A Bi-Directional DC_DC Converter for an Energy Storage System

A Bi-Directional DC/DC Converter for an Energy Storage System Shigenori Inoue, Student Member, IEEE, and Hirofumi Akagi, Fellow, IEEE Department of Electrical and Electronic Engineering Tokyo Institute of Technology S3-17, 2-12-1, O-okayama, Meguro, Tokyo, 152-8552, JAPAN E-mail: inoue@akg.ee.titech.ac.jp, akagi@ee.titech.ac.jp Abstract- This paper addresses a bi-directional dc/dc con- verter suitable for an energy storage system with an additional function of galvanic isolation. An energy storage device such as an electric double layer capacitor is directly connected to one of the dc buses of the dc/dc converter without any chopper circuit. Nevertheless, the dc/dc converter can continue operating when the voltage across the energy storage device droops along with its discharge. Theoretical calculation and experimental measurement reveal that power loss and peak current impose limitations on a permissible dc-voltage range. This information may be useful in design of the dc/dc converter. A laboratory model of the energy storage system rated at 200 V and 2.6 kJ designed and constructed in this paper verifies that the dc/dc converter can charge and discharge the capacitor bank properly. Moreover, the dc/dc converter can charge the capacitor bank from zero to the rated voltage without any external precharging circuit. I. INTRODUCTION Generally, electric power generated by renewable energy sources is unstable in nature, thus producing a bad effect on the utility grid. This fact spurs research on energy storage systems to smooth out active-power flow on the utility grid [1], [2]. Fig. 1 shows a conventional energy storage system employing a line-frequency (50- or 60-Hz) transformer, a PWM converter, a bi-directional chopper, and an energy storage device such as electric double layer capacitors (EDLCs) or lithium-ion batter- ies. The transformer is indispensable for some applications that require voltage matching and/or galvanic isolation between the utility grid and the energy storage device. Replacing the line-frequency transformer with a high-frequency and isolated dc/dc converter would result in a more compact and flexible energy storage system. Various bi-directional isolated dc/dc converters have been proposed as the interface to energy storage devices with focus on automotive or fuel cell applications. Most of the presented dc/dc converters have asymmetrical circuit configurations to couple the two dc buses having largely different voltages, several tens volts and several hundreds volts [3]-[9]. Fig. 2 depicts a bi-directional isolated dc/dc converter presented in 1991 [10], [11]. It had two symmetrical single- phase voltage-fed full-bridge converters. The dc/dc converter suffered from a low efficiency because the first-generation IGBTs were used as switching power devices [10]. However, advancement in power device technology over the last decade has enabled the dc/dc converter to operate at an efficiency as PWM Converter Bi-Directional Chopper vs is LgS 4I G ; ~L1 l J I L 50- or60-Hz ~~~VD2 or50 or60Hz~~~ ~ EDLC Transformer Fig. 1. A conventional energy storage system employing a 50- or 60-Hz transformer. bridge t bridge 2 si ~~La,2 La,2I VD1 vii ii t2 VD2 S2 4 20 kHz Figs. 6 and 7 describe operations of this leg. Fig. 2. A bi-directional isolated dc/dc converter. high as 97% [12]. A resonant dc/dc converter based on the similar topology has also achieved the same efficiency [13]. In addition, when the SiC power devices become available in the near future, the efficiency of the dc/dc converter in Fig. 2 may reach 99%. Therefore, the dc/dc converter in Fig. 2 has become a promising candidate as a power electronic interface for an energy storage system. Fig. 3 shows the energy storage system using the bi- directional isolated dc/dc converter in Fig. 2. Appropriately choosing the transformer turn ratio n enables to design the voltage range of the