# Modified Cascaded Z-Source High Step-Up Boost Converter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Converter and Principle of Operation

_{1}; one diode D

_{1}in the impedance network; two diodes in the cells D

_{2}and D

_{3}; and one output diode D

_{4}; six coupled inductors L

_{1}, L

_{2}, L

_{3}, L

_{4}, L

_{5}, and L

_{6}; four capacitors C

_{1}, C

_{2}, C

_{3}, and C

_{4}in the impedance network; two switched-capacitors C

_{5}and C

_{6}; and output capacitor C

_{7}.

_{2}can be considered not in the circuit due to being in parallel with input voltage source, and Figure 5 is provided to show the theoretical waveforms of the proposed converter. To simplify the steady state analysis, the following assumptions are made:

- The converter operates in continuous conduction mode (CCM);
- The switch, diodes, and all inductors and capacitors are assumed ideal;
- The magnetizing inductance is large enough to ignore its current ripple;
- The leakage inductances of all windings are equal;
- The output capacitor C
_{7}is large enough to make the output voltage constant; - The switching capacitors C
_{5}and C_{6}are equal.

#### Operation Principles

_{0}< t < t

_{1}] (Figure 4a): Before the t

_{0}input, diode D

_{1}is conducting, and the other semiconductor devices are off. At t

_{0}, the switch Q turns on, diode D

_{1}becomes reverse-biased, and (2 + n)V

_{C}− V

_{in}is applied across it. In addition, the current direction of capacitors C

_{3}and C

_{4}become reverse. In this operation mode, the capacitor voltage of C

_{3}and C

_{4}applies to inductors L

_{3}and L

_{4}, and consequently this voltage will be induced to other coupled inductors L

_{1}, L

_{2}, L

_{5}, and L

_{6}by considering the turn ratio. In this stage, the energy of leakage inductances L

_{1}and L

_{2}are recycled to the input voltage source, and the energy of leakage inductances L

_{5}and L

_{6}are absorbed by switched-capacitors C

_{5}and C

_{6}. The following equations are established in this time interval:

_{C}

_{5}(t

_{0}) and V

_{C}

_{6}(t

_{0}) are less than the coupled inductor’s voltage in their corresponding cells, so a resonance occurs between the leakage inductances and both C

_{4}and C

_{5}to charge the capacitors through D

_{2}and D

_{3}over the half resonance period. The current and voltage of capacitor C

_{5}can be expressed as:

_{3}and switch Q current are determined as:

_{C}

_{5}is given by (5).

_{2}and D

_{3}turn off at zero current.

_{1}< t < t

_{2}] (Figure 4b): At this operation mode, the switch Q is still on and all diodes are at the off state. In addition, the magnetizing inductance L

_{m}is still charging by C

_{3}and C

_{4}. Diodes D

_{2}and D

_{3}are off in this stage due to reversing the current of inductors L

_{5}and L

_{6}, which are blocked by diodes D

_{2}and D

_{3}, respectively. Therefore, the stored magnetic energy of the transformer leads to slightly increasing the current of other coupling windings. This mode ends when the switch Q turns off. The current of inductor L

_{1}can be expressed as:

_{1}is also equal to i

_{C}

_{4}(t

_{1}) by considering the turn ratio.

_{2}< t < t

_{3}] (Figure 4c): At t = t

_{2}, the switch Q turns off, diodes D

_{1}and D

_{4}turn on, and the energy transfers from the input to the output during this stage. The stored energy of the magnetizing inductance and of capacitors C

_{5}and C

_{6}also transfers to the load, and capacitors C

_{3}and C

_{4}will be charged through diode D

_{1}; however, capacitor C

_{1}is discharged in this operation mode. The resonance between leakage inductance L

_{5}and C

_{5}and also leakage inductance L

_{6}and C

_{6}occurs during the maximum time of the half-resonant interval. This stage ends when the resonant current of i

_{C}

_{5}becomes zero and provide the ZCS (zero current switching) turn-off for diode D

_{4}. In the following, the corresponding voltage and current equations are expressed:

_{3}< t < t

_{4}] (Figure 4d): In this stage, the switch is still off and the output diode D

_{4}is also off by reversing the current of L

_{5}, which occurred in the previous operation mode. However, the input diode D

_{1}remains on in this stage, which causes the capacitors C

_{3}and C

_{4}to keep their charging state on from the previous stage. In addition, capacitor C

_{1}is discharged the same way as operation mode 3. The current of L

_{1}can be stated as:

_{3}is equal to i

_{C}

_{4}(t

_{3}) by considering the turn ratio.

