Wenjuan Liang, Xuefeng Hu, Hao Chen, Guiyang Wu, Meng Zhang, and Guodong Tan

（School of Electrical Engineering, Anhui University of Technology, Ma’anshan, 243032 China）

Abstract: A novel DC-DC converter topology that uses a three-winding coupled inductor (TWCI) and a new voltagemultiplication technique is presented for achieving high voltage gain. The proposed converter comprises one boost unit, one passive absorption circuit, and two voltage-multiplier cells. The tertiary winding of the coupled inductor is connected to a capacitor and diode,and this combination acts as a secondary voltage-multiplier cell (SVMC). The SVMC, when combined with two capacitors, the secondary winding of the coupled inductor, a diode, and a switch, forms a primary voltage-multiplier cell, which can achieve a large voltage-conversion ratio that can be adjusted easily. The new voltage-multiplier technique can be used to decrease the number of capacitors and diodes, which improves the transformation efficiency. A prototype circuit with a nominal rating of 300 W is designed to verify the correctness of theoretical analysis.

Keywords: Three-winding coupled inductor, voltage multiplier, output diode stress, high step-up

1 Introduction1

Nowadays, renewable energy sources such as fuel cells, wind, and photovoltaic systems are becoming indispensable globally, owing to environmental concerns and energy shortage[1-5]. However, the output voltages of these renewable-energy powergeneration systems are relatively low, and need highstep-up DC-DC converters to convert the voltage of electric power[6-10]. Therefore, high-step-up DC-DC converters have been widely applied in renewable power generation systems.

In theory, a fundamental boost converter can obtain high-voltage gain when operated with extremely high duty cycles. However, because of the influence of the parasitic parameters of the power switches, diodes, conductors, and capacitors, it is difficult to achieve high gains (greater than 10) from a basic boost converter. Moreover, the extremely high duty cycle may result in large conduction and switching losses, and cause serious reverse-recovery problems[11-12]. Furthermore, the conversion efficiency for the increased voltage gain may be very low.

In order to increase the voltage gain and improve the conversion efficiency, several topologies were researched in many literatures[13-17]. The cascaded boost converter could provide high voltage gains under suitable duty cycles[18]. However, the voltage stress of the main switch was quite large, in this topology, and the stability of system had to be monitored. A family of high-step-up DC-DC converters was proposed, in which charging was performed through inductors and capacitors connected in parallel and discharging through inductors and capacitors connected in series [19]. Unfortunately, the diode reverse-recovery problem was serious when the converter was applied in high-step-up applications.Some isolated converters were presented to achieve high-step-up conversions without extreme duty cycles[20]. However, the leakage inductances of the transformers in these topologies caused increased the switch stress greatly, which affected the conversion efficiency significantly.

A new type of converter was proposed, which could obtain high step-up voltage gain by adjusting the turns ratio of the coupled inductor properly,instead of increasing the duty cycle[21-23]. In this configuration, the leakage-inductor energy could be recycled to improve the conversion efficiency, by using a clamp circuit. Some high-voltage-gain DC-DC converters based on coupled inductors and passive clamp circuits were proposed[24-28]. In these structures, the voltage spike of the main switch could be suppressed effectively. Although the active clamp technique could be reduce a high voltage spike and reduce the switching losses[29-30], the additional active switches complicated the structure and control.In [31], a high-step-up converter with low diode voltage stress was presented; however, a coupled inductor was used in this configuration, which increased the complexity of the module. A novel converter based on a Zeta converter was studied for high-step-up voltage conversion, in which the energy stored in the leakage inductance could be recycled to the load[32]. However, the input current in this configuration was not continuous, which degraded the DC voltage utilization. A new single-switch high-step-up DC-DC converter was presented, which utilized the three-winding coupled inductor(TWCI)[33-34]. This technique was expected to be suitable for power-conversion applications, to increase the power density.

In this paper, a novel single-switch DC-DC converter is presented, which is integrated with the TWCI and voltage-multiplier cells. A high step-up voltage gain is realized and the voltage stress on the active switch is reduced in the proposed converter.The tertiary winding of the coupled inductor is connected between the secondary winding of the coupled inductor and the output diode, which reduces the output-diode voltage stress. Moreover, the reverse-recovery problem of the output diode is greatly alleviated by the reasonable leakage inductance of the TWCI. The operating principles and steady-state analysis of the proposed converter are discussed in detail. Finally, a prototype circuit with a nominal rating of 300 W is fabricated in the laboratory, to verify the performance of the proposed converter.

