# A Coupled-Inductor DC-DC Converter with Input Current Ripple Minimization for Fuel Cell Vehicles

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

_{p}was employed in Reference [26] to simply reduce the input ripple current of a proton exchange membrane (PEM) fuel cell. However, it was only suitable for AC output applications. A pre-regulator was introduced in Reference [27] to interface with the main regulator for reducing the current ripple. However, the pre-regulator employed an interleaved structure that was not indispensable. The introduced pre-regulator reduced the power density and increased the cost of the proposed converter. To reduce the low-frequency input current ripple without the auxiliary circuit, a control method based on a front-end DC-DC converter was proposed in Reference [28]. This method intended to modify the DC bus voltage reference and control the DC bus voltage to fluctuate properly at 2f

_{o}, making the DC bus capacitor support nearly all of the fluctuating power. However, it was not suitable for high-frequency current ripples caused by a charging/discharging current flowing through the input inductor.

## 2. Topology

_{M}, a leakage inductance L

_{r}, and an ideal transformer whose turns ratio is n

_{p}:n

_{s}= 1:n. The inductor L

_{a}and the capacitor C

_{1}form an input current ripple minimization unit, and the diode D

_{1}and the capacitor C

_{4}form a passive lossless clamping circuit. Consequently, the voltage stress across the power switch Q can be clamped to the voltage across C

_{4}when Q is turned off. The voltage doubling unit is composed of the capacitor C

_{2}and the coupled inductor L

_{s}, while the capacitor C

_{3}and the capacitor C

_{4}are the energy storage capacitors in the high voltage side.

## 3. Analysis of Operating Principles and Characteristics

#### 3.1. Operating Principles

_{3}is still conducting, and the current flowing through capacitor C

_{1}starts to decrease. This mode ends when the current flowing in C

_{3}becomes zero.

_{3}is no longer able to provide energy for the load and continues to decrease. Accordingly, capacitor C

_{3}begins to discharge, and the current flowing through it increases. The trends of the currents flowing in other branches of the circuit remain the same. This mode ends when the current flowing through diode D

_{3}decreases to zero.

_{2}is turned on, and capacitor C

_{3}is still discharging. The coupled inductor transfers energy to capacitor C

_{2}, and it starts to charge. The capacitor C

_{1}continues to discharge, but its current decreases gradually. Meanwhile, capacitor C

_{4}continues to charge, and its current gradually decreases to zero, at which time this mode ends.

_{4}begins to reverse and gradually increase, and C

_{4}begins to discharge. The current flowing through capacitor C

_{1}continuously decreases, while the current flowing in diode D

_{2}rises gradually. This mode ends when the current flowing through capacitor C

_{1}is equal to the current flowing in diode D

_{2}.

_{2}continues to increase, and it is larger than the current flowing through capacitor C

_{1}. As a result, the current flowing through capacitor C

_{4}continues to rise. When the current flowing into capacitor C

_{1}decreases to zero, this mode ends.

_{1}starts to charge, and the current flowing in it increases gradually. Then the current decreases as the capacitor voltage rises.

_{2}is completed, and the current flowing in the secondary side of the ideal transformer n

_{s}reduces to zero. The current flowing in the primary side n

_{p}of the ideal transformer increases faster because there is no energy being transferred to the secondary side. This mode does not exist when the duty cycle is small (based on the magnetizing inductor).

_{M}discharges. As a result, the current flowing into the leakage inductance L

_{r}starts to decrease. Because of the conduction of diode D

_{1}, the voltage stress across Q is clamped at the voltage across the capacitor C

_{4}. The capacitor C

_{4}continues charging. Meanwhile, capacitor C

_{2}is still in the charging state because the currents flowing into both sides of the ideal transformer have not reversed yet. The diode D

_{2}remains turned on, and the current flowing through capacitor C

_{1}begins to decrease. This mode finishes when the current flowing in capacitor C

_{2}reduces to zero.

_{3}begins to decrease because of the conduction of D

_{3}. When the current flowing into C

_{3}decreases to zero, this mode ends.

_{3}continues to increase, and C

_{3}changes into a charging state. The current trends of other branches remain unchanged. This mode terminates when the current flowing into C

_{1}decreases to zero.

