# Design and Implementation of a High Efficiency, Low Component Voltage Stress, Single-Switch High Step-Up Voltage Converter for Vehicular Green Energy Systems

^{*}

## Abstract

**:**

## 1. Introduction

_{in}) of photovoltaic ranges between 20 V and 45 V. To effectively feed the photovoltaic energy into the grid, the voltage must be increased to 380 ± 20 V to facilitate the grid connection for the rear inverter [3,4,5] or charge/discharge battery of an electric vehicle (EV) by a bidirectional DC/DC converter [6,7,8]. In the front-end structure, a boost converter is employed to generate a step-up ratio of at least 1:8. Thus, many high step-up converter structures have been recently researched and developed.

## 2. Operating Principles of the Main Circuit

_{m}), magnetizing leakage inductance (L

_{k}

_{1}), and coupled inductors (turns ratio N

_{1}:N

_{2}:N

_{3}). A voltage multiplier circuit is composed of diodes D

_{1}and D

_{2}, capacitors C

_{1}and C

_{2}, coupled inductor L

_{2}, and coupled leakage inductance L

_{k}

_{2}. Another circuit cascaded with capacitor C

_{3}is composed of diodes D

_{4}and D

_{5}, capacitors C

_{4}and C

_{5}, coupled inductor L

_{3}, and coupled leakage inductance L

_{k}

_{3}. A complete cycle of the circuits comprises five operating modes, which are analyzed as follows.

- (1)
- The capacitance values of C
_{1}, C_{2}, C_{3}, C_{4}and C_{5}are high enough to be regarded as constant power sources; and - (2)
- The circuit is operated under the continuous conduction mode (CCM) and the magnetic inductance of each winding is substantially higher than the leakage.

#### 2.1. Mode I (t_{0} ≤ t < t_{1})

_{0}, the S, D

_{1}and D

_{4}are turned on, whereas D

_{2}, D

_{3}and D

_{5}are turned off. The current pathway is depicted in Figure 4a. In this mode, the V

_{in}stores energy through L

_{m}and L

_{k}

_{1}, yielding a linear rise of the inductive current. At the turn-on transient of S, L

_{k}

_{2}, and L

_{k}

_{3}of N

_{2}and N

_{3}continuously release energy to C

_{1}and C

_{4}through D

_{1}and D

_{4}, the cascade of C

_{3}, C

_{4}and C

_{5}transmits energy to the output load (R

_{L}) until the currents i

_{d}

_{1}and i

_{d}

_{4}= 0. When t = t

_{1}, this operating region ends and progresses into the next mode.

#### 2.2. Mode II (t_{1} ≤ t < t_{2})

_{2}and D

_{5}are turned on continuously, whereas D

_{1}, D

_{3}and D

_{4}are turned off. The current pathway is depicted in Figure 4b. In this mode, the V

_{in}stores energy through L

_{m}and L

_{k}

_{1}, yielding a linear rise of the inductive current. Meanwhile, coupled inductors based on turns ratios N

_{21}and N

_{31}and through D

_{2}and D

_{5}release energy to C

_{2}and C

_{5}in a forward manner. The cascade of C

_{3}, C

_{4}and C

_{5}transmits energy to the R

_{L}. When t = t

_{2}, this operating region ends and progresses into the next mode.

#### 2.3. Mode III (t_{2} ≤ t < t_{3})

_{2}, the S is turned off transiently. Since the inductive voltage has a continuous current characteristic and cannot be changed instantaneously, D

_{2}, D

_{3}and D

_{5}are turned on, whereas D

_{1}and D

_{4}are turned off. The current pathway is depicted in Figure 4c. In this mode, the V

_{in}is connected to V

_{C}

_{1}and V

_{C}

_{2}in series and transmits energy to C

_{3}through D

_{3}. As D

_{2}and D

_{5}are switched on, the coupled inductors maintain leakage currents i

_{Lk}

_{2}, i

_{Lk}

_{3}, from which energy is continuously released to C

_{2}and C

_{5}as the means to recover leakage. The cascade of C

_{3}, C

_{4}and C

_{5}transmits energy to the R

_{L}. When the t = t

_{3}, this operating region ends and enters the next mode.

