A Variable-Structure Multi-Resonant DC–DC Converter with ... - MDPI

energies Article

A Variable-Structure Multi-Resonant DC–DC Converter with Smooth Switching Mengying Chen 1 Haiyun Yan 3 1 2 3

*

ID

, Yifeng Wang 1, *

ID

, Liang Yang 2

ID

, Fuqiang Han 1 , Yuqi Hou 1 and

School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China; [email protected] (M.C.); [email protected] (F.H.); [email protected] (Y.H.) National Electric Power Dispatching and Control Center, State Grid Corporation of China, Beijing 100031, China; [email protected] State Grid Tianjin Maintenance Company, Tianjin 300250, China; [email protected] Correspondence: [email protected]; Tel.: +86-185-2206-2559; Fax: +86-022-2740-1479

Received: 5 August 2018; Accepted: 20 August 2018; Published: 27 August 2018







Abstract: In this paper, a variable-structure multi-resonant soft-switching DC–DC converter and its transient smooth control method are proposed. Through the introduction of auxiliary switches, the converter can flexibly adjust its structure among three operating modes. Two switching processes can be obtained. Thus, a wide voltage gain range is achieved within a narrow frequency range. Moreover, to eliminate the large voltage fluctuation during modes switching, a drive signal gradual adjustment control method is proposed. Consequently, smooth switching between different modes can be realized and the voltage fluctuation is suppressed effectively. Finally, a 200 W experimental prototype is established to verify the theoretical analyses. Soft-switching performances for power switches and diodes are both guaranteed. The highest efficiency is 98.2%. With the proposed transient control method, a basically constant 400 V output voltage is ensured within a wide input voltage range (80 V–600 V). In particular, the transient voltage fluctuations during two switching processes decrease from 38.4 V to 10.8 V and from 37.2 V to 8.4 V, respectively. Keywords: variable structure; multi-resonant; soft switching; DC–DC converter; transient control; smooth switching

1. Introduction In recent years, the problem of energy shortages has become increasingly serious. Wind power, as an important form of new energy power generation, has attracted much attention [1–4]. Compared to the large and medium-scale wind power generation systems (WPGSs) [5], small-scale WPGSs have the advantages of lower cost, more flexible installation and a higher utilization rate of wind energy [6–9]. Moreover, they can be divided into off-grid and grid-connected WPGSs [10]. For the latter, the collected wind power can be transmitted to the electric grid through the inverter. Thereby, the wind energy can be applied to various loads, which exhibits wider applicability and practicability. Typical small-scale grid-connected WPGSs mostly adopt the cascading structure of three-stage converters: AC–DC rectifier, DC–DC converter and DC–AC inverter. To meet the normal grid-connected demands, the DC input voltage of the inverter is close to 400 V, indicating that the DC output voltage of the DC–DC converter is constant at 400 V. As for the small-scale wind field, however, its energy density is too small due to the frequent low wind speed. This results in a small input voltage for the DC-DC converter. Moreover, the wind speed can be dynamic at some occasions, which also indicates that the input voltage range of the DC–DC converter is wide. Therefore, it is very difficult to realize the normal grid connection. To solve these problems, the DC–DC converter not only needs to Energies 2018, 11, 2240; doi:10.3390/en11092240

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provide sufficient voltage pumping capacity, but also should achieve a relatively wide voltage gain range to meet the different requirements of various wind speed. High conversion efficiency is another objective to fulfill. This contributes to more power delivered to the electric grid. In summary, it is necessary to study a DC–DC converter with such advantages, including high voltage gain, a wide voltage gain range, and high efficiency. The resonant converters are the important components of the DC–DC converters. They can exhibit many merits, such as high frequency, high conversion efficiency and high power density. Among them, due to its simple structure and soft-switching characteristics, the LLC resonant converter has become a research hotspot [11,12]. LLC is an abbreviation of a resonant circuit, which is composed of two inductors and a capacitor. Where ‘L’, ‘L’ and ‘C’ represent the total leakage inductor, the excitation inductor and the resonant capacitor, respectively. Some researchers have tried to improve the performances of the LLC converter from the new topological derivations and control strategies. Hence, outstanding properties are achieved [13–17]. In [18], a novel sLLC resonant converter with a half-bridge structure is proposed, where “s” represents the auxiliary switch. Through the introduction of an auxiliary switch, the converter is able to energize the resonant inductor with the bus voltage during the hold-up period. As a result, a higher voltage gain can be obtained, while the output voltage remains at the expected level. However, limited by the structure of the LLC resonant tank, its voltage gain curve becomes very flat within the range exceeding the resonant frequency. Thus, the converter cannot regulate the output voltage flexibly. In [19], a HB-2LLC resonant converter is proposed. A half-bridge (HB) inverter and the dual LLC resonant tanks are employed. These two resonant tanks are series-connected in the primary side of the transformer, which improves the voltage gain effectively. Meanwhile, high conversion efficiency within a wide output voltage range is also realized. Such converters, however, suffer from the issues of complicated structure, difficult parameter design and intricate selection of magnetic components. Based on the traditional LLC topology, another kind of multi-resonant converter is obtained by adding more components to the resonant tank [20–23]. Owing to the multiple resonant components, multi-resonant DC–DC converters possess many resonant frequency points, and have diverse performances. Therefore, they can meet various requirements of different working conditions. In literature [20], a multi-resonant DC–DC converter is proposed. It can realize zero voltage switching (ZVS) and zero current switching (ZCS) in bidirectional power flow, which effectively reduces power losses and improves the efficiency. Moreover, [21] studies an algorithm with dead-band control, switch control and soft start control for a CLLC DC–DC converter. The ‘C’ and ‘L’ denote the resonant components in the resonant tank. The converter adopts the symmetrical ‘LC’ series structure in both sides of the transformer, and thus bidirectional power flow is realized. Through the control algorithm, the soft change between bidirectional power flow is realized. Meanwhile, good voltage gain property is obtained. Furthermore, based on the LLC topology, a new LLC-LC resonant converter with a notch filter is proposed in [22]. It is derived from the combination of the LLC topology and ‘LC’ resonant components. By adding the LC notch filter to the secondary side of the transformer, a wide voltage gain range from zero to the rated value is acquired. Until now, some researchers have been improving performance from the aspects of promoting conversion efficiency, elevating voltage gain and widening voltage gain range. However, for these converters with a fixed structure, it is difficult to achieve these three advantages simultaneously. As a result, the aforementioned converters still cannot meet the requirements of the small-scale grid-connected WPGSs. Through the employment of auxiliary switches, another kind of resonant converter can be implemented. Different to the fixed-structure converters, their structures can be flexibly changed to meet various operating demands. In [24], a topology-transformative resonant converter is proposed that adopts the structure of dual transformers. Through the voltage superposition of two transformers, the voltage gain can be elevated effectively. However, it is still limited by the relatively narrow input voltage range. In [25], a LLC resonant converter with a semi-active variable-structure rectifier (SA-VSR) is proposed. The SA-VSR is comprised of two switches and two diodes. Through the

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different operating states of switches, the converter can achieve a wide output voltage range. In [26], a topology-transformative LLC-SAR (semi-active rectifier) resonant DC–DC converter is proposed. It has two different structures that can be transformed flexibly between each other. Furthermore, soft switching characteristics are realized and the circulating energy is reduced. The multi-resonant converters with variable structure can achieve outstanding performance, such as high adaptability, high efficiency and high voltage gain. However, they also suffer from some issues. When the states of power switches are changed directly during the transition process between different modes, a voltage fluctuation may occur and this has a bad influence on system safety. To achieve smooth switching between different modes, a method of setting a control dead zone is employed in literature [27]. That is, all power switches are turned off firstly when the transition process starts. From the control aspect, the duty ratio of the control signal is directly reduced to zero. After a period of control dead zone, the duty ratio is then directly restored from zero to the desired value again. The remarkable advantages of this control method are simplicity of implementation, reliability and strong portability. However, the control signal in this method increases or decreases sharply. It may cause the large fluctuation in DC output voltage during the transition process, which will affect the normal operation of the renewable energy generation system as a result. Thereby, to obtain high reliability for a variable-structure converter, it is of great significance to study a control method with smooth mode switching. In this paper, to satisfy the application of the small-scale grid-connected WPGSs, a variable-structure multi-resonant soft switching DC–DC converter is proposed. It not only contributes to providing sufficient voltage pumping capacity and high conversion efficiency, but also achieves a wide voltage gain range. By controlling the on/off states of auxiliary switches in the resonant tank, the structure of the converter can be changed flexibly. Correspondingly, the converter has three different operating modes: the FB-CLTCL mode (full bridge CLTCL), the FB-LCLCL mode (full bridge LCLCL) and the HB-LCLCL mode(half bridge LCLCL), respectively. Where, the ‘C’, ‘L’ and ‘T’ are the capacitor, inductor and transformer in the resonant tank, respectively. These all represent the resonant components. These three modes guarantee the wide voltage gain range to meet the demands of variable wind speeds. Moreover, the FB-CLTCL mode is designed to obtain high voltage gain to fulfill the situation of low collected wind energy, while the FB/HB-LCLCL modes realize high conversion efficiency. However, the converter still faces the challenge of output voltage instability during the mode-switching processes. Fortunately, a gradual adjustment control method is proposed to ensure smooth switching. Consequently, a stable output voltage is achieved during switching processes. Finally, based on the proposed converter, a 200 W experimental prototype is built. The validity of the proposed converter and the feasibility of the control strategy are both verified in this paper. The paper is organized as follows: In Section 2, a detailed analysis of the proposed converter is presented. In Section 3, a transient control method for smooth switching is discussed. In Section 4, some experiments are conducted to verify the validity of the theoretical analyses. In the last section, some conclusions are summarized. 2. Operating Principles of the Proposed Converter 2.1. Topological Structure The topology of the proposed variable-structure multi-resonant DC–DC converter is shown in Figure 1. It consists of three units in total: the inverter unit, the resonant tank unit and the rectifier unit. The inverter unit adopts the traditional full bridge (FB) structure, which aims to convert the input DC voltage into a series of square wave signals. The resonant tank unit is constituted by two pairs of inductors (Ls1 , Lp2 ) and capacitors (Cs1 , Cp2 ), two transformers (Tx1 , Tx2 ) and two auxiliary switches (Qa , Qb ). The resonant structure can be changed by controlling the on/off states of Qa and Qb reasonably to satisfy different operating requirements. The rectifier unit comprises four diodes, which is responsible for transforming the AC output voltage of resonant tank to DC voltage for the load.