2 High-voltage-gain coupled-inductor DC-DC converter

The coupled-inductor and switched-capacitor techniques have a wide range of applications in high-step-up conversions. Some coupled-inductor boost converters have been proposed in literatures[35-37], which achieve good performances. However,those converters have many drawbacks such as inflexibility of voltage-gain adjustment and high voltage stress on power devices. A modified boost converter with a coupled inductor is presented in this paper. This configuration has the following advantages:

(1) A high step-up voltage gain can be obtained easily.

(2) The converter exhibits flexible voltage-gain adjustment.

(3) The voltage stress on the power devices is reduced obviously.

Fig. 1 Circuit configuration of converters

The comparisons of the voltage gain and voltage stress on the output diode (VDo), of the different converter configurations are shown in Fig. 1,presented in Tab. 1 (where N is the turns ratio, D is the duty cycle). Although the voltage gain of the converter in Fig. 1c is equal to that of the proposed converter, its voltage stress on the output diode is more than that of the proposed converter. Moreover, the secondary and tertiary windings of the TWCI used in the proposed converter can be adjusted to achieve a high voltage gain and increase the capability of voltage-gain adjustment, respectively. As shown in Fig. 2, even when the secondary/tertiary winding turns (n2or n3) is equal to zero, the modified converter can be operated with superior performance.

Fig. 2 Modified converters based on the proposed converter

3 Proposed converter and operation principles

The equivalent circuit of the proposed converter is shown in Fig. 3. Lmand Lkare the magnetizing and total reflected leakage inductances, respectively, of the coupled inductor. The primary winding of the coupled inductor has n1turns, the secondary winding has n2turns, and the tertiary winding has n3turns. The turns ratio N2of the coupled inductor is defined as N2= n2/n1and the turns ratio N3is defined as N3= n3/n1. The coupling references of the coupled inductor are notated using “” as shown in Figs. 1, 2, and 3. The proposed converter consists of a main switch S, coupled inductor,clamp diode VD1, regenerative diode VD2(VD3), output diode VDo, clamp capacitor C2, series capacitor C1(C3),and output capacitor Co. To simplify the operation analyses, some assumptions are made:

(1) The capacitors (C1, C2, C3, and Co) are sufficiently large so that the voltages across them can be considered to be constant in one switching period.

(2) All components are ideal, except for the leakage inductance of the coupled inductor.

Fig. 3 Equivalent circuit of the proposed converter

3.1 Continuous-mode operational analysis

Fig. 4 depicts the key waveforms when the current iLmis operated in the continuous mode (CCM).The operating modes in one switching cycle are presented in Fig. 5.

Mode 1 [t0～t1] [Fig. 5a]: At t = t0, the switch S is turned on. The diodes VD1and VD3are turned off,while VD2and VDoare on. The current falling rates through VD2and VDoare controlled by the leakage inductance Lk, which can effectively relieve the diode reverse-recovery problems.

Mode 2 [t1～t2] [Fig. 5b]: During this interval, the switch S remains in the on state. At t = t1, the diode VD3begins to turn on, and the diodes VD1, VD2, and VDoare turned off. The magnetizing inductance Lmas well as the leakage inductance Lkare linearly charged by the input voltage. Meanwhile, the capacitor C1is charged by the capacitors C2and C3.The voltage across C1is approximately equal to (N1+N2) Vin+ VC2+ VC3.

Mode 3 [t2～t3] [Fig. 5c]: In this mode, the switch S is turned off and the diodes VD2and VDoare reverse-biased. The leakage inductance Lkreleases energy to the clamp capacitor C2through the clamp diode VD1. At t = t3, the current through the diode VD3is equal to zero, and this mode ends.

Mode 4 [t3～t4] [Fig. 5d]: During this transition interval, the switch S is still turned off and the diode VD3is turned off. The diodes VD1, VD2, and VDoare turned on. The capacitor C2continues to be charged via VD1. Meanwhile, the energy stored in the magnetizing inductor Lmand the capacitor C1is transferred to the output.

Mode 5 [t4～t5] [Fig. 5e]: At t = t4, the clamp diode VD1naturally turns off and there is no reverserecovery problem for VD1. The magnetizing inductance Lmstill delivers energy to the capacitor C3through the tertiary winding of the coupled inductor and the diode VD2. The diode VDois still in the turned-on mode,which leads to energy transfer to the output. This interval ends when the switch S is turned on at t = t5,which is the beginning of the next switching period.

