Extended Switched-Boost DC-DC Converters ...

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IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, VOL. 5, NO. 3, SEPTEMBER 2017

Extended Switched-Boost DC-DC Converters Adopting Switched-Capacitor/Switched-Inductor Cells for High Step-up Conversion Xiaoquan Zhu, Bo Zhang, Senior Member, IEEE, Zhong Li, Hong Li, Member, IEEE, and Li Ran, Senior Member, IEEE

Abstract— This paper proposes a family of switched-boost dc–dc converters for the high stepup voltage conversion applications, such as renewable energy power generation, uninterruptible power supply, and automobile high-intensity discharge headlamps. Compared with other dc–dc converters, the proposed switched-boost converter, which combines the traditional switched-boost network with the switched-capacitor/switchedinductor cells, has the following features: higher output voltage gain, a fewer passive components such as inductors and capacitors, and lower voltage stress across the output diode and power switches. Another advantage of the proposed topology is its expandability. If a higher voltage conversion ratio is required, additional cells can be easily cascaded by adding one inductor and three diodes. The structure, operating principle analysis, parameter design, and comparison with other dc–dc converters are also analyzed. Finally, both simulations and experimental results are presented to verify the effectiveness of the proposed converter. Index Terms— DC–DC converter, switched-boost network, switched capacitor (SC), switched inductor (SL).

I. I NTRODUCTION N RECENT years, with the development of modern industrial technology and the massive consumption of electrical energy, it is necessary to increase the electric power generation to fulfill the increasing energy demand. In this case, distributed generation technologies, which utilize the renewable energy sources to generate electrical power, have gained wide attention [1], [2]. Among this, the fuel cells and photovoltaic arrays are the main utilization method of the new energy resources, which have got rapid development [3], [4].

I

Manuscript received September 1, 2016; revised October 21, 2016 and November 28, 2016; accepted December 6, 2016. Date of publication December 19, 2016; date of current version July 31, 2017. This work was supported by the Key Program of National Natural Science Foundation of China under Grant 51437005. Recommended for publication by Associate Editor Zhikang Shuai. (Corresponding author: Bo Zhang.) X. Zhu and B. Zhang are with the School of Electric Power, South China University of Technology, Guangzhou 510640, China (e-mail: [email protected]; [email protected]). Z. Li is with the Faculty of Mathematics and Computer Science, FernUniversität in Hagen, 58084 Hagen, Germany (e-mail: [email protected]). H. Li is with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China (e-mail: [email protected]). L. Ran is with the State Key Laboratory of Power Transmission Equipment and System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JESTPE.2016.2641928

Fig. 1.

Typical schematic of the two-stage renewable energy system.

However, in the renewable power generation systems, the output voltage of fuel cells and photovoltaic arrays tend to be low, which is far away from the desired dc-link voltage level of the grid-connected inverters. Therefore, high stepup dc/dc converters, which are used as the interfacing converters between the renewable sources and the grid-connected inverters, are getting more and more attention and have been widely studied [4]–[30]. Fig. 1 shows a typical schematic of the two-stage renewable energy system, which is composed of renewable energy sources, a high stepup dc/dc converter, and a grid-connected inverter for ac power application [5]. While for many other industrial applications, such as electrical vehicle auxiliary power supplies, TV-CRTs, medical X-ray equipment systems, and automobile high-intensity discharge headlamps, the dc/dc converter with high voltage conversion ratio is also required [6], [7]. Generally, the conventional boost converter is one of the most commonly used topology for voltage stepup. However, when the desired output voltage is much higher than the input voltage, the operated duty ratio is almost approaching 1, which will induce high current ripple with low efficiency [8]. Various dc–dc converter topologies have been developed to produce a high voltage gain without an extremely large duty ratio. For the isolated dc/dc converters, it can produce a high voltage conversion ratio by increasing the turns ratio of the transformers [9], [10]. However, a large turns ratio will lead to a large leakage inductance, which may induce high voltage spikes and high voltage stress of the switching devices [11]. Moreover, the cost and system volume of the isolated converter is high with the isolated controllers and multiple dc/ac/dc power conversion stages. The nonisolated dc–dc converters can be employed to achieve low cost and high efficiency, and can be categorized as coupled inductor type and noncoupled inductor type. For the coupled-inductor-based dc/dc converters, by increasing the turns ratio of the coupled inductor appropriately, which is

