Novel High Step-Up DC–DC Converter with Three-Winding-Coupled-Inductors and Its Derivatives for a Distributed Generation System

: A novel step-up DC-DC converter with a three-winding-coupled-inductor which integrates a coupled-inductor and voltage-boost techniques for a distributed generation system is proposed in this paper. The two windings of the dotted terminal connection are charged by the input source; the proposed converter utilized smaller turn ratios, and can achieve higher gain when the active switch is turned on. The passive lossless clamped circuits not only can absorb the leakage energy, but also lower the switch voltage stresses; additionally, the reverse-recovery problem of diodes can be reduced to improve the system efﬁciency. Furthermore, the voltage stress of the output capacitor is reduced. The operating principle and corresponding theoretical analyses are discussed in detail. Finally, an experimental prototype with 50 kHz switching frequency, 40 V input voltage, 380 V output voltage and 400 W output power is set up to verify the validity of the proposed converter.


Introduction
In recent times, in order to reducing pollution caused by fossil fuels, new, clean, renewable energy systems have been rapidly developed. Multilevel inverters with higher performance and corresponding analysis methods are presented, and have been widely applied for many circumstances [1,2]. But new renewable energies can't provide higher DC voltage; DC-DC converters with high step-up voltage gains and high efficiencies must be connected between lower input DC voltage and inverters [3][4][5][6][7].
In theory, the basic boost converter with unlimited voltage gain is a preferable candidate, but the higher voltage gain will use the higher duty cycle ratio, which will result in many serious problems such as the reverse-recovery of diodes, higher losses, and higher voltage stress across passive components [8,9]. Boost converters in series are presented to realize the higher voltage gain, but this results in complicated systems and influences reliability due to the presence of additional switches and control units [10][11][12]. Quadratic boost converters based on cascaded technology can improve voltage gain and are applied extensively, but two switches and control circuits in quadratic boost converters increase the complexity and cost of systems, and the voltage gain still needs to be improved to meet many application circumstances.