energy storage device, independent of the utility voltage. The energy storage device is directly connected to one of the dc buses of the dc/dc converter without any chopper circuit. Nevertheless, the dc/dc converter continues operating even when the voltage across the energy storage device, VD2 droops along with its discharge. However, no paper has addressed the permissible voltage range of VD2 in terms of power loss and peak current. There has been no experimental verification based on the dc/dc converter. This paper analyzes the relationships between the power loss, the peak current, and VD2 in a dc/dc converter rated at 10 kW and 20 kHz with VD1 fixed to 320 V. Then, the dc/dc converter is constructed and experimentally tested to 1-4244-0714-1/07/$20.00 C 2007 IEEE. 761 Authorized licensed use limited to: North China University of Technology. Downloaded on September 26, 2009 at 08:55 from IEEE Xplore. Restrictions apply. Bi-Directional Isolated DC/DC Converter Transformer Fig. 3. An energy storage system based on the bi-directional isolated dc/dc converter. verify the analysis. A 2.6-kJ laboratory model of the energy storage system using an electrolytic capacitor bank, together with the dc/dc converter, demonstrates stable charging and discharging operation. Besides, the dc/dc converter can charge the capacitor bank from zero to the rated voltage without any external precharging or starting-up circuit. II. THE BI-DIRECTIONAL ISOLATED DC/DC CONVERTER A. Operation Principle and Simplified Theoretical Waveforms Fig. 4 illustrates simplified theoretical waveforms of the dc/dc converter where VD1 < VD2. The two single-phase voltage-fed full-bridge converters produce square voltages v1 and v2. The power transfer PD can simply be controlled by adjusting the phase shift between v, and v2, d as expressed by [10] PD VD1VD2 6 wL (1) VD1 VI - 0 VD2 --- V2 - 112 --- I t Fig. 6 describes ZVS operation in bridge 1 at this point. Fig. 4. Simplified theoretical waveforms used to analyze the power losses when VD1 < VD2. TABLE I CIRCUIT PARAMETERS OF THE DC/DC CONVERTER. Rated power 10 kW Rated DC voltage VD1, VD2 360 V DC capacitor CD 7,100 ,uF Unit capacitance constant H 46 ms Transformer core material Finemet FT-3M Transformer turn ratio 1: 1 Transformer leakage inductance Lt 1.6 ,uH (1.6%) Transformer winding resistance Rtrw 17 mQ (0.13%) Auxiliary inductor La /2 21 ,uH (19%) Auxiliary inductor core material Ferrite (PC44) Inductor winding resistance Ra/2 20 mQ (0.15%) Snubber Capacitor CEI 0.01 ,uF (1.6%) Switching Frequency f 20 kHz Based on single-phase 360 V, 10 kW, and 20 kHz. where w (= 27f) is the switching angular frequency of the two single-phase voltage-fed full-bridge converters, and L is the sum of the transformer leakage inductance Lt , and the inductance of the auxiliary inductors La. As can be seen in Fig. 4, this paper defines a set of two instantaneous values of the current i1 as "switching currents," Ill and 112 which are calculated as 11l and '12 (VD1 + VD2)-+ (VD1 -VD2)(y- ) 2wL (VD1 + VD2)6- (VD1 -VD2)(w -) 2wL (2) (3) 'Il and '12 are the instantaneous values of i1 when v, and v2 respectively change their polarity from negative to positive. In this paper, a single-phase voltage-fed full-bridge con- verter is referred to simply as a "bridge." In the following experiments, the transformer turn ratio is unity (n = 1) for the sake of simplicity. B. An Experimental Circuit of the DC/DC Converter Table I summarizes the circuit parameters of the dc/dc con- verter. Four auxiliary inductors, totally having La = 40 ,uH, are connected in series with the transformer to obtain an inductance of L = 41.6 puH together with the leakage induc- tance of the transformer, Lt, . The inductance of 41.6 ,pH is sufficient to maintain a control resolution of power transfer around 120 W because the time resolution of the controller is 50 ns that corresponds to 0.36° at 20 kHz. The following sections analyze relationships