_{1}begins to discharge, and energy is transferred to C

_{4}from C

_{1}. As the current flowing through L

_{a}does not change, the current flowing into the primary side n

_{p}falls. As a result, the current flowing into the secondary side n

_{s}begins to decrease. This mode terminates when the power switch Q turns on.

_{4}and its voltage ripple can be obtained as

#### 3.2. Analysis of Ripple Minimization Characteristics

_{1}, C

_{2}, C

_{3}, and C

_{4}are U

_{C1}, U

_{C2}, U

_{C3}, and U

_{C4}respectively; U

_{in}is the steady input voltage; u

_{La}is the instantaneous inductor voltage; the instantaneous current flowing into L

_{a}is i

_{La}and the average inductor current is I

_{La}; and the duty cycle is d.

_{a}, the capacitor C

_{1}, and the capacitor C

_{4}form a closed circuit loop, and the following equation can be derived by applying Kirchhoff’s Voltage Laws (KVLs):

_{in}is the instantaneous input voltage, and u

_{c1}and u

_{c4}are the instantaneous voltages across C

_{1}and C

_{4}.

_{a}satisfies the voltage second balance principle, and thus the average voltage across the inductor L

_{a}is zero in each switching period. Therefore, Equation (4) can be obtained. The voltage ripples across C

_{1}and C

_{4}are very close to zero, and the input voltage is regarded as constant in a switching period, so the instantaneous inductor voltage u

_{La}is very small, according to Equation (3). Therefore, the current ripple of the inductor current i

_{La}can be regarded as zero, which means that input current ripple minimization can be realized:

_{a}, u

_{C1}, and u

_{C4}. The capacitor voltage fluctuation is smaller if the capacitances of C

_{1}and C

_{4}are larger, which is beneficial to the realization of current ripple minimization.

#### 3.3. Voltage Gain Analysis

_{M}/(L

_{M}+ L

_{r}) is introduced.

_{p}of the ideal transformer is equal to kU

_{in}, while the voltage across the secondary side n

_{s}is U

_{C2}− U

_{C4}. Equation (5) can be obtained:

_{p}is changed to kU

_{C1}, and the voltage across the secondary side n

_{s}becomes U

_{C3}− U

_{C2}. Therefore, Equation (6) can be obtained:

_{M}yields Equation (7):

_{1}, C

_{2}, C

_{3}, and C

_{4}can be derived as

#### 3.4. Analysis of Passive Lossless Clamping Circuit

_{1}and the capacitor C

_{4}form a passive lossless clamping circuit. C

_{4}can absorb the energy stored in the leakage inductance through D

_{1}and limit the voltage stress across the power switch Q to U

_{C4}. This passive lossless clamping circuit provides a path for transmitting leakage inductance energy to the load. Moreover, it can raise the efficiency of the converter and suppress the voltage spike across the power switch Q caused by leakage inductance L

_{r}.

## 4. Voltage and Current Stresses and Performance Comparisons

#### 4.1. Voltage Stresses

_{4}are connected in parallel when Q is turned off, and D

_{2}is connected to the capacitor C

_{3}in parallel when D

_{2}is turned off. In other words, the voltages across Q and C

_{4}are equal, and the voltage stress across D

_{2}is U

_{C3}. The voltage stresses across Q and D

_{2}can be derived as

_{1}is U

_{C4}and the voltage stress across D

_{3}is U

_{C3}when Q is turned on. Thus, the voltage stresses across D

_{1}and D

_{3}can be derived as

_{1}are independent of the coupled inductors and are only related to the duty cycle d and the input voltage U

_{in}. The voltage stresses across diode D

_{2}and diode D

_{3}are not only related to d, but are also related to the turns ratio n. Hence, it is beneficial to choose a desired turns ratio n for the coupled inductors to obtain a trade-off between the voltage gain and the voltage stresses across D

_{2}and D

_{3}.

#### 4.2. Current Stresses

_{1}, C

_{2}, C

_{3}, and C

_{4}are I

_{C1on}, I

_{C2on}, I

_{C3on}, and I

_{C4on}; and the current flowing into L

_{a}is I

_{Laon}. I

_{npon}is the current flowing into the primary side of the ideal transformer, while I

_{nson}is the current flowing into the secondary side. Meanwhile, the current flowing into L

_{M}is I

_{LMon}, and the current flowing into L

_{r}is I

_{Lron}. I

_{D2}is the current of D

_{2}. I

_{inon}and I

_{outon}are the input current and the output current, respectively.