Fig. 4 Key waveforms of the proposed converter under CCM operation

Fig.5 Operational modes of the proposed converter under CCM operation

3.2 Discontinuous mode operation analyses

To simplify the discontinuous mode (DCM)analysis, the leakage inductance Lkof the coupled inductor is neglected. The coupled inductor can be modeled as a magnetizing inductor Lmand ideal transformer. The key waveforms of the proposed converter are shown in Fig. 6. There are five modes during one switching cycle. The operating modes are analyzed in Fig. 7. The detailed operation of each case is described as follows.

Mode 1 [t0～t1]: During this interval, the switch S is turned on. The diode VD3is on, but the diodes VD1,VD2, and VDoare all reverse-biased. The current-flow path is shown in Fig. 7a. The magnetizing inductance Lmis charged by the input voltage source Vin. Therefore, the current iLmincreases linearly. Simultaneously, because of the transformer function of the coupled inductor, the series capacitor C1is charged through the clamp capacitor C2, tertiary winding of the TWCI, regenerative diode VD3, secondary winding of TWCI, and switch S.At t = t1, the current through the regenerative diode VD3is equal to zero, and this interval ends.

Mode 2 [t1～t2]: At t = t1, the switch S remains on.All the diodes are reverse-biased, as shown in Fig. 7b.The magnetizing inductance Lmis charged continuously by the input voltage source Vin. The clamp diode VD1is forward-biased when the switch S is turned off at t =t2, and this interval ends.

Mode 3 [t2～t3]: During this transition interval, the switch S and regenerative diode VD3are maintained off. The diodes VD1, VD2, and VDoare turned on. The current-flow path is shown in Fig. 7c. The input voltage source and magnetizing inductance Lmrelease energy to the clamp capacitor C2through the diode VD1. Meanwhile, the series capacitor C1and secondary winding of the TWCI operate as a voltage source,which is in series, to achieve a high conversion ratio.This interval ends when iVD1is equal to zero at t = t3.

Mode 4 [t3～t4]: During this interval, the switch S is still turned off. The diodes VD1and VD3are also turned off. The current-flow path of this mode is shown in Fig. 7d. The energy stored in the magnetizing inductance Lmis transferred to the secondary side, and the energy stored in magnetizing inductance is decreased. The current through the regenerative diode VD2decreases quickly. When the current iVD2decreases to zero, this interval ends.

Mode 5 [t4～t5]: During this interval, the switch S remains in the turned-off mode. The magnetizing inductance current is zero at t4. The current-flow path is shown in Fig. 7e. The energy stored in the capacitor Cois discharged to the output. This interval ends when the switch S is turned on at t = t5.

Fig. 6 Key waveforms of the proposed converter under DCM operation

Fig. 7 Operation modes of the proposed converter under DCM operation

4 Steady-state performance analysis of the proposed converter

4.1 CCM operation

To simplify the circuit performance analysis of the proposed converter, the equivalent circuit of the proposed converter is redrawn as in Fig. 8.

Fig. 8 Simplified circuit configuration of the proposed converter

Modes 2 and 4 are considered, and Modes 1, 3,and 5 are neglected because of their relatively short durations.

When the switch S is turned on, the magnetizing inductance Lmis charged by the DC source Vin. The following equation is written for Fig. 5(b).

Where VLm,chargeis the voltage of magnetizing inductance during be charged.

Applying the voltage-second balance principle to the magnetizing inductance Lm, the following equation can be obtained

During Mode 4, the following voltage equations hold true

Since the average current of the diode VDois equal to the output current, the average current of VDocan be expressed as

The following equations can be obtained as

The voltage across the capacitor C1and the voltage across the leakage inductance Lkduring Mode 4 can be derived by applying the current-second balance to C1and the voltage-second balance to Lk, as

Where VLk,t34is the voltage of leakage inductance Lk.

The output voltage of the proposed converter is given by

From (2), (7), (8), and (9), the voltage gain of the proposed converter can be expressed as

Therefore, the output voltage gain M can be obtained as

When the leakage inductance Lkis assumed to be zero, Q is equal to zero. Therefore, the voltage gain M is rewritten as

From (12), it can be seen that the voltage-gain expression for the proposed converter has three degrees of freedom, which increases the flexibility of the voltage-gain adjustment.

