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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO.
Abstract—This paper describes the design and performance of a 6-kW, full-bridge, bidirectional isolated dc–dc converter using a 20-kHz transformer for a 53.2-V, 2-kWh lithium-ion (Li-ion) battery energy storage system. The dc voltage at the high-voltage side is controlled from 305 to 355 V, as the battery voltage at the lowvoltage side (LVS) varies from 50 to 59 V. The maximal efﬁciency of the dc–dc converter is measured to be 96.0% during battery charging, and 96.9% during battery discharging. Moreover, this paper analyzes the effect of unavoidable dc-bias currents on the magnetic-ﬂux saturation of the transformer. Finally, it provides the dc–dc converter loss breakdown with more focus on the LVS converter. Index Terms—Bidirectional isolated dc–dc converters, dc-bias currents, energy storage systems, lithium-ion (Li-ion) battery.
RC-snubber loss. Insulated-gate bipolar transistor (IGBT) equivalent collector–emitter resistance. Total HVS dc resistance. Total LVS dc resistance. MOSFET on-state resistance. HVS equivalent diode forward resistance. MOSFET lead resistances. HVS net dc voltage. LVS net dc voltage. PC40-core parameters. Maximum ac ﬂux.
LIST OF SYMBOLS Air-gap ﬂux density. Maximum dc-plus-ac ﬂux density. Net magnetomotive force. Magnetizing intensity. High-voltage-side (HVS) net dc-bias current. Low-voltage-side (LVS) instantaneous switching currents at speciﬁc times. LVS net dc-bias current. LVS dc-link capacitor ripple current. LVS magnetizing current. RC-snubber rms current. LVS stray inductance. HVS magnetizing inductance. LVS magnetizing inductance. Transformer turns ratio. Transformer HVS turns number. Transformer LVS turns number. Battery power. DC–DC converter power transfer.
40-A·h Li-ion battery bank. this paper considers the power ﬂow as shown in (1).6-V. and N is the transformer turns ratio. However. ω is the angular switching frequency. 50-Hz ac-side through the ac-link inductor Lac . and the switching-ripple-ﬁlter circuit is represented by LF . CF . Parallel connections of multiple capacitors are accompanied by bulkiness. and RF . increased cost. The circuit conﬁguration is similar to that in . the ac current. The so-called “dc-blocking capacitors” are typically used to prevent the transformer from magneticﬂux saturation. 40-A·h Li-ion battery modules connected in series. 2-kW·h Li-ion battery energy storage system based on the 6-kW full-bridge bidirectional isolated dc–dc converter using a 20-kHz transformer. voltage v2 leads voltage v1 .2 V. It provides experimental and theoretical discussions concerning the effect of dc-bias currents on the magnetic-ﬂux saturation of the high-frequency transformer. The battery bank consists of two 26. available high-frequency capacitors may not meet high-current requirements. L F = 44 μH (0. A lossless capacitor is connected in parallel with each of the IGBTs to achieve zero-voltage switching and to minimize . where L S is the background system impedance (<1%). and may damage the dc–dc converter in the worst case. The dc–dc converter with a symmetrical structure consists of two voltagesource converters that are referred to as bridge 1 and bridge 2 in this paper. EXPERIMENTAL SYSTEM A. this paper aims at demonstrating the performance of the bidirectional isolated dc–dc converter for low-voltage and high-current battery applications. This paper presents the 53. NO.  proposed a dc–dc converter power ﬂow model that takes into account the switching-device voltage drop and dead time. 3. The dc–dc converter is in the charging mode when voltage v1 leads voltage v2 . L is the sum of the transformer leakage inductance Ltrans and the auxiliary inductances LAL and LAH . 27. The dc–dc converter allows bidirectional power transfer by means of controlling the phase-shift angle δ [rad] between square voltages v1 and v2 as follows : PD = |δ| VD1 VB N δ 1− ωL π (1) II. and . and δ is denoted as negative. 1. the 6-kW bidirectional isolated dc–dc converter. Li-ion battery bank of 53. However.2 Ω (3%). . and C F = 150 μF (33%) on a three-phase 200-V. Krismer and Kolar  designed a 100-kHz transformer with a low magnetic-ﬂux density not only to achieve a low core loss but also to provide a large safety margin prior to the saturation ﬂux density. The PWM converter is connected at the point of common coupling to the 200-V. TABLE I CIRCUIT PARAMETERS OF THE BIDIRECTIONAL ISOLATED DC–DC CONVERTER 355 V to keep the dc-voltage ratio of the HVS to LVS close to the transformer turns ratio. and reliability. MARCH 2012 Fig. VOL. reduce efﬁciency.2-V. VB is the amplitude of v2 .2%). 40 A·h connected to the 6-kW bidirectional isolated dc–dc converter. and δ is denoted as positive. The high-voltage dc bus is adjusted between 305 and where VD1 is the amplitude of v1 . 6-kW. However. L A C = 280 μH (1. cost.2 V and the operating voltage range of 50–59 V are determined from a practical point of view. the LVS uses laminated bus bars so that ripple currents can ﬂow into the dc capacitor CD2 that is the combination of electrolytic capacitors and high-frequency ﬁlm capacitors. and the 53.3%). To minimize stray inductances. Klopper and Ferreira  proposed a sensor for measurement of ﬂux below a saturation level. In the discharging mode.2-V. This consideration helps in designing an appropriate air-gap length in high-frequency transformers with different voltage and current ratings. Table I summarizes the parameters of the electrical components in the bidirectional isolated dc–dc converter. and 50-Hz base.1238 IEEE TRANSACTIONS ON POWER ELECTRONICS. Xie et al. and decreased reliability. They cause additional current stress in the switching devices. they did not address any dc-bias current in the transformer. However. R F = 0. The overall loss breakdown of the dc–dc converter compares the loss distribution of the low-voltage high-current converter with that of the high-voltage low-current converter. Bridge 1 consists of four 600-V. Note that both the nominal battery voltage of 53. Each IGBT module contains two devices in series. considering system-level safety. 1 shows the experimental setup consisting of a threephase pulse-width-modulated (PWM) converter. 200-A trench-gate IGBTs (CM200DY-12NF). System Conﬁguration Fig.
