# The Suppression of Modular Multi-Level Converter Circulation Based on the PIR Virtual Impedance Strategy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MMC Analysis

#### 2.1. MMC Model

#### 2.1.1. MMC Basic Circuit

- (1)
- When the drive signal of the upper switch ${T}_{1}$ is placed on the submodule, ${T}_{1}$ is in the input state S = 1. When the bridge arm current ${i}_{jk}$ is positive, the current charges the capacitor through the anti-parallel diode $D1$ on the switch $T1$, the capacitance-voltage ${u}_{C}$ rises, and the output voltage ${u}_{jk}$ of the submodule is equal to the capacitance-voltage ${u}_{C}$, as shown in Figure 3a. When the bridge arm current ${i}_{jk}$ is negative, the current discharges the capacitance through the upper switch tube $T1$, then the capacitance-voltage ${u}_{C}$ drops and the output voltage ${u}_{jk}$ of the submodule is equal to the capacitance-voltage ${u}_{C}$, as shown in Figure 3b.
- (2)
- When the drive signal of the switch $T1$ is set to 0, the submodule $T1$ is in the bypass state S = 0. When the bridge arm current ${i}_{jk}$ is positive, the current bypasses the capacitance through $T2$, the capacitance-voltage ${u}_{C}$ remains unchanged, and the output voltage ${u}_{jk}$ of the submodule is 0, as shown in Figure 3c. When the bridge arm current ${i}_{jk}$ is negative, the current bypasses the capacitance through $D2$, and then the capacitance-voltage ${u}_{C}$ remains unchanged, and the output voltage ${u}_{jk}$ of the submodule is 0, as shown in Figure 3d.

#### 2.1.2. MMC Equivalent Circuit

#### 2.2. Circulation Analysis

#### 2.3. Modulation Method

## 3. MMC Circulation Control Strategy

#### 3.1. Controller Analysis

#### 3.1.1. PIR Control

#### 3.1.2. Virtual Impedance

#### 3.2. Controller Instruction

## 4. Simulation Analysis

#### 4.1. Simulation Parameters

#### 4.2. Simulation Result

#### 4.2.1. Output for the Steady-State Operation

#### 4.2.2. Comparison of the Control Effects

## 5. Discussion

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Working principle of an MMC half-bridge submodule. (

**a**) Working condition in S = 1, i

_{jk}> 0. (

**b**) Working condition in S = 1, i

_{jk}< 0. (

**c**) Working condition in S = 0, i

_{jk}> 0. (

**d**) Working condition in S = 0, i

_{jk}< 0.

**Figure 8.**(

**a**) FFT analysis of the three−phase output voltage. (

**b**) FFT analysis of the three−phase output current.

**Figure 11.**(

**a**) Harmonic current without the suppressor. (

**b**) FFT analysis of the bridge arm current without the suppressor.

**Figure 12.**(

**a**) Harmonic current with the PI control suppressor. (

**b**) FFT analysis of the bridge arm current with the PI control suppressor.

**Figure 13.**(

**a**) Harmonic current with the QPR control suppressor. (

**b**) FFT analysis of the bridge arm current with the QPR control suppressor.

**Figure 14.**(

**a**) Harmonic current with the PIR virtual impedance composite suppressor. (

**b**) FFT analysis of the bridge arm current with the PIR virtual impedance composite suppressor.

Simulation Variable | Parameter Setting |
---|---|

DC bus voltage/kV | 5.5 |

Number of single bridges Arm submodules n | 22 |

Submodule capacitance/mF | 7 |

Bridge arm reaction/mH | 8 |

Switching frequency/kHz | 10 |

Modulation ratio | 0.9 |

Load resistance/Ω | 1 |

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

K_{p} | 40 |

K_{i} | 600 |

K_{r1} | 1000 |

K_{r2} | 1000 |

${\omega}_{c}$ | 5 |

R_{v}/Ω | 1 |

L_{v}/mH | 10 |

Controller Use | THD of the Bridge Arm Current (%) |
---|---|

Without adding the current suppressor | 30.02 |

PI control suppressor | 6.79 |

QPR control suppressor | 4.48 |

PIR virtual impedance composite suppressor | 1.43 |

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## Share and Cite

**MDPI and ACS Style**

Wang, C.; Yan, W.; Wang, W.; Ni, H.; Chu, J.
The Suppression of Modular Multi-Level Converter Circulation Based on the PIR Virtual Impedance Strategy. *World Electr. Veh. J.* **2023**, *14*, 17.
https://doi.org/10.3390/wevj14010017

**AMA Style**

Wang C, Yan W, Wang W, Ni H, Chu J.
The Suppression of Modular Multi-Level Converter Circulation Based on the PIR Virtual Impedance Strategy. *World Electric Vehicle Journal*. 2023; 14(1):17.
https://doi.org/10.3390/wevj14010017

**Chicago/Turabian Style**

Wang, Chun, Wenxu Yan, Wenyuan Wang, Hongyu Ni, and Jie Chu.
2023. "The Suppression of Modular Multi-Level Converter Circulation Based on the PIR Virtual Impedance Strategy" *World Electric Vehicle Journal* 14, no. 1: 17.
https://doi.org/10.3390/wevj14010017