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ZHU et al.: EXTENDED SWITCHED-BOOST DC–DC CONVERTERS ADOPTING SC/SL CELLS

similar to the isolated transformer based converters, a high stepup voltage gain can be obtained [12], [13]. However, the voltage spikes across the power switches caused by leakage inductance of the coupled inductor should also be carefully taken into consideration. As a result, various active and passive voltage clamping strategies and additional snubber circuits have been proposed to absorb the energy stored in the leakage inductance [14], [15], leading to circuit complexity, high volume, and low overall efficiency. The noncoupled inductor type dc–dc converters can produce high voltage gain with minimized magnetic components. In [16], the boost converters can be cascaded in series to achieve a high voltage gain, but the system will be complicated due to too many components and additional control units. In [17], the nonisolated high stepup dc–dc converters with single-phase and multiphase voltage multiplier cells have been proposed, which have a low switch voltage stress and low commutation losses. In [18], a family of high stepup selflift dc/dc converters has been proposed by integrating the voltage lift technique into the conventional Cuk converter. And a transformerless dc–dc converter with high voltage gain has been presented in [19], which can be used to reduce the voltage and current stress, but the voltage gain is usually lower than five. In addition, some nonisolated high stepup dc–dc converters using the switched-capacitor (SC) cells have been proposed in [20]-[22]. Similarly, switched-inductor (SL) techniques can also be used in dc–dc converters to achieve high voltage gain as presented in [23]-[26]. Although the output voltage gain can be increased by adding more switched cells, the circuit topology will be very complex. Based on Z -source impedance network [27], a modified Z -source dc–dc converter is proposed in [28], which can produce a higher voltage gain than the conventional Z -source dc–dc converter. As similar to the Z -source network, a switched-boost converter has been presented in [29] and [30], which has a less number of passive components in the impedance network. However, the output voltage gain of the switched-boost converter is not higher than that of the traditional Z-source converter. In this paper, based on the conventional switched-boost converter topology, a high stepup switched-boost dc–dc converter adopting SC/SL cells is proposed, which has the following advantages: high output voltage gain, low voltage stress across the output diode and power switches, and easy to control. In addition, it can be extended to have a very high voltage conversion ratio by cascading additional cells. The operating principle and steady-state analysis of the proposed converters are discussed in detail, and the comparison with other dc–dc converter topologies reveal the advantages of the proposed converter, which are verified by both the simulation studies and the experimental results. II. T OPOLOGICAL D ERIVATION OF THE P ROPOSED C ONVERTER The proposed SC switched-boost converter (SC-SBC) is derived from the SC converter, as shown in Fig. 2, and the switched-boost converter, as shown in Fig. 3. The basic idea of the proposed SC-SBC is using an additional SC branch combined with another SC branch, which is

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Fig. 2.

SC converter in [21].

Fig. 3.

Switched-boost converter in [29].

Fig. 4.

Proposed switched-boost converters. (a) SC-SBC. (b) SC/SL-SBC.

hidden in the switched-boost network, to form an SC cell, as shown in Fig. 4(a). The switched-boost network is composed of inductor L, capacitor C1 , switch S1 , and diodes D1 and D3 , and the SC cell is consisted of capacitors C1 and C2 and diodes D1 and D2 . The power switches S1 and S2 share the same control signals, which is easy to control. By substituting the inductor L with an SL cell (L 1 , L 2 , D1a , D2a , and D3a ) in the switched-boost network. A new high stepup dc–dc converter can be constructed, named SC/SL-SBC, as shown in Fig. 4(b). Combining the SC/SL cell with the switched-boost network, when the switches are shutting OFF, the inductors are connected in series and the energy transferred from inductors is used to charge the capacitors in parallel; when the switches are turned ON, the inductors are connected in parallel and charged by the input source, and the SCs are operated in series connection to supply the load. Therefore, the converter can produce a higher output voltage gain. III. O PERATING P RINCIPLE OF THE P ROPOSED C ONVERTERS To simplify the analysis, we assume that all components in the converter are ideal, and the inductors, capacitors,

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Fig. 6. Equivalent circuits of the proposed SC-SBC in CCM operation. (a) Switches S1 and S2 are turned ON. (b) Switches S1 and S2 are turned OFF.

of Vi , C1 , Do , Co , R L , C2 , and S2 , where C1 and C2 are in series with the input source Vi to supply the load through S2 . By applying KVL, we have u L = Vi + VC1 Vo = Vi + VC1 + VC2 .

(1) (2)

2) Mode 2: During this state, the switches S1 and S2 are turned OFF, as shown in Fig. 6(b). Diodes D1 –D3 are ON and the output diode Do is reverse blocking. There are three loops in this state: 1) loop 1 is composed of L, D1 , C1 , and D3 , where the inductor L charges capacitor C1 ; 2) loop 2 is consisted of Vi , D3 , L, C2 , and D2 , where Vi and L discharge the energy to C2 ; and 3) loop 3 is composed of Co and R L . The load R L is powered by capacitor Co . Thus, we have u L + VC1 = 0 VC2 = Vi + VC1 . Fig. 5. Key waveforms of the proposed switched-boost converters in CCM. (a) SC-SBC. (b) SC/SL-SBC.

and resistors are all linear, time invariant, and frequency independent. And all the proposed converters operate in continuous conduction mode (CCM). Fig. 5 shows the key waveforms of the proposed converters in CCM operation. A. Operating Modes of the SC-SBC Converter When the converter operates in CCM, there exist two operating modes. And the topological equivalent circuits are shown in Fig. 6. 1) Mode 1: The power switches S1 and S2 are turned ON during this time interval, as shown in Fig. 6(a). Diodes D1 , D2 , and D3 are OFF due to the reverse parallel connection with capacitors. There are two loops in this state: 1) loop 1 is composed of Vi , C1 , S1 , L, and S2 , in which Vi and C1 discharge the energy to inductor L; 2) loop 2 is consisted