and the discharging operation is carried out from an initial voltage of 55. 2.7 V. the sum of the wire bond resistance. Photo of the two Li-ion battery modules used for experiment. Altera’s Max 7000s complex programmable logic device is used to generate eight gate signals for all the gate-drive circuits of the IGBTs in bridge 1 and the MOSFETs in bridge 2. 3–6 were observed through the Tektronix TDS3014B.8 V. 1 TABLE III ADJUSTMENT OF HVS DC-LINK VOLTAGE WITH BATTERY VOLTAGE Fig. vD1 and the battery voltage vB during battery charging and discharging. Each MOSFET module also contains two devices in series. However. The peak current of i2 is 153 A. The high-voltage dc bus is 355 V. turn off overvoltage across the collector–emitter terminals of the IGBT. Table III indicates the relation between the dc voltage at the HVS.: DESIGN AND PERFORMANCE OF A BIDIRECTIONAL ISOLATED DC–DC CONVERTER FOR A BATTERY ENERGY STORAGE SYSTEM 1239 TABLE II DATA OF THE LI-ION BATTERY MODULE USED IN THE EXPERIMENTAL CIRCUIT SHOWN IN FIG. The switching periods of bridges 1 and 2 are the same as 50 μs (20 kHz). Fig. The effect of stray inductance at the LVS is seen as the following change in voltage v2 . Adjustment of vD1 is carried out by changing the reference voltage of the three-phase PWM converter. The time resolution of the controller is 40 ns/bit. Li-Ion Battery Modules Table II presents the speciﬁcations of the Li-ion battery modules of the Li-ion battery bank shown in Fig. III. 3 presents the ac voltage and current waveforms of bridges 1 and 2 when the Li-ion battery is charged and discharged at PB = ±5. EXPERIMENTAL RESULTS This section demonstrates the performance of the designed dc–dc converter in charging and discharging the Li-ion battery bank by adjusting the HVS dc voltage vD1 . From the datasheet by Nihon Inter Electronics Corporation. In Fig. No voltage-balancing circuit is required for the series-connected battery modules. and its speciﬁc power to be 313 W/kg.78 μs. It may also cause MOSFET drain–source overvoltages and increase the switching loss.7 A/μs.36 A in i2 . contact resistance between the source and drain metallization and the silicon. with each of the four MOSFETs.5 mΩ.16 A in i1 . The rate of change of current causes a voltage drop of ∼4 V across the stray inductance in bridge 2.e. Bridge 2 is operated in synchronous rectiﬁcation mode to minimize conduction loss. For the duration of a phase-shift angle of δ = 5. The dc voltage vD1 is controlled with the battery voltage vB in such a way as to minimize the voltage change across the auxiliary inductors and transformer leakage inductor. (2) dt A nonnegligible stray inductance of a few tens of nanoHenries makes it difﬁcult to achieve soft switching at turn off at the LVS.TAN et al.9 V. A small-sized RC snubber is connected in parallel. i. each of which is rated at 26. Each of the modules consists of seven Li-ion battery cells connected in series.9 kW. where di2 + vB . as the battery voltage vB at the LVS varies. the rate of change of i2 (within the dotted lines) is calculated as di2 /dt = −46.6 V and 40 A·h.24 μs is set for each leg in bridges 1 and 2. RDS(ON) . 3(a). v1 leads v2 because the Li-ion battery is charged.. Bridge 2 consists of four 100-V. 0. Control Method The control method is based on an open-loop. feedforward control intended for investigating the basic operating performance of the dc–dc converter in the Li-ion battery energy storage system. The battery charging operation is carried out from an initial voltage of 54.6 nH from (2). Experimental Waveforms Fig. 1. and the battery voltage (the low-voltage dc bus) is 59 V. A. Due to the existence of ﬁnite turn on and turn off times of the IGBTs and MOSFETs. This gives the stray inductance as Lσ 2 = 85. v2 = Lσ 2 . where the nominal voltage of each battery cell is 3.29◦ /bit. C. the on-state resistance. the speciﬁc energy of the Li-ion battery module can be determined to be 63 W·h/kg. a dead time of 1. to reduce its switching loss and to damp out an overvoltage and the resultant ringings. The switching-frequency-based waveforms of Figs. The dc-bias current is 0. The initial voltage is measured at iB = 0. and −4.6 mΩ. 500-A MOSFETs (PDM5001). B. 2 shows the photo of the two Li-ion battery modules used in the experimental setup. From the speciﬁcations given. is as low as 0. and the contact resistance between the metallization and lead frame is not negligible because the total resistance Rwcm l reaches 0.
and iB .2 A/μs. (a) Battery charging at P B = 5. 5. V D 1 = 355 V. For the duration of a phase-shift angle of δ = 7. 3(b).35 μs. Waveforms of v D 1 . MARCH 2012 Fig. and V B = 59 V. v2 leads v1 because the Li-ion battery bank is discharged. and 6. NO.9 nH. Drain–source and gate–source voltages of a leg in bridge 2 at P B = 5.9 kW.5 V across the stray inductance in bridge 2.05 A in i2 . (b) Discharging mode at P B = −5.9 kW. The peak current of i2 is 171 A. v B . and the battery voltage is 50.9 kW (V D 1 = 305 V). This gives the stray inductance as Lσ 2 = 82. The high-voltage dc bus is 305 V.9 kW (V D 1 = 355 V). Experimental waveforms with dc-voltage control at the HVS. the rate of change i2 (within the dotted lines) is calculated as di2 /dt = −42.9 kW. (a) Charging mode at P B = 5. In Fig. .5 V.33 A in i1 . The dc-bias current is 0. 27. Fig.1240 IEEE TRANSACTIONS ON POWER ELECTRONICS. 3. VOL. 4. which is nearly equal to the value from Fig. 3. (b) Battery discharging at P B = −5. The rate of change of current causes a voltage drop of ∼3.