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Figure 1.1.Topology of the proposed converter. Figure1. Topologyof ofthe theproposed proposedconverter. converter. Figure Topology

The auxiliary switches employ the complementary conduction control. Thus, two different The auxiliary employ thethe conduction control.control. operating The auxiliary switches employ complementary conduction Thus, different operating circuits switches can be achieved for complementary various working conditions. WhenThus, Qa istwo off different andtwo Qb is on, the circuits can be achieved for various working conditions. When Q is off and Q is on, the converter works operating circuits can be achieved for various working conditions. When Q a is off and Qb is on, the a b converter works in the CLTCL circuit. On the contrary, when Qa is enabled and Qb is disabled, the in the CLTCL circuit. On the contrary, when Q is enabled and Q is disabled, the LCLCL circuit will converter works in the CLTCL circuit. On the contrary, when Q a is enabled and Q b is disabled, the a b LCLCL circuit will be utilized. In the following sections, these two circuits will be described in detail. be utilized.circuit In thewill following sections, these two circuits willthese be described in detail. LCLCL be utilized. In the following sections, two circuits will be described in detail. 2.2. Characteristic Analysis for the CLTCL Circuit 2.2. Characteristic CharacteristicAnalysis Analysisfor forthe theCLTCL CLTCL Circuit Circuit 2.2. In the CLTCL circuit, Qa is off and Qb is on. The transformer Tx2 participates in the resonant In the the CLTCL CLTCL circuit, circuit, Q Qaa is is off off and Qbb is on. The Tx2 participates in in the the resonant resonant x2 participates In and The transformer transformertoT process. In such way, the secondary side Q of Tisx2 on. is series-connected that of Tx1. Thereby, these two process. In such way, the secondary side of T is series-connected to that of T . Thereby, these x2 series-connected to that of Tx1. Thereby, x1 process. In such the secondary sidetoof Tx2load is two transformers canway, transmit active power the side simultaneously. Beneficial from thethese multiple two transformers can transmit active power to the load side simultaneously. Beneficial from the transformers can transmit active power to the load side simultaneously. Beneficial from the multiple components adopted in the resonant tank, the CLTCL circuit contains three resonant points fC1, fC2 multiple components adopted in the resonant the circuit CLTCLcontains circuit contains three resonant points components adopted in resonant thetank, CLTCL resonant points , fC2 and fC3. Furthermore, thethe voltage gaintank, curves are depicted in Figure 2 three for different loads. AsfC1seen f , f and f . Furthermore, the voltage gain curves are depicted in Figure 2 for different loads. C1 fC3 C2 C3 and . Furthermore, the voltage gain curves are depicted in Figure 2 for different loads. As seen from the figure, fC2 is the resonant zero point, where the voltage gain is constant zero and As seen the figure, f C2 resonant is the resonant zero point, where the voltage gain isconstant constantzero zero and and from thefrom figure, fC2 is the point, where therange voltage gain is to independent of load variation. Hence,zero a wide voltage gain from zero the maximum is independent of load variation. Hence, a wide voltage gain range from zero to the maximum independent of load variation. Hence,gain a wide voltage gainasrange from zero to the maximum isis guaranteed. Moreover, the DC voltage curves decrease the load increases. guaranteed.Moreover, Moreover, the the DC DC voltage voltage gain gain curves curves decrease decrease as as the the load load increases. increases. guaranteed.

Figure 2. DC voltage gain curves of the CLTCL circuit. Figure2.2.DC DCvoltage voltagegain gaincurves curvesof ofthe theCLTCL CLTCLcircuit. circuit. Figure

By using the fundamental harmonic approximation (FHA) method for model analysis, the By using thefundamental fundamental harmonic (FHA) method for model By using the method for analysis, relevant relevant Kirchhoff laws (KVL, harmonic KCL) can approximation be approximation established.(FHA) Consequently, themodel voltage gainanalysis, Vthe gainFC of the the relevant Kirchhoff laws (KVL, KCL) can be established. Consequently, the voltage gain V gainFC of the Kirchhoff laws (KVL, KCL) can be established. Consequently, the voltage gain V of the CLTCL CLTCL circuit is achieved, as shown in Equation (1). Limited by the length gainFC of this article, the CLTCL circuit derivative is achieved, as shown in Equation (1).presented Limited for by simplification: the length of this article, the corresponding process for VgainFC will not be corresponding derivative process for VgainFC will not be presented for simplification: 1 V gainFC  1j  V V  V gainFC  R eC ImC V R eC  j  V ImC

(1) (1)

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circuit is achieved, as shown in Equation (1). Limited by the length of this article, the corresponding derivative process for V gainFC will not be presented for simplification: VgainFC   

VReC =

1 ReC + j · VImC

= V

ωs ( Ls1 + Lm1 )− ωs1C +

  VImC = VReC ·

γω Req

−

s1 βω βω Req

(1)

ωs ( Lp2 + Lm2 ) αω

(2)

 α = 1 − ωs2 Cp2 ( Lp2 + Lm2 )    ω β ω = ωsnLm1 + ωsnL2m2 · α1ω 1 2    γω = ωs L2m1 + ωs L2m2 · 1−ωs Cp2 Lp2 αω n n

(3)

2

1

Req =

8 Ro π2

(4)

where, V gainFC represents the voltage gain of the CLTCL circuit. V ReC and V ImC are the real and imaginary parts of the denominator of V gainFC , respectively. Ls1 , Lp2 , Cs1 and Cp2 are the parameters of the resonant tank. Lm1 , Lm2 and n1 , n2 denote excitation inductances and turns ratios of transformers Tx1 and Tx2 , respectively. Req is defined as the equivalent load resistance, as shown in Equation (4). Moreover, αω , βω and γω are the intermediate variables. ω s = 2πf s is the angular frequency of the operating frequency f s . Equations (5)–(7) show the corresponding expressions of these three resonant points. If the imaginary part V ImC is set to zero, the expressions of resonant points f C1 and f C3 can be acquired, as shown in Equations (5) and (7), respectively. Besides, the expression of f C2 can be derived by equaling βω to zero. For the CLTCL circuit, the two transformers are both enabled and will participate in the resonant process. As a result, the voltage gain of this circuit can be effectively elevated.

f C1

v u Lm2 1 Lm1 u u Cs1 ( n2 + n2 ) 1 2 1 ×u = 2π t ( L + L + L + L )( Lm1 + Lm2 ) − ( Lm1 + p2 m2 s1 m1 n n2 n2 1

f C2

f C3

1 = × 2π

s

1

2

Lm2 2 n2 )

n1 + n2 1 · n2 Cp2 ( Lp2 + Lm2 )

v u u ( L + L + L + L )( Lm1 + Lm2 ) − ( Lm1 + p2 m2 m1 u s1 n1 1 n21 n22 = ×u t ( L + L ) L L ( L + L ) L L p2 m2 s1 m1 2π Cp2 [ p2 m2 + s1 m1 ] n2 n2 1

(5)

(6) Lm2 2 n2 )

(7)

2

2.3. Characteristic Analysis for the LCLCL Circuit Different with the CLTCL circuit, the auxiliary switch Qa is turned on, and Qb is turned off. At this time, the converter works as the LCLCL circuit. In this case, the secondary side of Tx2 is disabled, and thus it will no longer be involved in the transformation process. Furthermore, an equivalent inductor Leq2 is achieved, which is composed of Lm2 and Lp2 . It is then connected in parallel with Cp2 to constitute the LC notch filter. Therefore, only Tx1 in the resonant tank is adopted to transfer power to the load. Due to the multi-resonant feature of the circuit, three resonant points f L1 , f L2 and f L3 can be obtained as well. The voltage gain curves of different loads are shown in Figure 3. Similarly, f L2 is the resonant zero point, whose voltage gain is always zero. Owing to the introduction of f L2 , wide voltage gain range from zero to the maximum is ensured. Besides, the voltage gain is decreased with the increasing load.

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Figure 3. DC voltage gain curves of the LCLCL circuit. Figure 3. DC voltage gain curves of the LCLCL circuit.

