# Circulating Current Suppression Strategy Based on Virtual Impedance and Repetitive Controller for Modular Multilevel Converter Upper and Lower Bridge Arm Capacitance Parameter Asymmetry Conditions

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## Abstract

**:**

## 1. Introduction

## 2. MMC Analysis

#### 2.1. MMC Basic Circuit

#### 2.2. Circulating Current Analysis

- (1)
- The capacitors in the upper bridge arm of the A-phase deteriorate and their capacitance values all drop to 1/1 − n (n ≤ 0) times their rated value;
- (2)
- The remaining parameters, such as the inductance, remain symmetrical between the upper and lower bridge arms;
- (3)
- The capacitor voltage balancing control algorithm remains in effective operation and the average capacitor voltage remains stable.

## 3. Circulating Current Suppression Strategy

#### 3.1. Repetitive Controller Design

- (1)
- Low-pass filter $Q(z)$

- (2)
- Time-delay session ${z}^{-{N}_{rc}}$

- (3)
- Compensation session ${K}_{rc}S(z){z}^{d}$

#### 3.2. Additional Virtual Impedance Design

#### 3.3. VI-RC Structure

## 4. Simulation Studies

#### 4.1. Simulation Parameters

#### 4.2. Simulation Results

#### 4.2.1. Circulating Current Characteristics

- (1)
- Condition 1: The capacitance rating of the upper bridge arm SMs of the A-phase is set to 7 mF and the capacitance rating of the lower bridge arm SMs is set to 7 mF;
- (2)
- Condition 2: The capacitance rating of the upper bridge arm SMs of A-phase is set to 6.5 mF and the capacitance rating of the lower bridge arm SMs is set to 7 mF;
- (3)
- Condition 3: The capacitance rating of the upper bridge arm SMs of A-phase is set to 6 mF and the capacitance rating of the lower bridge arm SMs is set to 7 mF.

#### 4.2.2. VI-RC Control Effect

#### 4.2.3. Comparison of the Control Effects

- (1)
- PI controller

**Figure 19.**PI controller effect: (

**a**) circulating current waveform under PI controller; (

**b**) bridge arm current waveform under PI controller; (

**c**) circulating current FFT analysis under PI controller; (

**d**) bridge arm current FFT analysis under PI controller.

- (2)
- QPR controller

**Figure 20.**QPR controller effect: (

**a**) circulating current waveform under QPR controller; (

**b**) bridge arm current waveform under QPR controller; (

**c**) circulating current FFT analysis under QPR controller; (

**d**) bridge arm current FFT analysis under QPR controller.

- (3)
- Repetitive controller

**Figure 21.**Repetitive controller effect: (

**a**) circulating current waveform under RC; (

**b**) bridge arm current waveform under RC; (

**c**) circulating current FFT analysis under RC; (

**d**) bridge arm current FFT analysis under RC.

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Four normal operating states of SM, with the red lines indicating the current flow paths. (

**a**) $S=1$, ${i}_{ju,l}>0$; (

**b**) $S=1$, ${i}_{ju,l}<0$; (

**c**) $S=0$, ${i}_{ju,l}>0$; (

**d**) $S=0$, ${i}_{ju,l}<0$.

**Figure 6.**Controller structure: (

**a**) block diagram of RC-based circulating current control system; (

**b**) detailed block diagram of RC.

**Figure 14.**Condition 1 current FFT analysis: (

**a**) circulating current FFT analysis; (

**b**) bridge arm current FFT analysis.

**Figure 15.**Condition 2 current FFT analysis: (

**a**) circulating current FFT analysis; (

**b**) bridge arm current FFT analysis.

**Figure 16.**Condition 3 current FFT analysis: (

**a**) circulating current FFT analysis; (

**b**) bridge arm current FFT analysis.

**Figure 17.**Current key waveform under VI-RC: (

**a**) circulating current waveform under VI-RC; (

**b**) bridge arm current waveform under VI-RC.

**Figure 18.**Current FFT analysis under VI-RC: (

**a**) circulating current FFT analysis under VI-RC; (

**b**) bridge arm current FFT analysis under VI-RC.

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

Rated power/MW | 0.8 |

DC bus voltage/kV | 5.5 |

Number of SMs per arm | 22 |

Rated submodule capacitance/mF | 7 |

Arm inductance/mH | 1.35 |

System sampling frequency/kHz | 10 |

Controller Parameters | Parameter Setting |
---|---|

N_{rc} | 200 |

K_{rc} | 1 |

K_{p} | 30 |

K_{i} | 1 |

d | 4 |

R_{v}/Ω | 1 |

L_{v}/mH | 10 |

Condition | Fundamental Frequency Amplitude/A | Second Frequency Amplitude/A | THD of Bridge Arm Current/% |
---|---|---|---|

Condition 1 | 2.63 | 19.38 | 19.64 |

Condition 2 | 4.49 | 19.39 | 19.89 |

Condition 3 | 10.69 | 19.62 | 20.15 |

Controller Use | Fundamental Frequency Amplitude/A | Second Frequency Amplitude/A | THD of Bridge Arm Current/% |
---|---|---|---|

No controller | 4.49 | 19.39 | 19.89 |

PI | 0.48 | 5.53 | 5.75 |

QPR | 0.16 | 4.87 | 5.23 |

RC | 0.93 | 0.73 | 1.48 |

VI-RC | 0.09 | 0.56 | 0.98 |

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## Share and Cite

**MDPI and ACS Style**

Yao, M.; Ni, H.; Zhao, F.; Wang, W.; Yan, W.
Circulating Current Suppression Strategy Based on Virtual Impedance and Repetitive Controller for Modular Multilevel Converter Upper and Lower Bridge Arm Capacitance Parameter Asymmetry Conditions. *World Electr. Veh. J.* **2023**, *14*, 181.
https://doi.org/10.3390/wevj14070181

**AMA Style**

Yao M, Ni H, Zhao F, Wang W, Yan W.
Circulating Current Suppression Strategy Based on Virtual Impedance and Repetitive Controller for Modular Multilevel Converter Upper and Lower Bridge Arm Capacitance Parameter Asymmetry Conditions. *World Electric Vehicle Journal*. 2023; 14(7):181.
https://doi.org/10.3390/wevj14070181

**Chicago/Turabian Style**

Yao, Mincheng, Hongyu Ni, Feng Zhao, Wenyuan Wang, and Wenxu Yan.
2023. "Circulating Current Suppression Strategy Based on Virtual Impedance and Repetitive Controller for Modular Multilevel Converter Upper and Lower Bridge Arm Capacitance Parameter Asymmetry Conditions" *World Electric Vehicle Journal* 14, no. 7: 181.
https://doi.org/10.3390/wevj14070181