Improving Dynamic Performance and Efficiency of a Resonant Switched-Capacitor Converter Based on Phase-Shift Control

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1 Improving Dynamic Performance and Efficiency of a Resonant Switched-Capacitor Converter Based on Phase-Shift Control Kenichiro Sano, and Hideaki Fujita Department of Electrical and Electronic Engineering Graduate School of Science and Engineering Tokyo Institute of Technology S3-18, , Ookayama, Meguro-ku, Tokyo, , Japan Tel./Fax.: sano@akg.ee.titech.ac.jp, fujita@ee.titech.ac.jp Abstract This paper presents the output voltage regulation characteristics and the dynamic performance of an RSCC using a phase-shift control. The proposed phase-shift control realizes soft switching operation even if the output voltage was changed, and it achieves a higher conversion efficiency. A theoretical analysis shows that the RSCC can reduce its inductor volume compared with a buck converter when its output voltage range is limited within 19 81% of its input voltage. Experimental results verify the operation characteristics of the proposed method and show the improved conversion efficiency more than 99%. Index Terms inductor volume, phase-shift control, switchedcapacitor converter, zero-voltage switching. I. INTRODUCTION Dc dc converters are widely applied to dc power supplies, battery chargers, and power conditioners for photovoltaics and fuel cells. Most of the dc dc converters include magnetic components such as inductors or transformers to convert the power. The magnetic components occupy large volume and weight, and produce non-negligible losses in the converters. Switched-capacitor converters (SCC) [1] [3] have been widely used as a simple and low-cost dc dc converter in small power applications. The advantage of the SCC is its small volume because it needs no inductor or transformer. Recently, resonant switched-capacitor converters (RSCC) have been proposed to reduce the power losses and EMI []. The RSCC has an additional small inductor in series with the switched capacitor, leading to soft switching operation and low switching loss. As a consequence, the RSCC seems to be more suitable for high power applications than the SCC [5] [7]. The inductor used in the RSCC is much smaller than that in conventional buck converters because the main energy storage device in the RSCC is still capacitor like SCC. The mitigation of the conducted EMI is also reported in [8]. The RSCC can supply an output voltage which is almost half or double of the input voltage by feeding fixed periodic gate signals. This conventional method has a difficulty in the output voltage regulation, and the output voltage changes according to the input voltage fluctuations or voltage drops in the switching devices and the passive components. Some feedback methods have been proposed to regulate the output voltage by adjusting blanking [9], switching frequency [1], and duty cycle [11]. These methods make the RSCC continuously step-down the output voltage. However, these methods may cause increased switching and on-state losses due to its hard switching operation and large peak current, which lead the conversion efficiency to decline. The authors have proposed a new voltage-regulation method for RSCCs by adjusting a phase-shift angle. The control method realized a current amplitude control by adjusting the phase difference among gate signals. The method made the RSCC not only step-down but also step-up the output voltage continuously, and realized more flexible voltage regulation. The RSCC can continue zero-voltage switching (ZVS) even if the output voltage is changed. The basic characteristics have been analyzed on condition that the RSCC is used as a voltagebalancing circuit, and reported in [12]. This paper presents the output voltage regulation characteristics and the dynamic performance of an RSCC using a phase-shift control. The phase-shift control and mechanism of soft switching operations are explained. A theoretical analysis shows that the inductor volume of the RSCC is smaller than that of the buck converter in an output voltage range from 19 to 81% of