8% between PB = −1. However. especially during battery charging because a higher switching current causes a higher turn off overvoltage.6 kW. This is deduced from the rise time of the MOSFET drain–source voltage. The maximum efﬁciency of the converter is achieved around the onset of zero-voltage switching. 6(b) presents the time-expanded waveforms of vDS and iR C . and the battery power PB is calculated from measurements of vB and iB by using the Hioki 3139 power meter having a moving average function. 4(a) shows the waveforms of the dc voltage at the HVS.TAN et al. and the battery current when the battery is charged at PB = 5. The adjustment of vD1 with the variation of vB can minimize the rate of change of the currents i1 and i2 over the time interval of conduction. Additionally. it is observed from Fig. B. (a) Drain–source voltage and RC-snubber current. At battery charging. The losses in the Li-ion battery. Note that iD2 is 0 during the resonant transition time. this paper will consider the low-side dc-link voltage as the battery voltage vB . 5 presents the time-expanded waveforms of the drain– source and gate–source voltages of a leg in bridge 2 at PB = 5. 4 that the current iB .9 kW. Effects of the RC-snubber on a MOSFET in bridge 2 during battery charging at P B = 5. Note that both functions use the least-mean-square approximation. which is 6% during battery charging and 9% during battery discharging. This means that an amount of current ﬂows in the MOSFET during turn off. and that of the other diagonal MOSFET pair swings from vB to 0. the measured converter efﬁciency peaks at 96% at PB = 1.9 kW. At battery discharging. and that the current results in a nonnegligible turn off switching loss. 1 and Table I. which is almost simultaneous to the rise time of the RC-snubber current. RC snubbers mitigate the overvoltages and ringings across the MOSFET drain–source terminals. and VB = 59 V.9 μs. Fig. which is less than half of the MOSFET peak turn off current. Therefore. iB should contain a 40-kHz component. As bridge 2 is operated in synchronous rectiﬁcation. Fig. Since i2 has a frequency of 20 kHz. During the resonant-transition time. or out of. 7 shows the measured plots of the dc–dc converter efﬁciency and the battery terminal voltage when the battery is charged and discharged between 500 W and 5.9 kW. This stray inductance value is used to design the RC snubbers shown in Fig. 3(a).2 kW and PB = −2. This method contributes to minimizing the peak switching current. (b) Time-expanded waveform of v D S and iR C . the snubber loss due to hard switching or incomplete zero-voltage switching. VD1 = 355 V. On the other hand. the PWM converter.9 kW. Fig. 7 are ﬁtted with an exponential function. measured converter efﬁciency averages at 96. The .9 kW.: DESIGN AND PERFORMANCE OF A BIDIRECTIONAL ISOLATED DC–DC CONVERTER FOR A BATTERY ENERGY STORAGE SYSTEM 1241 Fig. which increases the turn off switching loss. The time taken to charge the snubber capacitor across the MOSFET to vB (resonant-transition time). ﬂowing into. 6. The current ﬂow in the RC snubber produces a snubber loss in bridge 2 that is estimated in Section V-A. Fig. and the cables connecting the battery and PWM converter to the dc–dc converter are not considered. An observable decrease in converter efﬁciency exists when the battery Fig. The ripples in the battery voltage vB are also negligible. and the switching loss in bridges 1 and 2 would dominate the loss at this low-power level. 6(a) shows the drain–source voltage vDS of a MOSFET in bridge 2 and the RC-snubber current iR C of the corresponding snubber circuit during battery charging at PB = 5. Therefore.9 kW. Pdc1 is calculated from measurements of vD1 and iD1 . The accuracies of the measuring instruments are listed in the Appendix. The conduction loss in bridge 1. Converter Efﬁciency Fig. the transformer. whereas the measured battery voltage points are ﬁtted with a ﬁrst-order polynomial function. In bridge 2. the current iB becomes a part of the rectiﬁed current of i2 . and that the ac current of bridge 2 i2 circulates in the four RC snubbers. Fig. A 40-kHz ripple voltage exists at the HVS. the conduction loss in bridge 2 should not be signiﬁcant at a low conduction current. The efﬁciency of the dc–dc converter is less than 92% at low power levels (<1 kW). 4(b) shows those when the battery is discharged at PB = −5. the drain–source voltage of one diagonal MOSFET pair swings from 0 to vB . Power at the HVS. The measured efﬁciency points in Fig. including the settling time of the voltage ringings (parasitic-resonance time) is approximately 0. 6(b) implies that the turn off switching loss in bridge 2 may not be negligible. the Li-ion battery voltage. Fig. indicating that the snubber capacitor is not large enough to minimize the rate of change of the MOSFET drain–source voltage. voltages vGSU and vDSU show that zero-voltage switching at turn on is achieved in the upper MOSFET with a negligible turn on switching loss. a rather ﬂat top ac current is observed in i1 and i2 . the peak current in the RC snubber is 22 A. and the LVS auxiliary inductors. Moreover. The so-called “Miller effect” that lasts for approximately 400 ns is observed from the gate–source voltage of the lower MOSFET vGSL . the Li-ion battery bank have almost none of the 40-kHz ripples.2 kW.
Almost no power ﬂows when the reference phase-shift angle is about −4◦ . The experimental phase-shift angle is the reference angle from the controller. The maximum ac-ﬂux density Bac can be calculated as Bac = VD1 = 0. at δ = 0. When charging. and δ=− π + 2 ωπLPD π2 + 4 VD1 VB N (4) Table IV presents the speciﬁcations of the 20-kHz transformer with an air-gap length of 1 mm. and VB are substituted into (3) or (4). In order to calculate the theoretical phase-shift angle. 3. The curves for the theoretical and experimental points are ﬁtted with the function in (1) using the least-meansquare approximation. 27. The absolute value of the power transfer increases. The magnetizing inductance at the LVS is equivalent to 48. power is between ±3 and ±6 kW. The deviation is more severe when the dc-voltage ratio of the HVS to the LVS is not equal to the transformer turns ratio. Power Transfer Versus Phase-Shift Angle Fig.1242 IEEE TRANSACTIONS ON POWER ELECTRONICS. its LVS-referred peak and rms . where the core material is ferrite PC40. The estimation of loss breakdown is shown in Section V. (a) Battery charging. but it is considered reasonable in making the comparison. Bidirectional power transfer versus phase-shift angle. PD is equal to the power at the HVS Pdc1 and it is denoted as negative. Fig. 7.76 mH/36). VOL. as the phase-shift angle increases in the positive and negative directions. but is 500 W. the power transfer is not zero.  have proposed a more accurate power transfer model for the dc–dc converter. IV. 8. Measured dc–dc converter efﬁciencies and battery voltages. TRANSFORMER OF 20 KHZ This section discusses the dc-bias current phenomenon observed in the transformer. and switching losses. An air-gap length of 1 mm is inserted to prevent the transformer from magnetic-ﬂux saturation. This is the result from an increase in conduction.9 μH (=1. 8 compares the experimental and theoretical power transfer PD versus phase-shift angle δ during battery charging and discharging. A. ohmic. The calculation of the theoretical phase-shift angle is derived from (1) to be δ= π − 2 ωπLPD π2 − 4 VD1 VB N (3) in the calculation. When discharging. MARCH 2012 Fig. C. the theoretical and measured curves are seen to be in good agreement because the dc-voltage ratio of the HVS to the LVS is kept close to the transformer turns ratio. The model is useful for accurate power management when vD1 = N vB . Note that the theoretical calculation is not entirely idealized due to the usage of the experimental values where VD1 = 360 V is the rated voltage at the HVS. the power transfer PD is equal to the battery power PB and it is denoted as positive. and at the battery voltage of 59 V. The magnetizing current is triangular. resulting in a power transfer that deviates from the converter power transfer model in (1). copper. even in the worst case that considers transient conditions and a margin of manufacturing and component tolerances. VD1 . For the charging and discharging modes of operation. Xie et al. The dead time in the converter causes a phase difference between voltages v1 and v2 .104 T 4N1 Ae f (5) during battery discharging. the measured values of PD . Based on the experimental results. which is divided into eight different regions of operation. NO. Maximum AC-Flux Density and Magnetizing Current during battery charging. as the operating current increases to 100 A during battery charging. (b) Battery discharging. and to 120 A during battery discharging at the LVS.