Proposed High Step-Up Converter and Corresponding Operating Principles
The integration processes of the proposed converter are shown in Figure 1. Figure 1a shows the conventional boost DC-DC converter. To improve the voltage gain, a two-winding coupled inductor boost converter is structured by replacing inductor L 1 with two winding coupled inductors, whose topology is shown in Figure 1b. Through the addition of auxiliary diodes (D 1 and D 2 ) and capacitors (C 1 and C 2 ), the voltage-double two-winding coupled inductor boost converter are presented to further produce higher voltage gain, as shown in Figure 1c. So, through adding one winding N 3 and the corresponding voltage-double capacitors and diodes, the proposed three-winding coupled inductor high step-up converter is constructed by a three-winding coupled inductors, a switch S, four diodes D 1 -D 4 , and four capacitors C 1 -C 4 , as shown in Figure 1d. Meanwhile, a passive clamped circuit which is made of C 1 and D 1 can suppress the voltage spike on the switch caused by inductor leakage, and recycle the inductor leakage energy. The capacitor C 2 is used to step-up and reduced the voltage stress on the diode D 3 . The voltage stress of the capacitor C 3 can be reduced by connection with the capacitor C 4 in series.
Three-winding coupled-inductor cell can be modeled as an ideal transformer, and the following conditions are assumed: (1) The capacitors in this converter are large enough that the voltages of those capacitors can be considered constant in one period. (2) Switches and diodes are considered as ideal, and will not be discussed in transient states.
(3) The coupled inductor's coupling coefficient K is equal to L M /(L M + L K ).  increase linearly. The current 2 N i is increased too. Meanwhile, the capacitor C2 is charged by the clamped capacitor C1, the source, and the winding N3. The capacitor C4 is powered by the winding N2. The capacitor C3 and the secondary-side winding N2 provide their energy to the load R. When 2 D i is equal to zero at t = t1, D2 is naturally turned off, and the operating mode ends.
(2) Mode II [t1, t2]: during this time interval, the switch S is still turned on. The current-flow path is shown in Figure 3b. D3 is still turned off. The currents M L i and K L i are still rising, and the winding N3 of the coupled inductor is charged by the input source. The energy of the load is supplied by the secondary-side winding N2 and the capacitor C3. When the switch is turned off, this operating mode ends.
(3) Mode III [t2, t3]: at t = t2, the switch S is turned off. Diodes D1 and D3 are turned on. Meanwhile, diodes D2 and D4 are turned off in Figure 3c. The energy of the clamped capacitor C1 is provided by the primary side N1 and secondary side winding N3 of the coupled inductor; thus the voltage of the switch S is clamped by the input source and clamped capacitor C1. The capacitor C3 is charged by the source and primary-side winding N1 and the secondary-side winding N2 of the coupled inductor and the multiplier capacitor C2. The energy of the load is supplied by the input source, the secondary-side winding N1 and the primary-side winding N2 of the coupled inductor and the multiplier capacitor C2 the capacitor C4. When the current 1 D i is equal to zero at t = t3, diode D1 is turned off, ending operating mode.  (1) Mode I [t 0 , t 1 ]: at t = t 0 , the switch S is turned on. D 1 , D 2 and D 4 are turned on, and D 3 is off as shown in Figure 3a. In this interval, the power source charges the magnetizing inductor L M and the leakage inductor L K , and the currents i L M and i L K increase linearly. The current i N 2 is increased too. Meanwhile, the capacitor C 2 is charged by the clamped capacitor C 1 , the source, and the winding N 3 . The capacitor C 4 is powered by the winding N 2 . The capacitor C 3 and the secondary-side winding N 2 provide their energy to the load R. When i D 2 is equal to zero at t = t 1 , D 2 is naturally turned off, and the operating mode ends.
(2) Mode II [t 1 , t 2 ]: during this time interval, the switch S is still turned on. The current-flow path is shown in Figure 3b. D 3 is still turned off. The currents i L M and i L K are still rising, and the winding N 3 of the coupled inductor is charged by the input source. The energy of the load is supplied by the secondary-side winding N 2 and the capacitor C 3 . When the switch is turned off, this operating mode ends.
(3) Mode III [t 2 , t 3 ]: at t = t 2 , the switch S is turned off. Diodes D 1 and D 3 are turned on. Meanwhile, diodes D 2 and D 4 are turned off in Figure 3c. The energy of the clamped capacitor C 1 is provided by the primary side N 1 and secondary side winding N 3 of the coupled inductor; thus the voltage of the switch S is clamped by the input source and clamped capacitor C 1 . The capacitor C 3 is charged by the source and primary-side winding N 1 and the secondary-side winding N 2 of the coupled inductor and the multiplier capacitor C 2 . The energy of the load is supplied by the input source, the secondary-side winding N 1 and the primary-side winding N 2 of the coupled inductor and the multiplier capacitor C 2 the capacitor C 4 . When the current i D 1 is equal to zero at t = t 3 , diode D 1 is turned off, ending operating mode.
(4) Mode IV [t 3 , t 4 ]: during this time interval, the switch S is still turned off. The current-flow path is shown in Figure 3d.The input source connects in series with the primary-side winding N 1 , the secondary-side winding N 2 of the coupled inductor, the capacitor C 2 and the capacitor C 4 to provide energy for the load through D 3 . This mode ends at t = t 4 when the switch S is turned on at the beginning of the next switching period. (4) Mode IV [t3, t4]: during this time interval, the switch S is still turned off. The current-flow path is shown in Figure 3d.The input source connects in series with the primary-side winding N1, the secondary-side winding N2 of the coupled inductor, the capacitor C2 and the capacitor C4 to provide energy for the load through D3. This mode ends at t = t4 when the switch S is turned on at the beginning of the next switching period.  (4) Mode IV [t3, t4]: during this time interval, the switch S is still turned off. The current-flow path is shown in Figure 3d.The input source connects in series with the primary-side winding N1, the secondary-side winding N2 of the coupled inductor, the capacitor C2 and the capacitor C4 to provide energy for the load through D3. This mode ends at t = t4 when the switch S is turned on at the beginning of the next switching period.