the input voltage. Experimental results verify the operation characteristics of the proposed control method and show the improved conversion efficiency more than 99%. II. RESONANT SWITCHED-CAPACITOR CONVERTERS A. Circuit Configuration Fig. 1 shows a circuit configuration of a resonant switchedcapacitor converter (RSCC) [5]. This circuit steps down the input voltage V in and feeds the output voltage to a load. The RSCC consists of two half-bridge inverters with four switching devices and a series resonant circuit and. Addition of the small inductor is the only difference from a conventional SCC in circuit configuration, resulting in a great suppression of spike currents, power losses, and EMI issues. B. Phase-Shift Control Fig. 2 shows switching modes in the RSCC. Because the RSCC consists of two half-bridge inverters, it has four switching modes /9/$ IEEE 359

2 C s Reference points Reference signal k 1 k k 1 k 2 T/2 T/2 T/2 ON OFF ON OFF V in i out i load T/ T/ ON OFF ON OFF T 1k T 1k1 OFF ON OFF ON Load ON OFF ON OFF v S T 1k /2 T 1k1 2 OFF ON OFF ON Fig. 1. A resonant switched-capacitor converter. T 1k /2 T 1k1 2 ON i out V v in Cr 2 Mode t (a) (b) OFF Fig. 3. Switching sequence in the phase-shift control. v out K p K i s Phase-shift controller based on a feed-forward method I out T 1 I out 2K r RSCC i load 1 sco Fig.. Block diagram of the output voltage controller with current feedforward method. (c) Fig. 2. Four switching modes in the RSCC. (a) Mode 1. (b) Mode 2. (c) Mode 3. (d) Mode. Fig. 3 illustrates the switching sequence and waveforms of the phase-shift control for a power flow from the voltage source V in to the load. They are drawn under the condition that = V in /2. The switching frequency is set at a higher frequency than the resonant frequency of the series resonant circuit f r (= ωr 2π = 1 2π ). Therefore, the resonant circuit acts as an inductive impedance. In this situation, the amplitude of is controllable by the phase difference between the two half-bridge inverters. The reference signal is a square wave with a period T (= 1/ ) and a 5% duty cycle. The gate signals of and lead from the reference signal by T 1 /2, while and lag by T 1 /2. Therefore, mode 2 or appears for a short duration of T 1 between mode 1 and 3. Since the resonant-capacitor voltage is V in /2 on average, ±V in /2 is applied across the resonant inductor during mode 2 and. As a result, the resonant current has a trapezoidal waveform. The output current i out is the rectified current of. Therefore, the average value of i out is proportional to the amplitude of. When and lag from and (T 1 < ), power is regenerated from to V in. In a conventional control method, the power flow was decided only by the output voltage. However, the phase- (d) shift control enables the RSCC to control i out bidirectionally by adjusting the phase-shift T 1 regardless of. The averaged output current I out is derived from the relation between transferred power and T 1 in the RSCC [12], which is expressed as follows: I out = 2V in sin ω r T 1 sin ω r T 2 ωrl 2 r T 1cosω r T 1 cos ω r T 2 cos ωrt, (1) 2 where T 2 = T/2 T 1. A first order approximation of (1) around T 1 =yields I out V in Z r tan ω rt ( ) T1, (2) T where Z r is the characteristic impedance of the resonant circuit, given by Z r = /. C. Control Scheme Fig. shows the block diagram of the output voltage controller for the RSCC. The output voltage can be regulated by applying voltage feedback with proportional and integral (PI) gains. The reference of the averaged output current Iout is given as follows: ( Iout(s) = K p K ) i {V s out(s) V out (s)}, (3) where K p is a proportional gain and K i is an integral gain. This feedback control realizes an accurate voltage regulation 351