between power transfer and power losses in the dc/dc converter. The power losses depend not only on the power transfer, but also the dc voltage VD2. When VD2 droops along with discharge of the energy storage device, power loss increases at a given power transfer. III. SNUBBER LOSS A. Operating Points and ZVS Conditions In Fig. 2, a snubber capacitor CQt is connected in parallel with each IGBT both to reduce switching loss and to damp out overvoltage. If the IGBT is turned on with its snubber capacitor charged, the capacitor is shorted out by the IGBT, and the energy stored in the capacitor is dissipated, thus resulting in power loss. This paper refers to this power loss as "snubber loss." When both dc voltages are equal (VD1 = VD2), and the power transfer is sufficiently large around its rating, each IGBT is turned on in ZVS (zero-voltage switching) manner to generate no snubber loss. However, when VD1 7& VD2, and the power transfer is small, the IGBT is not necessarily turned on in ZVS manner. Fig. 5 shows simplified theoretical waveforms when the IGBTs in bridge 1 is turned on in hard-switching manner. 762 771 T T Authorized licensed use limited to: North China University of Technology. Downloaded on September 26, 2009 at 08:55 from IEEE Xplore. Restrictions apply. A S1 D1 CEI 2Wvc VD1 S2 II<0 D2 CEIIll (> 0) ,., A Si D1C :VDI 1 'VDI O0 VD IX 11V2 off 0 O- VD1I CB + Fig. 7 describes hard-switching operation in bridge 1 at this point. Fig. 5. Waveforms when a positive III forces bridge 1 to operate in hard- switching manner. The power transfer is less than that in Fig. 4 although the dc voltages VD1 and VD2 are the same as those in Fig. 4. The switching current Ill is now positive in Fig. 5 in contrast to negative Ill in Fig. 4. With a positive Ill, the so-called "re- verse recovery" occurs in the free-wheeling diodes in bridge 1, leading to hard-switching operation. Turn-on operations of the IGBTs in bridge 1 and bridge 2 can be classified into the following three: (1) ZVS operation, (2) incomplete ZVS operation, and (3) hard switching operation, depending on the phase shift 6, the dc voltages VD1 and VD2, and the dead time Td. The incomplete ZVS and hard-switching operations can take place only in one bridge whose dc voltage is lower than the other. Therefore, the four IGBTs in bridge 2 are turned on in ZVS manner because VD1 < VD2. The following calculations mainly focus on phenomena in bridge 1 because those in bridge 2 can be described alike. B. Calculations of the Snubber Loss 1) ZVS operation: Fig. 6 shows circuit modes when a leg in bridge 1 (for example, consisting of Si and S2) operates in ZVS manner. Before the dead time, a current of Ill is flowing in S2 (see Fig. 6(a)). When S2 is turned off, the dead time starts. The current flowing in S2 commutates to the snubber capacitors Cd, and C& Resonance between the inductance L (see Fig. 2), C, , and C6 begins. Cb discharges from VD1 to zero while C6 charges from zero to VD1. The energy stored in Cd, is transferred to C6 When Cd, discharges down to zero, the current commutates to D1 (see Fig. 6(c)). An amount of energy stored in L is regenerated back to VD1 through D1. Providing a gating signal while D1 is conducting can turn Si on in ZVS manner. This operation results in no snubber loss. 2) Incomplete ZVS Operation: IGBTs in bridge 1 can not necessarily be turned on in ZVS manner even with a negative Ill. If the magnitude of Ill, or ~Iii is smaller than I,, CGi is not discharged down to zero, and Ca is not charged up to VD1 where [11] 2 VD1VD2 (4) Zr and IL Zr = / *(5) VCffi (a) off VI.I ii VDD1S2 _ 2 RIB (c) (b) 0 VD1 (d) Fig. 6. ZVS on a leg in bridge 1: (a) just before the dead time starts, (b) just after the dead time starts, (c) diode free wheeling, (d) current polarity alternates after the dead time. In this case, the operation of the leg makes a direct transition from Fig. 6(b) to (d), not through (c). Turning S1 on with CE charged results