# Comparative Study of Classical and MPC Control for Single-Phase MMC Based on V-HIL Simulations

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## Abstract

**:**

## 1. Introduction

## 2. MMC Overview

#### 2.1. Topology

#### 2.2. Mathematical Model

#### 2.3. Control Objectives

#### 2.3.1. AC Current Control

#### 2.3.2. Circulating Current Control

#### 2.3.3. Submodule Capacitor Voltage Control

#### 2.4. Parameter Settings

#### 2.5. Submodule Capacitance Selection

#### 2.6. Arm Inductance Selection

#### 2.6.1. Resonant Frequency

#### 2.6.2. Circulating Current Second Order Harmonic Amplitude

## 3. Classical Control

#### 3.1. AC Current Control

#### 3.2. Total Leg Voltage Control

#### 3.3. Circulating Current Control

#### 3.4. Leg Energy Distribution Control

#### 3.5. Modulation

## 4. OSS-MPC

## 5. Results

#### 5.1. Control Parameter Selection

#### 5.2. Steady-State

#### 5.3. Dynamic Performance

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

^{®}for their help and support. This paper is the product of the research supported by FONDECYT Regular 1191028 and FONDAP/SERC Chile 15110019.

## Conflicts of Interest

## References

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**Figure 6.**Steady-state performance of Classical Control (

**left**) and OSS-MPC (

**right**): AC current reference set to 10 A; (1) AC current reference (blue) and AC current response (red); (2) circulating current; (3) sum of upper submodule voltages (blue) and sum of lower submodule voltages (red); (4) total sum of submodule voltages.

**Figure 7.**Dynamic performance of Classical Control (

**left**) and OSS-MPC (

**right**): Amplitude of AC current reference changed from 10 A to 5 A at $t=0.075$ s; (1) AC current reference (blue) and AC current response (red); (2) circulating current; (3) sum of upper submodule voltages (blue) and sum of lower submodule voltages (red); (4) total sum of submodule voltages.

Parameter Name | Designation | Value |
---|---|---|

DC bus voltage | ${V}_{dc}$ | 3 kV |

Number of submodules per arm | N | 6 |

Load resistance | R | 80 Ω |

Load inductance | L | 0.19 H |

Switching frequency | ${f}_{pwm}$ | 6 kHz |

Fundamental AC frequency | f | 50 Hz |

Parameter Name | Designation | Value |
---|---|---|

DC bus voltage | ${V}_{dc}$ | 3 kV |

Number of submodules per arm | N | 6 |

Load resistance | R | 80 Ω |

Load inductance | L | 0.19 H |

Switching frequency | ${f}_{pwm}$ | 6 kHz |

Fundamental AC frequency | f | 50 Hz |

Submodule capacitance | ${C}_{sm}$ | 10 mF |

Arm inductance | ${L}_{arm}$ | 5 mH |

Arm resistance | r | 100 mΩ |

Parameter Name | Designation | Value |
---|---|---|

AC current PR controller proportional gain | ${k}_{prp}^{ac}$ | 600 |

AC current PR controller resonant gain | ${k}_{prr}^{ac}$ | 20,000 |

Circulating current PR controller proportional gain | ${k}_{prp}^{z}$ | 753.6 |

Circulating current PR controller resonant gain | ${k}_{prr}^{z}$ | 2 |

Circulating current PI controller proportional gain | ${k}_{p}^{z}$ | 79 |

Circulating current PI controller integral gain | ${k}_{i}^{z}$ | 39 |

Total leg voltage PI controller proportional gain | ${k}_{p}^{tlv}$ | 10 |

Total leg voltage PI controller integral gain | ${k}_{i}^{tlv}$ | 20 |

Leg energy distribution control factor | ${k}_{B}$ | 50 |

Parameter Name | Designation | Value |
---|---|---|

AC current weighting factor | ${\lambda}_{ac}$ | 0.95 |

Circulating current weighting factor | ${\lambda}_{z}$ | 0.16 |

Submodule capacitor voltage weighting factor | ${\lambda}_{sm}$ | 1 |

Criteria | Classical Control | OSS-MPC |
---|---|---|

AC current reference tracking | Excellent | Excellent |

AC current THD | 3.03% | 1.18% |

AC voltage THD | 15.93% | 17.74% |

Submodule capacitor voltage balancing | Excellent | Good |

Total submodule voltage control | Excellent | Poor |

Circulating current tracking | Poor | Good |

Circulating current THD | 17% | 8.8% |

Number of control parameters | 9 | 3 |

Computational complexity | Low | High |

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**MDPI and ACS Style**

Majstorovic, M.; Rivera, M.; Ristic, L.; Wheeler, P. Comparative Study of Classical and MPC Control for Single-Phase MMC Based on V-HIL Simulations. *Energies* **2021**, *14*, 3230.
https://doi.org/10.3390/en14113230

**AMA Style**

Majstorovic M, Rivera M, Ristic L, Wheeler P. Comparative Study of Classical and MPC Control for Single-Phase MMC Based on V-HIL Simulations. *Energies*. 2021; 14(11):3230.
https://doi.org/10.3390/en14113230

**Chicago/Turabian Style**

Majstorovic, Milovan, Marco Rivera, Leposava Ristic, and Patrick Wheeler. 2021. "Comparative Study of Classical and MPC Control for Single-Phase MMC Based on V-HIL Simulations" *Energies* 14, no. 11: 3230.
https://doi.org/10.3390/en14113230