3 v out K p K i s Phase-shift controller based on a current feedback method i load I out T 1 I out 1 K r RSCC sco ON OFF v S1 Fig. 5. Block diagram of the output voltage controller with current feedback method. in spite of the input voltage fluctuation or voltage drops in devices. According to the relation in (2), T 1 is calculated by the reference value of the output current Iout as follows: ON OFF i S1 id1 i Cs1 (a) i S1 id1 i Cs1 (b) T 1 =2K r I out, () v S3 where K r is a control gain depending on circuit parameters, given by Z r T K r = 2V in tan ωrt. This feed-forward control method simply decides T 1 to be in proportion to the Iout, and do not need any current sensor. III. CURRENT FEEDBACK METHOD The phase-shift controller based on the feed-forward method using () is simple and easy to implement, but may cause some error and/or overcurrent in transient states. In order to eliminate the error, a feedback control loop can be added to T 1 in (), and the phase-shift is represented by T 1 =2K r I out G(I out I out ). (5) The first term is the same as (), and the second term is a feedback component to eliminate the disturbance in I out.if the feedback gain is set as G = K r based on a deadbeat control technique, I out settles to I out a half switching cycle after the reference change. Therefore, the phase-shift is given by T 1 = K r (I out I out ). (6) Fig. 5 shows the block diagram of the proposed current controller refining the dynamic performance. The output current I out is sampled at the reference points shown in Fig. 3. Even if the resonant current includes error in transient states, the current feedback operates to reduce the error. This control is suitable for applications which require a quick transient response. In the actual circuits, the resonant current is detected instead of direct sensing of i out to reduce the impedance of the output current pass. The estimated output current Îout is given by { air (in Mode 1) Î out = (7) a (in Mode 3), where a is the coefficient to convert the sampled current value to average current value, given by a = ωrt ω rt sin [12]. i S3 id3 i Cs3 i S3 id3 i Cs3 (c) (d) Fig. 6. Voltage and current waveforms of the switching devices in case of a soft switching operation. (a) turn-off of the. (b) turn-on of the.(c) turn-off of the. (d) turn-on of the. A. Soft Switching Operation IV. SOFT SWITCHING The phase-shift control makes the RSCC accomplish soft switching operations by using the parasitic output capacitance of the MOSFET or additional snubber capacitors C s. Fig. 6 shows waveforms of the gate signal, the drain-tosource voltage, and the drain current when the and are turned on or off. The drain current is expediently separated to a MOSFET forward current i S, a diode current i D, and a snubber-capacitor or output capacitance current i Cs. The inductor current bypasses the switching devices via in the turn-off process shown in (a) and (c), resulting in a zerovoltage switching (ZVS). The energy stored in C s does not cause any power loss because discharges C s before the next turn-on transition as shown in (b) and (d). In the turnon process, the diode current automatically commutates from diode to the corresponding MOSFET when the polarity of changes, resulting in a zero-voltage zero-current switching (ZVZCS). and also turn-off under ZVS and turn-on under ZVZCS as well as and. B. Requirement to Achieve Soft Switching If the inductor current is small during the commutation, the RSCC can not fully discharge C s before the turn-on transition. In such case, the energy remained in C s is lost during the turn-on process. The other snubber capacitor connected to the complementary MOSFET of the half-bridge inverter also generates loss at the same because it is suddenly charged to V in /2. The voltage of C s changes from V in /2 to during a blanking T D, and thus, the snubber voltage v Cs is 3511

4 I min I max T 1 T 2 Slope: (.5 m) V in Slope: V in 2 V in L c i out Load i out Fig. 8. A buck converter. Mode Fig. 7. Current waveforms of the RSCC in case of <m.5. calculated by v Cs = V in 2 1 dt. (8) 2C s v Cs has to be equal to zero at t = T D in order to discharge C s completely. If is assumed to be constant during a blanking T D, the current to discharge the snubber capacitor is derived as I SW = VinCs T D. The inductor current has to be greater than I SW at the switching timing to achieve a turn-on under ZVZCS. V. ENERGY STORED IN THE INDUCTOR In order to evaluate the inductor volume of the RSCC applying the phase-shift