Similarly, through thethe corresponding KVL/KCL equations can can be obtained as well. Similarly, throughthe theFHA FHAmethod, method, corresponding KVL/KCL equations be obtained as By proper manipulation, the voltage gain VgainFL the LCLCL derivedisinderived Equations (8) and (9): well. By proper manipulation, the voltage gainfor VgainFL for the circuit LCLCLis circuit in Equations (8) and (9): 1 (8) VgainFL = 1 j · VImL VReL + V gainFL  (8) V R eL  j  V Im L  Cp2 Lp2 ( Ls1 + Lm1 )ωs2 −1+(Cs1 Ls1 +Cp2 Lp2 +Cs1 Lp2 +Cs1 Lm1 )ωs2   VReL = − 2 Lm1 n1 (Cp2 Lp2 ωs2−1) Cs1 Lm1 n1 ωs2 (Cp2 Lp2 ωs2 −1) (9)  C p2 L p2 (CLs1 L L ) ( Cωs12L C p2 L p2  C s1 L p2  C s1 L m 1 ) s2  1n [1− 3s m1ω s1  L ( C p2 p2 s1 1 s1 Ls1 +Cp2 Lp2 +Cs1 Lp2 )] s s V ReLV  =    2 2 + ImLL m1 n1R( C(p2CL p2L s2ω 2− 2  1) C L n  ( C L  1) Cs1 Rs1eq ωms1(C1p2sLp2 ωp2s −p2 1) s  eq p2 p2 s 1)  (9) 3 2    C L L  n [1  ( C L C L C p2 s1 p2 s 1 s s1 s1 and p2 imaginary p2 s1 L p2 )]parts of the voltage gain where, V ReL andVVImL real ImL denote the2 denominator’s   R eq ( C p2 L p2  s  1) C s1 R eq  s ( C p2 L p2  s2  1)  V gainFL , respectively. The relevant expressions of three resonant points of the LCLCL circuit are shown in where, VReL and VImL denote the denominator’s real and imaginary parts of the voltage gain VgainFL, Equations (10)–(12), respectively, where, Leq2 = Lp2 + Lm2 . respectively. The resonant zero point f L2 is introduced by the parallel structure of Leq2 and Cp2 . The relevant expressions of three resonant points of the LCLCL circuit are shown in Equations Meanwhile, by setting V ImL to zero, the expressions of f L1 and f L3 can be achieved. (10)–(12), respectively, where, Leq2 = Lp2 + Lm2. s q parallel structure of Leq2 and Cp2. Meanwhile, The resonant zero point fL2 is introduced by the ( Ls1 Cs1 + Leq2 Cp2 + Leq2 Cs1 )− ( Ls1 Cs1 + Leq2 Cp2 + Lp2 Cs1 )2 −4Ls1 Leq2 Cs1 Cp2 1 by setting VImLfto be achieved. = 2π the × expressions of fL1 and fL3 can (10) L1 zero, 2Ls1 Leq2 Cs1 Cp2 f L1 

1  2π

L

s1

C s1  Leq2 C p2  Leq2 C s1  1 ( Ls1C1s1  Leq2 C p2  Lp2 C s1 ) 2  4 Ls1 Leq2 C s1C p2

f L2 =

p 2π 2 Ls1LLeq2 Cs1C p2 eq2 p2

s f L3 =

1 2π

×

( Ls1 Cs1 + Leq2 Cp2 + Leq2 Cs11)+ f L2 

2π

(11) (10)

q

( Ls1 Cs1 + Leq2 Cp2 + Lp2 Cs1 )2 −4Ls1 Leq2 Cs1 Cp2 1 2Ls1 Leq2 Cs1 Cp2

L eq2 C p2

(12) (11)

Furthermore, these resonant points can be carefully designed to achieve the preferable resonant characteristics. In this paper, they are reasonably placed according to Equation (13). As a result, the 1st Ls1C s1  Leq2 C p2  Leq2 C s1   ( Ls1C s1  Leq2 C p2  Lp2 C s1 ) 2  4 Ls1 Leq2 C s1C p2  1 and the 3rdf L3harmonics are both utilized to transmit active power. Thereby, the reactive circulating (12)   2π 2 Ls1 Leq2 C s1C p2 power in the resonant tank is reduced, which promotes the efficiency of the converter. f L3 = 1 : designed 3 (13) Furthermore, these resonant points canf L1 be: carefully to achieve the preferable resonant characteristics. In this paper, they are reasonably placed according to Equation (13). As a result, the 1st and the 3rd harmonics are both utilized to transmit active power. Thereby, the reactive circulating power in the resonant tank is reduced, which promotes the efficiency of the converter.

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f L1： f L3 = 1 : 3

7 of 21 (13)

2.4. Operating Operating Modes Modes of of the the Converter Converter 2.4.

For For the the proposed proposed converter, converter, its its structure structure can can be be flexibly flexibly changed changed according according to to different different requirements requirements of of operating operating conditions. conditions. This Thisisis the the predominant predominant advantage advantage compared compared to to the the other other multi-resonant with fixed fixed structures. structures.Moreover, Moreover,based basedon onthe thedifferences differences and similarities multi-resonant converters with and similarities of of CLTCL LCLCL circuits, the structure of the proposed can be by thethe CLTCL and and LCLCL circuits, the structure of the proposed converterconverter can be altered by altered reasonably reasonably on/off states oftransient relevantswitches. transient switches. To the sumproposed up, the proposed controlling controlling the on/off the states of relevant To sum up, converter converter caninoperate in three different modes. Thatfull is, bridge the fullCLTCL bridge CLTCL (FB-CLTCL) mode, can operate three different modes. That is, the (FB-CLTCL) mode, the full the fullLCLCL bridge(FB-LCLCL) LCLCL (FB-LCLCL) and the LCLCL half bridge LCLCL mode. (HB-LCLCL) mode. The bridge mode and mode the half bridge (HB-LCLCL) The corresponding corresponding structures in areFigure illustrated in Figure 4. structures are illustrated 4.

(a)

(b)

(c) Figure modes of of thethe proposed converter. (a) Full bridge (FB)(FB) CLTCL; (b) Figure 4.4. Three Threedifferent differentworking working modes proposed converter. (a) Full bridge CLTCL; FB-LCLCL; (c) half bridge (HB)(HB) LCLCL. (b) FB-LCLCL; (c) half bridge LCLCL.

Mode a: the four switches in the inverter unit run in the full bridge structure. The auxiliary Mode a: the four switches in the inverter unit run in the full bridge structure. The auxiliary switch switch Qa is always off, while Qb is permanently conducting. This indicates that the converter Qa is always off, while Qb is permanently conducting. This indicates that the converter operates in operates in the FB-CLTCL mode. In this mode, two transformers Tx1 and Tx2 are both activated to the FB-CLTCL mode. In this mode, two transformers Tx1 and Tx2 are both activated to transfer active transfer active power to the load. As a consequence, high voltage gain can be acquired. In this paper, power to the load. As a consequence, high voltage gain can be acquired. In this paper, the maximum the maximum gain value of the proposed converter is placed at the peak gain of the FB-CLTCL mode. gain value of the proposed converter is placed at the peak gain of the FB-CLTCL mode. Mode b: in this mode, the inverter unit still employs the full bridge structure. Contrary to Mode a, Mode b: in this mode, the inverter unit still employs the full bridge structure. Contrary to Mode Qa is conducting, and Qb remains off-state. Thus, the transformer Tx2 is disabled. In such a way, the a, Qa is conducting, and Qb remains off-state. Thus, the transformer Tx2 is disabled. In such a way, excitation inductor Lm2 and resonant inductor Lp2 form an equivalent inductor Leq2. Moreover, Leq2 is the excitation inductor L and resonant inductor Lp2 form an equivalent inductor Leq2 . Moreover, Leq2 parallel-connected to Cp2m2 , which results in an LC notch filter. This mode is defined as the FB-LCLCL is parallel-connected to Cp2 , which results in an LC notch filter. This mode is defined as the FB-LCLCL

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mode. By placing the resonant points appropriately, the 1st and 3rd harmonic components can be mode. By placing the resonant appropriately, theof1st harmonic components can be transmitted simultaneously. Thepoints effective employment theand 3rd3rd harmonic reduces the circulating transmitted simultaneously. The effective employment of the 3rd harmonic reduces the circulating energy in the resonant tank. As a result, it is greatly beneficial to the improvement of efficiency. energy in the resonant result, it is greatly beneficial of efficiency. Mode c: similar totank. ModeAs b, athe resonant tank unit remainstoasthe theimprovement LCLCL architecture. However, Mode c:unit similar b, the resonant tankthrough unit remains as theconduction LCLCL architecture. the inverter workstoasMode the half bridge structure, the constant of Q4 and However, the inverter unit works the half operates bridge structure, throughmode, the constant conduction non-conducting of Q2. Therefore, theasconverter in the HB-LCLCL whose voltage gain of of Q2 . Therefore, converteritoperates in the HB-LCLCL mode, whose is Q half of non-conducting that in the FB-LCLCL mode. Inthe particular, can work in the step-down condition. 4 and voltage gain isdue halftoofthe that in the FB-LCLCL mode. In particular, can work component in the step-down Furthermore, same LCLCL structure as Mode b, the 3rdit harmonic is still condition. due to the same LCLCL structure as Mode b, the is employed Furthermore, to transfer active power. Consequently, the performance of 3rd highharmonic efficiencycomponent can also be still employed transfer active power. Consequently, the performance of high efficiency can also be achieved in thistomode. achieved in this mode. Combining Equations (1)–(13), the integrated DC voltage gain curve of the proposed converter Combining Equations integratedof DC voltage gainand curve the proposed converter is illustrated in Figure 5. As(1)–(13), seen, itthe is composed three curves, theofcorresponding operating is illustrated in Figure 5. as Asthe seen, it is show. composed of threethe curves, andisthe operating process is demonstrated arrows In addition, A point thecorresponding peak voltage gain point, process is demonstrated as the arrows show. In addition, the A point is the peak voltage gain whose value is designed at 5 reasonably. With the increasing of input voltage, the converterpoint, runs whose 5 reasonably. With increasing of input voltage, runs from Avalue pointistodesigned B point at gradually. During thisthe process, the converter operatesthe in converter the FB-CLTCL from point to B pointthe gradually. this process process, from the converter operates in the FB-CLTCL mode. mode.A Subsequently, transientDuring switching FB-CLTCL to FB-LCLCL (named as the Subsequently, the transient process from FB-CLTCL to FB-LCLCL (named as the transient transient switching process switching a) is enabled at B point. After the transition, the converter switches to the switching is enabled at Binterval point. After the transition, converter switches to thetoFB-LCLCL FB-LCLCLprocess mode.a)The working of the FB-LCLCLthe mode is from C point D point. mode. The D working the FB-LCLCL is from point to Dtopoint. Moreover, D point is Moreover, point isinterval the nextofswitching point,mode namely from C FB-LCLCL HB-LCLCL (named as the the next switching namely FB-LCLCL HB-LCLCL (named as the transient switching transient switchingpoint, process b). At from this moment, theto HB-LCLCL mode is enabled, which corresponds process b). At from this moment, theGHB-LCLCL is G enabled, corresponds to the and section from E to the section E point to point on themode curve. point iswhich the resonant zero point its voltage point to G point on the at curve. point is the resonant zero pointcase andcan its voltage gain always remainsthe at gain always remains zero.GFurthermore, the step-down be employed to broaden zero. the step-down case can be employed to broaden the range of voltage gain. rangeFurthermore, of voltage gain.

