A Low-Cost High-Performance Interleaved Inductor-Coupled Boost Converter for Fuel Cells

Long-Yi Chang 1,2, Jung-Hao Chang 2, Kuei-Hsiang Chao 2,* and Yi-Nung Chung 1 1 Department of Electrical Engineering, National Changhua University of Education, Changhua 50074, Taiwan; lychang@ncut.edu.tw (L.-Y.C.); ynchung@cc.ncue.edu.tw (Y.-N.C.) 2 Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung 41170, Taiwan; iop5u0@gmail.com * Correspondence: chaokh@ncut.edu.tw; Tel.: +886-4-2392-4505 (ext. 7272); Fax: +886-4-2392-2156


Introduction
Despite the recent plunge in oil prices, the development of alternative energy sources remains a key issue for CO 2 emissions reduction due to global warming and climate change.So far, fuel cells, solar energy, and wind power stand as examples of the most successfully developed renewable energy sources.Yet fuel cells have the disadvantage of providing a low output voltage, and are unable to operate in parallel with other types of energy sources [1].Furthermore, the output voltage provided by a fuel cell is found to vary with its load, according to which a power conditioner is required to boost the output voltage to a specified level for a DC linked load [2][3][4][5][6][7].
Currently, there exist a wide variety of boost converters in the literature.As presented in [8][9][10], conventional boost converters are characterized as being simple in structure and easy to control, while a major concern is the damage to overheated power switches caused by an overlong duty cycle.An isolated boost converter [11,12] has the same advantage as conventional boost converters, and is designed to provide a high voltage gain and to reduce the voltage rating by means of output capacitors connected in series.In such configuration, a high turns ratio between coupled inductors leads to a high voltage gain, but also gives rise to a large input current ripple, meaning that high current rated power switches are required.Consequently, the price paid reflects a rise in the facility's costs and volume.As presented in [2,13], although the aim of a high voltage gain can be achieved using coupled inductors connected in series in inductor-coupled boosters, this configuration creates an excessive amount of parasitic capacitance between the coupled inductors and the power switches.As a result, circuit resonance is seen and power switches are damaged due to excessive surge voltage across and inrush current through the switches.Hence, a snubber is introduced into the configuration for switch damage prevention.Over recent years, there have been a number of interleaved boost converters published in the literature [14][15][16][17].The configurations of interleaved boost converters not only have the same advantages as conventional counterparts, but also lower the current stress in inductors and power switches using an interleaving mechanism, and suppress the input current ripple.They cannot be applied to high output voltage operation, due to the fact that they provide the same voltage gain as a boost converter.In contrast, the interleaved boost converters, as presented in [18][19][20], have a high voltage gain advantage over those in [14][15][16][17] using capacitor of voltage doublers, and the voltage stress across power switches are lowered accordingly.Yet they are unable to boost the output voltage of fuel cells to a high voltage level due to an inadequate voltage gain.As presented in [21], a pair of high voltage ratio interleaved DC-DC converters operate in parallel, such that the input current splits into four branches and the pair of converters delivers power to its load in an interleaving manner.Even though this move is able to successfully suppress the ripples of input current and output voltage, this parallel configuration, as opposed to a single counterpart, doubles the converter cost, requires a complicated control mechanism, and occupies an oversized volume, while the voltage gain remains exactly the same.As presented in [4], voltage multiplier cells are employed to achieve a high voltage gain in an interleaved boost converter, but the voltage gain can be further improved at the cost of more voltage multiplier cells.In addition, this parallel configuration requires higher current rated power switches, due to an interleaved path.Although a two-phase interleaved converter, as presented in [22], provides the same voltage gain as those in [18][19][20], and the aim of voltage double can be achieved using capacitors connected in series, this configuration gives rise to high current stress in power switches, i.e., a rise in the implementation cost, and provides a voltage gain inadequate for high output voltage applications.A modular high step-up interleaved boost converter, presented in [23], is developed as a combined form of an inductor-coupled boost converter, as in [2,13], and an interleaved voltage double boost converter, as in [18][19][20].This configuration provides a high voltage gain by use of coupled inductors connected in series with capacitor of voltage doublers, which involves a larger number of components, higher current rated power switches and higher voltage rated diodes.The coupled inductor connected in series was adopted in [24] to achieve a high voltage conversion ratio, but it increased the voltage rating and current rating of the switches.In addition, when the leakage inductance of the coupled inductor and the stray capacitance of the switches produce resonance, it will cause excess surge voltage and inrush current to the switches.As a result, switches with higher voltage and current rating were needed.As for [25], it operated two sets of capacitor voltage doublers, adopting interleaved control.By doing so, not only was the voltage gain of the converter increased, but the input current ripple and the voltage rating were reduced.However, it caused a problem by increasing the current stress of the switches.Hence, it is important to develop a high-voltage gain converter with low voltage/current power switches for keeping the facility costs down.
This paper presents an interleaved inductor-coupled converter as a way to resolve the above-stated problems.It is designed to provide a high voltage conversion ratio, using coupled inductors and capacitor of voltage doublers.In this manner, the voltage ratings of the involved power switches and diodes stay unaffected as the output voltage is boosted.In addition, the current stress on the coupled inductors and the power switches can be lowered, and the ripple level in the input current can be suppressed using an interleaving mechanism.