and the equivalent diode forward resistance have a role in reducing the dc-bias currents in the dc–dc converter. 9 shows the theoretical digital control signals for the two diagonal-pair MOSFETs. DC-Bias Currents at the HVS and LVS The bidirectional isolated dc–dc converter produces squarewave ac voltages that are applied to the HVS and LVS of the 20-kHz transformer. The same situation can appear in square-wave voltage v1 at the HVS.16 mΩ. Table V presents the measured dc-resistance values of the passive components and connecting cables in the dc–dc converter. As shown in Fig. The dash-line waveform of v2 represents the ac voltage at the LVS under the ideal condition. the presence of the delay-time differ- Fig.5 V.75 mΩ from the same data sheet. However. The solid-line waveform of v2 shows the following difference caused by the delays: The diagonal-lined voltage-time area is larger than the gray-shaded voltage–time area. 5) unequal turn on and turn off times of the IGBTs and MOSFETs. Based on the calculated dc resistance Rdc2 . 9.TAN et al. the polarity of v2 changes from negative to positive when the gate signal for diagonal-pair 2 changes from high to low. and no transient overvoltage is considered in Fig. Manufacturing and component tolerances make it impossible to predict accurate degrees of mismatches in the IGBTs/MOSFETs and their gate-drive circuits at the stage of system design. resulting in a positive or negative net dc voltage every switching cycle. ence deﬁned by Δt(=t1 − t2 ) yields a net positive dc voltage in the LVS every switching cycle. and it is estimated as 7. A constant current source of Idc = 5 A was connected across the transformer HVS. In this case.3 and 8. possible delays in the turn on and turn off times of the MOSFETs and the output signals from their gate-drive-circuits can defer the polarity change in v2 . and the ensuing square-wave ac voltage v2 at the LVS under both ideal and practical conditions. which excludes the threshold voltage from the iA –vAK curve of the diode. Similarly. and cables. B.05 A at the rated power in the discharging mode. An unequal voltage–time area in each ac voltage would result in a net dc voltage in either side of the transformer. the IGBT equivalent collector–emitter resistance. The total dc resistance at the LVS in the charging and discharging modes Rdc2 is expressed as Rdc2 = 2RDS(ON) + 2Rwcm l + RALo + R2o = 3. Fig. This burdens the switching devices with additional current stress. 2) unequal saturation voltage in the IGBTs. the voltage–time area for one half of a switching cycle is equal to that for the other half of the switching cycle. The dc-bias current in the LVS was measured as 6. (6) The total dc resistance at the HVS in the charging and discharging modes Rdc1 is expressed as Rdc1 = 2RFW D (or 2RCE ) + RAHo + R1o + RCBLo = 42 mΩ(or 33. These include the following: 1) unequal gate-drive circuits. RCE is the equivalent collector–emitter resistance in the charging mode. the delay-time difference Δt is calculated as Vdc2 T = 19 ns (8) Δt = VB where T = 50 μs and VB = 50. other components. . It shows that at times ta and tc . the net dc voltage of v2 Vdc2 is deduced as 19. An optimal design in the air-gap length results in a reasonable magnetizing current in the transformer. A net negative dc voltage is also possible. Note that the on-state resistance across each MOSFET is assumed equal. There are several factors that can cause dc-bias currents in the transformer. 3. whereas Idc = 25 A was connected across the transformer LVS. From Fig. and the terminal dc voltage of each of them was measured. and may damage the dc–dc converter. 4) asymmetry in transient overvoltages across the IGBTs and MOSFETs. Note that the MOSFET on-state resistance. 9. A dc-bias current can cause magnetic-ﬂux saturation that produces high current pulses in the transformer.8 mΩ from the datasheet by Mitsubishi Electric. Hence. 9.1 mV. and it is estimated as 3.9 A. an amount of dc-bias current was observed in the experimental waveforms.9 mΩ) (7) where RFW D is the equivalent diode forward resistance in the discharging mode. which excludes the threshold voltage from the iC –vCE curve of the IGBT.: DESIGN AND PERFORMANCE OF A BIDIRECTIONAL ISOLATED DC–DC CONVERTER FOR A BATTERY ENERGY STORAGE SYSTEM 1243 TABLE IV SPECIFICATIONS OF THE 20-KHZ TRANSFORMER USED IN EXPERIMENT currents are 15. 3) unequal on-state resistance of the MOSFETs. Theoretical MOSFET gate signals and the resultant ac voltage v 2 at the LVS that emphasizes on the time delay during the dead time. the polarity of v2 changes from positive to negative when the gate signal for diagonal-pair 1 changes from high to low. reduces converter efﬁciency. At the time tb . respectively.