Fig. 9 shows the relationships between the voltage gain and the duty cycle of the proposed converter and the converters in [28] and [33]. It is clear that the proposed converter can achieve a higher voltage gain for the same duty cycle and turns ratio of the coupled inductor.

Fig. 9 Voltage gain comparison of the proposed converter and the converters in [28] and [33]

From the aforementioned analysis of the operating modes, the voltage stresses on the switch S,diodes VD1～VD3, and output diode VDocan be derived.

The voltage stress of the switch S is expressed as

The voltage stresses of the diodes are given by

Fig. 10 demonstrates the relationship between the normalized power-device voltage stress and the turns ratio. It can be seen that the stress of voltage on the main switch and diodes VD1and VD2is a quarter of the output voltage when the turns ratio of the coupled inductor is 1. Furthermore, as the turns ratio increases,the main-switch voltage stress and the voltage stress on VD1will decrease rapidly. Although the voltage stresses on diodes VD2and VD3increase with the increase in the turns ratio, the voltage stress on VD2is less than one half of the output voltage and the voltage stress on VD3is always less than the output voltage. It is obvious that the turns ratio has no effect on the voltage stress of the output diode VDowhen N1is equal to N2.

Fig. 10 Voltage-stress curve of power devices (N1=N2=N)

4.2 DCM operation

During DCM operation, there are five modes. The key waveforms are shown in Fig. 6. During Mode 1,the switch S is turned on. The following equations hold true

During Mode 3, the switch S and diode VD3are turned off. The following equations can be derived from Fig. 7c.

If DXis defined as the duty cycle of the magnetizing inductor current, from the peak point ramped down to zero, by applying the volt-second balance principle to the magnetizing inductance Lm,the following equation can be derived as

From (25), the voltages of C1, C2, and C3can be rewritten as

Substituting (27) into (24), the output voltage is obtained as

According to (29), the duty cycle DXcan be expressed as

The peak value of the magnetizing inductor current ILmpis derived as

The average current iCoof the output capacitor is expressed as

By applying the current-second balance principle to the output capacitor, and substituting (30) and (31)to (32), the voltage gainof the proposed converter can be obtained as

where fsis the switching frequency.

4.3 Boundary conduction mode operation

The boundary normalized time constant of the magnetizing inductor can be expressed as

The plot of τLm,Bis shown in Fig. 11. If τLmis larger than τLm,B, the coupled inductor is operated in CCM. In the case of practical applications, one should make subtle adjustments.

Fig. 11 Boundary condition of the proposed converter under N1=N2=1

4.4 Calculation of efficiency

Before analyzing the losses of the converter in the CCM mode, the parasitic parameters of the converter must be defined as follows:

(1)The equivalent resistances of the primary,secondary, and tertiary windings of the coupling inductor are rLa, rLb, and rLc, respectively.

(2) The on-resistance of the switch S is rS.

(3) The forward voltage drops of the diodes VD1,VD2, VD3, and VDoare,,, and,respectively, and their equivalent resistances are rVD1,, and, respectively.

In order to simplify the analysis, the effect of leakage inductance is neglected. The turns ratio of the coupling inductance N1=N2=N. The equivalent circuit of the converter with losses is shown in Fig. 12. Fig.13a shows a diagram of the converter with losses during the on period of the switch and Fig. 13b shows a diagram of the converter with losses during the off period of the switch.

Fig. 12 Equivalent circuit of proposed converter with losses

Fig. 13 Circuit diagrams of the proposed converter with losses during on and off periods of the switch

From Fig. 13a, the following equations can be obtained as

From Fig. 13b, the following equations can be obtained as

The average current of diode VD3can be expressed as

The average currents of diodes VD1, VD2, and VDocan be expressed as

From (43) and (41), the following equation can be obtained as

When (42) and (44) are substituted into (36), the following results are obtained as According to the volt-second balance principle,the following equations can be obtained as

From (45) and (46)

By substituting (42) to (45), and (47) into(37)～(40), the voltage gain of the converter with losses can be derived as

From (48), it can be inferred that the on-resistance of the active switch has a great influence on the voltage gain of the converter. Therefore, a switch with small on-resistance should be selected to improve the voltage gain of the converter. The efficiency of the proposed converter, considering losses, can be derived as in (49).