Fuel Cells
Among fuel cells consisting of various types of electrolytes, a proton exchange membrane (PEM) fuel cell is the most common type seen in practical applications due to the advantages of: (1) a low operating temperature leading to a high speed switching; (2) a low operating temperature for safety concerns; (3) easy modularization and a superior response to load variation; and (4) low emissions as well as a high conversion ratio.In light of this, a pair of Horizon (H-500XP) PEM fuel cells, as specified in Table 1 [26], is adopted as the electricity source in this work.

Inductor Coupled Interleaved Converter with High Voltage Conversion Ratio
As a low-voltage, high-current power source, a fuel cell requires a step-up converter for parallel operation with other types of power sources.Hence, this paper presents an interleaved inductor-coupled converter, as illustrated in Figure 1.It mainly involves a pair of boost converters, a flyback converter, and a clamp capacitor.Designed with a high voltage conversion ratio, this circuit configuration requires a low duty cycle, giving rise to a considerable reduction in the voltage ratings of power switches, in the conduction and switching loss of power switches.Besides, the input current ripple can be suppressed and the current rating of power switches can be reduced using an interleaving mechanism.

Inductor Coupled Interleaved Converter with High Voltage Conversion Ratio
As a low-voltage, high-current power source, a fuel cell requires a step-up converter for parallel operation with other types of power sources.Hence, this paper presents an interleaved inductorcoupled converter, as illustrated in Figure 1.It mainly involves a pair of boost converters, a flyback converter, and a clamp capacitor.Designed with a high voltage conversion ratio, this circuit configuration requires a low duty cycle, giving rise to a considerable reduction in the voltage ratings of power switches, in the conduction and switching loss of power switches.Besides, the input current ripple can be suppressed and the current rating of power switches can be reduced using an interleaving mechanism.A good design of a boost converter with coupled inductor needs to achieve high voltage gain, low voltage and current ratings of switches, low voltage rating of diodes, and minimum additional elements.Table 2 lists the expected good design performance of the proposed boost converter with coupled inductors.A good design of a boost converter with coupled inductor needs to achieve high voltage gain, low voltage and current ratings of switches, low voltage rating of diodes, and minimum additional elements.Table 2 lists the expected good design performance of the proposed boost converter with coupled inductors.

Operation Principle
This section is devoted to the mode analysis on the presented interleaved inductor-coupled converter.There are four operation modes involved in this converter, and the respective voltage and current waveforms across and through components are illustrated in Figure 2.For illustration purposes, the duty cycle is set to greater than 0.5 in continuous conduction mode (CCM), and the following assumptions are made.