control, the energy stored in the inductor is derived and compared with a conventional buck converter. Fig. 7 shows waveforms of the resonant current and the output current i out when the output voltage is lower than V in /2. Here, the voltage conversion ratio is defined as m = /V in. Because the resonant capacitor voltage is equal to V in /2 on average regardless of, V in /2 applies to in mode 2 and. Therefore, the slope of is ± Vin 2 in mode 2 and. In mode 1, the sum of V in,, and applies to, and the slope of is (.5 m) Vin. In mode 3, the sum of and applies to, and the slope of is (m.5) Vin. Therefore, is a factor to decide these slopes. The decrease of increases the slopes of, resulting in the increase of I max and decrease of I min. When <m.5, a geometric analysis by Fig. 7 yields d dt = V in = I max I min (in Mode 2, ) (9) 2 T 1 d dt = (.5 m)v in = I max I min (in Mode 1, 3). (1) T 2 The averaged output current I out is expressed as follows: I out = (I max I min )T 2. (11) 2(T 1 T 2 ) The maximum energy stored in the inductor is given by E L = 1 2 I 2 max. (12) Substituting (9), (1), and (11) to (12) results in E L = 1 2m 16 V in I out ( ) 2 Imax I min Imax I min (13) I max I min I max I min V in and are constants decided by the specifications, and m and I out are fixed on a rated load condition. Both I max and I min are functions of. To minimize E L, the inductor should be set to 1 = m (1 m) 2 V in ( <m.5), (1) I out and the minimum E Lmin is given by E Lmin = 1 2m VinI out ( <m.5). (15) In case of.5 <m 1, similar analysis gives and E Lmin as follows: = m V in m 2 (.5 <m 1) (16) I out E Lmin = 12m VinI out (.5 <m 1). (17) Fig. 8 shows a buck converter. The energy stored in the inductor L c becomes minimum if L c is designed to make the peak value of the ripple current equal to the averaged value of the output current. In such condition, E Lmin is given as follows [13]: E Lmin = m(1 m) V ini out. (18) The maximum energy stored in the inductor shown in (15), (17), and (18) are plotted in Fig. 9 by the voltage conversion ratio m. The RSCC is smaller in the stored energy than the buck converter in a range of.19 <m<.81, and E Lmin is minimum around m =.5 in the RSCC. If m is limited in.5 <m<.55, the RSCC is ten s smaller in inductor volume than the conventional buck converter. 1 Applying the inequality of arithmetic and geometric means, I maxi min I max I min I 2 maxi min I max I min =2. I max I min I maxi min I max I min I maxi min I That equality holds if maxi min I = max I min,i.e.i I max I min I maxi min =. min 3512

5 Energy stored in the inductor ( ELmin V in ) Iout Buck converter RSCC.5 1 Voltage conversion ratio m Fig. 9. Relationship between the voltage conversion ratio and the energy stored in the inductor E Lmin, shown in (15), (17), and (18). TABLE I PARAMETERS OF THE EXPERIMENTAL CIRCUITS. Section VI-A, VI-C VI-B Input voltage V in V 2 V Output voltage V out V 1 V Voltage ratio m = V out/v in Output current I out 1 A 5 15 A Output capacitor 2, μf 1, μf Resonant inductor 27 μh 1 μh Resonant capacitor 9. μf 1 μf Snubber capacitor C s not connected.3 μf Switching frequency 2 khz 3kHz VI. EXPERIMENTAL RESULTS The proposed methods were evaluated using a 2.8-kW experimental circuit. The circuit parameters are summarized in Table I. The inductor is designed to realize soft switching operation in a range of.6 m.5 (±8% in the output voltage). is slightly larger than the theoretical value given by (1) and (16) in order to realize the soft switching in all operating range. Fig. 1 is the photograph of the resonant circuit used in the following experiments. Film capacitors (.7 μf, 63 V, two in parallel) were used for the resonant capacitor and a ferrite core inductor (27 μh, 22 A) was used for the resonant inductor. The volume of the capacitors and inductor were 87 cm 3 and 27 cm 3, respectively. The maximum energy stored in the inductor is 6.5 mj. On the other hand, a 2.8-kW buck converter has to store 7 mj in the inductor as presented in (18). Therefore, RSCCs can reduce the volume of the inductor by a factor of ten compared with buck converters. Fig. 1. Resonant capacitor (87 cm 3 ) Resonant inductor (27 cm 3 ) scale: mm Components for the resonant circuit. 