in an amount of snubber loss. This paper refers to this as "incomplete ZVS operation." Snubber loss caused by incomplete ZVS operation can be calculated as follows. The collector-emitter voltage of Si, vy in Fig. 6(b) can be expressed as ( ) (VD1 + VD2) + (VD1 -VD2) COSWrt ~~~~2 Zr Ill sinfrt 2 (6) where t is the time after the beginning of the dead time, and Wr (= 1/ ) is the resonant angular frequency of CRb and L. At the end of the dead time (t = Td), vy (Td) is not zero beacuse II11 < I, . Cb is shorted out and quickly discharges from vy (Td) to zero. C( suddenly charges from VD1 -vE (Td) to VD1. As a result, a joule loss of W«b =Cb {VE (Td)}2 (7) is dissipated in S1, where Cb = C = C Note that charging Ca as well as discharging Cb contributes to the joule loss. W«b represents an amount of energy lost at one switching per leg. The snubber loss P«b in bridge 1, having two legs, is calculated as PF = 4 f Whb 4 fCb {V (Td)}2. (8) 3) Hard-Switching Operation: Fig. 7 shows circuit modes when the leg operates in hard-switching manner. If VD, < VD2, and the following equation is satisfied, the switching 763 VD1 ---1 VI VD2 --- V2 - 112 i1 il Il I: I Authorized licensed use limited to: North China University of Technology. Downloaded on September 26, 2009 at 08:55 from IEEE Xplore. Restrictions apply. Large currents flowing B. Copper Loss in the Transformer and the Inductors The rms value of il, or 11 can be expressed by VVD 1. A|D2 ,+,2+(VD1 VD2)2VuVL 712 VD1VD2 (3 regardless of the switching manner. The copper loss in the transformer and the auxiliary inductors, PP is obtained as (a) (b) (c) Pp =(Rt +Ra) N , Fig. 7. Hard switching on a leg in bridge 1: (a) just before the dead time ends, (b) rapid charging/discharging of CE, and CB (c) after commutation. current Ill becomes positive, and the IGBTs in bridge 1 are turned on in hard-switching manner: [10] < VD2 VD1 (9) 2VD2 Before the end of the dead time, CQ is charged at VD1 (see Fig. 7(a)). Just after S1 is turned on, reverse recovery occurs in D2. CQ rapidly discharges from VD1 to zero, and Ca charges from zero to VD1 (see Fig. 7(b)). The charging/discharging currents result in a joule loss of W« = CLb VD1 in S1. Then, the snubber loss P«b in bridge 1 is calculated as P«b 4 f W«b 4 fCb VD1. (10) As can be seen in (8) and (10), the snubber loss P«b is proportional to the capacitance of the snubber capacitors CQ1b . Minimizing parasitic inductances in the dc/dc converter circuit is necessary so that small snubber capacitors can damp out the overvoltage appearing across the IGBTs without causing an excessive snubber loss. IV. PROFILE OF THE CURRENT il AND RELATED LOSSES A. Conducting Loss in the IGBTs This paper approximates both the on-state voltage across the IGBT, Vi , and the forward voltage drop across the free-wheeling diode, VF, to be 1.5 V, independently of the current flowing in them [12]. The conducting loss in the IGBTs and diodes, Pod can be calculated from the average of the absolute value of the current il, or ,i1D. When both bridge 1 and bridge 2 is operated in ZVS or incomplete ZVS manner, calculation on Fig. 4 yields VD1VD 2 62 w(VD1 -VD2 (i1I wL=.L(VD + VD2) { 4VD1VD On the other hand, when either bridge 1 or bridge 2 is operated in hard-switching manner, calculation on Fig. 5 derives: I VD1VDI22 wiL VD1 -VD2~ VD2,}. To calculate ( i1 , Ili and 112 should be obtained first, and then either (11) or (12) should be applied, depending on the switching manner. where Rt = 17 mQ is the winding resistance of the transformer, and Ra = 40 mQ is that of the auxiliary inductors. C. Core Loss in the Auxiliary Inductors The four auxiliary inductors were constructed using ferrite (TDK PC44) cores. The effective cross-sectional area of each core was Ae = 3.3 cm2, the effective volume was Ve 37.2 cm3, and the turn number was N = 6. An air gap of g = 1.5 mm was introduced in the magnetic path. Thus, the instantaneous magnetic flux density bhd is approximately