# Analysis of a Single-Phase Z-Source Inverter for Battery Discharging in Vehicle to Grid Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. DC Side Current of Single-Phase ZSI

_{d}(t) I

_{d}(t) stand for DC-link voltage and current, d

_{s}for shoot-through duty ratio, M for modulation index, Z and Φ for load impedance and power factor, ω for inverter output angular frequency. Note that the effects brought by switching frequency components are neglected. The term (1 − d

_{s}) indicates that shoot-through state is not involved in energy transfer process from DC to AC side. Hence, DC side current drawn by the inverter bridge can be expressed as:

_{d}(bar) and i

_{d}(t) denote the average and oscillating value of DC side current, respectively. Since this paper focuses on the design of a Z-Source network, the inverter bridge can be modeled as a current source I

_{d}(t), which is shown in right side of Figure 1. Equation (2) indicates that in addition to the DC component, the current also contains a sinusoidal component at twice the output frequency. The DC side current of a three-phase ZSI only contains the DC component, which solely results in high-frequency DC-link voltage ripple [12]. The situation of single-phase ZSI, nevertheless, is more complicated: (1) the DC component yields similar results to the three-phase case; (2) the sinusoidal component leads to a sinusoidal oscillation of the DC-link voltage, also at twice the output frequency. Therefore, both high and low frequency ripples need to be taken into consideration when sizing the Z-Source network.

## 3. High-Frequency Ripple Analysis of Single-Phase ZSI

_{c}(s) and peak ripple value of inductor current ΔI

_{l}(s) during S-1 state could be expressed by:

_{s}stands for carrier time period, L and C for inductance and capacitance of Z-Source network, E

_{s}for DC source voltage, V

_{c}

_{(s)}(bar) and I

_{l}

_{(s)}(bar) for average value of capacitor voltage and inductor current during S-1 state.

_{c}

_{(A)}and peak ripple value of inductor current ΔI

_{l}

_{(A)}during A-1 state could be expressed by:

_{c}

_{(A)}(bar) and I

_{l}

_{(A)}(bar) stand for average value of capacitor voltage and inductor current during A-1 state. Figure 4 shows the waveforms of capacitor voltage and inductor current analyzed above.

_{vc}

_{(H)1}as the targeted high-frequency ripple factor set by the designer, high-frequency ripple factor of capacitor voltage k

_{vc}

_{(H)}should be smaller than k

_{vc}

_{(H)1}(k

_{vc}

_{(H)}≤ k

_{vc}

_{(H)1}). Likewise, high-frequency ripple factor of inductor current k

_{il}

_{(H)}should be smaller than k

_{il}

_{(H)1}chosen by the designer (k

_{il}

_{(H)}≤ k

_{il}

_{(H)1}). Hence, the critical capacitance and inductance can be obtained by:

## 4. Low-Frequency Ripple Analysis of Single-Phase ZSI

_{d}(t), respectively.

_{c}(t) i

_{l}(t) v

_{d}(t) are corresponding low-frequency oscillations. Hence, based on Equation (2) DC side current could be modified as:

## 5. Z-Source Network Design Approach

- ■
- targeted high-frequency capacitor voltage ripple factor k
_{vc}_{(H)1} - ■
- targeted high-frequency inductor current ripple factor k
_{il}_{(H)1} - ■
- targeted low-frequency capacitor voltage ripple factor k
_{vc}_{(L)1} - ■
- targeted low-frequency inductor current ripple factor k
_{il}_{(L)1}

- (1)
- calculating C based on k
_{vc}_{(H)1}constraint - (2)
- calculating L based on k
_{il}_{(H)1}constraint - (3)
- checking whether k
_{vc}_{(L)1}constraint is met, modifying C if not - (5)
- checking whether k
_{il}_{(L)1}constraint is met, modifying L if not

Output Voltage/Frequency | DC Source (E_{s}) | Load Resistance/Inductance | Carrier Frequency (f_{s}) | Shoot-through Duty Ratio (d_{s}) | Modulation Index (M) |
---|---|---|---|---|---|

55 V/50 Hz | 70 V | 10 Ω/2 mH | 10 kHz | 0.1 | 0.8889 |

Design Input | Design Output | Simulation Comparison | |||||
---|---|---|---|---|---|---|---|

k_{vc}_{(H)1} | k_{il}_{(H)1} | k_{il}_{(L)1} | k_{vc}_{(L)1} | (k_{v}_{(L)}) | L/mH | C/uF | k_{vc}_{(L)} |

2% | 2% | 10% | 1.00% | (1.80%) | 2.29 | 7679 | 0.96% |

1.50% | (2.70%) | 2.29 | 5355 | 1.40% | |||

2.00% | (3.60%) | 2.29 | 4192 | 1.79% | |||

3.00% | (5.40%) | 2.29 | 3029 | 2.50% |

## 6. Experimental Verification

Z-Source Network Parameters | Low-Frequency Capacitor Voltage Ripple Factor k_{vc}_{(L)} | ||
---|---|---|---|

L/mH | C/uF | Theoretical Predictions | Experimental Results |

2.29 | 2700 | 3.49% | 3.09% |

2.29 | 3640 | 2.38% | 2.24% |

2.29 | 4580 | 1.80% | 1.97% |

2.29 | 5400 | 1.49% | 1.41% |

2.29 | 6340 | 1.24% | 1.27% |

2.29 | 7280 | 1.06% | 1.10% |

**Figure 9.**Experimental waveforms of DC source voltage (blue) (10 V/div), inverter output voltage (green) (25 V/div) and capacitor voltage (red) (1 V/div) (AC coupling) with different groups of L and C combinations; measured peak to peak ripple of capacitor voltage (

**a**) 4.80 V, (

**b**) 3.48 V, (

**c**) 3.08 V, (

**d**) 2.20 V, (

**e**) 1.98 V, (

**f**) 1.72 V; measured average capacitor voltage (

**a**) 77.57 V, (

**b**) 77.83 V, (

**c**) 78.15 V, (

**d**) 78.03 V, (

**e**) 78.01 V, (

**f**) 78.11,V.

## 7. Conclusions

## Acknowledgments

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## Share and Cite

**MDPI and ACS Style**

Yu, Y.; Zhang, Q.; Liang, B.; Liu, X.; Cui, S.
Analysis of a Single-Phase Z-Source Inverter for Battery Discharging in Vehicle to Grid Applications. *Energies* **2011**, *4*, 2224-2235.
https://doi.org/10.3390/en4122224

**AMA Style**

Yu Y, Zhang Q, Liang B, Liu X, Cui S.
Analysis of a Single-Phase Z-Source Inverter for Battery Discharging in Vehicle to Grid Applications. *Energies*. 2011; 4(12):2224-2235.
https://doi.org/10.3390/en4122224

**Chicago/Turabian Style**

Yu, Yifan, Qianfan Zhang, Bin Liang, Xiaofei Liu, and Shumei Cui.
2011. "Analysis of a Single-Phase Z-Source Inverter for Battery Discharging in Vehicle to Grid Applications" *Energies* 4, no. 12: 2224-2235.
https://doi.org/10.3390/en4122224