# Analysis of the THD and Common-Mode Voltage of the Three-Phase Boost-Buck EV Traction Inverter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Operating Principle

_{2}for S3.

_{1}for S1. In this mode, the output voltage is filtered by the dc link capacitor of the phase module.

## 3. CM Voltage, THD, and Interleaving Method

#### 3.1. CM Voltage and Current

_{an}, v

_{bn}, and v

_{cn}, referenced to the negative dc rail), as well as the CM voltage v

_{CM}that is equal to the load neutral voltage v

_{on}, i.e.,

#### 3.2. THD of the Output Current

_{an}, the load neutral voltage v

_{on}with respect to the negative dc rail, the load phase voltage v

_{ao}= v

_{an}− v

_{on}, and the load phase current i

_{a}. Note that these waveforms follow the same pulse pattern during the buck mode.

_{i}of the BBI will decrease as the overall modulation index M increases. This is because a higher M means a higher output voltage, which, in turn, means a wider duration of the boost operation mode of the BBI, and the inherent filtering effect becomes more significant.

#### 3.3. Phase Swapping Interleaving Method

## 4. Simulation Evaluation

_{an}is a pulse-width-modulated voltage when the commanded value is lower than the input voltage (buck mode), and it is a filtered smooth waveform when the commanded value is higher than the input voltage (boost mode). The resulting line-to-line voltage is a partially filtered waveform with drastically lower high-frequency harmonics than that with the B-VSI. The total harmonic distortion of the output current (THDi) obtained by the BBI is only 0.85%, 5.2 times lower than the THDi value of 4.40% with the B-VSI.

_{llm}is not greater than the input voltage V

_{in}, the boost switch-legs are bypassed. The BBI is the same as the B-VSI, and both of them work as the regular three-phase two-level inverter. Their THDi levels are the same. When M > $2/\sqrt{3}$, i.e., the peak value of the output line-to-line voltage V

_{llm}is greater than the input voltage V

_{in}, the boost switch-legs are actively operating. For the B-VSI, the dc-link voltage is boosted from the input voltage, and the inverter stage is always operating at the maximum modulation index of SVPWM. The THDi level increases linearly with the overall modulation index. For the BBI, a higher M means longer durations of the boost operation mode and shorter durations of the buck mode, hence longer durations of the filtered smooth current waveform, i.e., lower THDi. The simulated THDi of the BBI matches very well with the analytically derived results based on Equation (21).

## 5. Experimental Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Circuit topology of (

**a**) B-VSI: voltage source inverter with a preceding booster stage and (

**b**) BBI: boost-buck inverter.

**Figure 3.**The characteristic waveforms of phase module A of the boost-buck inverter. (

**a**) The input voltage V

_{in}, reference output voltage v

_{an}, (

**b**) duty cycle d

_{1}for the boost switch leg, duty cycle d

_{2}for the buck switch leg, (

**c**) input current i

_{La}, and average output current i

_{a}are shown.

**Figure 5.**The characteristic waveforms of (

**a**) the module output voltage v

_{an}, load neutral voltage v

_{on}, (

**b**) the phase voltage v

_{ao}, and (

**c**) current i

_{a}of the load.

**Figure 6.**Simulated output voltage and current waveforms of the (

**a**) BBI and (

**b**) B-VSI. (

**a.i**,

**b.i**) Phase voltages, (

**a.ii**,

**b.ii**) phase-to-phase voltages, and (

**a.iii**,

**b.iii**) output currents.

**Figure 7.**Simulated ripple characteristics of the output current of the (

**a**) BBI and (

**b**) B-VSI. (

**a.i**,

**b.i**) Ripple component of the output current and (

**a.ii**,

**b.ii**) instantaneous (green) and averaged (red) waveform of the output current.

**Figure 9.**Simulated output CM voltage and current of the (

**a**) BBI and (

**b**) B-VSI. (

**a.i**,

**b.i**) Instantaneous (green) and averaged (red) waveform of the CM voltage and (

**a.ii**,

**b.ii**) CM current.

**Figure 10.**Zoomed-in detail of the CM voltage and current waveforms. (

**a**) BBI and (

**b**) B-VSI. (

**a.i**,

**b.i**) CM voltage and (

**a.ii**,

**b.ii**) CM current.

**Figure 11.**Simulated waveforms of the ripple of the three summed input inductor currents (

**a**) without and (

**b**) with the phase swapping interleaving method.

**Figure 13.**Experimental waveforms of the output phase voltages (v

_{an}and v

_{bn}), phase-to-phase voltage v

_{ab}, and three-phase currents (i

_{a}, i

_{b}, and i

_{c}) of the BBI.

**Figure 14.**Experimental waveforms of the output phase voltages (v

_{an}and v

_{bn}), phase-to-phase voltage v

_{ab}, and three-phase currents (i

_{a}, i

_{b}, and i

_{c}) of the B-VSI.

**Figure 15.**Measured waveforms of the CM voltage and current of (

**a**) BBI and (

**b**) B-VSI. (

**a.i**,

**b.i**) Waveform over a fundamental cycle. (

**a.ii**,

**b.ii**) Zoomed-in detail of the waveforms.

**Figure 16.**Measured waveforms of the input inductor currents (i

_{La}, i

_{Lb}, i

_{Lc}, i

_{sum}= i

_{La}+ i

_{Lb}+ i

_{Lc}) of the BBI. (

**a**) Without interleaving. (

**b**) With interleaving. (

**a.i**,

**b.i**) Waveforms over a fundamental cycle. (

**a.ii**,

**b.ii**) Zoomed-in detail of the waveforms.

Parameter | Value |
---|---|

Nominal power (kW) | 10 |

Input DC voltage (V) | 200 |

Output voltage, L-L RMS (V) | 400 |

Input filter inductance (uH) | 240 |

DC bus Capacitance (uF) | 12 |

Switching frequency (kHz) | 50 |

Load inductance (mH) | 0.5 |

Topology | Efficiency | THDi | CM Current RMS |
---|---|---|---|

BBI | 97.7% | 1.74% | 86 mA |

B-VSI | 96.8% | 12.52% | 776 mA |

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**MDPI and ACS Style**

Han, Y.; Zhu, Y.; Wu, D.
Analysis of the THD and Common-Mode Voltage of the Three-Phase Boost-Buck EV Traction Inverter. *World Electr. Veh. J.* **2022**, *13*, 114.
https://doi.org/10.3390/wevj13070114

**AMA Style**

Han Y, Zhu Y, Wu D.
Analysis of the THD and Common-Mode Voltage of the Three-Phase Boost-Buck EV Traction Inverter. *World Electric Vehicle Journal*. 2022; 13(7):114.
https://doi.org/10.3390/wevj13070114

**Chicago/Turabian Style**

Han, Yongjie, Yuan Zhu, and Deliang Wu.
2022. "Analysis of the THD and Common-Mode Voltage of the Three-Phase Boost-Buck EV Traction Inverter" *World Electric Vehicle Journal* 13, no. 7: 114.
https://doi.org/10.3390/wevj13070114