Fig. 14 shows the relationship between the efficiency of the converter and the duty cycle. It can be seen that when the duty cycle is too large, the efficiency decreases rapidly. Therefore, in order to achieve high-efficiency transformation, the duty cycle should not be too large.

Fig. 14 Efficiency curve of the proposed converter

5 Performance comparison

To demonstrate the performance of the proposed converter, some comparisons with other high-step-up converters described in [28], [32], and [33] are presented in Tab. 2.

Tab. 2 Performance comparisons of high-step-up converters

The comparisons of the voltage stresses of the main switch and output diode are shown in Fig. 15 and Fig. 16, respectively. It can be seen that the proposed converter obtains higher voltage gains and that the voltage stress across the main switch is lower than that of the conventional ones. Meanwhile, the voltage stress on the output diode is also lower than that of the converters introduced in [27] and [28]. Furthermore, a low-voltage-rated diode can be used, which reduces the output-diode conduction losses. Therefore, the proposed converter is more suited for high-step-up voltage conversion applications, where it effectively increases the conversion efficiency.

Fig. 15 Comparison of normalized voltage stresses of the proposed converter and other converters in the literature.

Fig. 16 Voltage-stress curve of the output diode

6 Experimental verification

In order to verify the operation and evaluate the performance of the proposed converter, an experimental prototype of the structure with the TWCI was designed in a laboratory. The specifications of the components used in the prototype are provided in Tab. 3. The experimental results are shown in Fig. 17, under the full load of 300 W.

Fig. 17a shows the gate signal of the switch S,and the currents through the primary-side leakage inductor Lkand the switch S. The current iLk1through the leakage inductance Lkis the input current iin.

Tab.3 Utilized components and specifications of the prototype

In Fig. 17b, the gate signal of the switch S, the voltage stress on it, and the voltage on the clamp capacitor C2are presented. When the switch S is turned off, the voltage on the switch S is clamped by the clamp capacitor C2and clamp diode VD1. It can be observed that the voltage stress Vdsis a quarter of the output voltage during the steady-state period.Therefore, low voltage ratings and low on-state resistance levels can be obtained for the active switch of the proposed converter, to improve the conversion efficiency.

Fig. 17 Experimental results under the full load of 300 W

The ZCS performance of the clamp diode VD1is illustrated in Fig. 17c. One can see that the current through the clamp diode, iVD1, decreases to zero before the switch S is turned on. Thus, the reverse-recovery problem is efficiently alleviated.

Fig. 17d and Fig. 17e show the voltages and currents of the regenerative diodes VD2and VD3,respectively. The reverse recovery of the regenerative diode current is effectually alleviated.

Fig. 17f illustrates the voltage and current stresses on the output diode VDo. The voltage stress is approximately half of the output voltage in the steady-state period. In addition, the reverse-recovery problem of the output diode can be effectively alleviated, which improves the conversion efficiency.

Fig. 18 shows the dynamic response between 400 W and 300 W, under a step load variation. The output voltage is maintained at 400 V because of the closed-loop voltage to be added. In the open-loop state,we assume that the resistance before the load change is R1, the output voltage is V1, the resistance after change is R2, and the output voltage is V2. The output power is assumed to remain unchanged when the load changes.In this case,

Fig. 18 Dynamic response waveforms from 400 W to 300 W

According to (50), the output voltage will change when the load resistance changes. On comparing with the experimental waveforms, which add closed-loop control, it can be seen that the closed-loop voltage has successfully realized the function of maintaining the output voltage.

Fig. 19 shows the experimental conversion efficiency of the proposed converter. The maximum efficiency of the proposed converter is approximately 95.27% at Po= 150 W and the full-load efficiency is 94.43%. The results demonstrate that the proposed converter can realize high conversion efficiencies.

Fig. 19 Experimental conversion efficiency

7 Conclusion

A novel single-switch converter based on the TWCI and voltage-multiplier techniques, which was suited for high-step-up industry applications, was introduced in this paper. The voltage stress of the switch was reduced by the clamped circuit and the energy stored in the leakage inductance could be recycled to improve the conversion efficiency. In addition, the output-diode reverse-recovery problem was greatly alleviated and its voltage stress was low.Thus, a low-voltage-rated diode with low RDS(on)could be used. The proposed converter exhibited the advantages of continuous input current and high conversion ratio, which is appropriate for high-step-up applications.