#### 2.4. Mode IV (t_{3} ≤ t < t_{4})

_{3}, S is permanently turned off and D

_{1}, D

_{3}and D

_{4}are turned on, whereas D

_{5}is turned off. The current pathway is depicted in Figure 4d. In this mode, because the preceding mode releases energy continuously until currents i

_{Lk}

_{2}and i

_{Lk}

_{3}reach zero, the polarity of the coupled inductors is reversed. The energy at N

_{1}is transmitted through a flyback method and switched on through D

_{1}and D

_{4}to C

_{1}and C

_{4}, thereby increasing i

_{d}

_{1}and i

_{d}

_{4}. The V

_{in}is continuously connected to V

_{C}

_{1}and V

_{C}

_{2}in series to transmit energy to C

_{3}through D

_{3}. At the output end, similarly, the cascade of C

_{3}, C

_{4}and C

_{5}transmits energy to the R

_{L}until the i

_{Lk}

_{1}current reaches zero. When t = t

_{4}, this operating region ends and progresses into the next mode.

#### 2.5. Mode V (t_{4} ≤ t < t_{5})

_{in}becomes an open circuit because of the zero i

_{Lk}

_{1}current. D

_{1}and D

_{4}are on, whereas D

_{2}, D

_{3}and D

_{5}are off. The current pathway is depicted in Figure 4e. In this mode, the L

_{m}couples energy into C

_{1}and C

_{4}through the coupled inductors. Since the magnetizing inductance is the only source that supplies the required energy, the magnetizing inductance current i

_{Lm}and i

_{d}

_{1}and i

_{d}

_{2}continue to drop until t = t

_{5}. Upon the conclusion of this operating region, a complete switching cycle T

_{S}is achieved.

## 3. Steady-State Analysis

- (1)
- The capacitance values of C
_{1}, C_{2}, C_{3}, C_{4}and C_{5}are high enough to be regarded as constant power sources; - (2)
- The S, D
_{1}, D_{2}, D_{3}, D_{4}and D_{5}are ideal circuit elements; - (3)
- The magnetizing inductance of each winding is substantially higher than the leakage, which can, thus, be ignored; and
- (4)
- The converter is operated under the CCM.

#### 3.1. Step-Up Conversion Ratio

_{in}− V

_{L}

_{1}= 0

_{C}

_{2}= N

_{21}× V

_{L}

_{1}

_{C}

_{5}= N

_{31}× V

_{L}

_{1}

_{21}= N

_{2}:N

_{1}and N

_{31}= N

_{3}:N

_{1}.

_{C}

_{3}= V

_{in}+ V

_{C}

_{1}+ V

_{C}

_{2}− V

_{L}

_{1}

_{C}

_{1}= N

_{2}× V

_{L}

_{1}

_{C}

_{4}= N

_{31}× V

_{L}

_{1}

_{O}= V

_{C}

_{3}+ V

_{C}

_{4}+ V

_{C}

_{5}, substituting Equations (10)–(12) into the equation can render a voltage gain ratio of converters, as expressed in Equation (13):

#### 3.2. Component Voltage Stress

_{1}, D

_{3}, and D

_{4}. The corresponding equations are expressed as follows:

_{2}and D

_{5}are calculated using Equations (18) and (19), as follows:

#### 3.3. Loss Analysis

#### 3.3.1. Switch Element (S)

_{r}represents the rise time of the switch and T

_{f}represents the fall time of the switch.

_{conduction-loss}= I

_{load}

^{2}× R

_{DS}(on)

_{driver-loss}= 16/3 × C

_{gs}× V

_{in}× f

_{sw}

_{turn_on-loss}= 1/2 × T

_{r}× I

_{load}× V

_{in}× f

_{sw}

_{turn_off-loss}= 1/2 × T

_{f}× I

_{load}× V

_{in}× f

_{sw}

#### 3.3.2. Magnetic Energy Storage Element (L)

_{copper-loss}= I

_{load}

^{2}× R

#### 3.3.3. Capacitor (C)

_{leakage}= K × C × V

#### 3.3.4. Diode (D)

_{f}occurs to lower the voltage; when current I

_{load}flows through the potential barrier, power losses occur, as expressed in Equation (26):

_{forward-loss}= V

_{f}× I

_{load}× D

_{d}) exists in the diodes and can cause power losses when the I

_{load}flows through it. The equation is expressed in Equation (27):

_{Rd-loss}= I

_{load}

^{2}× R

_{d}× D

_{rm}) and the period during which it occurs is called the reverse recovery time (T

_{rr}). The area resembling an inverse triangle formed by I

_{rm}and the T

_{rr}is called the reverse storage charge (Q

_{rr}). Without appropriate recycling mechanisms, the energy accumulates and cause losses, as expressed in Equation (28):

_{sw}is the switching frequency and V

_{R}is the reverse-bias voltage of the diode.