_{1}, C

_{2}, C

_{3}, and C

_{4}are I

_{C1off}, I

_{C2off}, I

_{C3off}, and I

_{C4off}; the current flowing into L

_{a}is I

_{Laoff}; and the currents flowing into both sides of the ideal transformer are I

_{npoff}and I

_{nsoff}. I

_{LMoff}is the current flowing into L

_{M}, and the current flowing into L

_{r}is I

_{Lroff}. I

_{D1}is the current of D

_{1}, while I

_{D3}is the current of D

_{3}. The input current and the output current are I

_{inoff}and I

_{outoff}, respectively.

_{1}–C

_{4}, the equations can be derived as

_{a}and L

_{M}are assumed to be constant, Equation (17) can be derived:

_{2}can be obtained according to Figure 4a, Equations (18) and (19):

_{1}and D

_{3}can be obtained by means of Figure 4b, Equations (18) and (19):

#### 4.3. Performance Comparisons

_{1}was larger than the output voltage in the converter of Reference [29], while the voltage stresses across all semiconductors in the proposed converter were less than the output voltage. Moreover, the proposed converter could achieve a much higher voltage gain at the cost of one more diode and one more capacitor. The voltage gain M versus the duty cycle d is shown in Figure 5 when the turns ratio n is equal to 1 and 2.

## 5. Experimental Results and Analysis

_{in}= 30–100 V was used as the input of the converter to simulate a fuel cell source. The output voltage was controlled to 400 V by a voltage loop implemented on a digital signal processor (DSP) TMS320F28335. The experiment parameters are listed in Table 2. According to Equation (1), the current ripple coefficient α is defined as 0.2, and a large L

_{a}can reduce the input current ripple: Therefore, L

_{a}and L

_{M}were taken as 241 μH and 368 μH, respectively. From Equation (2), the voltage ripple Δu is defined as 0.5 V. Considering practical experience and the laboratory conditions, C

_{2}–C

_{4}were taken as 540 μF, and C

_{1}was taken as 270 μF.

_{out}= 400V are shown in Figure 7. Figure 7a shows the voltage stresses across Q and D

_{1}, which were equal to 133 V, while Figure 7b shows the voltage stresses across D

_{2}and D

_{3}, which were 267 V, which was consistent with the theoretical analysis. In addition, the energy stored in the leakage inductance was released through the diode D

_{1}when Q was turned off. As a result, the voltage spike across the power switch Q was reduced significantly. The current flowing into the inductor L

_{a}and the voltage across the capacitor C

_{1}are shown in Figure 8. The input current I

_{in}, which flowed into L

_{a}, had no fluctuation in each switching period, and neither did the voltage across C

_{1}. Thus, it could be concluded that input current ripple minimization was achieved, as analyzed in Section 3.2. Figure 9 shows the currents flowing into both sides of the coupled inductors. The capacitor C

_{2}received energy from the coupled inductors when Q was turned on. On the contrary, the current I

_{Lp}flowing into the primary side started to decrease when Q was turned off, C

_{2}started to discharge, and the current I

_{Ls}flowing into the secondary side transferred energy to the load through D

_{3}. The experimental results were consistent with the theoretical analysis.

_{out}could be kept constant at 400 V, even when the input voltage U

_{in}varied from 30 V to 100 V continuously. This demonstrated that the proposed converter could operate well in a wide voltage gain range from 13.33 to 4.

_{in}= 100 V and the load power P = 400 W, the proposed converter reached a maximum conversion efficiency of 95.12%. The minimum efficiency was 89.24% when the input voltage U

_{in}= 40 V and the load power P = 400 W. To sum up, with the same power, as the voltage gain increased (i.e., the input voltage decreased), the efficiency of the proposed converter decreased. Since the input current rose as the low-side voltage decreased, the copper loss and the switching losses of the converter rose. Therefore, the efficiency of the converter appeared to degrade at a high voltage gain.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The proposed coupled-inductor DC-DC converter. (

**a**) The topology; (

**b**) the equivalent circuit.

**Figure 2.**Current flow paths of the proposed converter in one switching period. (

**a**) Mode A; (

**b**) Mode B; (

**c**) Mode C; (

**d**) Mode D; (

**e**) Mode E; (

**f**) Mode F; (

**g**) Mode G; (

**h**) Mode H; (

**i**) Mode I; (

**j**) Mode J; (

**k**) Mode K.

**Figure 3.**The simplified current waveforms of the converter. Mode A: End with i

_{C3}dropping to 0; Mode B: End with i

_{D3}dropping to 0; Mode C: End with i

_{C4}dropping to 0; Mode D: End with i

_{C1}equaling i

_{D2}; Mode E: End with i

_{C1}dropping to 0; Mode I: End with i

_{C3}dropping to 0; Mode J: End with i

_{C1}dropping to 0.