This means that the operating condition is almost at the saturation ﬂux density because Fig.35 T at 120 ◦ C. the net magnetomotive force can be expressed as Fnet = N2 I2o − N1 I1o = 24. 10(b) indicates that the change in ﬂux with current is approximately 0. the positive dc-bias currents at both HVS and LVS produce a dc ﬂux that has a slight cancellation effect. Therefore. Each dc-bias current produces a dc ﬂux that has a slight cumulative effect. The net magnetomotive force is expressed as Fnet = −(N2 I2o + N1 I1o ) = −31. Note that VD1 is much higher than Vdc1 . the initial dc-ﬂux density Bdc is 0. Net DC Magnetomotive Force In the discharging mode of Fig. and μ0 (=4π × 10−7 H/m) is the permeability of air. 0.9 A·turns in the charging mode. the calculated delay-time differences are only approximations. (a) Comparison between the transformer with no air gap and four different air-gap lengths. the net dc voltage of v1 Vdc1 is deduced as 13. 10(b).33 A at the rated power in the discharging mode.0 mm at a temperature of 120 ◦ C. 10 shows the relationship of the magnetic ﬂux density and ﬂux with the magnetomotive force of the transformer with no air gap and air-gap lengths of 0. (b) The magnetomotive force is expanded.0. From Fig.9 A·turns. This means that the controller resolution is not responsible for the dc-bias currents. As a result. 3(b). measurements with reasonable accuracy are challenging. Since the delaytime differences are very small. 3. The saturation ﬂux density of the core reduces to 0.5% to 2% of reading). VOL. Design of an Optimal Air-Gap Length In the worst case of the experimental results.3 ns VD1 (9) where VD1 = 305 V. NO. and that measurements of the net dc voltages Vdc1 and Vdc2 cannot be carried out because reasonable accuracy is unachievable as v1 and v2 also include transient overvoltages. 1.241 T for the transformer with no air gap. magnetomotive force and magnetic ﬂux density: F = Hlc + lg Bg μ0 (12) where I1o and I2o are the dc-bias currents at the HVS and LVS. The following assumption is made: Neither fringing effects at the air gap nor leakage ﬂux exists. Based on the dc resistance Rdc1 . and Lm 1 = 1. as shown in (11). MARCH 2012 TABLE V DC-RESISTANCE VALUES OF THE PASSIVE COMPONENTS IN THE DC–DC CONVERTER The dc-bias current in the HVS was measured as 0. D. (11) where H is the magnetizing intensity.9 mV. Considering that the measured values are subjected to the accuracies of the measuring instruments (0.008 mWb/A in the transformer with the air-gap length of 1 mm. and 2. 3(a). The delay-time difference Δt is calculated as Δt = Vdc1 T = 2.1244 IEEE TRANSACTIONS ON POWER ELECTRONICS.008 mWb/A di N2 (13) where N = 6 from Table I.2. Bg is the air-gap ﬂux density. Fig.4 A·turns (10) Fig. Ferrite-core (PC 40) ﬂux density and ﬂux versus magnetomotive force at 120 ◦ C. The dc-bias currents can also be of opposite polarity. C. as shown in the charging mode of Fig. the dc-bias currents at the HVS and LVS accumulate to produce a net magnetomotive force of 31.76 mH and N2 = 6 from Table IV. the delay-time differences in (8) and (9) are calculated based on the measured dc-bias currents in the HVS and LVS and the measured dc resistances that are shown in Table V. This theoretical value is in good agreement with the one calculated from the measured magnetizing inductance value as follows: (Lm 1 /N 2 ) dφ = = 0. The delay-time differences are seen to be less than the controller resolution (40 ns). respectively. 10. 27.5. These curves are derived based on the B–H curve obtained from the datasheet of ferrite PC40 with the help of the following basic relationship between .
the transformer with an air-gap length of 1 mm has an initial dc-ﬂux density of 0.139 T.6 W. Although the method of loss breakdown is the same as that in the previous papers . and k = 150 W · Hz−1 · T−2 · m−3 from the datasheet. V. From the measured waveform of iR C in Fig.4% of the rated current. which is close to the saturation ﬂux density. for various air-gap lengths. respectively. the RC snubbers in the LVS produce an amount of loss.4 W.9 kW and PB = 4. which could increase the copper loss. the inductor core losses in the HVS and LVS at PB = 5. and that for the dc-ﬂux density could come from a margin of manufacturing and component tolerances. LOSS BREAKDOWN This section presents the estimated loss distribution in the dc–dc converter under the following two battery charging conditions: One is at PB = 4.5 to 1 mm. At PB = 4. However. Assuming that the same rms current ﬂows in the other three RC snubbers. the magnetizing inductance.9 kW. Core Loss in Auxiliary Inductors The voltage drop across the high-voltage and LVS inductors are deduced from the rate of change of currents i1 and i2 per switching cycle. For an air-gap length of 0. The effect of dc-bias currents on the transformer would become more severe when SiC-MOSFETs are employed in the HVS. respectively.1 kW.345 T.86 T. in which the nanocrystalline soft-magnetic material with a saturation ﬂux density of 1. which is obtained from the curves in Fig. AND DC-FLUX DENSITY FOR VARIOUS AIR-GAP LENGTHS AT 120 ◦ C the gate-drive circuits could aid in minimizing or even canceling the dc magnetomotive force at the primary and secondary sides with the same voltage and current ratings. the maximum dc-plusac ﬂux density in the possible worst case would be 0. Note that the maximum dc-plus-ac ﬂux density in the possible worst case for the transformer with an air-gap length of 1 mm.9 kW and PB = 4.035 × 2) = 0. B.3 and 37.9 A·turns. VD1 = 340 V.1 kW. The total loss can also be calculated from its energy loss for one switching cycle as follows: 2 PR C = 4CSL VB f. Using the Steinmetz parameters and the improved generalized Steinmetz equation. The dc–dc converter in . β = 2. and IB = 70 A.035 T. . . and Lm 2 is the magnetizing inductance at the LVS.3 T (14) where the doubling factor for the ac-ﬂux density could come from start-up and transient conditions. This would result from using the same IGBTs and gate-drive circuits. However. Manufacturing and component tolerances are unavoidable in any practical bidirectional isolated dc–dc converter.278 < 0.14 A. and calculates the auxiliary-inductor core loss using an improved generalized Steinmetz equation  that is suitable for nonsinusoidal excitation waveforms.6 and 4. the rms magnetizing current would be 14. These RC-snubber losses agree fairly well with those calculated from the measured RC-snubber current. VD1 = 355 V.1 kW. the rms current IR C is 2. Slight component mismatches in bridges 1 and 2 produce a net dc magnetomotive force in the transformer with different voltage and current ratings in the primary and secondary sides.27 A at PB = 5. 