(3) (4)

Based on the volt–second balance principle of inductor L and defining the duty ratio of switches S1 and S2 as D = TON /Ts , where Ton is the ON time of the switches and Ts is the switching period, the following equations can be obtained: D Vi (5) VC1 = 1 − 2D 1− D Vi VC2 = (6) 1 − 2D 2(1 − D) Vi . (7) Vo = 1 − 2D Therefore, the output voltage gain of the proposed SC-SBC converter can be derived as Vo 2(1 − D) G= . (8) = Vi 1 − 2D B. Operating Modes of the SC/SL-SBC Converter Fig. 7 shows the topological equivalent circuits of the SC/SL-SBC converter in CCM operation, and can be divided into two operating modes.


Fig. 7.

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Fig. 8.

Schematic of the Mc-SC/SL-SBC.

Fig. 9.

Output voltage gains of the Mc-SC/SL-SBC.

Equivalent circuits of the proposed SC/SL-SBC in CCM operation.

1) Mode 1: The switches S1 and S2 are turned ON simultaneously, as shown in Fig. 7(a). Diodes D1 –D3 and D2a are OFF. The two inductors L 1 and L 2 are charged by Vi and C1 in parallel. Meanwhile, Vi , C1 , and C2 supply the load R L through S2 . Thus, we have u L 1 = u L 2 = Vi + VC1 Vo = Vi + VC1 + VC2 .

(9) (10)

2) Mode 2: During this time interval, S1 and S2 are turned OFF, as shown in Fig. 7(b). Diodes D1 –D3 and D2a are ON and D1a , D3a , and Do are reverse biased. Inductors L 1 and L 2 discharge the energy to capacitor C1 in series. Meanwhile, L 1 and L 2 are in series with Vi to charge capacitor C2 . And the load R L is powered by capacitor Co . By applying the KVL, we have u L 1 + u L 2 + VC1 = 0 Vi = VC2 − VC1 .

(11) (12)

Based on the volt–second balance principle of inductors L 1 and L 2 , one can obtain 2D Vi 1 − 3D 1− D Vi VC2 = 1 − 3D 2(1 − D) Vi . Vo = 1 − 3D

VC1 =

(13) (14) (15)

Therefore, the voltage gain of the SC/SL-SBC converter can be expressed as G=

Vo 2(1 − D) . = Vi 1 − 3D

(16)

Comparing the output voltage gain of (8) with that of (16), one can find that the output voltage gain of SC/SL-SBC is much higher than that of SC-SBC.

C. Multicell SC/SL-SBC The topology of a multicell SC/SL-SBC (Mc-SC/SL-SBC) is shown in Fig. 8. It can be extended to produce a higher voltage conversion ratio by cascading more cells, and the structure of a cell is shown in the bottom-left corner of Fig. 8. It is composed of one inductor L n+1 and three diodes D3na , D(3n−1)a , D(3n−2)a for the nth cell. When S1 and S2 are turned ON, the diodes D3na , D(3n−2)a , and Do are ON, whereas diodes D1 –D3 and D(3n−1)a are OFF. All the inductors from L 1 to L n operate in parallel connection, and all inductors are charged by both the input source Vi and capacitor C1 . When S1 and S2 are turned OFF, the diodes D1 , D2 , D3 , and D(3n−1)a are ON, whereas diodes D3na , D(3n−2)a , and Do are OFF. All the inductors from L 1 to L n operate in series connection, and all inductors are discharged to capacitor C1 . Using a similar method as the SC/SL-SBC, the output voltage gain of the Mc-SC/SL-SBC can be derived as G=

Vo 2(1 − D) . = Vi 1 − (2 + n)D

(17)

Fig. 9 shows the output voltage gains with varying duty ratio when n is changed from 0 to 3. The Mc-SC/SL-SBC without a cell (n = 0) becomes SC-SBC and the Mc-SC/SL-SBC with one cell (n = 1) becomes the SC/SL-SBC. Therefore, the output voltage gain of the Mc-SC/SL-SBC can be easily increased by cascading more cells. D. Small-Signal Transfer Function Analysis For the proposed SC/SL-SBC converter, the open-loop small-signal transfer function from the duty ratio to the output

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TABLE I V OLTAGE S TRESS OF THE P ROPOSED C ONVERTERS

Fig. 10.

Bode diagram of the open-loop system.

Fig. 11.