_{d}, and capacitor losses. The total impedance of the winding was set to 60 mΩ, resistance of switching conduction R

_{DS}(on) as 10 mΩ, diode V

_{f}as 0.55 V, and f

_{s}as 50 kHz for calculation. In this paper, the measurement device was limited, so component power losses were roughly estimated. We neglected some difficult evaluation parameters (for example. eddy-current, capacitance ESR, print circuit board (PCB) (parasitic impedance losses, and capacitance impedance losses, etc.), and the full load efficiency estimation compared with measurement can meet within ±1%. The total component power losses of the system were much smaller than the system power.

#### 3.3.5. Estimated Conversion Efficiency Analysis

_{rr}, coupled coefficient losses and leakage of coupled inductance, and equivalent series inductance of electrolytic capacitors were ignored. The parasitic effects of elements that were considered were the parasitic internal resistance of coupled inductance (r

_{L}

_{1}, r

_{L}

_{2}and r

_{L}

_{3}), the forward conduction voltage drop of diodes (V

_{D}

_{1}, V

_{D}

_{2}, V

_{D}

_{3}, V

_{D}

_{4}and V

_{D}

_{5}), the series internal resistance of diodes (r

_{D}

_{1}, r

_{D}

_{2}, r

_{D}

_{3}, r

_{D}

_{4}and r

_{D}

_{5}), the ESR of capacitors (r

_{C}

_{1}, r

_{C}

_{2}, r

_{C}

_{3}, r

_{C}

_{4}and r

_{C}

_{5}), and the internal R

_{DS}, as depicted in Figure 6.

_{o}) to the input power, as expressed in Equation (30):

_{L}

_{1}–r

_{L}

_{3}are assumed to be 50 mΩ, r

_{D}

_{1}–r

_{D}

_{5}as 20 mΩ, R

_{DS}as 10 mΩ, r

_{C}

_{1}–r

_{C}

_{5}as 20 mΩ, diode conduction voltage drop as 0.55 V, V

_{in}as 40 V, output voltage as 400 V, and R

_{L}as 355.56 Ω. The relationship among efficiency, gain ratio, and duty cycle is shown in Figure 7.

#### 3.4. Comparison of the Proposed Structure with Extant Structures

_{2}represents the ratio of coils N

_{2}to N

_{1}; n

_{3}represents the ratio of N

_{3}to N

_{1}; and D represents the operating duty cycle ratio. The voltage gain comparison in Table 2 is depicted in Figure 5, where the turns ratio is N

_{1}:N

_{2}:N

_{3}= 1:2:2.

## 4. Experiment Results

_{1}–D

_{3}voltage waveform; (c) D

_{4}and D

_{5}voltage waveform; (d) D

_{1}–D

_{3}current waveform; (e) D

_{4}and D

_{5}current waveform; and (f) voltage waveform of C

_{1}, C

_{3}, C

_{4}, and output. From the experimental waveforms of Figure 13 compared with the steady-state analysis before, the proposed converter had been proved that the component voltage stress of the active switch and diodes are less than 100 V, and was consistent with the results of steady-state analysis.

_{in}, output voltage, and output power for the proposed converter were 40 V, 400 V and 450 W, respectively. The output power of [9,16,21] were only 200, 400 and 300 W, respectively. These curves were measured under a distinct P

_{o}. Under a light-load P

_{o}of 50 W, the proposed structure yielded a 94.511% efficiency. Under a full-load P

_{o}of 450 W, the efficiency became 93.2%. The optimal efficiency (95.346%) was reached under a P

_{o}of 250 W. The efficiency under all power conditions was higher than 93%.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Block diagram of application of vehicular green energy systems. PV: photovoltaics; and MPPT: maximum power point tracking.

**Figure 4.**Mode operating under CCM: (

**a**) Mode I; (

**b**) Mode II; (

**c**) Mode III; (

**d**) Mode IV; and (

**e**) Mode V.

**Figure 13.**The operating waveforms of each element measured under the power loading of 450 W, (

**a**) V

_{gs}: 10 V/div, V

_{ds}: 50 V/div, I

_{LK}

_{1}: 25 A/div, I

_{ds}: 25 A/div, time: 5 μs/div; (

**b**) V

_{gs}: 10 V/div, V

_{D}

_{1}: 100 V/div, V

_{D}

_{2}: 100 V/div, V

_{D}

_{3}: 50 V/div, time: 5 μs/div; (

**c**) V

_{gs}: 10 V/div, V

_{D}

_{4}: 100 V/div, V

_{D}

_{5}: 100 V/div, time: 5 μs/div; (

**d**) V

_{gs}: 20 V/div, I

_{D}

_{1}: 5 A/div, I

_{D}

_{2}: 5 A/div, I

_{D}

_{3}: 25 A/div, time: 5 μs/div; (

**e**) V

_{gs}: 20 V/div, I

_{D}

_{4}: 5 A/div, I

_{D}

_{5}: 5 A/div, time: 5 μs/div; and (

**f**) V

_{C}

_{1}: 50 V/div, V

_{C}

_{3}: 250 V/div, V

_{C}

_{4}: 50 V/div, V

_{O}: 200 V/div, time: 25 μs/div.