**Figure 5.**Curves of voltage gain versus duty cycle for two types of converters with input current ripple minimization.

**Figure 7.**Voltage stresses across all semiconductors when U

_{in}= 50 V and U

_{out}= 400 V: (

**a**) Voltage stresses across Q and D

_{1}; (

**b**) voltage stresses across D

_{2}and D

_{3}.

**Figure 11.**Efficiencies of the proposed converter with different output powers at different input voltages (i.e., different voltage gains) when U

_{out}= 400 V.

Characteristics | Converter in [29] | Proposed Converter |
---|---|---|

Voltage Gain | $(nd+1)/(1-d)$ | $(n+2)/(1-d)$ |

Voltage Stress of power switch | $\frac{1}{1-d}{U}_{\mathrm{in}}$ | $\frac{1}{1-d}{U}_{\mathrm{in}}$ |

Voltage Stress of diodes | ${D}_{\mathrm{C}}:\frac{1}{1-d}{U}_{\mathrm{in}}$ | ${D}_{1}:\frac{1}{1-d}{U}_{\mathrm{in}}$ |

${D}_{1}:\frac{n+1}{1-d}{U}_{\mathrm{in}}$ | ${D}_{2},{D}_{3}:\frac{n+1}{1-d}{U}_{\mathrm{in}}$ | |

Current Stress of power switch | $\frac{nd+1}{\left(1-d\right)d}{I}_{\mathrm{out}}$ | $\frac{n+2d}{\left(1-d\right)d}{I}_{\mathrm{out}}$ |

Current Stress of diodes | ${D}_{\mathrm{C}}:\frac{nd+1}{2\left(1-d\right)d}{I}_{\mathrm{out}}$ | ${D}_{1},{D}_{3}:\frac{1}{1-d}{I}_{\mathrm{out}}$ |

${D}_{1}:\frac{nd+1}{\left(1-d\right)d}{I}_{\mathrm{out}}$ | ${D}_{2}:\frac{1}{d}{I}_{\mathrm{out}}$ | |

Number of power switches | 1 | 1 |

Number of diodes | 2 | 3 |

Ripple-minimization input current | Yes | Yes |

Parameters | Values |
---|---|

Rated power P_{n} | 400 W |

Switching frequency f_{s} | 20 kHz |

Capacitor C_{1} | 270 μF |

Capacitors C_{2}, C_{3}, and C_{4} | 540 μF |

Inductor L_{a} | 241 μH |

Magnetizing inductor L_{M} | 368 μH |

Leakage inductance L_{r} | 3.25 μH |

Turns ratio n_{p}:n_{s} | 1:1 |

Output voltage U_{out} | 400 V |

Input voltage U_{in} | 30–100 V |

Power switch Q | IXTH88N30P |

Diodes D_{1}–D_{3} | DPG60C300HB |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yan, F.; Li, J.; Du, C.; Zhao, C.; Zhang, W.; Zhang, Y.
A Coupled-Inductor DC-DC Converter with Input Current Ripple Minimization for Fuel Cell Vehicles. *Energies* **2019**, *12*, 1689.
https://doi.org/10.3390/en12091689

**AMA Style**

Yan F, Li J, Du C, Zhao C, Zhang W, Zhang Y.
A Coupled-Inductor DC-DC Converter with Input Current Ripple Minimization for Fuel Cell Vehicles. *Energies*. 2019; 12(9):1689.
https://doi.org/10.3390/en12091689

**Chicago/Turabian Style**

Yan, Fuwu, Jingyuan Li, Changqing Du, Chendong Zhao, Wei Zhang, and Yun Zhang.
2019. "A Coupled-Inductor DC-DC Converter with Input Current Ripple Minimization for Fuel Cell Vehicles" *Energies* 12, no. 9: 1689.
https://doi.org/10.3390/en12091689