expressed as (15)bhd Nil, 9 where ,u0 is the permeability of vacuum. The datasheet of PC44 indicates that its core loss per volume is 0.6 W/cm3 when the maximum flux density is 0.2 T at a frequency of 100 kHz in a temperature of 25°C. If the core loss per volume in PC44 can be approximated by kfB2, where f is the fre- quency of magnetization, the coefficient k = 0.15 mW/HzT2. This paper assumes that a 20-kHz sinusoidal current having an rms value as large as I1 is responsible for the core loss in the auxiliary inductors. Under this assumption, the core loss in the four auxiliary inductors can be calculated as PL# 4kf (LON 21i)V 8kfP9N2Ve 2 y2 -2 (1 6) where 2 is the coefficient to transform an rms value into an amplitude. Therefore, the core loss in the auxiliary inductors can be treated as an equivalent winding resistance of 8kfION2Ve 23 mQ. 92 (17) The core loss in the auxiliary inductors can be calculated as a part of copper loss. V. POWER LOSSES AND LOWER LIMIT OF VD2 A. Comparison between Theoretical and Experimental Losses Theoretical losses described above are compared to mea- surement results on the basis of an experimental dc/dc con- verter rated at 10 kW and 20 kHz. The circuit configuration and the circuit parameters are the same as those in Fig. 2 and Table I, respectively. A regulated dc power supply is connected to the dc bus of bridge 1. The dc bus of bridge 2 is connected back to that of bridge 1 so that the transferred power can be regenerated back to the dc power supply. Thus, the power 764 (14) Authorized licensed use limited to: North China University of Technology. Downloaded on September 26, 2009 at 08:55 from IEEE Xplore. Restrictions apply. Theoretical loss (excluding switching loss) -----Conducting loss Pnd ----- Snubber loss Pb . -----Copper loss P. including 118 W inductors core loss P.PO Experimental overall loss 2 4 6 Transferred Power PD [kW] 300k 200 100 Trans. I --Core Loss 8 10 18W 2 4 6 8 1( Transferred Power PD [kW] Fig. 8. Comparison between calculated and experimental power losses at VD1 = VD2 = 350 V. coming from the dc power supply equals the overall loss in the dc/dc converter. Both theoretical calculation and measurement are carried out under VD1 = VD2 = 350 V. Fig. 8 shows comparisons between the theoretical and ex- perimental losses. The solid line corresponds to the theoretical overall loss, Ptby although it excludes the switching loss in the IGBTs, or P, . When PD = 10 kW, the theoretical losses were as follows. The conducting loss was Pod = 189 W. The snubber loss was Pb = 0 W. The copper loss both in the transformer and the inductors PP = 73 W including the core loss in the inductors, P,O The core loss in the transformer was Po) = 18 W almost independently of the power transfer. The theoretical overall loss Pt by was 282 W. The experimental value of the overall loss, on the other hand, was 400 W. Thus, the difference between the theoretical and measurement results were 118 W. It would correspond to the switching loss in the IGBTs that was excluded from the theoretical overall loss. In [12], the switching loss in the IGBTs was 90 W when a power of 10 kW was transferred. Although the error of 118W 90W = 28 W remains uniden- tified, the theoretical calculations above can be valid because the error of 28 W corresponds to 0.28% of the power transfer of 10 kW, and 7% of the measured overall loss of 400 W. B. Thermal Limit and VD2 Fig. 9 shows theoretical calculation results of conducting and snubber losses in the IGBTs (Pod + P«b ) when the power transfer PD is positive. In Fig. 9, one dc voltage VD1 was kept constant at 320 V, while the other dc voltage VD2 was changed as a parameter. Achieving ZVS operation becomes difficult with VD1, VD2, compared to VD1 = VD2 = 320 V, resulting in an increased snubber loss around 3 kW. Fig. 9 defines Pod + Pb = 212 W at VD1 = VD2 320 V as a "thermal limit." In the dc/dc converter, the losses in the IGBTs, which are the most domi