2 1 v S [μs] Fig. 11. Experimental waveforms when the output voltage was regulated as V out = 185 V. 2 1 v S [μs] Fig. 12. Experimental waveforms when the output voltage was regulated as V out = 2 V. 2 1 v S [μs] Fig. 13. Experimental waveforms when the output voltage was regulated as V out = 215 V. A. Voltage Regulation Characteristics Figs. 11, 12, and 13 are the experimental waveforms of the 2.5 kw conversion when the output voltage V out was regulated at 185 V, 2 V and 215 V. The phase of and led to the phase of and. The zero-voltage switching operation was realized, and switching surge was very small. The voltage applies to and, and V in applies to and.the average of these voltage V in /2 (= 2 V) is the average of the resonant capacitor voltage, which is constant regardless of the output voltage V out. 3513

6 Output voltage Vout (V) V out = 215 V V out = 2 V V out = 185 V Output power V outi out (kw) Fig. 1. Output voltage regulation characteristics under different load conditions. 1 I out 1 3 i out Fig. 15. Experimental waveforms by the feed-forward method whose phaseangle is given by (). 1 I out 1 3 i out Fig. 16. Experimental waveforms by the proposed current feedback method whose phase-angle is given by (6). Fig. 1 shows the characteristics of the output voltage regulation under different load conditions when the output voltage reference Vout was set to 185 V, 2 V, and 215 V. The error in the output voltage was regulated within.2% in all operating range. B. Transient Characteristics under a Load Change Figs. 15 and 16 show experimental waveforms when the output current reference Iout was suddenly changed between 2. A and 9. A. A 1-V voltage source was connected instead of the load in order to verify the current control characteristics. In Fig. 15, the phase-shift control based on 3 i load i out Fig. 17. Experimental waveforms by the output voltage controller with the current feed-forward method shown in Fig.. 3 i load i out Fig. 18. Experimental waveforms by the output voltage controller with the proposed current feedback method shown in Fig. 5. the feed-forward method given by () was applied as a current regulator. The current included an oscillation in the resonant frequency, and the peak value reached 22 A just after the step change. Fig. 16 was obtained by using the current feedback method given by (6). No overshoot was observed even if step changes were given to Iout. The current feedback method can improve the transient characteristics in the RSCC. Figs. 17 and 18 show experimental waveforms under a step change in the load current i load while the output voltage was regulated to V out = V in /2=1 V. Fig. 17 was obtained by the voltage controller with the feed-forward method shown in Fig.. The current had an oscillation and its peak reached 3 A. Fig. 18 was obtained by the voltage controller with the current feedback method shown in Fig. 5. No oscillation was observed in. The proposed method can reduce the peak current flowing through the resonant circuit, resulting in the reduction of the current rating in the inductor. C. Efficiency and Classified Power Losses Conversion efficiency was measured using Power MOS- FETs (IXYS HiPerFET, IXFN13N3) for the switching devices. External snubber capacitors C s were not connected because MOSFET s parasitic output capacitance (ss = 2.7 nf at V DS = 25 V) was enough to achieve soft switching. Power meters (Yokogawa WT13) were attached to the dc 351

