# Integration of Photovoltaic Power Units to Power Distribution System through Modular Multilevel Converter

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## Abstract

**:**

## 1. Introduction

## 2. Modelling of GC-MMC

_{u}, i

_{l}, V

_{Ci_u}, V

_{Ci_l}are upper/lower values for arm currents and capacitor voltages receptively. Moreover, d

_{i}V

_{dc}and V

_{a}are gating signal of the upper gate of the i-th cell, DC-link voltage and phase a voltage separately.

## 3. Fuzzy-Sliding Mode Control (FSMC) of GC-MMC

_{dc-ref}is the reference dc-link voltage and V

_{dc}is the actual dc-link voltage. The PV array’s voltage is remained close to a reference dc-link voltage. Then, the power control is implemented. To achieve this goal, current control strategy based on fuzzy sliding mode control is established. The details of suggested current controller are explained as follow.

_{dp_ref}, i

_{qp_ref}, i

_{dn_ref}and i

_{qp_ref}are reference currents of symmetrical dq components, respectively.

_{c,ref}is the reference SM capacitor voltage.

_{c,j}for each SM is obtained by the formula below:

_{k,j}is arm current and T

_{s}is the control time period.

_{ref}is a vector which it is included the reference values for state variables.

_{eq}+ k

_{w}·sgn(s)

_{w}is the switching gain.

## 4. Simulation Results and Analysis

## 5. Experimental Results

_{dc}≈ 20 V, it is expected the average value across any submodule at any given time, when the sorting algorithm is active, should be approximately 10.

_{fc}and the number of rule bases during designing of the fuzzy controller and it influences on both simulation and experimental results. From the simulation result, it is evident that the controller is capable to reduce the impact of the external events such as asymmetric grid voltage fault and it is very important during connection of photovoltaic systems to weak grid. From the simulation results, it can be observed that the proposed current controllers let retaining power as requested by the DC current source during and after the event. Despite the unbalance of AC voltages, the AC current controller can balance the resulting AC currents. As a result, the active as well as reactive powers start oscillating with double frequency of AC grid. Thanks to the developed current controller, the applied event is damped by the stored energy inside the MMC and consequently does not disturb the DC current and voltage.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Dynamic response (generated active and reactive powers and capacitor voltage) of the GC-MMC during unbalanced voltage sag.

u_{fs} | $\mathit{s}$ | |||||||
---|---|---|---|---|---|---|---|---|

$\dot{s}$ | PB | PM | PS | ZE | NS | NM | NB | |

PB | NB | NB | NB | ZE | ZE | ZE | ZE | |

PM | NB | NB | NB | ZE | ZE | ZE | PS | |

PS | NB | NB | NM | ZE | ZE | PS | PM | |

ZE | NB | NM | NS | ZE | PS | PM | PB | |

NS | NM | NS | ZE | ZE | PM | PB | PB | |

NM | NS | ZE | ZE | ZE | PB | PB | PB | |

NB | ZE | ZE | ZE | ZE | PB | PB | PB |

Nominal Parameters | |
---|---|

SM capacitor initial voltage | 5892 V |

Rated line-line voltage | 10 kV |

Number of Cells per arm | 6 |

Arm inductance | 1.59 mH |

Arm resistance | 0.04 mΩ |

Cell capacitance | 100 µF |

Rated frequency | 60 Hz |

Carrier frequency | 600 Hz |

Real power reference | 0.05 MW |

Reactive power reference | 0.2 MVAr |

k_{fs} | 20 |

δ | 10% of rated values |

ε | 25% of rated value |

Arm inductance | 5 mH |

DC link voltage | 20 V |

Cell capacitance | 3.3 mF |

Rated frequency | 50 Hz |

Carrier frequency | 2000 Hz |

Sampling frequency | 10 kHz |

k_{fs} | 15 |

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**MDPI and ACS Style**

Hakimi, S.M.; Hajizadeh, A.
Integration of Photovoltaic Power Units to Power Distribution System through Modular Multilevel Converter. *Energies* **2018**, *11*, 2753.
https://doi.org/10.3390/en11102753

**AMA Style**

Hakimi SM, Hajizadeh A.
Integration of Photovoltaic Power Units to Power Distribution System through Modular Multilevel Converter. *Energies*. 2018; 11(10):2753.
https://doi.org/10.3390/en11102753

**Chicago/Turabian Style**

Hakimi, Seyed Mehdi, and Amin Hajizadeh.
2018. "Integration of Photovoltaic Power Units to Power Distribution System through Modular Multilevel Converter" *Energies* 11, no. 10: 2753.
https://doi.org/10.3390/en11102753