Operation Principle
This section is devoted to the mode analysis on the presented interleaved inductor-coupled converter.There are four operation modes involved in this converter, and the respective voltage and current waveforms across and through components are illustrated in Figure 2.For illustration purposes, the duty cycle is set to greater than 0.5 in continuous conduction mode (CCM), and the following assumptions are made.(1) All the components involved are ideal, meaning that the parasitic capacitance and the conduction resistance of each switch and the voltage drop across a forward-biased diode are not taken into account.(2) For simplification purposes, it is assumed that L m1 = L m2 = L, and i The equivalent circuit in this mode is illustrated in Figure 3.Both S 1 and S 2 are switched on, and the input voltage V i is applied to L m1 and L m2 .With both inductors as energy storage devices, i Lm1 and i Lm2 rise linearly with time, expressed as: The voltage drops across the reverse-biased diodes D 1 -D 4 are respectively described as: The energy is released from the output capacitors C o1 -C o3 toward the load.
Energies 2016, 9, 792 5 of 22 (1) All the components involved are ideal, meaning that the parasitic capacitance and the conduction resistance of each switch and the voltage drop across a forward-biased diode are not taken into account.(2) For simplification purposes, it is assumed that Lm1 = Lm2 = L, and iLm1 = iLm2.Hence, vLm1 = vLm2 = vL and iLm1 = iLm2 = iLm = 1/2ii.

Mode 1 (t0-t1)
The equivalent circuit in this mode is illustrated in Figure 3.Both S1 and S2 are switched on, and the input voltage Vi is applied to Lm1 and Lm2.With both inductors as energy storage devices, iLm1 and iLm2 rise linearly with time, expressed as: The voltage drops across the reverse-biased diodes D1-D4 are respectively described as: The energy is released from the output capacitors Co1-Co3 toward the load.

Mode 2 (t 1 -t 2 )
The equivalent circuit in this mode is illustrated in Figure 4. S 1 is switched off, while S 2 stays switched on.Meanwhile, i Lm1 decreases linearly with time, formulated as: The stored inductive energy is released by way of D 4 to the clamp capacitor C 1 .In the same manner, the energy is released via D 1 to the output capacitor C o1 due to the reversed polarity of N 12 , and the output voltage across C o1 is expressed as: Furthermore, L m2 serves as an energy storage device as in Mode 1, and i Lm2 is given as: The voltage drops across the reverse-biased diodes D 2 and D 3 are respectively expressed as: Energies 2016, 9, 792 6 of 22

Mode 2 (t1-t2)
The equivalent circuit in this mode is illustrated in Figure 4. S1 is switched off, while S2 stays switched on.Meanwhile, iLm1 decreases linearly with time, formulated as: The stored inductive energy is released by way of D4 to the clamp capacitor C1.In the same manner, the energy is released via D1 to the output capacitor Co1 due to the reversed polarity of N12, and the output voltage across Co1 is expressed as: ) Furthermore, Lm2 serves as an energy storage device as in Mode 1, and iLm2 is given as: The voltage drops across the reverse-biased diodes D2 and D3 are respectively expressed as:

Mode 3 (t2-t3)
The equivalent circuit in this mode is illustrated in Figure 5.As in Mode 1, S1 and S2 both are switched on, and the input voltage Vi is applied to the inductors Lm1 and Lm2.Consequently, the currents through inductors, as given in Equations ( 1) and (2), rises linearly with time, and all the diodes are reverse-biased, as described in Equations ( 3)-( 6).Hence, the electricity is delivered from Co1-Co3 to the load.

Mode 3 (t 2 -t 3 )
The equivalent circuit in this mode is illustrated in Figure 5.As in Mode 1, S 1 and S 2 both are switched on, and the input voltage V i is applied to the inductors L m1 and L m2 .Consequently, the currents through inductors, as given in Equations ( 1) and (2), rises linearly with time, and all the diodes are reverse-biased, as described in Equations ( 3)-( 6).Hence, the electricity is delivered from C o1 -C o3 to the load.

Mode 4 (t3-t4)
The equivalent circuit in this mode is illustrated in Figure 6.S1 remains switched on, while S2 is switched off.In the meantime, iLm1 and iLm2 rises and decreases linearly with time respectively, described as: Electricity is released to Co3 via C1 and D3, owing to a reversal of the voltage polarity across Lm2.Likewise, the energy is released to Co2 by way of D2 due to the voltage polarity reversal across N22, and the voltage drop across Co2 is expressed as: The voltage drops across D1 and D4 are respectively expressed as:

Mode 4 (t 3 -t 4 )
The equivalent circuit in this mode is illustrated in Figure 6.S 1 remains switched on, while S 2 is switched off.In the meantime, i Lm1 and i Lm2 rises and decreases linearly with time respectively, described as: Electricity is released to C o3 via C 1 and D 3 , owing to a reversal of the voltage polarity across L m2 .Likewise, the energy is released to C o2 by way of D 2 due to the voltage polarity reversal across N 22 , and the voltage drop across C o2 is expressed as: The voltage drops across D 1 and D 4 are respectively expressed as: Following the inductor volt second balance principle, the combined use of Equations ( 1), ( 2), ( 7), and ( 13) gives: Back substitution of Equation (17) into Equation ( 18) now gives: Rearrangement of Equation (19) gives the voltage drop across the clamp capacitor: Substitution of Equation ( 20) into either Equation (18) or Equation (19) gives the voltage drop across the output capacitor Co3: VCo1-VCo3 are summed as the total output voltage, formulated as: Substitution of Equations ( 8), (14), and (21) into Equation (22) gives: or, expressed in a concise form: As a graphic representation of Equation ( 24), a family of voltage gain-duty cycle curves is illustrated in Figure 7, with N = N12/N11 = N22/N21 as a parameter.Following the inductor volt second balance principle, the combined use of Equations ( 1), ( 2), (7), and (13) gives: Back substitution of Equation (17) into Equation ( 18) now gives: Rearrangement of Equation (19) gives the voltage drop across the clamp capacitor: Substitution of Equation ( 20) into either Equation (18) or Equation (19) gives the voltage drop across the output capacitor C o3 : V Co1 -V Co3 are summed as the total output voltage, formulated as: Substitution of Equations ( 8), (14), and (21) into Equation (22) gives: or, expressed in a concise form: As a graphic representation of Equation ( 24), a family of voltage gain-duty cycle curves is illustrated in Figure 7, with N = N 12 /N 11 = N 22 /N 21 as a parameter.

Performance Comparison
To demonstrate the performance superiority of this work, Table 3 gives a comparison on the voltage gain, voltage/current ratings of power switches, voltage rating of diodes, and the numbers of the required inductors, capacitors, and diodes in this proposal and other representative pieces of work [4,17,19,[22][23][24][25].
As can be seen in Table 3, the presented converter is found to outperform its counterparts in terms of the number of components required and the voltage ratings of switches and diodes.It also meets the expected performance listed in Table 2.

Converter Design
The presented interleaved inductor-coupled converter is developed as a combined form of a boost converter and a flyback one.Table 4 lists the electrical specifications of the boost converter.

Performance Comparison
To demonstrate the performance superiority of this work, Table 3 gives a comparison on the voltage gain, voltage/current ratings of power switches, voltage rating of diodes, and the numbers of the required inductors, capacitors, and diodes in this proposal and other representative pieces of work [4,17,19,[22][23][24][25].
As can be seen in Table 3, the presented converter is found to outperform its counterparts in terms of the number of components required and the voltage ratings of switches and diodes.It also meets the expected performance listed in Table 2.

Converter Design
The presented interleaved inductor-coupled converter is developed as a combined form of a boost converter and a flyback one.Table 4 lists the electrical specifications of the boost converter.(1) Choice of inductance Turns ratio of L m1 to L m2 is specified as 1:2 herein, and then substituted into Equation ( 24), simplified as: For simplification purposes, the inevitable power loss in each component is not taken into account, meaning that the input power completely reaches the output of the converter, i.e., Substitution of the turns ratio and Equation ( 24) into Equation ( 26) gives the average inductor current: As illustrated in Figure 2, the maximum and minimum currents through L m1 and L m2 can be expressed in terms of the average value and the current swing, respectively, as: For operation in CCM, it is requested that I Lm1,2(min) be greater than zero, that is, Rearrangement of Equation (30) gives the lower bound of inductance: Designed to operate in CCM under a light load of 300 W, the presented converter must drive a 400 Ω load.Accordingly, Equations ( 24) and (31) give a duty cycle (D) of 0.78 and a minimum inductance of 23 µH, respectively.In consideration of redundancy, a 35 µH inductor is employed herein.
(2) Choice of capacitance In the vast majority of DC/DC converters, the output is followed by a shunt capacitor as a way to reduce the output ripple voltage caused by on/off switching.With C o1 = C o2 = C o3 = C o , as illustrated in Figure 8, it is observed that i Co1 -i Co3 share the same waveform, and the change of charge is given as: Rearrangement of Equation (32) gives: Under arbitrary load conditions, substitution of a ripple ratio below 0.5% to Equation (33) gives C o = 50 µF.Hence, a commercially available 470 µF/450 V capacitor is employed herein.
Under arbitrary load conditions, substitution of a ripple ratio below 0.5% to Equation (33) gives Co = 50 μF.Hence, a commercially available 470 μF/450 V capacitor is employed herein.The above analysis indicates an equivalent impedance of 122.5 Ω and an output voltage of approximately 15 V at an output power of 1000 W in a fuel cell.Substitution of the above results into Equation (24) gives D = 0.78, and Equation (28) results in ILm1,2(max) ≈ 41 A. Furthermore, Figure 2 illustrates the waveforms of the current through and the voltage drop across the power switches and the diodes, according to which commercially available IGBT MMG100J030U (600 V/100 A) switches (IXYS, Milpitas, CA, USA) and IQBD30E60A1 (600 V/60 A) diodes (IXYS, Milpitas, CA, USA) are employed herein.

