# Novel Switching Frequency FCS-MPC of PMSG for Grid-Connected Wind Energy Conversion System with Coordinated Low Voltage Ride Through

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## Abstract

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## 1. Introduction

- Overcoming the variable switching frequency of the two-level converter problem by designing a modulation algorithm that obtains a fixed switching frequency.
- A coordinated pitch angle control and low voltage-ride through (LVRT) algorithm is designed and inserted in the vector control of the grid side converter (GSC) to supply reactive power to the grid during fault for ensuring safe operation of the inverter.
- A comparison with conventional FCS-MPC is made to show the effectiveness of the proposed method.

## 2. Principle of Wind Energy Conversion System

## 3. Mathematical Modeling of Direct-Driven Permanent Magnet Synchronous Generator

## 4. Modelling of Machine Side Converter

## 5. Conventional FCS-MPC of the MSC Scheme

## 6. Proposed Modulated Model Predictive Control for the MSC

## 7. Modelling and Control of Grid-Side Converter

## 8. Coordinated Low Voltage-Ride through Algorithm

#### 8.1. Control Strategy of Grid Side Converter

#### 8.2. Pitch Angle Control Strategy

## 9. Simulation Results and Case Studies

**Case 1:**For balanced grid voltage operation, the proposed MMPC algorithm performance under step increase in wind speed from 8 m/s to 12 m/s at time t = 2 s will be evaluated as shown in Figure 11.

**Case 2:**The effectiveness of the proposed modulated model predictive control (MMPC) with the grid-side LVRT controller is enabled (${i}_{dg}^{*}\left(k\right)={i}_{dg,LVRT}^{*}\left(k\right),{i}_{qg}^{*}\left(k\right)={i}_{qg,LVRT}^{*}\left(k\right)$) in this case of study. Moreover, the pitch angle controller is also enabled as described in Figure 10. The control scheme is tested under transient operation with a fixed wind speed of 12 m/s and a three-phase grid voltage dip is applied from rated value to 10% of its rated at t = 1 s with a duration of 150 ms. The corresponding results of a fixed switching frequency MMPC algorithm are depicted in Figure 13.

## 10. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Variable | Definition |

P_{m} | mechanical power |

ρ | air density |

C_{p} | the wind turbine power coefficient |

A_{r} | Blade swept area |

V_{w} | Wind speed |

V_{sd}, V_{sq} | dq − axis stator voltage of the generator |

i_{sd}, i_{sq} | dq − axis stator current of the generator |

φ_{sd}, φ_{sq} | dq − axis stator flux linkage |

L_{d}, L_{q} | dq − axis synchronous inductance |

T_{e} | electromagnetic torque |

R_{s} | stator resistance |

P | number of pole pairs |

φ_{r} | rotor flux linkage. |

ω_{e} | angular rotor speed. |

V_{dg}, V_{qg} | dq component of grid voltages |

i_{dg}, i_{qg} | dq component of grid currents |

R_{g}, L_{g} | Filter resistance and inductance |

v_{dc}, v_{qc} | dq component of grid-side converter voltages and is determined by the switching function S |

ω_{g} | Grid voltage angular frequency. |

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**Figure 1.**Kinetic to electric energy conversion system based on direct-driven permanent magnet synchronous generator (PMSG) topology.

**Figure 3.**Traditional schematic diagram of finite control set-model predictive controller (FCS-MPC) system.

**Figure 10.**Coordinated low voltage-ride through (LVRT) algorithm: (

**a**) Control structure of grid side converter; (

**b**) Pitch control structure diagram.

**Figure 11.**Simulation results of proposed scheme under step change of wind speed: (

**a**) grid voltage; (

**b**)grid current; (

**c**) stator current; (

**d**) Zoom of grid current; (

**e**) dq-axis of grid current; (

**f**) active and reactive grid power; (

**g**) dc bus voltage; (

**h**) rotor speed.

**Figure 12.**Simulation results: Comparison of machine-side converter voltage, current spectra and total harmonic distortions (THDs) for (

**a**) conventional FCS-MPC and (

**b**) Proposed MMPC.

**Figure 13.**Simulation results of proposed MMPC under three phase grid voltage dip and grid-side converter LVRT capability.

FCS_MPC | MMPC | |
---|---|---|

THD% | 5.82% | 5.27% |

Total Execution time of Simulation (s) | 329.67 | 160.98 |

Execution time of controller (s) | 1.5468 | 0.7553 |

Reduction in time (%) | 51.17% |

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## Share and Cite

**MDPI and ACS Style**

Ghany, A.A.; Shehata, E.G.; Elsayed, A.-H.M.; Mohamed, Y.S.; Haes Alhelou, H.; Siano, P.; Diab, A.A.Z.
Novel Switching Frequency FCS-MPC of PMSG for Grid-Connected Wind Energy Conversion System with Coordinated Low Voltage Ride Through. *Electronics* **2021**, *10*, 492.
https://doi.org/10.3390/electronics10040492

**AMA Style**

Ghany AA, Shehata EG, Elsayed A-HM, Mohamed YS, Haes Alhelou H, Siano P, Diab AAZ.
Novel Switching Frequency FCS-MPC of PMSG for Grid-Connected Wind Energy Conversion System with Coordinated Low Voltage Ride Through. *Electronics*. 2021; 10(4):492.
https://doi.org/10.3390/electronics10040492

**Chicago/Turabian Style**

Ghany, Asmaa A., E. G. Shehata, Abo-Hashima M. Elsayed, Yahia S. Mohamed, Hassan Haes Alhelou, Pierluigi Siano, and Ahmed A. Zaki Diab.
2021. "Novel Switching Frequency FCS-MPC of PMSG for Grid-Connected Wind Energy Conversion System with Coordinated Low Voltage Ride Through" *Electronics* 10, no. 4: 492.
https://doi.org/10.3390/electronics10040492