Figure 5. 5. Integrated Integrated DC DC voltage voltage gain gain curve. curve. Figure

In conclusion, the converter consists of three operating modes in total, corresponding to the In conclusion, the converter consists of three operating modes in total, corresponding to the working range from A point to G point. Moreover, two transient switching processes are also working range from A point to G point. Moreover, two transient switching processes are also included. included. They are transient switching processes a and b, respectively. They are transient switching processes a and b, respectively. 3. Transient Switching Control Algorithm 3. Transient Switching Control Algorithm In order to alleviate the output voltage fluctuation during mode switching processes, a transient In order to alleviate the output voltage fluctuation during mode switching processes, a transient control algorithm for the variable-structure converter is proposed in this paper. As mentioned control algorithm for the variable-structure converter is proposed in this paper. As mentioned above, above, the proposed converter has two transient switching processes, namely the transient switching the proposed converter has two transient switching processes, namely the transient switching process process a and the transient switching process b. By gradually regulating the duty ratio of relevant

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a and thethe transient switching process b. By gradually the duty ratioThereby, of relevant switches, switches, large transient voltage fluctuation can beregulating constrained effectively. a relatively the large transient voltage fluctuation can be constrained effectively. Thereby, a relatively stable output stable output voltage is maintained. voltage is maintained. 3.1. Operating Principles of the Proposed Control Algorithm 3.1. Operating Principles of the Proposed Control Algorithm Through the on/off control of power switches, various operating modes and the corresponding Through control power switches, variousdifferent operatingmodes, modesthe andtraditional the corresponding transitions canthe beon/off achieved. Forofthe transitions between control transitions can be achieved. For the transitions between different modes, the traditional control method method usually turns on or off the relevant switches suddenly. The control is simple and easy to usually turns on or off the relevant switches suddenly. The control is simple and easy to implement. implement. However, it may lead to a large fluctuation for the output voltage. The fluctuation can be However,by it may lead to a large fluctuation output voltage. fluctuation canwill be reduced by using reduced using a large capacitor, but for thethe volume, cost andThe power density be affected. To a large capacitor, but the volume, cost and power density will be affected. To overcome this problem, a new overcome this problem, a new transient control method, named as the gradual adjustment control transientiscontrol method, named as The the gradual adjustment controlmethod method,isisgradually discussedadjusting in this paper. method, discussed in this paper. main idea of this control the The main idea of this control method is gradually adjusting the duty ratio during transient switching duty ratio during transient switching processes. Compared to the traditional method, the proposed processes. Compared the voltage traditional method, the proposed Furthermore, method can suppress voltage fluctuation method can suppresstothe fluctuation effectively. smooththe switching between effectively. Furthermore, smooth switching between different modes is realized. different modes is realized. The digital digital implementation implementation block block diagram The diagram for for transient transient switching switchingprocess processaaisisshown shownininFigure Figure6. Where, V and V are the sample and reference values of output voltage, respectively. V is 6. Where, out Vout and Vout_ref out_ref are the sample and reference values of output voltage, respectively. Verror error is the error error between between V and V out . count Ncount denotes maximum count valueofofdigital digitalslope slopefor forPWM PWM the Vout_ref out_ref and Vout .N denotes thethe maximum count value (Pulse Width Modulation) signals. T represents the clock cycle. T and N are defined as CLK trans1 trans1 (Pulse Width Modulation) signals. TCLK represents the clock cycle. Ttrans1 and Ntrans1 are defined as the the counting period of the transient counter and its real-time output value, respectively. counting period of the transient counter and its real-time output value, respectively.

Figure 6. Digital implementation block diagram for transient switching process a. Figure 6. Digital implementation block diagram for transient switching process a.

During the transient switching process a, the proposed transient control method is applied to During the transient process a, the proposed transient control method is applied to auxiliary switches Qa and Qswitching b. While the four switches, in the inverter unit, remain employing the full auxiliary switches Q and Q . While the50%. fourFrom switches, in6,the unit, remain employing the a b ratios of bridge state with constant duty Figure theinverter error Verror , produced by Vout_ref and bridge state with constant duty ratios of 50%. From Figure 6, the error V error , produced by Vfull out, is sent to a PI (Proportional Integral) controller, whose output is denoted as N count. Besides, the V and V , is sent to a PI (Proportional Integral) controller, whose output is denoted Ncount out out_ref operating period of carrier Ts = 2NcountTCLK, and its corresponding frequency fs = 1/Ts. Asasfor the . Besides, the operating period of carrier T = 2N T , and its corresponding frequency f = 1/T s count CLK s transient counter, its maximum count value is limited to Ncount. Initially, the count value is set to 0.s . As for the the transient transient switching counter, itscondition maximum value limited to Ncount . Initially, the count When is count reached, theiscounting value starts to increase fromvalue 0 to is set to 0. When the transient switching condition is reached, the counting value starts to increase Ncount gradually. Meanwhile, a real-time output value Ntrans1 is obtained. Since then, both of Ntrans1 and from 0 to N gradually. Meanwhile, a real-time output value N is obtained. Since then, both count trans1 the digital slope are delivered to a comparator to generate the control signals for Qa and Qb. As stated of Ntrans1 the digital slopeQare delivered to a comparator to generate the control signals for Q before, theand control of Qa and b is complementary. By using this control method, the adjustmenta and Q . As stated before, the control of Q complementary. By using thisthe control a and Q b isgradually. processb of duty ratios for Qa and Qb are carried out As a consequence, large method, voltage the adjustment process of duty ratios for Q and Q are carried out gradually. As a consequence, a b fluctuation during the switching process is suppressed effectively. This is the main superiority of the proposed large voltage fluctuation during the switching process is suppressed effectively. This is the main the control method. superiority of the proposed control method. The digital implementation block diagram for transient switching process b is shown in Figure 7. The digital implementation block diagram for transient switching output processvalue b is shown Figure 7. Where Ttrans2 and Ntrans2 denote the counting cycle and the real-time of theintransient Where T and N denote the counting cycle and the real-time output value of the transient trans2 trans2 counter, respectively. counter, respectively.

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Figure process b. b. Figure 7. 7. Digital Digital implementation implementation block block diagram diagram for for transient transient switching switching process