Voltage loop control of the proposed converter.

voltage G vd (s) is obtained as G vd (s) =

b0 + b1 s + b2 + a1 s 2 + a2 s + a3 s2

a0

s3

TABLE II C URRENT S TRESS OF THE P ROPOSED C ONVERTERS

(18)

where a0 = 2LC1 Co , a1 = 2LC1 /R a2 = (1 − D)(1 − 3D)Co , a3 = (1 − D)(1 − 3D)/R 4DC1 Vi b0 = 2LC1 Vo /R D, b1 = − 1 − 3D and 2(1 + D)Vo (1 − D)(1 − 3D)Vo − . b2 = RD (1 − D)R The detailed derivation of G vd (s) can be found in the Appendix. By choosing the parameters in Section VI and assuming D = 0.2, the Bode diagram of the duty ratio to the output voltage open-loop transfer function G vd (s) is shown in Fig. 10. From Fig. 10, it can be observed that the slope inclination is about −20 dB/dec on the crossing frequency, and when the radian frequency ω approaches infinity, the corresponding phase angle is about −90°, which indicates that the stability of this open-loop system can be guaranteed. In order to obtain a better performance of the proposed converter, the voltage loop control strategy can be implemented, as shown in Fig. 11, based on the developed small-signal model. IV. PARAMETER D ESIGN Normally, parameter design of the passive components mainly depends on their voltage stresses and current stresses, which have been summarized in Tables I and II, respectively. This is because the SC/SL-SBC converter has a simple circuit configuration and a higher voltage gain. Therefore, we will take it as the example to discuss the parameter design in this section. A. Parameter Design of Inductors 1) Switched Inductors L1 and L2 : When switches S1 and S2 are turned ON, the inductors are charged by Vi and C1 .

Therefore, the inductors can be designed based on following differential equation: L = uL

dt di L

(19)

where u L is the voltage of the corresponding inductor during the ON state, u L = Vi + VC1 . dt = DTs is the time interval of the ON state, and di L is the corresponding inductor current ripple within this time interval. For a given permitted fluctuation range x L % of the inductor current I L , di L is restricted by the following equation: di L = x L %I L .

(20)

Substituting the expression of u L and (20) into (19), the inductance can be expressed as L1 = L2 =

D(1 − 3D)R L . 4x L % fs

(21)

Hence, for a given duty ratio D and load R L , the inductance will be determined by (21) directly.


Fig. 12.

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Boundary condition of the proposed SC/SL-SBC converter. Fig. 13.

2) Boundary Condition Between CCM and DCM: In order to ensure that the proposed SC/SL-SBC operates in CCM, the inductor current i L should keep continuous in a whole switching period, that is

Comparison of voltage gains. TABLE III C OMPARISON OF THE N UMBER OF C OMPONENTS

1 I L − i L ≥ 0. (22) 2 Substituting the expression of I L and (20) into (22), we have L fs D (1 − 3D) . (23) ≥ RL 8 Denoting τ = Lf s /R L and τ B = D(1 − 3D)/8, Fig. 12 shows a plot of the critical τ B as a function of duty ratio D at the CCM and DCM boundaries. When τ > τ B , the converter operates in CCM; when τ < τ B , the converter operates in DCM. B. Parameter Design of Capacitors 1) Switched Capacitors C1 and C2 : Similar to the parameter design of inductors, when S1 and S2 are ON, capacitor C1 and C2 are in series with the input source Vi to supply the load R L . However, due to the sum of Vi , VC1 and VC2 are slightly higher than the output voltage Vo , and there exists a small voltage ripple VC on capacitors at the switching frequency. In order to limit VC to a small range, the capacitor voltage ripple is restricted by a permitted fluctuation range x C % as dvC = x C %VC .

(24)

During the ON state of S1 and S2 , the capacitors can be designed based on the following differential equation: C = IC_ON

dt . dvC

(25)

where dt = DTs is the ON time of S1 and S2 , IC_ON is the corresponding capacitor current as S1 and S2 are ON, and IC1_ON = −(1 + D)I L /(2D), IC2_ON = 2I L + IC1_ON . Substituting these two equations and (24) into (25) leads to ⎧ (1 + D)Io ⎪ ⎪C 1 = ⎨ 2Dx C %Vi f s (26) ⎪ (1 − 3D)Io ⎪ ⎩C 2 = . (1 − D)x C %Vi f s Therefore, the capacitance of capacitor C1 and C2 can be determined by (26) directly.

2) Output Capacitor Co : When S1 and S2 are turned OFF, the output diode Do is reverse blocking. The current flow through capacitor Co is equal to the load current Io . Then Co =

Io dt Io dt = dvCo x Co %Vo

(27)

where dt = (1 − D)Ts . Substituting (15) into (27), the capacitance of the output filter capacitor Co can be derived as Co =

(1 − 3D) Io . 2x Co %Vi f s

(28)

C. Parameter Design of Switching Devices Generally, The semiconductor switches S1 and S2 and diodes can be selected according to their voltage stresses and current stresses, as tabulated in Tables I and II, to keep them operating in their safe operating area. V. C OMPARISON W ITH OTHER DC–DC C ONVERTERS A. Comparison of Output Voltage Gains The output voltage gains of the proposed SC-SBC and SC/SL-SBC are given in Fig. 13 and compared with the existing SC boost (SC-Boost) converter with two SC cells in [21], SL boost (SL-Boost) converter with three SL cells in [23], 3-Z network boost (3-Z-Boost) converter in [26], the symmetrical hybrid SL (SH-SLC) converter in [24], and the

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TABLE IV C OMPARISON OF S TRESSES FOR THE S AME Vi , Iin , AND G

Fig. 14.