Simulation Results
Power simulation (PSIM) software simulations are conducted on an interleaved inductorcoupled converter with a high voltage conversion ratio as illustrated in Figure 9.With a fuel cell output voltage of 15 V, illustrated in Figure 10 are the simulated input and output voltage/current waveforms of the presented DC/DC converter at an output voltage of 350 V and an output power of 1000 W. Exhibited in Figures 11 and 12 are the simulated waveforms of the trigger signals for S1 and S2, the currents through the diodes ids1 and ids2 and the voltage drops across the power transistors vds1 and vds2.Presented in Figure 13 are the simulated waveforms of the currents through the coupled inductors Lm1 and Lm2, while in Figures 14-17 are the simulated voltage/current waveforms across/through the diodes D1-D4, and in Figure 18 are the simulated current waveforms through the capacitors iCo1-iCo3.A good agreement is found between all the above-stated simulation results and Figure 2.
. Switch control signals and the current waveforms through the output capacitors over an operating cycle (t 0 -t 4 ).
The above analysis indicates an equivalent impedance of 122.5 Ω and an output voltage of approximately 15 V at an output power of 1000 W in a fuel cell.Substitution of the above results into Equation (24) gives D = 0.78, and Equation (28) results in I Lm1,2(max) ≈ 41 A. Furthermore, Figure 2 illustrates the waveforms of the current through and the voltage drop across the power switches and the diodes, according to which commercially available IGBT MMG100J030U (600 V/100 A) switches (IXYS, Milpitas, CA, USA) and IQBD30E60A1 (600 V/60 A) diodes (IXYS, Milpitas, CA, USA) are employed herein.

Simulation Results
Power simulation (PSIM) software simulations are conducted on an interleaved inductor-coupled converter with a high voltage conversion ratio as illustrated in Figure 9.With a fuel cell output voltage of 15 V, illustrated in Figure 10 are the simulated input and output voltage/current waveforms of the presented DC/DC converter at an output voltage of 350 V and an output power of 1000 W. Exhibited in Figures 11 and 12 are the simulated waveforms of the trigger signals for S 1 and S 2 , the currents through the diodes i ds1 and i ds2 and the voltage drops across the power transistors v ds1 and v ds2 .Presented in Figure 13 are the simulated waveforms of the currents through the coupled inductors L m1 and L m2 , while in Figures 14-17 are the simulated voltage/current waveforms across/through the diodes D 1 -D 4 , and in Figure 18 are the simulated current waveforms through the capacitors i Co1 -i Co3 .A good agreement is found between all the above-stated simulation results and Figure 2.

Experimental Results
This section is devoted to the experimental validation of PSIM simulations on a DC/DC converter with the electrical specifications listed in Table 5.A photo of the realized converter is presented in Figure 19, and Figure 20

Experimental Results
This section is devoted to the experimental validation of PSIM simulations on a DC/DC converter with the electrical specifications listed in Table 5.A photo of the realized converter is presented in Figure 19, and Figure 20 illustrates the measured output voltage and current waveforms