The transient switching process b is changing the operating state of the four switches in the The transient switching process b is changing the operating state of the four switches in the inverter unit, while the structure of the resonant tank remains unchanged. That is, Qa is constant off, inverter unit, while the structure of the resonant tank remains unchanged. That is, Qa is constant and Qb is constant on. As seen from Figure 7, Verror is delivered to the PI link, and Ncount can be off, and Qb is constant on. As seen from Figure 7, V error is delivered to the PI link, and Ncount can be obtained. Similarly, the maximum of the digital slope is set as Ncount. The control signals of Q1–Q4 can obtained. Similarly, the maximum of the digital slope is set as Ncount . The control signals of Q1 –Q4 be divided into two channels: Q1 and Q3, Q2 and Q4, respectively. On one hand, a constant Ncount/2 can can be divided into two channels: Q1 and Q3 , Q2 and Q4 , respectively. On one hand, a constant be obtained through a proportional element of 1/2. By comparing Ncount/2 with the digital slope in Ncount /2 can be obtained through a proportional element of 1/2. By comparing Ncount /2 with the comparator 1, the constant complementary control signals of 50% for Q1 and Q3 are acquired. On the digital slope in comparator 1, the constant complementary control signals of 50% for Q1 and Q3 are other hand, for the transient counter, its original count value is 0 and the maximum count value is acquired. On the other hand, for the transient counter, its original count value is 0 and the maximum set to Ncount/2. When the transition occurs, the transient counter begins to count from 0 to Ncount/2, and count value is set to Ncount /2. When the transition occurs, the transient counter begins to count from outputs the count value Ntrans2 in real time. Moreover, another signal of Ncount/2 can be obtained, 0 to Ncount /2, and outputs the count value Ntrans2 in real time. Moreover, another signal of Ncount /2 can which is devoted to produce Ncount/2 + Ntrans2 by adding up Ntrans2. At this moment, Ncount/2 + Ntrans2 and be obtained, which is devoted to produce Ncount /2 + Ntrans2 by adding up Ntrans2 . At this moment, the digital slope are delivered to comparator 2, thus the control signals of Q2 and Q4 are obtained. It Ncount /2 + Ntrans2 and the digital slope are delivered to comparator 2, thus the control signals of Q2 and is noted that the operating states of Q2 and Q4 are complementary and changing gradually. Q4 are obtained. It is noted that the operating states of Q2 and Q4 are complementary and changing Specifically speaking, the duty ratio of Q2 decreases from 50% to 0%. Conversely, the duty ratio of Q4 gradually. Specifically speaking, the duty ratio of Q2 decreases from 50% to 0%. Conversely, the duty increases from 50% to 100%. Compared with the traditional method of abruptly changing the duty ratio of Q4 increases from 50% to 100%. Compared with the traditional method of abruptly changing ratio of the relevant transient switches, the proposed control method has a smaller output voltage the duty ratio of the relevant transient switches, the proposed control method has a smaller output fluctuation. Thereby, a smooth switching for the variable-structure converter is achieved. voltage fluctuation. Thereby, a smooth switching for the variable-structure converter is achieved. As mentioned above, the proposed converter has two mode-switching processes in total. For As mentioned above, the proposed converter has two mode-switching processes in total. For both both transitions, a detailed comparison between the traditional control method and the proposed transitions, a detailed comparison between the traditional control method and the proposed control control method is conducted as follows. method is conducted as follows. 3.2. Transient Analysis from FB-CLTCL to FB-LCLCL 3.2. Transient Analysis from FB-CLTCL to FB-LCLCL When the converter runs in the FB-CLTCL mode, the auxiliary switch Qa is maintained at When the converter runs in the FB-CLTCL mode, the auxiliary switch Qa is maintained at constant off-state. That is, the duty ratio of drive signal for Qa is constant 0%. Correspondingly, Qb constant off-state. That is, the duty ratio of drive signal for Qa is constant 0%. Correspondingly, Qb remains constant on-state, illustrating that the duty ratio of drive signal for Qb is constant 100%. By remains constant on-state, illustrating that the duty ratio of drive signal for Qb is constant 100%. contrast, when the converter is operating in the FB-LCLCL mode, Qa is enabled and Qb is disabled. By contrast, when the converter is operating in the FB-LCLCL mode, Qa is enabled and Qb is disabled. Hence, the duty ratios of drive signals for them are constant 100% and 0%, respectively. Hence, the duty ratios of drive signals for them are constant 100% and 0%, respectively. For the transient switching process a, the change process of the duty ratios for Qa and Qb is For the transient switching process a, the change process of the duty ratios for Qa and Qb is shown in Figure 8. This process works by the traditional control method. The red line is defined as shown in Figure 8. This process works by the traditional control method. The red line is defined as the the comparative value of PWM signals. comparative value of PWM signals.

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Figure 8. Adjustment of duty ratio for Qa and Qb with traditional control method during transient Figure 8. Adjustment of duty ratio for Qa and Qb with traditional control method during transient Figure 8. Adjustment switching process a. of duty ratio for Qa and Qb with traditional control method during transient switching process a. switching process a.

Under the FB-CLTCL mode, the comparative value of the PWM control signal is set to 0. Under the FB-CLTCL mode, the comparative value of the PWM control signal is set to 0. Thereby, Qa runs in the constant 0 (off) Correspondingly, its complementary switchisQset b works Under the FB-CLTCL mode, the state. comparative value of the PWM control signal to 0. Thereby, Qa runs in the constant 0 (off) state. Correspondingly, its complementary switch Qb works in the constant (on) When switching conditions are met, the comparative valueQbofworks control Thereby, Qa runs1 in thestate. constant 0 (off) state. Correspondingly, its complementary switch in in the constant 1 (on) state. When switching conditions are met, the comparative value of control signals for Q a and Q b directly rises from 0 to the maximum digital slope count N count . As a result, the the constant 1 (on) state. When switching conditions are met, the comparative value of control signals signals for Qa and Qb directly rises from 0 to the maximum digital slope count Ncount. As a result, the duty a increases directly, leading to the sudden Qa. Bythe contrast, Qb for Qratio andof Q Qdirectly risesfrom from0 0toto1the maximum digital slope countconduction Ncount . As aofresult, duty ratio duty aratio ofbQa increases from 0 to 1 directly, leading to the sudden conduction of Qa. By contrast, Qb operates in a complementary working state with Q a . Its duty ratio decreases from 1 to 0 sharply, of Qa increases from 0 to 1 directly, leading to the sudden conduction of Qa . By contrast, Qb operates operates in a complementary working state with Qa. Its duty ratio decreases from 1 to 0 sharply, indicating that Qb is abruptly turned In such a way, the transient switching process a is in a complementary working state with Qoff. a . Its duty ratio decreases from 1 to 0 sharply, indicating that indicating that Qb is abruptly turned off. In such a way, the transient switching process a is completed suddenly. Qb is abruptly turned off. In such a way, the transient switching process a is completed suddenly. completed suddenly. As As aa comparison comparison with with the the gradual gradual adjustment adjustment control control method, method, the the adjusting adjusting process process of of control control As a comparison with the gradual adjustment control method, the adjusting process of control signals for Q a and Q b during transient switching process a is shown in Figure 9. In the figure, tonthe is signals for Qa and Qb during transient switching process a is shown in Figure 9. In the figure, ton is signals for Qa and Qb during transient switching process a is shown in Figure 9. In the figure, ton is the on-time of the switches within a period, toffthe is the off-time. on-time of the switches within a period, andand toff is off-time. the on-time of the switches within a period, and toff is the off-time.

Figure Adjustment of ratio for Qa and Qb with during transient Figure 9. 9. of duty duty with the the gradual gradual control control method method Figure 9. Adjustment Adjustment of duty ratio ratio for for Q Qaa and and Q Qbb with the gradual control method during during transient transient switching process a. switching process a. switching process a.

Similar to the traditional method, the converter runs in the FB-CLTCL mode before switching. Similar to the traditional traditional method, method, the the converter converter runs runs in in the the FB-CLTCL FB-CLTCL mode mode before before switching. switching. The comparative value of PWM control signals is 0. Qa works in a constant off-state, and Qb remains inina aconstant off-state, and QbQremains in The comparative comparative value valueof ofPWM PWMcontrol controlsignals signalsisis0.0.QQ a works constant off-state, and b remains a works in constant on-state. During the process of this transition, the comparative value of PWM control constant on-state. During the process of this the comparative value of PWM signals in constant on-state. During the process of transition, this transition, the comparative value of control PWM control signals for Qa and Qb is increasing from 0 to the maximum Ncount gradually. Hence, the adjusting for Qa and is increasing from 0 to the maximum Ncount gradually. Hence, the adjusting process signals for Qab and Qb is increasing from 0 to the maximum Ncount gradually. Hence, the adjusting process of drive signals for the relevant switches is gradual. Specially, as for Qa, its duty ratio of the of driveof signals the relevant switches is gradual. Specially, as for Q its Q duty the of drive process drive for signals for the relevant switches is gradual. Specially, asa ,for a, itsratio dutyof ratio the drive signal is increasing from 0 to 1 gradually. Conversely, for Qb, the corresponding value is signal signal is increasing from 0 to 1 gradually. Conversely, for Qb , thefor corresponding value is decreasing drive is increasing from 0 to 1 gradually. Conversely, Qb, the corresponding value is decreasing from 1 to 0 gradually. Finally, the duty ratios of drive signals for Qa and Qb are stable at from 1 to 0 gradually. the duty ratios driveratios signals Q signals and Q for areQstable and 0%, decreasing from 1 to 0Finally, gradually. Finally, theofduty of for drive a and at Qb100% are stable at 100% and 0%, respectively. At this point, the transient switchinga processb a ends and the converter respectively. this point, the process a ends process and the aconverter into the 100% and 0%,Atrespectively. At transient this point,switching the transient switching ends andenters the converter enters into the FB-LCLCL mode. Compared to the traditional method, the proposed transient control enters into the FB-LCLCL mode. Compared to the traditional method, the proposed transient control method reduces the voltage fluctuation effectively. method reduces the voltage fluctuation effectively.

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3.3. Transient Transient Analysis from FB-LCLCL to HB-LCLCL During the thetransition transition from FB-LCLCL to HB-LCLCL, the resonant tank unit remains from FB-LCLCL to HB-LCLCL, the resonant tank unit remains unchanged, unchanged, while unit the inverter unit differs them. Thereby, switches two auxiliary switches Qaconstant and Qb while the inverter differs among them. among Thereby, two auxiliary Qa and Qb keep keep constant on and off state, respectively. on and off state, respectively. In the FB-LCLCL mode, mode, for the inverter inverter unit, all four switches operate operate with constant constant 50% 50% duty duty ratio. Where, Q11 and Q 4 adopt the same control signal, while Q 2 and Q 3 employ another pair of same and Q4 adopt the same control 2 3 employ another signal. Moreover, Moreover,these thesetwo twopairs pairs control signals are complementary to other. each other. However, of of control signals are complementary to each However, under under the HB-LCLCL Q2 remains in constant off-state, Q4 at works at the constant on-state. the HB-LCLCL mode, mode, Q2 remains in constant off-state, and Q4and works the constant on-state. At this At thisintime, in the inverter unit,Q only Q1 Q and Q3 operate frequency PWM mode, while time, the inverter unit, only withwith highhigh frequency PWM mode, while Q4Qis4 isa 1 and 3 operate anormally-on normally-onswitch. switch. Figure 10 shows the adjusting process of duty ratios during the transient switching process b with the traditional traditional control controlmethod. method.In Inthe thefigure, figure,the theblue blueline lineindicates indicates that the comparative value that the comparative value of of PWM control signals iscount Ncount /2.Other Otherdefinitions definitionsof ofthe thevariables variablesare areidentical identicalwith withFigure Figure9.9. PWM control signals is N /2.