6(b). Table VI summarizes the peak and rms magnetizing currents. The peak magnetizing current at the LVS is calculated as N2 φac (15) Im 2 = Lm 2 where φac is the maximum ac ﬂux.2 and 20.8 V. For an air-gap length of 2 mm. PR C = 30. and the dc-ﬂux density that would be present when the net magenetomotive force is 31. the maximum dc-plus-ac ﬂux density reaches 0. the total loss in the four RC snubbers is given by 2 PR C = 4IR C RSL = 34.1 kW are 39. Table VI suggests that the acceptable air-gap length would be in the range of 0. The component mismatches are due to the dc–dc converter employing different switching devices and gate-drive circuits. because the on-state resistance of the SiC-MOSFETs is expected to be one-ﬁfth as low as that of the Si-MOSFETs . Bm ax is given by Bm ax = (0.3 T.5 mm. . leaving a decent margin prior to the saturation ﬂux density. VB = 59 V.: DESIGN AND PERFORMANCE OF A BIDIRECTIONAL ISOLATED DC–DC CONVERTER FOR A BATTERY ENERGY STORAGE SYSTEM 1245 TABLE VI CALCULATED MAGNETIZING INDUCTANCE AND CURRENT AT THE LVS. The maximum dc-plus-ac ﬂux density reaches 0. Finally. The Steinmetz parameters of ferrite PC44 are α = 1. in consideration of the possible worst case. This transformer with no air gap did not experience any magneticﬂux saturation. and  had a toroidal-core transformer with a turns ratio of 1:1. VB = 57. (17) The total loss at PB = 5. However. . A.1 kW. 10.9 kW are 3.33 T. RC-Snubber Loss Zero-voltage switching is achieved in both the HVS and LVS at PB = 5.TAN et al.9 kW. was used and the ac magnetic ﬂux density was designed as 0. inserting an appropriate air gap into the transformer ensures stable operation of the dc–dc converter without causing magnetic-ﬂux saturation. named Finemet.104 × 2) + (0. the following differences exist: This paper takes into account the RC-snubber and dc-capacitor losses at the LVS.2 W. Therefore. the inductor core losses in the HVS and LVS are 1. where good matches in the IGBTs and (16) At PB = 4.6 W. the air-gap length of 1 mm is concluded to be optimal for this system. respectively. and IB = 100A .8 W. since IR C = 2. and the other is at PB = 5.
measurements of the currents iD2 and iCD2 are restricted.0 V. Based on the estimated losses in earlier sections.1246 IEEE TRANSACTIONS ON POWER ELECTRONICS. Inoue and Akagi  showed that the total switching loss for the 350-V bidirectional isolated dc–dc converter using IGBTs was estimated as 90 W at 10 kW. respectively.9 kW. the ESR loss in CD2 is 16 W. transformercore. which include the transformer and auxiliary inductors at the rated power. VOL. the LVS switching loss is 93 W. The analysis of iD2 and iCD2 are based on the following assumptions: Since Fig.9 kW. 3. the rms current of iCD2 can be calculated from Fig. it can be assumed that the ripple current ﬂows into the dc capacitors CD2 .1 kW are estimated as 334 W (424 W − 90 W) and 145 W (225 W − 80 W). Therefore. Assuming that the switching loss is proportional to the power transferred. where iD2 can be analyzed from the charging operation.9 μs.1 kW or PB = 5. The total loss in the switching devices.9 kW. inductor-core. V D 1 = 355 V. As specially designed laminated bus bars are used at the LVS.4 A so that the ESR loss in CD2 is 5 W. Relationship between the dc–dc converter loss and switching frequency at P B = 4. VB = 59.52 μs. MARCH 2012 Fig. and IB = 100 A. and at P B = 5. Therefore. the measured dc– dc converter loss and efﬁciency are 424 W and 93.1 kW. respectively. which include conduction and switching . The experimental data were ﬁtted with a ﬁrst-order polynomial and extrapolated to zero switching frequency. Because the waveform of iB contains almost no 40-kHz ripple. 13 shows the estimated overall loss breakdown at battery charging powers of 4.9 kW.8 V. the LVS switching loss is 200 W.8 V. 11(a) shows the experimental waveforms of i2 and iB at PB = 5. V D 1 = 340 V. The total ohmic loss in the dc–dc converter is deduced to be in a range of 4–10 W at PB = 4. VD1 = 355 V. the currents I21 and I22 are measured to be 99 and 73 A. the switching loss in bridge 1 is 27 W at PB = 5. 14 presents the loss distribution in bridges 1 and 2. and V B = 59 V.2 mΩ. and iCD2 is the ripple current ﬂowing in the dc capacitors at the LVS. and switching loss. E. At PB = 5. 12 shows the experimental results relating the dc–dc converter loss with the switching frequency between 10 and 20 kHz for battery powers of 5. The ripple current is obtained as iCD2 = iD2 − iB . Observed and simpliﬁed theoretical current waveforms at P B = 5. At PB = 5. including the conduction. Therefore. HVS switching loss. The estimated loss. Estimated Loss Distribution and Considerations Fig.9 kW. Hence. VB = 57. The ﬁgure illustrates that the switching loss of 200 W in bridge 2 is the largest portion (47%) of the loss in the dc–dc converter. the calculation for the switching currents can be found in  and . They include LVS snubber loss. only the dc and fundamental components are considered in the simpliﬁed waveforms. VD1 = 340 V.9 kW.1 and 5. DC-Capacitor Loss at the LVS Fig. Fig. Fig.1 kW. 6(c) shows that the resonant transition time of i2 is less than 0. The estimated loss excluding the LVS switching loss is 132 W. this time in which iD2 is 0 is negligible with respect to its fundamental frequency (40 kHz). The contactpoint ohmic losses can be estimated to be in the range of 2–5 W. Fig. and IB = 70 A. Hence.1 kW. and the magnetic components. the measured dc–dc converter loss and efﬁciency are 225 W and 94. 27. copper. Referring to the datasheets. 11(b) to be 71.9 and 4.9 kW. C. 11. At PB = 4.9 kW and PB = 4.1 kW and δ = 3. The ohmic loss is considered to be mainly contributed by the contact points and laminated bus bars at the LVS.3%. is 224 W.1 A. 11(b) shows the simpliﬁed waveforms of iD2 and iCD2 . and ohmic loss. and V B = 57. the equivalent series resistance (ESR) of the ﬁlm and electrolytic capacitors can be approximated to be 3. At PB = 4. In addition. The frequency-dependent losses at PB = 5. the switching loss is the most dominant of the frequency-dependent loss. NO.9 kW.1 kW. HVS Switching Loss and Ohmic Loss Fig.8%. the rms current of iCD2 can be calculated to be 39. While the values of I21 and I22 in this section are obtained from experiments. (a) Observed waveforms of i2 and iD 2 . ESR. and 18 W at PB = 4. transformer-core and inductorcore losses. (b) Simpliﬁed waveforms of iD 2 and iC D 2 . Note that I21 and I22 are deﬁned as the instantaneous switching currents of bridge 2 at speciﬁc times. 12. RC-snubber. D.