Experimental Results
This section is devoted to the experimental validation of PSIM simulations on a DC/DC converter with the electrical specifications listed in Table 5.A photo of the realized converter is presented in Figure 19, and Figure 20 illustrates the measured output voltage and current waveforms at an output power of 1000 W. With an extremely low level of ripples in the input and output current i i and i o , the converter was found to be able to boost an input voltage of 18 V to an output voltage of 350 V.For comparison purposes, the waveforms measured at P o = 350 W are presented in Figure 21.As expected, a good performance agreement is seen once more between the simulation and experimental results.Figures 22 and 23 illustrate the measured waveforms of the trigger signals for the main switches S 1 and S 2 , the currents i ds1 and i ds2 , and the voltage drops v ds1 and v ds2 .As before, there is a good agreement between the simulation and experimental results, the converter configuration meets the design requirement of components' current/voltage ratings.Moreover, Figure 24 illustrates the measured current waveforms through the coupled inductors L m1 and L m2 , where the ripple level of the input current i i is suppressed using an interleaving mechanism.Figures 25-28 illustrate the measured current and voltage waveforms through and across the diodes D 1 -D 4 .A good agreement is seen again between the simulation and experimental results.

Parameter Specification
Range of input voltage range (V i ) at an output power of 1000 W. With an extremely low level of ripples in the input and output current ii and io, the converter was found to be able to boost an input voltage of 18 V to an output voltage of 350 V.For comparison purposes, the waveforms measured at Po = 350 W are presented in Figure 21.
As expected, a good performance agreement is seen once more between the simulation and experimental results.Figures 22 and 23 illustrate the measured waveforms of the trigger signals for the main switches S1 and S2, the currents ids1 and ids2, and the voltage drops vds1 and vds2.As before, there is a good agreement between the simulation and experimental results, and the converter configuration meets the design requirement of components' current/voltage ratings.Moreover, Figure 24 illustrates the measured current waveforms through the coupled inductors Lm1 and Lm2, where the ripple level of the input current ii is suppressed using an interleaving mechanism.Figures 25-28 illustrate the measured current and voltage waveforms through and across the diodes D1-D4.
A good agreement is seen again between the simulation and experimental results.

Conclusions
This paper presents an interleaved inductor-coupled converter to boost the output voltage of fuel cells to a high voltage level and to overcome the problems of the voltage ratings of the involved power switches and diodes.By using the proposed circuit scheme of the converter, not only was the voltage gain increased, but the voltage ratings of power switches were also reduced.In addition, the current stress on the coupled inductors can be lowered, and the ripple level in the input current can be suppressed by using an interleaving mechanism.It is validated by simulation and experimental means to provide a high voltage conversion ratio, boosting an input voltage of 15 V to an output voltage of 350 V.In addition, as the output voltage is boosted, the voltage rating of power switches stays at Vi/(1 − D), meaning that it has no dependence on the output voltage, and the current rating is merely one half the input current.In conclusion, this paper presents a DC/DC converter with low cost but high performance due to a smaller number of required components, a high voltage conversion ratio, and low voltage and current stress on power switches.

Figure 1 .
Figure 1.Configuration of the presented interleaved inductor-coupled boost converter.

Figure 1 .
Figure 1.Configuration of the presented interleaved inductor-coupled boost converter.

Figure 2 .
Figure 2. Respective waveforms of the current through and the voltage across the components in the converter in Figure 1.

Figure 2 .
Figure 2. Respective waveforms of the current through and the voltage across the components in the converter in Figure 1.

Figure 7 .
Figure 7.A family of voltage gain-duty cycle curves with N as a parameter.

Figure 7 .
Figure 7.A family of voltage gain-duty cycle curves with N as a parameter.

Figure 8 .
Figure 8. Switch control signals and the current waveforms through the output capacitors over an operating cycle (t0-t4).

Figure 10 .
Figure 10.Simulated input and output voltage/currents at an input voltage of 15 V, an output voltage of 350 V, and an output power of 1000 W.

Figure 10 .
Figure 10.Simulated input and output voltage/currents at an input voltage of 15 V, an output voltage of 350 V, and an output power of 1000 W.

Figure 10 . 22 Figure 11 .
Figure 10.Simulated input and output voltage/currents at an input voltage of 15 V, an output voltage of 350 V, and an output power of 1000 W.

Figure 14 .
Figure 14.Simulated voltage and current waveforms for the diode D1.

Figure 14 .
Figure 14.Simulated voltage and current waveforms for the diode D1.

Figure 14 .
Figure 14.Simulated voltage and current waveforms for the diode D 1 .