Comparison of the switch voltage stress.

Fig. 15.

Comparison of the output diode voltage stress.

multicell SL/SC active network converters (M-SL/SC-ANCs, n = 1 and m = 1) in [25]. The expressions of the ideal output voltage gain are shown in Table IV. And all the seven converters are noncoupled inductor type topologies. As can be seen from Fig. 13, the output voltage gains of the proposed SC-SBC and SC/SL-SBC converter are higher than those of the SL-Boost converter (with three SL cells), 3-Z-Boost converter, and the SH-SLC converter in the whole duty ratio range. Compared with

Fig. 16. Simulation results for the proposed SC/SL-SBC. (a) D = 0.2, (b) D = 0.25.

the SC-Boost converter (with two SC cells), the proposed SC/SL-SBC converter can achieve a higher voltage gain when the duty ratio D is larger than 0.18 (D > 0.18). And compared with the M-SL/SC-ANCs (n = 1, m = 1), the proposed SC/SL-SBC converter can produce a higher output voltage gain when the duty ratio is larger than 0.22 (D > 0.22).


Fig. 17.

Experimental waveforms when D = 0.2.

B. Comparison of the Number of Components Table III shows the comparison of the number of active and passive components used in these seven converters. As can be seen, compared with the SL-Boost converter (with three SL-cells), 3-Z-Boost converter and the SH-SLC converter, the proposed SC-SBC and SC/SL-SBC converter can provide a much higher output voltage gain but with the similar number of passive components used in the converter. Although the SC-Boost converter (with two SC cells) and the M-SL/SC-ANC(n = 1, m = 1) can produce a higher voltage gain when 0 < D < 0.18 and 0 < D < 0.22, they require a little more passive components than the proposed SC/SL-SBC converter. C. Comparison of Stresses This section compares the voltage and current stresses of these seven dc–dc converters under the condition of same input voltage Vi , input current Iin , and voltage gain G. The stresses of these converters have been summarized in Table IV. The comparison of the switch voltage stress in these seven converters is shown in Fig. 14. As can be seen, to produce a same output voltage gain, the proposed converters present a lower switching voltage stress than the SL-Boost converter (with three SL cells), 3-Z-Boost converter, and the SH-SLC converter, but a little higher than the SC-Boost converter (with 2 SC-cells) and the M-SL/SC-ANC (n = 1, m = 1). In addition, as shown in Fig. 15, to obtain the same voltage gain G, the proposed converters have only a higher output

Fig. 18.

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Experimental waveforms when D = 0.25.

Fig. 19. Experimental results with the load transient variation between full load and half load of the proposed SC/SL-SBC converter.

diode voltage stress than the SC-Boost converter, but lower than the other four dc–dc converters. VI. S IMULATION R ESULTS The simulation parameters are selected according to the parameter design in Section IV: the input voltage Vi = 10 V, switched capacitors C1 = C2 = 330 μF, switched inductors L 1 = L 2 = 220 μH, output filter capacitor Co = 470 μF, switching frequency f s = 30 kHz, and the load R L = 100 . The simulation results of the proposed SC/SL-SBC are shown in Fig. 16. As shown in Fig. 16(a), when D = 0.2, the capacitor voltages VC1 and VC2 are boosted to 10 and 20 V, respectively, and the output voltage Vo is boosted to 40 V. When the duty ratio D increases to 0.25, as shown in

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observed that there are some differences between them, which are mainly caused by the nonidealities of the components. Finally, the measured efficiency of the proposed SC/SL-SBC converter is plotted in Fig. 21. As can be seen, the proposed converter can realize a high efficiency when the output power is high.

Fig. 20.

Comparison between the experimental and theoretical values.

Fig. 21.

Measured efficiency of the proposed SC/SL-SBC converter.

