# A Discontinuous Modulation Method with Variable Clamping Interval Width of the Modular Multilevel Converter

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle of Modular Multilevel Converter

_{1}is ON and T

_{2}is OFF, the state of the submodule is defined as ON, and the output voltage of the submodule is u

_{c}; on the contrary, if T

_{1}is OFF and T

_{2}is ON, the state of the submodule is defined as OFF, and the output voltage of the submodule is 0.

_{x}and i

_{x}

_{z}are the phase current and differential current flowing through the arm, which can be expressed as:

## 3. Conventional Discontinuous Modulation Method

_{m}is the amplitude of the reference voltage.

_{max}= max{u

_{A},u

_{B},u

_{C}} and u

_{min}= min{u

_{A},u

_{B},u

_{C}}. Thus, the expression of zero-sequence voltage can be further expressed as:

## 4. Discontinuous Modulation Method with Variable Clamping Interval

#### 4.1. Calculation of Power Factor

#### 4.2. Discontinuous Modulation Method with Variable Clamping Interval

_{z}= 0, while in the clamping interval:

#### 4.3. Capacitor Voltage Dynamic Balance Algorithm

- (1)
- Determining the total number of submodules which need to be put in, then subsequently sorting the submodules into numerical order according to the amplitude of the capacitor voltage;
- (2)
- Judging the direction of the current i
_{xy}. When the direction of i_{xy}is positive, set S = 0, otherwise, set S = 1; - (3)
- Determining the index number of submodules according to the direction of i
_{xy}. The expression of the index number is as follows:$${N}_{\mathrm{in}}={\mathrm{C}}_{N}\times S+\left(N-1-{\mathrm{C}}_{N}\right)\times \left(1-S\right)$$ - (4)
- The ON and OFF of each submodule is determined by the calculation result of step (3);
- (5)
- Judging the change of the number of submodules in the ON state. If the number of submodules in the ON state is not changed, there will be no switching behavior, and the switching loss will be reduced.

## 5. Experimental Verification

#### 5.1. Switching Loss

#### 5.2. Capacitor Voltage Ripple of Submodule

#### 5.3. Total Harmonic Distortion

#### 5.4. Strategy Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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State | T_{1} | T_{2} | u_{sm} |
---|---|---|---|

ON | ON | OFF | u_{c} |

OFF | OFF | ON | 0 |

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

DC voltage U_{dc} | 200 | V |

Number of submodules N | 4 | - |

Submodule capacitance C | 5.04 | mF |

arm inductance L_{m} | 2.7 | mH |

Carrier frequency f_{c} | 2 | kHz |

Output frequency f | 50 | Hz |

Load resistance R | 5 | Ω |

Load inductance L | 5 | mH |

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## Share and Cite

**MDPI and ACS Style**

Gu, X.; Ma, L.; Zhang, G.; Jin, X.
A Discontinuous Modulation Method with Variable Clamping Interval Width of the Modular Multilevel Converter. *World Electr. Veh. J.* **2023**, *14*, 1.
https://doi.org/10.3390/wevj14010001

**AMA Style**

Gu X, Ma L, Zhang G, Jin X.
A Discontinuous Modulation Method with Variable Clamping Interval Width of the Modular Multilevel Converter. *World Electric Vehicle Journal*. 2023; 14(1):1.
https://doi.org/10.3390/wevj14010001

**Chicago/Turabian Style**

Gu, Xin, Langang Ma, Guozheng Zhang, and Xuefeng Jin.
2023. "A Discontinuous Modulation Method with Variable Clamping Interval Width of the Modular Multilevel Converter" *World Electric Vehicle Journal* 14, no. 1: 1.
https://doi.org/10.3390/wevj14010001