vol.” Proc. no. 1–8. F. Inoue and H. Kheraluwala. and ID 2 = 70 A. 2007. 1744–1756. Mar. and Y. V D 1 = 355 V. respectively. Liu.05% of full scale. V D 2 = 59 V. and M. Available: http://www.TAN et al. D. 13. V D 1 = 355 V. 63–73. “A bidirectional isolated dc-dc converter as a core circuit of the next-generation medium-voltage power conversion system. Nov. M. One of the best methods of improving the efﬁciency of the dc–dc converter is to operate it at a lower switching frequency.. 6. 2. at a switching frequency of 10 kHz. Appl. However. the dc–dc converter can . B. pp. IEEE. A. pp. no. and that at P B = 5. this class of MOSFET is more optimal at lower switching frequencies to minimize the switching loss. Ind. Ind. pp. Estimated loss breakdown at P B = 4. The results have veriﬁed the proper operation of the Li-ion battery energy storage system. Gascoigne. A. Kheraluwala. 12. M. Crow. 1294–1301. APPENDIX The 9602 ac/dc clamp-on meters of Hioki 3139 have the following speciﬁcations: 1) Voltage meter a) DC-voltage measurement range: 0–600 V. W. REFERENCES  New Energy and Industrial Technology Development Organization (NEDO). CONCLUSION This paper has presented the experimental results from the combination of a 53. The transformer with an air-gap length of 1 mm has been shown experimentally to be robust against magnetic-ﬂux saturation. 22. 2001. Ribeiro. and E. The MOSFET employed in bridge 2 has a very low on-state resistance (0.  R.. 28.  S. and IB = 100 A. Estimated loss distribution in bridges 1 and 2. V D 2 = 59 V. Johnson. L. and the magnetic components at P B = 5.9 kW.2% of full scale. For example.9 kW. D. V B = 57. 12 indicates that the efﬁciency of the 6-kW bidirectional isolated dc–dc converter at the rated power can be improved when the switching frequency of the dc–dc converter is reduced. (2008). “A threephase soft-switched high-power-density dc/dc converter for high power applications. K. “Performance characterization of a high-power dual active bridge dc-todc converter.” IEEE Trans. K. “Energy storage systems for advanced power applications.2-V. no. Fig. Appl. D. “Advancement of energy storage devices and applications in electrical power system. Power Electron. Feb. Smith. The dc-current ranges for the 9278 universal clamp-on current transducer at the HVS and LVS are 0–50 and 0–200 A. Discussions focusing on magneticﬂux saturation due to unavoidable dc-bias currents at the highvoltage and LVSs have been carried out. M. 1991. A. b) accuracy: ±0. From the estimation of loss distribution in the dc–dc converter.” IEEE Trans. Fig.  M. Jul. this method is accompanied by acoustic noise generation and a bulky transformer.1 kW. is 71% of the loss in the dc–dc converter at the rated power. Divan. vol. a large portion of the loss at the rated power is caused by the turn off switching loss at the LVS.2% of full scale. 89. Global warming counter measures: Japanese technologies for energy savings/GHG (greenhouse gases) emissions reduction (Revised ed.” IEEE Trans. Akagi. As a result of a tradeoff.: DESIGN AND PERFORMANCE OF A BIDIRECTIONAL ISOLATED DC–DC CONVERTER FOR A BATTERY ENERGY STORAGE SYSTEM 1247 achieve an efﬁciency as high as 97% at a switching frequency of 5 kHz at the expense of generating acoustic noise and requiring a bulky transformer. General Meeting. and IB = 100 A./Dec. Fig. C. the very low onstate resistance compromises the switching loss in the MOSFET. vol. P. Divan. VI. W. vol. no. Baumann. Sen.” in Proc. R.. 2008. H. De Doncker. pp.5 mΩ). 1992. Their accuracies are ±0. 1.  P.go. 40-A·h Li-ion battery bank with a single-phase full-bridge bidirectional isolated dc–dc converter. 535–542. [Online].). Kroposki. 14. the overall efﬁciency of the dc–dc converter can be improved by 2–3% at the rated power. The extrapolation based on the experimental results shows that at the rated power. 2) Current meter a) DC-current range: 0–500 A (depending on the rating of the clamp-on current transducer). The bidirectional isolated dc–dc converter exhibits high efﬁciency in the low-voltage and high-current operation. Dec. b) accuracy: ±0. V D 1 = 340 V. H. Therefore. 27. IEEE Power Energy Soc.8 V.nedo. losses. and B.jp  S. pp. Arsoy. even in the worst cases.