Figure 10. Adjustment of duty ratio for Q Q11–Q44 with with the the traditional traditional control method during transient switching process b.

As seen from Figure 10, at the beginning the comparative value of control signals for all the As seen from Figure 10, at the beginning the comparative value of control signals for all the switches is Ncount/2. Thereby, the corresponding duty ratios for Q1–Q4 are 50%, and the converter switches is Ncount /2. Thereby, the corresponding duty ratios for Q1 –Q4 are 50%, and the converter operates in the full-bridge (FB) mode. When this transition starts, the comparative value of control operates in the full-bridge (FB) mode. When this transition starts, the comparative value of control signals for Q1 and Q3 keeps at Ncount/2, and the corresponding switches operate with constant 50% signals for Q1 and Q3 keeps at Ncount /2, and the corresponding switches operate with constant 50% duty ratio. However, the comparative value of control signals for Q2 and Q4 rises from Ncount/2 to duty ratio. However, the comparative value of control signals for Q2 and Q4 rises from Ncount /2 to Ncount directly. Thereby, the duty ratio of Q2 decreases from 50% to 0% rapidly; while, for Q4, its duty Ncount directly. Thereby, the duty ratio of Q2 decreases from 50% to 0% rapidly; while, for Q4 , its duty ratio increases from 50% to 100% suddenly. Since then, the converter completes the switching ratio increases from 50% to 100% suddenly. Since then, the converter completes the switching process, process, and starts to operate at HB-LCLCL mode. and starts to operate at HB-LCLCL mode. By contrast, the adjusting process of the duty ratios with the gradual adjustment control By contrast, the adjusting process of the duty ratios with the gradual adjustment control method method is shown in Figure 11. The variables are defined as the same as Figure 10. is shown in Figure 11. The variables are defined as the same as Figure 10.

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Figure 11.Adjustment Adjustmentof of duty Q1–Q4 with gradual control method during transient Figure 11. duty ratioratio for Qfor 1 –Q4 with gradual control method during transient switching switching process b. process b.

Similar to the traditional method, the converter operates in the FB-LCLCL mode initially. That Similar to the traditional method, the converter operates in the FB-LCLCL mode initially. is, the duty ratios of control signals for Q1–Q4 are all 50%. However, once the transition starts, the That is, the duty ratios of control signals for Q1 –Q4 are all 50%. However, once the transition starts, comparative value of control signals for Q1 and Q3 remains at Ncount/2, as the blue line shows in the the comparative value of control signals for Q1 and Q3 remains at Ncount /2, as the blue line shows in figure. It indicates that Q1 and Q3 operate with the 50% duty ratio, while, the comparative value of the figure. It indicates that Q1 and Q3 operate with the 50% duty ratio, while, the comparative value duty ratios for Q2 and Q4 increases from Ncount/2 to the maximum Ncount gradually, which can be of duty ratios for Q2 and Q4 increases from Ncount /2 to the maximum Ncount gradually, which can verified by the red line with gradual increase. Thus, the change of drive signals for Q2 and Q4 is be verified by the red line with gradual increase. Thus, the change of drive signals for Q2 and Q4 is gradual. To be more specific, as for Q2, the duty ratio of its drive signal decreases from 50% to 0% gradual. To be more specific, as for Q2 , the duty ratio of its drive signal decreases from 50% to 0% gradually. Conversely, for Q4, the duty ratio of its drive signal increases from 50% to 100% gradually. gradually. Conversely, for Q4 , the duty ratio of its drive signal increases from 50% to 100% gradually. Finally, the transition from FB-LCLCL to HB-LCLCL is completed. Compared to the traditional Finally, the transition from FB-LCLCL to HB-LCLCL is completed. Compared to the traditional control control method, the output voltage fluctuation is constrained effectively. Consequently, smooth method, the output voltage fluctuation is constrained effectively. Consequently, smooth switching switching between different modes is implemented. between different modes is implemented. 4. Experimental 4. Experimental Results Results To verify verifythe thevalidity validityofof proposed topology the transient switching control algorithm, a To thethe proposed topology andand the transient switching control algorithm, a 200 W 200 W experimental prototype is built and tested in the laboratory. The main parameters of the proposed experimental prototype is built and tested in the laboratory. The main parameters of the proposed converter converter areTable listed1.inBesides, Table 1. the Besides, the experimental prototype shown in12. Figure 12. Moreover, the are listed in experimental prototype is shownisin Figure Moreover, the digital digital controller is TMS320F28379D manufactured by Texas Instruments (Dallas, TX, USA). controller is TMS320F28379D manufactured by Texas Instruments (Dallas, TX, USA). Table 1. Main the proposed proposed converter. converter. Table 1. Main parameters parameters of of the

Parameters Parameters Inductance Ls1 Inductance Inductance Lp2 Ls1 Inductance Lp2 Excitation inductance Lm1 Excitation inductance Lm1 Excitation inductance Lm2 Lm2 Excitation inductance Capacitance C s1 Capacitance Cs1 Capacitance Capacitance Cp2 Cp2 Turns n1 Turns ratio nratio 1 Turns ratio n2 Turns ratio n2

Values 73.67 uH 73.67 2.07 uH uH 2.07 uH 290 uH 290 uH 67uH uH 67 15 nF 15 nF 99nF nF 1.75 1.75 7.5 7.5 Values

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Figure12. 12.Experimental Experimentalprototype. prototype. Figure

The experimental experimental waveforms waveforms at at A point point of of Figure Figure 55 are are shown shown in in Figure Figure 13. 13. This point point is the the The The experimental waveforms at AApoint of Figure 5 are shown in Figure 13. This This point is theispeak peak gain point for the proposed converter, where the converter works in the FB-CLTCL mode. In peakpoint gain for point the proposed converter, where the converter in the FB-CLTCL mode. In gain thefor proposed converter, where the converter works in works the FB-CLTCL mode. In the figure, DS-Q1 and iQ1 represent the voltage and current of switch Q1, respectively. Vout is the output the figure, V the figure, VDS-Q1 and iQ1 represent the voltage and current of switch Q1, respectively. Vout is the output V DS-Q1 and iQ1 represent the voltage and current of switch Q1 , respectively. V out is the output voltage, voltage, and D1 denotes the current of diode D1. voltage, and iiD1 denotes the current D1. and iD1 denotes the current of diodeofDdiode 1.

Figure Experimental Figure13. 13.Experimental Experimentalwaveforms waveformsat atthe thepeak peakvoltage voltagegain gainpoint. point. Figure 13. waveforms at the peak voltage gain point.

From the figure, the input voltage 78.8 V, while while the output output voltagevoltage stays at atstays 400.2 V. V. Thereby, From the figure, figure,the the input voltage is 78.8 V, while the output at Thereby, 400.2 V. From input voltage isis 78.8 V, the voltage stays 400.2 Q1 that its phase lags behind that of the the the voltage gain is 5.07. It can be seen from the waveform of i Thereby, thegain voltage gainIt iscan 5.07. It canfrom be seen from the waveform its phase its iphase behindlags thatbehind of the voltage is 5.07. be seen the waveform of iQ1 that of Q1 thatlags voltage V DS-Q1 , so the ZVS is realized. At the same time, i Q1 is approximately zero at the turn-off that of theVDS-Q1 voltage , so the ZVS is realized. the same is approximately zeroatatthe the turn-off turn-off voltage , soVthe ZVS is realized. At theAt same time,time, iQ1 isiQ1approximately zero DS-Q1 period, thus, the converter obtains quasi ZCS as well. In addition, i D1close is close to zero both at turn-on period, thus, the converter obtains quasi ZCS as well. In addition, i is to zero both at turn-on and period, thus, the converter obtains quasi ZCS as well. In addition, D1 iD1 is close to zero both at turn-on and turn-off periods, and the quasi ZCS soft-switching performance is achieved. Consequently, the turn-off periods, and the quasi soft-switching performance is achieved. Consequently, the switching and turn-off periods, and the ZCS quasi ZCS soft-switching performance is achieved. Consequently, the switching losses are areconstrained, effectively constrained, constrained, and the the efficiency reaches 97.4% at at this this point. point. losses are effectively and the efficiency reaches 97.4%reaches at this point. switching losses effectively and efficiency 97.4% Figure14 14illustrates illustratesthe theexperimental experimentalwaveforms waveformsof ofthe therated ratedpoint. point. At this point, theoperating operating Figure At this point, the point. frequency is 100 kHz. The converter operates in the FB-LCLCL mode, which corresponds to the D D frequency operates in the FB-LCLCL mode, which corresponds to theto D the point frequency isis100 100kHz. kHz.The Theconverter converter operates in the FB-LCLCL mode, which corresponds point in Figure Figure 5. Where, Where, VD1 D1 is defined as the the voltage voltage ofD diode Dinput 1. The input voltage isV,228.6 228.6 V, the the in Figure 5. Where, VD1 is V defined as the as voltage of diode is 228.6is the output point in 5. is defined of diode D 1. The voltage input voltage V, 1 . The output voltage is 400.5 V. The voltage gain is 1.752, which is consistent with the theoretical design. voltage is 400.5 is V. 400.5 The voltage is 1.752, is consistent with the theoretical design. From the output voltage V. Thegain voltage gain which is 1.752, which is consistent with the theoretical design. From the the figure, figure, both of iiin Q1 and D1 are in shape, the saddle-wave saddle-wave shape, indicating the successful successful figure, both of iQ1 and iD1 of are indicating theshape, successful transmission of the 1st From both Q1 the andsaddle-wave iiD1 are in the indicating the transmission ofthe the1st 1stin and the 3rdharmonics harmonics in the circuit.the Moreover, byadopting adopting the3rd 3rd harmonic and the 3rd harmonics thethe circuit. Moreover,in bythe adopting 3rd harmonic to transmit active power, transmission of and 3rd circuit. Moreover, by the harmonic to transmit active power, the reactive circulating energy in the resonant tank is effectively reduced. the reactive active circulating energy in the resonant tank is effectively reduced.tank Thereby, the performance to transmit power, the reactive circulating energy in the resonant is effectively reduced. Thereby, the performance performance of Compared high efficiency efficiency isFB-LCLCL achieved.mode, Compared to the thegain FB-LCLCL mode, the the of high efficiency is achieved. to theis the voltage of the HB-LCLCL Thereby, the of high achieved. Compared to FB-LCLCL mode, voltage gain of the HB-LCLCL mode is half of that of the former. In addition to that, there is no mode is half of that of the former. In addition to that, there is no difference between two modes for the voltage gain of the HB-LCLCL mode is half of that of the former. In addition to that, there is no difference between two modes for the performance of the converter. Limited by the length of this performance of the converter. Limited the length ofofthis they Limited are not repeatedly given. difference between two modes for theby performance thearticle, converter. by the length of this article, they are not repeatedly given. article, they are not repeatedly given.