Fig. 16(b), the capacitor voltages VC1 and VC2 are 20 and 30 V and the output voltage Vo is 60 V, which are fit well with the theoretical analysis. VII. E XPERIMENTAL R ESULTS In this section, a prototype of the proposed SC/SL-SBC converter is built to verify the operating principles. And the experimental parameters are chosen the same as the simulation parameters. The power MOSFET S1 and S2 (type: FQA90N15) are driven by the isolated amplifier (TLP250), and the MBR30200F are used for all the diodes. As shown in Fig. 17, when the duty ratio D = 0.2, the measured experimental values of capacitor voltages and output voltage are VC1 = 8.4 V, VC2 = 18.2 V, and Vo = 36.8 V, while the theoretical values are VC1 = 10 V, VC2 = 20 V, and Vo = 40 V. In addition, the voltage stresses across the switches VS1 and VS2 and the diode voltages V D1, V Do , V D3, and V D1a are measured in Fig. 17(b) and (c), respectively. When D = 0.25, as shown in Fig. 18, the measured values of capacitor voltages and output voltage are VC1 = 17.8 V, VC2 = 27.6 V, and Vo = 54.8 V, whereas the expected values are VC1 = 20 V, VC2 = 30 V, and Vo = 60 V. Fig. 18(b) shows the switch voltage stresses VS1 and VS2 . Fig. 18(c) shows the diode voltages V D1, V Do , V D3, and V D1a . In order to evaluate the dynamic response performance of the proposed SC/SL-SBC converter, the experimental results of the output voltage Vo and the output current i o under the load transient variation between full load and half load are depicted in Fig. 19. It can be seen that the output voltage of the proposed converter is insensitive to the load variation. The comparison between the desired output voltage values and the experimental values is plotted in Fig. 20. It can be

VIII. C ONCLUSION This paper proposes a family of switched-boost dc–dc converters, which are based on the SC/SL cells and the switchedboost network. The operation principle, parameter design, and comparison with other dc–dc converters have been described in detail. In comparison with other converters, the proposed SC/SL-SBC converter can achieve higher voltage gain with a small duty ratio. And by combining the SC cell and SL cell into the converter, the proposed converters have a low voltage stress across the output diode and power switches. In addition, it can be easily extended to produce a very high voltage gain by cascading more cells. Therefore, it will provide a very potential application for the high stepup voltage conversion occasions. Finally, the simulations and experimental results are presented to verify the effectiveness of the proposed converters. A PPENDIX The small-signal transfer function analysis of the proposed SC/SL-SBC converter is derived based on the state-space averaging method. Here, we choose the capacitor voltages vC1 (t), vC2 (t), and vCo (t) and inductor currents i L1 (t) and i L2 (t) as state variables, and the input voltage vi (t) and the input current i in (t) are chosen as the input variables. The corresponding state space differential equations can be obtained from the equivalent circuits for operation mode 1 and operation mode 2, as shown in Fig. 7(a) and (b), respectively. The differential equations for operation mode 1 can be written as ⎧ di L 1 (t) ⎪u ⎪ = vi (t) + vC1 (t) ⎪ L 1_ON = L 1 ⎪ dt ⎪ ⎪ ⎪ di (t) ⎪ ⎪u L 2_ON = L 2 L 2 = vi (t) + vC1 (t) ⎪ ⎪ dt ⎪ ⎪ ⎪ dv (t) ⎪ ⎨i C1 (t) = C1 C1 = −i in_ON (t) dt (29) dvC2 (t) ⎪ ⎪ = i (t) = C (t) + i (t) − i (t) i ⎪ C 2 L L in_ ON 2 1 2 ⎪ ⎪ dt ⎪ ⎪ dvCo (t) ⎪ ⎪ = −i L 1 (t) − i L 2 (t) i Co (t) = Co ⎪ ⎪ ⎪ dt ⎪ ⎪ vCo (t) ⎪ ⎩ . + i in_ON (t) − R Similarly, from the equivalent circuit in Fig. 7(b), the differential equations for operation mode 2 can be obtained as ⎧ −vC1 (t) di L 1 (t) ⎪ u L 1_OFF = L 1 ⎪ = ⎪ ⎪ dt 2 ⎪ ⎪ −vC1 (t) di L 2 (t) ⎪ ⎪ ⎪u L 2_OFF = L 2 = ⎪ ⎪ dt 2 ⎨ dvC1 (t) (30) = i L 1 (t) − i in_OFF (t) i C1 (t) = C1 ⎪ dt ⎪ ⎪ dvC2 (t) ⎪ ⎪ ⎪ = i in_OFF (t) i C2 (t) = C2 ⎪ ⎪ dt ⎪ ⎪ ⎪ ⎩i (t) = C dvCo (t) = − vCo (t) . Co o dt R