Analysis in Continuous Conduction Mode
In modes I and II based Figure 3a,b, the following equations can be obtained as follows: During the time of modes III and IV, the following equations can be expressed based on Figure 3c,d: Using the volt-second balance principle on L M and L K yields: From Equations (1)-(10), the voltage gain can be expressed as: where n 21 = N 2 N 1 and n 31 = N 3 N 1 are the turns ratios of the proposed converter. The relationship between the voltage gain, the duty ratio, and the coupling coefficients of coupled inductor is shown in Figure 4a. It shows that the coupling coefficient results in a decline of voltage gain. It can be seen clearly that a smaller turns ratios can achieve a higher gain. If the coupled coefficient K is equal to 1 without considering the impact of the leakage inductance of the coupled inductor, then the ideal voltage gain can be expressed as: In Figure 4b, the curve shows voltage gain comparisons among the proposed converter and the converters in [19,20] at CCM operation under N 3 :N 2 :N 1 = 2:1:4. As shown in Figure 4b, the proposed converter has the higher voltage gain compared to the converters in [19,20], when using the same turn ratios and duty ratios.  In the proposed converter, the diode D4 is turned on during one switching period when N3 = 0. At the same time, the capacitor C4 can be ignored because the across its voltage is equal to zero. Therefore Figure 5 can be obtained. The voltage gains of converters in Figure 5a,b,c under different winding turns are listed in Table 1.      In the proposed converter, the following inequalities are satisfied: When the winding turns N 2 and N 3 are changed, some converters are derived as follows.
In the proposed converter, the diode D 4 is turned on during one switching period when N 3 = 0. At the same time, the capacitor C 4 can be ignored because the across its voltage is equal to zero. Therefore Figure 5 can be obtained. The voltage gains of converters in Figure 5a-c under different winding turns are listed in Table 1.  In the proposed converter, the diode D4 is turned on during one switching period when N3 = 0. At the same time, the capacitor C4 can be ignored because the across its voltage is equal to zero. Therefore Figure 5 can be obtained. The voltage gains of converters in Figure 5a,b,c under different winding turns are listed in Table 1.

Condition
Voltage Gain Converter

Voltage Stress Analysis
The switch voltage stresses, voltages of capacitors C 1 -C 4 and diodes D 1 -D 4 are expressed as follows:

Derivative Converters
According to the different connection position, the proposed circuits can be derived in Figure 6. When applying series-connected voltage-lift networks (VLN), the voltage gain is enhanced by adding some VLN modules in Figure 6a. The voltage gain equation is derived from: Likewise, the voltage gain can be directly enlarged by applying a multiple windings coupled-inductor and multiple diode-capacitor networks to the proposed converter, as shown in Figure 6b. The voltage gain equation can be expressed as follows: The converter with a high step-up voltage gain also can be obtained by an input-parallel-output-series technique. In this technique, the primary and second winding of the coupled-inductor are parallel charged when switch is turned on, and discharged in series when it is turned off. The improved topology is shown in Figure 6c. The detailed features of the aforementioned improved converters are listed in Table 2. The voltage gain equation can be expressed as follows: Energies 2018, 11, x 8 of 11

Experimental Verifications
An experimental prototype with 50 kHz switching frequency, 40 V input voltage, 380 V output voltage and 400 W output power is set up and corresponding parameters have been listed in Table  3.

