Research Affairs, Konkuk University; and from 2002 to 2004, he was the Dean of Academic Affairs, Konkuk University. From 2007 to 2008, he was the President of the Korean Institute of Power Electronics (KIPE), Seoul, Korea. From 2012 to 2013, he was the Vice President of Konkuk University. His current research interests include active power filters, PWM control, ac voltage regulators, inverter welding machines, the PCS design of photovoltaic generation and fuel cell generation, and the technologies for DC distribution, EV chargers and electrical safety.