Figure 15 .
Figure 15.Simulated voltage and current waveforms for the diode D2.

Figure 16 .
Figure 16.Simulated voltage and current waveforms for the diode D3.

Figure 15 . 22 Figure 15 .
Figure 15.Simulated voltage and current waveforms for the diode D 2 .

Figure 16 .
Figure 16.Simulated voltage and current waveforms for the diode D3.

Figure 16 .
Figure 16.Simulated voltage and current waveforms for the diode D 3 .

Figure 17 .
Figure 17.Simulated voltage and current waveforms for the diode D4.

Figure 17 . 22 Figure 17 .
Figure 17.Simulated voltage and current waveforms for the diode D 4 .

Figure 18 .
Figure 18.Simulated waveforms for the output capacitor current i Co1 -i Co3 .

Figure 19 .
Figure 19.A photo of the realized interleaved inductor-coupled boost converter.Figure 19.A photo of the realized interleaved inductor-coupled boost converter.

Figure 19 . 22 Figure 20 .
Figure 19.A photo of the realized interleaved inductor-coupled boost converter.Figure 19.A photo of the realized interleaved inductor-coupled boost converter.

Figure 21 .
Figure 21.Measured voltage and current waveforms in the input and output at an output power of 350W for the implemented boost converter.

Figure 22 .
Figure 22.Measured waveforms related to the power switch S1.

Figure 20 . 22 Figure 20 .
Figure 20.Measured voltage and current waveforms in the input and output at an output power of 1000 W for the implemented boost converter.

Figure 21 .
Figure 21.Measured voltage and current waveforms in the input and output at an output power of 350W for the implemented boost converter.

Figure 22 .
Figure 22.Measured waveforms related to the power switch S1.

Figure 21 . 22 Figure 20 .
Figure 21.Measured voltage and current waveforms in the input and output at an output power of 350 W for the implemented boost converter.

Figure 21 .
Figure 21.Measured voltage and current waveforms in the input and output at an output power of 350W for the implemented boost converter.

Figure 22 .
Figure 22.Measured waveforms related to the power switch S1.Figure 22. Measured waveforms related to the power switch S 1 .

Figure 22 . 22 Figure 23 .
Figure 22.Measured waveforms related to the power switch S1.Figure 22. Measured waveforms related to the power switch S 1 .

Figure 24 .
Figure 24.Measured current waveforms through the coupled inductors Lm1 and Lm2.

Figure 25 .
Figure 25.Measured voltage and current waveforms for the diode D1.

Figure 23 . 22 Figure 23 .
Figure 23.Measured waveforms related to the power switch S 2 .

Figure 24 .
Figure 24.Measured current waveforms through the coupled inductors Lm1 and Lm2.

Figure 25 .
Figure 25.Measured voltage and current waveforms for the diode D1.

Figure 24 .
Figure 24.Measured current waveforms through the coupled inductors Lm1 and Lm2.

Figure 25 .
Figure 25.Measured voltage and current waveforms for the diode D1.Figure 25.Measured voltage and current waveforms for the diode D 1 .

Figure 25 . 22 Figure 26 .Trigger signal of S 2 50VFigure 27 .
Figure 25.Measured voltage and current waveforms for the diode D1.Figure 25.Measured voltage and current waveforms for the diode D 1 .

Figure 28 .
Figure 28.Measured voltage and current waveforms for the diode D4.

Figure 28 .
Figure 28.Measured voltage and current waveforms for the diode D4.

Figure 28 .
Figure 28.Measured voltage and current waveforms for the diode D4.Figure 28.Measured voltage and current waveforms for the diode D 4 .

Figure 28 .
Figure 28.Measured voltage and current waveforms for the diode D4.Figure 28.Measured voltage and current waveforms for the diode D 4 .

Table 2 .
The expected good design performance of the proposed boost converter with coupled inductor.

Table 2 .
The expected good design performance of the proposed boost converter with coupled inductor.

Table 3 .
Performance and requirement comparison among representative types of boost converters and this proposal.

Table 3 .
Performance and requirement comparison among representative types of boost converters and this proposal.

Table 4 .
Design parameters and settings for the presented boost converter.

Table 5 .
Electrical specifications and component model numbers involved in the implemented boost converter.

Table 5 .
Electrical specifications and component model numbers involved in the implemented boost converter.