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⎧ ⎪ d(I L 1 + iˆL 1 ) ⎪ ˆ − (VC1 + vˆ C1 ) (D − d) ˆ ⎪ L1 = (Vi + vˆ i + VC1 + vˆ C1 )(D + d) ⎪ ⎪ dt 2 ⎪ ⎪ ⎪ d(I L 2 + iˆL 2 ) ⎪ ⎪ ˆ − (VC1 + vˆ C1 ) (D − d) ˆ ⎪ L2 = (Vi + vˆ i + VC1 + vˆ C1 )(D + d) ⎪ ⎪ dt 2 ⎨ d(VC1 + vˆ C1 ) ˆ + (I L 1_OFF + iˆL 1 − Iin_OFF − iîn )(D − d) ˆ (31) C1 = (−Iin_ON − iîn )(D + d) ⎪ dt ⎪ ⎪ ⎪ d(VC2 + vˆ C2 ) ⎪ ⎪ ˆ + (Iin_OFF + iîn )(D − d) ˆ = (I L 1_ON + iˆL 1 + I L 2_ON + iˆL 2 − Iin_ON − iîn )(D + d) C2 ⎪ ⎪ ⎪ dt ⎪ ⎪ d(VCo + vˆ Co ) (VCo + uˆ Co ) ⎪ ⎪ ˆ − (VCo + uˆ Co ) (D − d) ˆ ⎩C o = −I L 1_ON − iˆL 1 − I L 2_ON − iˆL 2 + Iin_ON + iîn − (D + d) dt R R D 2s 2 L 1 L 2 C1 IDo − 2sC1 (L 1 + L 2 ) 1−3D Vi + IDo (1 − D) (1 − 3D) L 2 − 1+D vˆ Co (s) 1−D Io (L 1 + L 2 ) = (34) 2L L C (s) = 0 v ˆ (1−D)(1−3D) 2s i 1 2 1 ˆ d(s) 2s 3 L 1 L 2 C1 Co + + s L 2 Co (1 − D) (1 − 3D) + L2 R R iîn (s) = 0 D Vi + IDo (1 − D) (1 − 3D) − 2 1+D 2s 2 LC1 IDo − 4sC1 1−3D vˆ Co (s) b0 s 2 + b1 s + b2 1−D Io G vd (s) = = (35) = 2 vˆ i (s) = 0 ˆ a0 s 3 + a1 s 2 + a2 s + a3 d(s) 2s 3 LC1 Co + 2s RLC1 + sCo (1 − D) (1 − 3D) + (1−D)(1−3D) R iîn (s) = 0 G vd (s) =

By applying the small-signal perturbations, vî (t) to the input ˆ to the duty ratio of voltage, iîn (t) to the input current, and d(t) switch S are shown by vi (t) = Vi + vî (t), i in (t) = Iin + iîn (t) ˆ and d(t) = D + d(t). Thus, we have (31), shown at the top of this page, where D = 1 − D. Separating the dc components, then we have ⎧ 2D 2 ⎪ ⎨VC1 = Vi Io IL1 = IL2 = 1 − 3D 1 − 3D (32) 1+ D Io ⎪ ⎩ Iin_ON = Io Iin_OFF = D (1 − 3D) 1− D which are in consistent with the values shown in Tables I and II, respectively. Separating the ac components, and after Laplace transformation, the ac small-signal transfer functions can be obtained as ⎧ 3 3D − 1 ⎪ ˆ ˆ ⎪ vˆ C1 (s) Dˆvi (s)+ ⎪s L 1 i L 1 (s) = Vi + 2 VC1 d(s)+ ⎪ 2 ⎪ ⎪ ⎪ 3 3D − 1 ⎪ ⎪ ˆ ⎪ vˆ C1 (s) s L 2 iˆL 2 (s) = Vi + VC1 d(s)+ Dˆvi (s)+ ⎪ ⎪ 2 2 ⎪ ⎪ ⎪ (−1 − D) Io ⎪ ⎪ ˆ d(s) ⎪sC1 vˆ C1 (s) = ⎪ ⎪ D(1 − D)(1 − 3D) ⎨ + (1 − D)iˆL 1 (s) − iîn (s) (33) ⎪ −Io ⎪ ⎪ ˆ ˆ ⎪ d(s) + Di L 1 (s) sC2 vˆ C2 (s) = ⎪ ⎪ D(1 − D) ⎪ ⎪ ⎪ ˆ ˆ ⎪ ⎪ ⎪ + Di L 2 (s) + (1 − 2D)i in (s) ⎪ ⎪ 1 Io ˆ ⎪ ⎪ vˆ Co (s) = d(s) − DiˆL 1 (s) sCo + ⎪ ⎪ ⎪ R D ⎪ ⎩ − DiˆL 2 (s) + Diîn (s). To obtain the transfer function from the duty ratio the output voltage, which implies that the perturbations the input voltage and the input current are assumed be zero. Therefore, we have (34), shown at the top this page,