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Figure 14. Experimental waveforms at the rated point. Figure 14. Experimental waveforms at the rated point.

The traditional is,is, thethe duty ratios of The traditional control control method method turns turns on on or oroff offthe theswitches switchessuddenly. suddenly.That That duty ratios the relevant switches increase from 0% to 100%, or decrease from 100% to 0%. Thereby, a sudden The traditional method or off or thedecrease switches from suddenly. is, theThereby, duty ratios of of the relevant switchescontrol increase from turns 0% toon100%, 100%That to 0%. a sudden switching occurs. In particular for Q b, 0% its duty ratio drops from 100% to 0% abruptly, corresponding the relevant switches increase from to 100%, or decrease from 100% to 0%. Thereby, a sudden switching occurs. In particular for Qb , its duty ratio drops from 100% to 0% abruptly, corresponding to a switching occurs. In particular for Qb, its duty ratio drops from 100% to 0% abruptly, corresponding to a sudden turn-off. sudden turn-off. to a sudden turn-off. With thetraditional traditional control method, Figure 15 shows the experimental waveforms of the With the control method, Figure 15 shows the experimental waveforms of the transient With the traditional control method, Figure 15 shows the experimental waveforms ofauxiliary the transient switching process a. In the figure, V Qb represents the PWM control signal of switching process a. In the figure, VQb represents the PWM control signal of auxiliary switch Qb ; transient switching process a. In the figure, VQb represents the PWM control signal of auxiliary switch Q b; VQb-avg denotes the duty ratio average value of VQb; Vin and Vout are defined as the input V denotes duty ratio average value of VQbvalue ; V in of and V;out the input voltage Qb-avg switch Qb; Vthe Qb-avg denotes the duty ratio average VQb Vin are anddefined Vout are as defined as the input and voltage and the output voltage, respectively. ΔV out is the absolute value of the deviation between the the output respectively. of the deviation between the reference out is the absolute voltagevoltage, and the output voltage, ∆V respectively. ΔVout is thevalue absolute value of the deviation between the reference output voltage(400 V) and the maximum fluctuation. output voltage(400 V) and the maximum fluctuation. reference output voltage(400 V) and the maximum fluctuation.

(a)

(a)

(b) Figure 15. Experimental waveforms of transient switching process a with traditional control

Figure 15. Experimental waveforms of transient switching process a with traditional control method. (b) detailed method. (a) Overall switching waveforms; (b) Enlarge waveforms. (a) Overall switching waveforms; (b) Enlarge detailed waveforms. Figure 15. Experimental waveforms of transient switching process a with traditional control method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms.

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At first, since the converter works in the FB-CLTCL mode, Qb is turned on. From Figure 15a, Energies 2018, 11, x FOR PEER REVIEW 16 of 21 its PWM control signal VQb is always 3.3 V, (corresponding to the ‘1’), and its resulting duty ratio average value VQb-avg is converter 1. When works the input voltage is 79.6 V, the output is Figure stable15a, at 400.2 At first, since the in the FB-CLTCL mode, Qb is turnedvoltage on. From its V, PWMclamped control signal Qb is 3.3 V, (corresponding ‘1’),V,and resultingenters duty ratio and then at 400VV. Asalways the input voltage increasestotothe 114.4 theits converter into the average value VQb-avg is 1.a.When thetime, inputVvoltage is 79.6 drops V, the output is stable at 400.2VV, transient switching process At this from 1 voltage to 0, and accordingly Qb suddenly Qb-avg and then clamped at 400 V. As the input voltage increases to 114.4 V, the converter enters into the also decreases from 1 to 0 sharply. During this process, the output voltage suffers from a large transient switching process a. At this time, Qb suddenly drops from 1 to 0, and accordingly VQb-avg fluctuation and the maximum fluctuation is V 38.4 V, which is about 9.6% of the rated output voltage. also decreases from 1 to 0 sharply. During this process, the output voltage suffers from a large Since then, as the input voltage keeps rising to 200 V, the converter stays in the FB-LCLCL mode at last. fluctuation and the maximum fluctuation is 38.4 V, which is about 9.6% of the rated output voltage. The output voltage is again stable and maintained at 400 V. Since then, as the input voltage keeps rising to 200 V, the converter stays in the FB-LCLCL mode at Figure shows the enlarged detailed waveformsatof400 Figure last. The15b output voltage is again stable and maintained V. 15a. During the switching process, the sudden changes of VQb VQb-avg can waveforms be observed clearly15a. in During Figure the 15b.switching Initially,process, under the Figure 15b shows the and enlarged detailed of Figure FB-CLTCL mode, both of V and V are 1 (constantly open). Once the transition begins, Qb-avg the sudden changes of VQb Qb and VQb-avg can be observed clearly in Figure 15b. Initially, under the VQb dropsFB-CLTCL from 100% to 0% directly, and the corresponding VQb-avg decreases from 1 to 0 simultaneously. mode, both of VQb and VQb-avg are 1 (constantly open). Once the transition begins, VQb drops from 100% the to 0% directly, and the corresponding VQb-avg decreases 1 to 0 simultaneously. In addition, through traditional control method, the situation of V outfrom deviating from the reference In addition, through the traditional control method, voltage (400 V) can be seen clearly from Figure 15b. the situation of Vout deviating from the reference voltage (400 V) can be seen clearly from Figure By contrast, the corresponding waveforms15b. of the same transition with the proposed transient By contrast, the corresponding of the same transition with theonproposed transient control method are presented in Figure waveforms 16. The main difference is the situation the transient process. control method are presented in Figure 16. The main difference is the situation on the transient For the traditional control method, the related control signal changes from one state to another state process. For the traditional control method, the related control signal changes from one state to directly. It may result in a large voltage fluctuation. However, the switching process is smoother by another state directly. It may result in a large voltage fluctuation. However, the switching process is the proposed control. The control signal gradually changes from one state another. smoother transient by the proposed transient control. The control signal gradually changes fromtoone state toAs a result, a stable guaranteed. another. Asoutput a result,voltage a stableisoutput voltage is guaranteed.

(a)

(b) Figure 16. Experimental waveforms of transient switching process a with gradual adjustment

Figure 16. Experimental waveforms of transient switching process a with gradual adjustment control control method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms. method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms.

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The The above above description description can be verified by the waveforms shown in Figure 16. From the figure, when decreasefrom from11to to00 gradually. gradually. when the the transient transientswitching switchingprocess processbegins, begins,both bothofofVVQb Qb and and V VQb-avg Qb-avg decrease Moreover, fluctuation is is 10.8 10.8 V, V, Moreover, aa more more stable stable output output voltage is achieved. Specifically, the maximum fluctuation which 2.7% of the output voltage. Compared to the traditional control method, which accounts accountsfor foronly only 2.7% of rated the rated output voltage. Compared to the traditional control the maximum fluctuation of outputofvoltage from 9.6%from to 2.7%. that, withthat, the method, the maximum fluctuation outputdecreases voltage decreases 9.6%Ittoindicates 2.7%. It indicates proposed transitiontransition control method, better output voltage is obtained. with the proposed controlamethod, a better outputregulation voltage regulation is obtained. In In Figure Figure 16b, 16b, the the corresponding corresponding enlarged enlarged waveforms waveforms of of the the transition transition are are given. given. The The gradual gradual variation andVQb-avg VQb-avg during switching process can be clearly seen. the From the both figure, variation of VVQb during this this switching process can be clearly seen. From figure, of Qband both them decrease from 100% 0% gradually, which agrees wellwith withthe the theoretical theoretical analyses. themofdecrease from 100% to 0%to gradually, which agrees well Moreover, it is is basically basically constant constant at at 400 400 V V during the transient process. Moreover, as as for forVVout out,, it With control method, the experimental waveforms of transient switchingswitching process b With the thetraditional traditional control method, the experimental waveforms of transient are shown in Figure In the figure, VQ4figure, represents the controlthe signal of Qsignal ; V is the average process b are shown17. in Figure 17. In the VQ4 represents control of Q 4 ; V Q4-avg is the 4 Q4-avg value of V . average value Q4 of VQ4.

