# Performance analysis of grid-integrated brushless doubly fed reluctance generator-based wind turbine: modelling, control and simulation

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## Abstract

Due to the absence of the rotor windings, the brushless doubly fed reluctance generator (BDFRG) presented a much better efficiency with less complicated control and modelling than that introduced by the brushless doubly fed induction generator. As a result, the BDFRG gained more preference than that of the doubly fed induction generator. Moreover, this result led to the emerging of the (BDFRG) as one of the most promising generators in the new modern wind turbines. This paper introduces modelling as well as control strategy for the grid-connected BDFRG-based wind turbine systems. This study was carried out using MATLAB/Simulink environment.

## Keywords

Modelling Simulation BDFRG Wind turbine Control## Abbreviations

- WECS
Wind energy conversion system

- BDFRG
Brushless doubly fed reluctance generator

- BDFIG
Brushless doubly fed induction generator

- IFOC
Indirect field-oriented control

- MPPT
Maximum power point tracking

- MSC
Machine-side converter

- GSC
Grid-side converter

- SPWM
Sinusoidal pulse-width modulation

- IFOC
Indirect field-oriented control

- PLL
Phase-locked loop

## List of symbols

*ω*Speed of reference frame of power winding

*ω*_{r}Electrical speed of rotor

*v*_{dp}Direct voltage component for power winding

*v*_{qp}Quadrature voltage component for power winding

*v*_{dc}Direct voltage component for control winding

*v*_{qc}Quadrature voltage component for control winding

*r*_{p}Resistance of power winding

*r*_{c}Resistance of control winding

*λ*_{dp}Direct flux component for power winding

*λ*_{qp}Quadrature flux component for power winding

*λ*_{dc}Direct flux component for control winding

*λ*_{qc}Quadrature flux component for control winding

*i*_{dp}Direct current component for power winding

*i*_{qp}Quadrature current component for power winding

*i*_{dc}Direct current component for control winding

*i*_{qc}Quadrature current component for control winding

*L*_{p}Inductance of power winding

*L*_{c}Inductance of control winding

*L*_{pc}Mutual inductance between power and control winding

*T*_{e}Electrical torque produced from the generator

*p*_{r}Number of poles for rotor

*T*_{m}Mechanical torque from turbine

*n*_{g}Turns ratio for gear box

*ω*_{rm}Mechanical speed of rotor

*J*_{r}Moment of inertia for wind turbine

*J*_{g}Moment of inertia for generator

*D*_{1}Constant

*ω*_{p}Angular speed for power winding

*ω*_{s}Angular speed for control winding

*P*_{t}Mechanical power from wind turbine

*ρ*Air density

*C*_{p}Power coefficient

*R*Wind turbine blade radius

*β*Pitch angle of blade

*V*_{w}Wind speed

*λ*Tip-speed ratio

*θ*_{p}Primary flux angle

*θ*_{g}Grid current angle

## 1 Introduction

- (1)
Doubly fed variable-speed WECS improves the efficiency of energy conversion, because the doubly fed variable-speed WECS has the ability to extend generator speed range (± 30%). Moreover, the doubly fed variable-speed WECS improves dynamic performance.

- (2)
Doubly fed variable-speed WECS has the ability to decrease the mechanical stress mainly caused by wind fluctuations. This result has a positive impact on the design of the structure and mechanical parts of the turbine. Moreover, this result led to the creation of a large wind turbines.

Doubly fed machines became much popular. Moreover, they became a research field for a lot of researchers. This is due to their capability to be used as a partially rated converter. In particular, the BDFIG is preferred than the conventional doubly fed induction machine; this preference is based on the ability to eliminate the slip rings. However, the BDFIG with time loss popularity mainly due to the rotor losses and the rotor construction is complicated [1]. Sometimes, the BDFRG is considered as an anther solution to the problems of BDFIG and DFIG [2]. After the improvement of the reluctance rotor, the BDFRG has a simpler control and a higher efficiency than those obtained by the BDFIG. These reasons increased the popularity of the BDFRG in comparison with other types of doubly fed machines. Due to the information mentioned above, the BDFRG is considered a preferable choice for using doubly fed machines with wind turbines.

## 2 Brushless doubly fed reluctance generator

## 3 Dynamic model of brushless doubly fed reluctance generator

## 4 Wind turbine characteristics

The MPPT technique function detects the preferable rotor speed related to the wind speed. Generator control systems are used for obtaining the optimal shaft speed. Some of the MPPT techniques need to measure the wind speed, while others don’t need. This paper used the tip-speed ratio MPPT method. This method calculates the optimal rotor speed to achieve MPPT.

## 5 Studied system

The first part from the MSC controller compared the reference speed extracted from MPPT method with actual speed for rotor. From this comparison, the resulting error inter in a PI controller that will give the reference torque. The reference torque will be input in equation of indirect field-oriented control IFOC in order to give reference quadrature current. The reference quadrature current will be compared with actual quadrature current of the control winding. From this comparison, the resulting error inter in a PI controller that will give the reference quadrature voltage.

The second part from the MSC controller compared the primary reactive power with the reference reactive power (that equals zero in this study for unity power factor). From this comparison, the resulting error inter in a PI controller that will give the reference direct current. The reference direct current will be compared with the actual direct current of the control winding. From this comparison, the resulting error inter in a PI controller that will give the reference direct voltage.

The reference quadrature voltage results from the first part of the MSC controller, and the reference direct voltage results from the second part of the MSC controller transformed from dq frame to abc frame by using \((\theta_{s} ).\) This transformation in order to obtain suitable gate signals for the switches of the MSC from SPWM.

## 6 Simulation Results

BDFRG parameters and wind turbine data

| |

Rated line voltage | 380 V |

Rated frequency | 50 Hz |

| 3.781 Ω |

| 2.441 Ω |

| 0.41 H |

| 0.316 H |

| 0.3 H |

| |

Rotor inertia, | 0.2 kg m |

Rated power | 6 KW |

Turbine radius, | 4 m |

Wind speed range | 2–12 m/s |

Turbine inertia, | 1.5 kg m |

Gearbox ratio, | 7.5 |

- (1)
DC voltage controller: it is the first controller that compares the actual DC link voltage with the reference value of the DC link voltage (equal to 710 V).

- (2)
The second controller and the third controller produce the reference direct voltage and the reference quadrature voltage, respectively. These reference voltages are transformed from dq frame to abc frame. This transformation produces suitable gate signals for the switches of the GSC from SPWM.

Some results from the overall system under study were presented here. As illustrated from the results, the system approximately reaches steady-state condition after 0.4 s from the starting point.

## 7 Conclusion

The grid-connected BDFRG model, control and its simulation can be show validity from results. As mentioned previously, all results approximately reach steady-state condition after 0.4 s from the starting point. The results of the primary current and the secondary current have different frequencies in order to produce electrical torque.

Active power delivers rated value to the grid after reaching the steady-state condition, while the reactive power has a zero magnitude (reference value) to improve the power factor. Rotor speed reaches reference value after a small time, and the reference value of the rotor speed is taken from MPPT method [tip-speed ratio in this study]. The power coefficient reaches a preferable value in order to extract a maximum power from the wind turbine [0.48 for this wind turbine]. Moreover, the DC link voltage reaches its reference value when the steady-state condition starts.

## Notes

### Compliance with ethical standards

### Conflict of interest

The author(s) declare that they have no conflict of interest.

## References

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