7 1 1 Efficiency Power loss (W) Output power V outi out (kw) Fig. 19. Conversion efficiency at V out = 2 V. output capacitance loss Output power V outi out (W) Fig. 2. Classified power losses of the RSCC. wire resistance loss inductor loss MOSFET on-state loss power source and the load. The power consumed in the control circuit and the gate drive circuit was not included in the loss. Fig. 19 shows the conversion efficiency in difference load conditions. The output voltage was regulated as V out = V in /2 = 2 V and output current I out was changed. The negative power means the regeneration from load side to power source using a voltage source instead of the load. The efficiency was more than 99% in a range from 1% to the full load. Fig. 2 shows the classified power losses. Measured losses are also plotted together. The on-state loss and output capacitance loss in the MOSFET are calculated based on the value in its data sheet. The loss in the resonant inductor, resonant capacitor, and wires connecting the components are calculated based on the resistances measured by a LCR meter. When the output power is less than 5 W, the resonant current is not large enough to operate under soft switching condition. Therefore, the output capacitance loss is dominant. When the output power is more than 5 W, the resonant current increases and the soft switching is achieved. The on-state loss of the MOSFET is % of the total loss. The inductor loss is only 2% of the total loss because its volume is quite small. The capacitor losses in and are less than.1 W and they are negligible. The difference between the measured and calculated losses is assumed to be switching losses. Fig. 21 shows the conversion efficiency when the output voltage was changed in the range of 2 ± 16 V (m = 5 ± %). The reduction of the transferred power limits the voltage range available to achieve soft switching. Therefore, the farther m goes from.5 (V out = 2 V), the lower the efficiency becomes. Efficiency Fig kw 2. kw 1.5 kw 1. kw Output voltage V out (V) Conversion efficiency in case of changing output voltage. VII. CONCLUSION The output voltage regulation characteristics, dynamic performance, the inductor volume, and the efficiency of the resonant switched-capacitor converter (RSCC) applying a phaseshift control are discussed in this paper. A current feedback method is proposed to improve the dynamic performance of the RSCC. The analysis of the inductor volume revealed that the inductor volume of the RSCC is smaller than the buck converter when the converter is operated in a range of 19 81% in voltage conversion ratio. Experimental setup rated at 2.8 kw confirmed the steady-state and transient-state operation. The conversion efficiency of the experimental setup reached more than 99%. REFERENCES [1] I. Oota, T. Inoue, and F. Ueno, A realization of low-power supplies using switched-capacitor transformers and its analysis, Trans. IECE Japan, vol.j66-c, no.8, pp , Aug (in Japanese) [2] A. Ioinovici, Switched-capacitor power electronics circuits, IEEE Circuits and Systems Magazine, vol.1, no.3, pp.37 2, 21. [3] F. Zhang, L. Du; F.Z. Peng; Z. Qian, A new design method for high-power high-efficiency switched-capacitor dc dc converters, IEEE Trans. on Power Electronics, vol.23, no.2, pp.832 8, Mar. 28. [] K.W.E. Cheng, New generation of switched capacitor converters, Proc. IEEE PESC 98, vol.2, pp , May [5] M. Shoyama, T. Naka, and T. Ninomiya, Resonant switched capacitor converter with high efficiency, Proc. IEEE PESC, vol.5, pp , Jun. 2. [6] O. Keiser, P.K. Steimer, and J.W. Kolar, High power resonant switchedcapacitor step-down converter, Proc. IEEE PESC 8, pp , Jun. 28. [7] M. Shen, F.Z. Peng, and L.M. Tolbert, Multilevel dc dc power conversion system with multiple dc sources, IEEE Trans. on Power Electronics, vol.23, no.1, pp.2 26, Jan. 28. [8] M. Shoyama, F. Deriha, and T. Ninomiya: Evaluation of conducted noise of resonant switched capacitor converter, Proc. IEEE INT- ELEC 6, 1-3, Sep. 26. [9] Y. C. Lin, and D. C. Liaw, Parametric study of a resonant switched capacitor DC-DC converter, Proc. IEEE TENCON 21, vol.2, pp , Aug. 21. [1] M. Shoyama, and T. Ninomiya, Output voltage control of resonant boost switched capacitor converter, Proc. PCC-Nagoya 27, LS3--, pp , Apr. 27. [11] D. Qiu, B. Zhang, and C. Zheng, Duty ratio control of resonant switched capacitor DC-DC converter, Proc. ICEM5, vol.2, pp , Sep. 25. [12] K. Sano, and H. Fujita, Voltage-balancing circuit based on a resonant switched-capacitor converter for multilevel inverters, IEEE Trans. on Industry Applications, vol., no.6, pp , Nov./Dec. 28. [13] J. G. Kassakian, M. F. Schlecht, and G. C. Verghese, Principles of Power Electronics, pp , Addison-Wesley,