Experimental Verifications
An experimental prototype with 50 kHz switching frequency, 40 V input voltage, 380 V output voltage and 400 W output power is set up and corresponding parameters have been listed in Table 3.
Duty cycle of the switch is about 0.58, and the switch voltage are about 87 V, as shown in Figure 7a. The switch voltage of active switch S and the voltage of primary winding N 1 of the coupled inductor are shown in Figure 7b; it can be seen that the winding N 1 are charged when the active switch S is turned on. The peak voltages of diodes (D 1 , D 2 , D 3 and D 4 ) are about 97 V, 193 V, 255 V, and 90 V, as shown in Figure 7c-f. From Figure 7c-f, it can be also seen that the current waveforms of diodes (D 1 , D 2 , D 3 and D 4 ) are consistent with theory analysis. It shows that the currents of diodes (D 1 , D 2 , D 3 and D 4 ) are decreased to zero quickly when the diodes are turned off, which means that losses can be reduced. The winding currents of the three-winding coupled inductor is shown in Figure 7a,g. As shown in Figure 7a,g, the operation states of three windings (N 1 , N 2 , N 3 ) are consistent with theory analysis through the switch sequence of active switch S. Duty cycle of the switch is about 0.58, and the switch voltage are about 87 V, as shown in Figure 7a. The switch voltage of active switch S and the voltage of primary winding N1 of the coupled inductor are shown in Figure 7b; it can be seen that the winding N1 are charged when the active switch S is turned on. The peak voltages of diodes (D1, D2, D3 and D4) are about 97 V, 193 V, 255 V, and 90 V, as shown in Figure 7c-f. From Figure 7c-f, it can be also seen that the current waveforms of diodes (D1, D2, D3 and D4) are consistent with theory analysis. It shows that the currents of diodes (D1, D2, D3 and D4) are decreased to zero quickly when the diodes are turned off, which means that losses can be reduced. The winding currents of the three-winding coupled inductor is shown in Figure 7a,g. As shown in Figure 7a,g, the operation states of three windings (N1, N2, N3) are consistent with theory analysis through the switch sequence of active switch S.    Figure 8 shows the tested efficiency curve of the proposed converter. The power range is 40-400 W, and the efficiency is tested per 40 W. From Figure 8, it can be seen that the efficiency of the proposed converter is about 91.9% when output power is 400 W, while the maximum efficiency of proposed converter is about 95.6% when output power is 160 W.

Conclusions
In this paper, a novel three-winding coupled-inductor dc-dc converter is proposed with analysis of its operating modes. The proposed converter can produce a higher voltage gain. Also, a passive lossless clamping circuit which belongs to the part of the step-up is used to suppress voltage spikes across the switch. The proposed converter has the following advantages: (1) It utilized smaller turns ratios, and can therefore achieve a higher voltage conversion gain in a normal small duty cycle; (2) A reduced magnetic size can be applied in this converter to achieve high voltage gain. It is suitable for DG system based on distributed generation system; (3) Two diodes avoid the reverse-recovery problem by achieving turn-off naturally; (4) The presented converter can recycle the leakage inductance energy to improve performance.

Conclusions
In this paper, a novel three-winding coupled-inductor dc-dc converter is proposed with analysis of its operating modes. The proposed converter can produce a higher voltage gain. Also, a passive lossless clamping circuit which belongs to the part of the step-up is used to suppress voltage spikes across the switch. The proposed converter has the following advantages: (1) It utilized smaller turns ratios, and can therefore achieve a higher voltage conversion gain in a normal small duty cycle; (2) A reduced magnetic size can be applied in this converter to achieve high voltage gain. It is suitable for DG system based on distributed generation system; (3) Two diodes avoid the reverse-recovery problem by achieving turn-off naturally; (4) The presented converter can recycle the leakage inductance energy to improve performance. Turns of winding (N 1 , N 2 , and N 3 ) n 31 , n 21 Turns ratios among windings (N 1 , N 2 , and N 3 ) K Coupling coefficients of coupled inductor V C 1 , V C 2 , V C 3 , V C 4 Voltages across capacitors (C 1 , C 2 , C 3 and C 4 ) M CCM Voltage gain D Duty ratio