## 3. The Proposed Converter Analysis and Design Considerations

#### 3.1. Conversion Ratio

_{1}is on, the capacitors C

_{3}and C

_{4}charge by the input voltage source through magnetizing inductance L

_{m}. However, at the on-state of switch Q, the capacitors C

_{3}and C

_{4}discharge themselves to L

_{m}, which causes the voltage gain of the converter to increase. By applying the magnetizing inductor L

_{m}, the voltage-second balance equation V

_{C}can be calculated as:

_{C}

_{5}and V

_{C}

_{6}can be expressed as:

#### 3.2. Voltage Stresses of Switch and Diodes

_{1}and D

_{4}can be determined as:

_{2}and D

_{3}can be determined by considering interval 2 as:

#### 3.3. Converter Analysis and Design Guideline

_{2}, D

_{3}and D

_{4}for the sake of resonance between leakage inductances of L

_{5}(or L

_{6}) and C

_{5}(or C

_{6}). The full-resonance can be done if the following equation is satisfied:

_{4}is conducting current only in time interval 3 (t

_{2}< t < t

_{3}). Therefore, it can be concluded that the average current of D

_{4}is equal to the output current:

_{3}− t

_{2}can be considered as the maximum DT

_{SW}. In addition, the magnetizing inductance can be also calculated as the following by considering the desirable current ripple $\Delta {I}_{L}$:

_{3}can be calculated with regard to the current flow over the switched-on interval:

_{3}.

#### 3.4. High Step-up Converters Comparison

## 4. Experimental Results

_{DS}of the MOSFET resulted in low conduction power loss.

_{1}; the voltage and current waveforms of the switch are shown in Figure 13. It can be seen that regarding the output voltage of 300 V, which is illustrated in Figure 15, the stress voltage of MOSFET is 100 V. Finally, the voltage and current of diode D

_{4}can be seen in Figure 14.

## 5. Conclusions

_{2}, D

_{3}, and D

_{4}turn off under a ZCS condition. The low input current ripple of this converter makes it appropriate to apply in renewable energy sources. A laboratory prototype of the proposed converter in order to justify the theoretic analysis was built, and experimental waveforms were presented for a 100 W output power converter.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Equivalent circuits of the proposed converter for each operation mode. (

**a**) interval 1, (

**b**) interval 2, (

**c**) interval 3, (

**d**) interval 4.

Converter | Voltage Gain (M) | Switch Voltage Stress | Input Current | Number of Ferrite Core |
---|---|---|---|---|

Conventional Z-source [12] | 1 − D/1 − 2D | (2M − 1)V_{in} | Discontinuous | 3 |

Converter in [18] | 1/(1 − D)^{2} | MV_{in} | Discontinuous | 2 |

Converter in [19] | 2n + 1/1 − 2D | V_{in}/(1 − 2D) | Discontinuous | 2 |

Proposed Converter | 2n + 1/(1 − (2 + n)D) | V_{in}/(1 − (2 + n)D) | Continuous | 1 |

Parameters | Value |
---|---|

Input voltage V_{in} | 25 V |

Output voltage V_{o} | 300 V |

Output power P_{o} | 100 W |

Switching frequency (f_{sw}) | 50 kHz |

Switch Q | IRFP3710 |

Input diode D_{1} | MUR880 |

Diodes D_{2}, D_{3}, D_{4} | MUR460 |

Coupled inductors core | 380 µH |

L_{1}, L_{2}, L_{3}, L_{4}, L_{5}, L_{6} | |

Turns of (L_{1} … L_{6}) | 90 turns |

Turns ratio n | 1 |

Z-source network capacitors (C_{1}, C_{2}, C_{3} and C_{4}) | 15 µF/100 V |

Switched capacitors C_{6}, C_{7} | 560 nF/100 V |

Output capacitors C_{8} | 10 µF/400 V |

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**MDPI and ACS Style**

Salehi, N.; Martínez-García, H.; Velasco-Quesada, G. Modified Cascaded Z-Source High Step-Up Boost Converter. *Electronics* **2020**, *9*, 1932.
https://doi.org/10.3390/electronics9111932

**AMA Style**

Salehi N, Martínez-García H, Velasco-Quesada G. Modified Cascaded Z-Source High Step-Up Boost Converter. *Electronics*. 2020; 9(11):1932.
https://doi.org/10.3390/electronics9111932

**Chicago/Turabian Style**

Salehi, Navid, Herminio Martínez-García, and Guillermo Velasco-Quesada. 2020. "Modified Cascaded Z-Source High Step-Up Boost Converter" *Electronics* 9, no. 11: 1932.
https://doi.org/10.3390/electronics9111932