to of to of

Due to L 1 = L 2 = L in the SC/SL-SBC converter, the transfer function G vd (s) can be simplified as (35), shown at the top of this page, where a0 = 2LC1 Co , a1 = 2LC1 /R, a2 = (1 − D)(1 − 3D)Co a3 = (1 − D) (1 − 3D)/R, b0 = 2LC1 Vo /R D, b1 = −(4DC1 Vi /(1 − 3D)), and b2 = (((1 − D)(1 − 3D)Vo )/R D) − ((2(1 + D)Vo )/((1 − D)R)). R EFERENCES [1] F. A. Farret and M. G. Simões, Integration of Alternative Sources of Energy, 1st ed. Hoboken, NJ, USA: Wiley, 2006. [2] M. H. Nehrir et al., “A review of hybrid renewable/alternative energy systems for electric power generation: Configurations, control, and applications,” IEEE Trans. Sustain. Energy, vol. 2, no. 4, pp. 392–403, Oct. 2011. [3] M. W. Ellis, M. R. von Spakovsky, and D. J. Nelson, “Fuel cell systems: Efficient, flexible energy conversion for the 21st century,” Proc. IEEE, vol. 89, no. 12, pp. 1808–1818, Dec. 2001. [4] W. Li and X. He, “Review of nonisolated high-step-up DC/DC converters in photovoltaic grid-connected applications,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1239–1250, Apr. 2011. [5] C.-T. Pan and C.-M. Lai, “A high-efficiency high step-up converter with low switch voltage stress for fuel-cell system applications,” IEEE Trans. Ind. Electron., vol. 57, no. 6, pp. 1998–2006, Jun. 2010. [6] W. Li, J. Liu, J. Wu, and X. He, “Design and analysis of isolated ZVT boost converters for high-efficiency and high-step-up applications,” IEEE Trans. Power Electron., vol. 22, no. 6, pp. 2363–2374, Nov. 2007. [7] J. C. Rosas-Caro, J. M. Ramirez, F. Z. Peng, and A. Valderrabano, “A DC-DC multilevel boost converter,” IET Power Electron., vol. 3, no. 1, pp. 129–137, Jan. 2010. [8] A. Ioinovici, Power Electronics and Energy Conversion Systems. Hoboken, NJ, USA: Wiley, 2013. [9] B. Gu, J. Dominic, J.-S. Lai, Z. Zhao, and C. Liu, “High boost ratio hybrid transformer DC–DC converter for photovoltaic module applications,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 2048–2058, Apr. 2013. [10] H.-M. Hsu and C.-T. Chien, “Multiple turn ratios of on-chip transformer with four intertwining coils,” IEEE Trans. Electron Devices, vol. 61, no. 1, pp. 44–47, Jan. 2014. [11] J.-H. Lee, T.-J. Liang, and J.-F. Chen, “Isolated coupled-inductorintegrated DC–DC converter with nondissipative snubber for solar energy applications,” IEEE Trans. Ind. Electron., vol. 61, no. 7, pp. 3337–3348, Jul. 2014.

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Xiaoquan Zhu was born in Anhui, China, in 1990. He received the B.S. degree from the School of Information and Control engineering, China University of Mining and Technology, Xuzhou, China, in 2014. He is currently pursuing the Ph.D. degree in electrical engineering with the School of Electric Power, South China University of Technology, Guangzhou, China. His current research interests include high step-up power electronic converters and renewable energy power generation systems.

Bo Zhang (M’03–SM’15) was born in Shanghai, China, in 1962. He received the B.S. degree in electrical engineering from Zhejiang University, Hangzhou, China, in 1982, the M.S. degree in power electronics from Southwest Jiaotong University, Chengdu, China, in 1988, and the Ph.D. degree in power electronics from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1994. He is currently a Professor with the School of Electric Power, South China University of Technology, Guangzhou, China. He has authored or co-authored more than 350 papers and holds 50 patents. His current research interests include nonlinear analysis and control of power supplies and ac drives.

Zhong Li received the B.Sc. degree from Sichuan University, Chengdu, China, in 1989, the M.Sc. degree from Jinan University, Guangzhou, China, in 1996, the Ph.D. degree from the South China University of Technology, Guangzhou, in 2000, and the D.Sc. (Habilitation) degree from FernUniversitat, Hagen, Germany, in 2007. He is currently an Adjunct Professor with FernUniversitat. He has authored four books with Springer-Verlag, 18 book chapters, 53 journal papers, and 44 conference papers. His current research interests include fuzzy logic and fuzzy control, chaos theory and chaos control, intelligent computation and control, complex networks, and swarm intelligence. Dr. Li serves as the Associate Editor for six international journals.

Hong Li (S’07–M’09) received the B.Sc. degree from the Taiyuan University of Technology, Taiyuan, China, in 2002, the M.Sc. degree from the South China University of Technology, Guangzhou, China, in 2005, and the Ph.D. degree from Fernuniversitaet, Hagen, Germany, in 2009. She is currently an Associate Professor with the Electrical Engineering School, Beijing Jiaotong University, Beijing, China. She has authored one book, 20 journal papers, and 36 conference papers, and has also applied 15 patents. Her current research interests include nonlinear control and its applications, EMI suppressing methods for power electronic system, widebandgap power devices, and applications.

Li Ran (M’98–SM’07) received the Ph.D. degree in power systems engineering from Chongqing University, Chongqing, China, in 1989. He was a Research Associate with the University of Aberdeen, Aberdeen, U.K., The University of Nottingham, Nottingham, U.K., and Heriot-Watt University, Edinburgh, U.K. He became a Lecturer of Power Electronics with Northumbria University, Newcastle upon Tyne, U.K., in 1999, and was seconded to Alstom Power Conversion, Kidsgrove, U.K., in 2001. Between 2003 and 2012, he was with Durham University, Durham, U.K. In 2012, he joined the University of Warwick, Coventry, U.K., as a Professor of Power Electronics - Systems. His current research interests include the application of power electronics for electric power generation, delivery, and utilization.