(a)

(b) Figure 17. Experimental waveforms of transient switching process b with traditional control Figure 17. Experimental waveforms of transient switching process b with traditional control method. method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms. (a) Overall switching waveforms; (b) Enlarge detailed waveforms.

Firstly, the converter operates in the FB-LCLCL mode, and Q4 works at on-state with the duty theCorrespondingly, converter operatesthe in duty the FB-LCLCL mode, and Q works athalf on-state the duty ratio ratioFirstly, of 50%. ratio average VQ4-avg is4 exactly of VQ4with . When the input of 50%. Correspondingly, the duty ratio average V is exactly half of V . When the input voltage Q4-avg Q4 stably in the FB-LCLCL voltage is 119.8 V, the output voltage is 400.2 V, the converter operates is 119.8 V, the output voltage is 400.2 V, the converter operates stably in the FB-LCLCL mode. When the mode. When the input voltage increases to 228.6 V, the converter enters into the transient switching input voltage increases to 228.6 V, the converter enters into the transient switching process b. At this process b. At this time, VQ4 increases from 50% to 100% directly. Thereby, VQ4-avg rises from 0.5 to 1 simultaneously. During this transition, the output voltage suffers from instability. The maximum fluctuation is 37.2 V, which accounts for 9.3% of the rated output voltage. After that, the input

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time, VQ4 increases from 50% to 100% directly. Thereby, VQ4-avg rises from 0.5 to 1 simultaneously. During transition, the600 output voltage suffers from instability. The maximum fluctuation 37.2 V, voltage this keeps rising to V, the converter switches into the HB-LCLCL mode, and theis output which 9.3%atof400 theV.rated output voltage. After that, the input voltage keeps rising to 600 V, voltageaccounts is stablefor again the converter switches into the HB-LCLCL mode, and theofoutput is stable again 400 V. that Figure 17b shows the enlarged detailed waveforms Figurevoltage 17a. In the figure, it is at obvious Figure 17b shows the enlarged detailed waveforms of Figure 17a. In the figure, it is obvious that both both VQ4 and VQ4-avg increase sharply during the switching process. Initially, VQ4-avg is 0.5, which V sharply during switching Initially, VQ4-avg is 0.5, which indicatesfrom that Q4 and Vthat Q4-avg indicates Q4increase operates with the dutythe ratio of 50%.process. Once the transition starts, VQ4-avg increases Q operates with the duty ratio of 50%. Once the transition starts, V increases from 0.5 to 1 directly. 4 to 1 directly. At the same time, VQ4 rises from 50% to 100% Q4-avg 0.5 abruptly. Furthermore, it can be At the same time,Figure VQ4 rises 100% voltage abruptly.isFurthermore, it can be observed from 17b observed from 17bfrom that50% the to output unstable, and it deviates from theFigure reference that the output voltage is unstable, and it deviates from the reference voltage (400 V). voltage (400 V). By By contrast, contrast, Figure Figure 18 18 shows shows the the corresponding corresponding waveforms waveforms of of the the same same transition transition with with the the proposed proposed transient transient control control method. method.

(a)

(b) Figure 18. Experimental waveforms of transient switching process b with gradual adjustment Figure 18. Experimental waveforms of transient switching process b with gradual adjustment control control method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms. method. (a) Overall switching waveforms; (b) Enlarge detailed waveforms.

As seen in Figure 18a, the converter operates in the FB-LCLCL mode before switching. The duty Figure 18a, the converter in the ratioAs of seen Q4 isin50%, and VQ4-avg is half ofoperates VQ4. When theFB-LCLCL transition mode starts,before VQ4-avgswitching. rises fromThe 0.5duty to 1 ratio of Q is 50%, and V is half of V . When the transition starts, V rises from Q4-avg Q4 change from 50% to 100% of the Q4-avg gradually,4 indicating the gradually incremental duty ratio. In 0.5 to 1 gradually, indicating the gradually incremental change from 50% to 100% of the duty ratio. addition, a more stable output voltage is acquired through the transient method. In other word, the In addition,fluctuation a more stable output voltage is for acquired through the output transient method. In other word, maximum is 8.4 V, accounting 2.1% of the rated voltage. Compared to the the maximum fluctuation is 8.4 V, accounting for 2.1% of the rated output voltage. Compared the traditional control method, the maximum fluctuation of output voltage decreases from 9.3% toto 2.1%. With the proposed transient control method, a smoother switching process is achieved. Figure 18b shows the enlarged detailed waveforms of Figure 18a. It clearly indicates the gradually incremental change of VQ4 and VQ4-avg during this switching process. Both of them increase

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traditional control method, the maximum fluctuation of output voltage decreases from 9.3% to 2.1%. 19 of 21 With the proposed transient control method, a smoother switching process is achieved. shows the enlarged detailed with waveforms of Figureanalyses. 18a. It clearly indicates the gradually from Figure 0.5 to 118b gradually, which is consistent the theoretical Furthermore, as for Vout, it incremental change of V and V during this switching process. Both of them increase from Q4-avg is basically constant at 400Q4V during the transient switching process b. 0.5 to 1 gradually, which is consistent with the theoretical analyses. Furthermore, as for V , is out it is Finally, the efficiency is tested by a power analyzer YOKOGAWA WT3000, and the result basically at Since 400 V the during the transient switching b. modes in total, three efficiency shown in constant Figure 19. converter comprises three process operating Finally, the efficiency is tested by a power analyzer YOKOGAWA WT3000, and the result is shown in curves are included. Figure 19. Since the converter comprises three operating modes in total, three efficiency curves are included.

Efficiency(%)

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99

HB-LCLCL

98.5

FB-LCLCL

98

FB-CLTCL

97.5 97 96.5 0

1

2 3 Voltage gain

4

5

6

Figure19. 19.Efficiency Efficiencycurve. curve. Figure

From Fromthe thefigure, figure,the theconverter converterachieves achievesthe thehighest highestefficiency efficiencyof of98.2% 98.2%in inthe theHB-LCLCL HB-LCLCLmode. mode. Moreover, at the rated point D (voltage gain is 1.75), the efficiency is 97.9% under Moreover, at the rated point D (voltage gain is 1.75), the efficiency is 97.9% under the the FB-LCLCL FB-LCLCL mode. the conversion conversion efficiency efficiencyofofthe theFB-CLTCL FB-CLTCL mode is lower than of the other mode. Moreover, Moreover, the mode is lower than thatthat of the other two two modes. The main reason is that, under the high-voltage-gain condition, the input voltage is modes. The main reason is that, under the high-voltage-gain condition, the input voltage is small. small. thevalue RMS of value the current input current be relatively large, which increases the Thus, Thus, the RMS the of input will bewill relatively large, which furtherfurther increases the power power losses of the converter. Consequently, the efficiency of this mode is reduced. Despite this, the losses of the converter. Consequently, the efficiency of this mode is reduced. Despite this, the proposed proposed still obtains a relatively high efficiency (≥97.2%) in this mode. converterconverter still obtains a relatively high efficiency (≥97.2%) in this mode. 5. 5.Conclusions Conclusions In this this paper, paper, a variable-structure variable-structure multi-resonant multi-resonant DC–DC DC–DC converter converter is is proposed. proposed. Through Through the the In adoption of of auxiliary switches, its structure of adoption structure can canbe beflexibly flexiblyadjusted adjustedtotomeet meetdifferent differentrequirements requirements high voltage gain andand highhigh conversion efficiency. The converter has three operating modes of high voltage gain conversion efficiency. The converter has different three different operating in total.inCorrespondingly, two transient switchingswitching processes processes are obtained. order to In alleviate modes total. Correspondingly, two transient are In obtained. order the to alleviate the output voltage instability during the modes’ switching, a transient method is output voltage instability during the modes’ switching, a transient control method control is proposed whose proposed whose main principle is the gradual adjustment of the duty ratios. Finally,analyses the above main principle is the gradual adjustment of duty ratios. Finally, above theoretical are theoretical analyses are validated experiments onconverter a 200 W prototype. converter acquires the validated by experiments on a 200 by W prototype. The acquires theThe highest efficiency of 98.2%. highest efficiency of 98.2%. of the control method proposed Moreover, comparison of theMoreover, traditionalcomparison control method andtraditional proposed transient control and method shows transient control method shows that the output voltage is voltage effectively stabilized. Thetwo maximum that the output voltage is effectively stabilized. The maximum fluctuations of the transient voltage fluctuations the twofrom transient switching 9.6% to 2.7% and from switching processes of decrease 9.6% to 2.7% andprocesses from 9.3%decrease to 2.1%, from respectively. 9.3% to 2.1%, respectively. Author Contributions: M.C., Y.W. and L.Y. designed the main parts of the study, including the circuit design, control method research and experiment. F.H., Y.H. and H.Y. helped in the hardware design, experiment and Author Contributions: Y.W., M.C. and L.Y. designed the main parts of the study, including the circuit design, some theoretical analysis. control method research and experiment. F.H., Y.H. and H.Y. helped in the hardware design, experiment and Funding: This research received no external funding. some theoretical analysis. Conflicts of Interest: The authors declare no conflict of interest. Funding: This research received no external funding.

Conflicts of Interest: The authors declare no conflict of interest.

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