Component | Loss Calculation | Unit |
---|---|---|

Switch Conduction Loss | 2.166 | W |

Switch Switching Loss | 1.726 | W |

Inductor Copper Loss | 12.612 | W |

Inductor Iron Loss | 0.28 | W |

Total Diode Loss | 7.324 | W |

Total | 24.108 | W |

Calculated Efficiency | 94.642% | - |

Measured Efficiency | 93.159% | - |

Comparison of Studies | Voltage Gain Ratio | Switch Voltage Stress | Diode Voltage Stress | Number of Capacitors | Number of Inductors | Number of Diodes |
---|---|---|---|---|---|---|

Proposed structure | $\frac{1+D+{n}_{2}+{n}_{3}}{1-D}$ | $\frac{{V}_{in}}{1-D}$ | $\frac{{n}_{2}\times {V}_{in}}{1-D}$ | 5 | 3 | 5 |

Reference [9] | $\frac{2+n+nD}{1-\mathrm{D}}$ | $\frac{{V}_{in}}{1-D}$ | $\frac{\left(1+n\right){V}_{in}}{1-D}$ | 4 | 2 | 4 |

Reference [16] | $\frac{1+{n}_{2}\times D}{{\left(1-D\right)}^{2}}$ | $\frac{\left(1+{n}_{2}\right){V}_{in}}{1-D}$ | $V\mathrm{o}+{\mathrm{n}}_{3}{V}_{in}$ | 3 | 3 | 4 |

Reference [21] | $\frac{1+nD}{{\left(1-D\right)}^{2}}$ | $\frac{Vo}{1+nD}$ | $\frac{nVo}{1+nD}$ | 3 | 2 | 4 |

Parameter | Specification | |
---|---|---|

Input DC Voltage V_{in} | 36–48 V | |

Output DC Voltage V_{O} | 400 V | |

Max output power P_{o} | 450 W | |

Switching frequency f_{s} | 50 kHz | |

Coupled inductors turns ratio | N_{1}:N_{2}:N_{3} = 1:2:2 | |

Component | Model | Specification |

S_{1} | IRFP4110 | 100 V, 120 A |

D_{1}, D_{2}, D_{4}, D_{5} | MBR20200 | 200 V/20 A |

D_{3} | NF020 | 200 V/40 A |

L | MPPRing core | 125 μH |

C_{1}, C_{2} | MPP Film Capacitor | 10 μF/100 V |

C_{3} | Electrolytic Capacitor | 300 μF/400 V |

C_{4}, C_{5} | MPP Film Capacitor | 22 μF/100 V |

V_{in} | Load | Weight Efficiency | |||||
---|---|---|---|---|---|---|---|

10% | 20% | 30% | 50% | 75% | 100% | ||

36 V | 94.018 | 94.287 | 94.441 | 94.608 | 93.983 | 92.648 | 94.119 |

40 V | 94.447 | 94.768 | 95.086 | 95.268 | 94.375 | 93.159 | 94.610 |

48 V | 94.836 | 95.322 | 95.482 | 95.712 | 94.898 | 93.541 | 95.090 |

- | 4% | 5% | 12% | 21% | 53% | 5% | - |

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## Share and Cite

**MDPI and ACS Style**

Wu, Y.-E.; Wu, Y.-L.
Design and Implementation of a High Efficiency, Low Component Voltage Stress, Single-Switch High Step-Up Voltage Converter for Vehicular Green Energy Systems. *Energies* **2016**, *9*, 772.
https://doi.org/10.3390/en9100772

**AMA Style**

Wu Y-E, Wu Y-L.
Design and Implementation of a High Efficiency, Low Component Voltage Stress, Single-Switch High Step-Up Voltage Converter for Vehicular Green Energy Systems. *Energies*. 2016; 9(10):772.
https://doi.org/10.3390/en9100772

**Chicago/Turabian Style**

Wu, Yu-En, and Yu-Lin Wu.
2016. "Design and Implementation of a High Efficiency, Low Component Voltage Stress, Single-Switch High Step-Up Voltage Converter for Vehicular Green Energy Systems" *Energies* 9, no. 10: 772.
https://doi.org/10.3390/en9100772