M. L. Xie. 771–781. Malaysia. He is the recipient of the 2001 IEEE William E. Klopper and J. the 2004 IEEE Industry Applications Society Outstanding Achievement Award. “Transformercoupled multiport ZVS bidirectional dc-dc converter with wide input range. “An Isolated Three-Port Bidirectional DC-DC Converter With Decoupled Power Flow Management. Kolar. 3.” IEEE Trans.. Int.. Tokyo.. in 1976 and 1979. 2002. Power Electron.Eng. Okayama University. “A sensor for balancing ﬂux in converters with a high-frequency transformer link. degree in international development engineering. both from Tokyo Institute of Technology. IEEE Power Electron. Nov.) degree from the University of Shefﬁeld. high-frequency resonant inverters for induction heating and corona discharge treatment processes. pp. Y.S.Eng. she has been a Senior Lecturer in the Department of Electrical Power Engineering. S. no. M. Power Electron. Zhao. Tarui. “A 6-kW. 2003. Oomori. Int.D. Abe.  D. 23. Sun. Jun. 2. Tan is a Graduate Member of the Institution of Engineers Malaysia (IEM) and a Member of the Institution of Engineering and Technology (IET). Conf. Fujihira. degrees from the Tokyo Institute of Technology. Walter and W. “Hybrid modulation for dual-activebridge bidirectional converter with extended power range for ultracapacitor application. Conf.” IEEE Trans.. vol. vol. Kotsopoulos. He has made presentations many times as a Keynote or Invited Speaker internationally. 2008.D. Imaizumi. 25. W. Weischedel and G.. respectively. “Voltage balancing of a 320-V. Available: http://home. 422–429. vol. Tokyo Institute of Technology. “A symmetry correcting pulsewidth modulator for power conditioning applications. Japan. C. Kobayashi. active and passive electromagnetic interference (EMI) ﬁlters. The total citation index for all his papers in Google Scholar is more than 15. vol. MARCH 2012  J.” IEEE Trans.” in Proc. and utility applications of power electronics. Ind.  S. He has received ﬁve IEEE Transactions Prize Paper Awards and nine IEEE Conference Prize Paper Awards. 774–779. no. U. R. Mar. Japan. 21.. His current research interests include power conversion systems. 2008. no. Jul. Zhu. motor drives.” in Proc. (2007). T. Since October 2010. respectively. vol. 2443–2453.  K. “A novel soft-commutating isolated boost full-bridge ZVS-PWM dc-dc converter for bidirectional high power applications. 1434–1442. 46–52. “Accurate power loss model derivation of a high-current dual active bridge converter for an automotive application. and the M. 2006. no. [Online].. 3. Mar. pp. pp. Westerman. Kola. 2755–2765.1248 IEEE TRANSACTIONS ON POWER ELECTRONICS. degree from Tokyo Institute of Technology. 23. Ind. Japan. Madison. Kinouchi. and M. Spec. he was a Visiting Scientist at Massachusetts Institute of Technology (MIT). pp. He was elected as a Distinguished Lecturer of the IEEE Power Electronics and Industry Applications Societies for 1998–1999. in 2010. Nov. no.gsyuasa. W. 2008. Ferreira. Her current research interests include power conversion systems and bidirectional isolated dc–dc converters. 6. pp.” in Proc.2 kV 4H-SiC MOSFETs with the very low on-state resistance of 5 mΩcm2 .  H. Yuasa. Duarte. Akagi was the President of the IEEE Power Electronics Society for 2007–2008. no. He received the B.. Hendrix. 3. Venkatachalam. M. Power Electron.” in Proc. the M. Since January 2000. Freudenberg. “Successful development of 1. and Ph. Jun. L. and S. in 1987.  C. VOL. Tan. degree in electrical and electronic engineering. She received the B. pp. 2-kWh lithium-ion battery energy storage system using a bidirectional isolated dc-dc converter. (PESC). Appl. “Middle-frequency isolation transformer design issues for the high-voltage dc-dc converter.  L. Power Electron. 22. pp.K.  N. Jun. D. IEEE Power Electron. 318–322. “Power ﬂow characterization of a bidirectional galvanically isolated high-power dc/dc converter over a wide operating range. Krismer and J.  H. Tokyo. Power Electron. J. Japan. IEEE Workshop Comput. 27–32. Vinnikov. Laugis. Abdallah. 12-F electric double-layer capacitor bank combined with a 10kW bidirectional isolated dc-dc converter. 1930–1936. he was a Professor in the Department of Electrical Engineering. M. on August 19. where he became an Associate Professor in the Department of Electrical Engineering. pp. NO. From March to August 1996.S. and then at MIT.  S. and J. Appl. vol. Hirofumi Akagi (M’87–SM’94–F’96) was born in Okayama. Tacca. Miura.S. Newell Power Electronics Award. self-commutated back-to-back (BTB) systems. degree from the Nagoya Institute of Technology. and the Ph.” IEEE Trans. Inoue. M. 23. and T. and the M. In 1979. no. 36–41. Ind. Takahiro Abe was born in Ibaraki. Jun. pp. in 1974. Conf. S.html  N. no.” IEEE Trans. Akagi. 2008. and the 2008 IEEE Richard H. no. pp. S. 2007. 27.S. and H. Sep.” in Proc.” IEEE Trans. T. Tokyo. Khambadkone. Tokyo. Power Electron. and ﬂexible ac transmission systems (FACTS) devices. vol. He has authored and coauthored more than 100 IEEE Transactions papers and two invited papers published in the Proceedings of the IEEE in 2001 and 2004.-I. R. L.  Y. Japan. pp. Cambridge. he was a Visiting Professor at the University of Wisconsin. Power Electron. and H. Mar. “A bidirectional dc-dc converter for an energy storage system with galvanic isolation. Tan. Ind. for ten months. He was involved in the research on bidirectional isolated dc–dc converters at Tokyo Institute of Technology. Spec. A. Akagi.000. W. and I Galkin. May/Jun.  G. all in electrical engineering. 1997. degree from Universiti Tenaga Nasional. . 2006. pp. May/Jun. 54–66. such as active ﬁlters. Kajang. as an Assistant Professor. in 2002. “High-power galvanically isolated dc-dc converter topology for future automobiles. Inoue and H.” IEEE Trans.  H.” IEEE Trans. Dr. Symp. A.gyps. Nagoya. 1. Y. 5. S. Zhou and A. all in electrical engineering. 881–891. 2010.  F. 1–4. “Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters. From 1991 to 1999. 2299–2306. no. J. 33.. Industrial Use Lithium-Ion Battery (LIM40/LIM80 Series) (in Japanese). in 2009 and 2011. Tao.. Sullivan. 1951. 45. pp. T. A. 4. pp. Dr. Japan. Watanabe. Okayama. Kaufmann Technical Field Award. Nadia Mei Lin Tan (S’07–M’10) was born in Kuala Lumpur. (IPEC). During 1987. he joined Nagaoka University of Technology. 1. and H. Power Semicond. Universiti Tenaga Nasional.com/products/li/lim40. in 2007. Power Electron. 2. Jan. vol. He is currently working for JFE Steel Corporation./Aug. vol. 2010. Electron. 57. (Hons.” IEEE Trans.  N. Appl. K. pp. vol.. A.” IEEE Trans. J. He received the B. 1973.. 3. and is currently the Senior Past President. he has been a Professor in the Department of Electrical and Electronic engineering. 2010. (PESC). 2009. Round. 6. Nakao. Jun. Akagi. IA-9. Shefﬁeld. Malaysia. Japan. vol. De Doncker. Devices Ics (ISPSD).

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