# Crowbar System in Doubly Fed Induction Wind Generators

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## Abstract

**:**

## Nomenclature

DFIG | Doubly Fed Induction Generator |

VRRIG | Variable Rotor Resistance Induction Generator |

SCIG | Squirrel Cage Induction Generator |

EESG | Electrical Excited Synchronous Generator |

PMSG | Permanent Magnet Synchronous Generator |

IGBT | Insulated Gate Bipolar Transistor |

TSO | Transmission System Operator |

RSC | Rotor Side Converter |

GSC | Grid Side Converter |

DC | Direct Current |

CB | Circuit Breaker |

## 1. Introduction

**Table 1.**World Top 10 in cumulative capacity of installed wind power generation published in [2].

Rank | Country | MW | % |
---|---|---|---|

1 | USA | 25.170 | 20.8 |

2 | Germany | 23.903 | 19.8 |

3 | Spain | 16.754 | 13.9 |

4 | China | 12.210 | 10.1 |

5 | India | 9.645 | 8.0 |

6 | Italy | 3.736 | 3.1 |

7 | France | 3.404 | 2.8 |

8 | UK | 3.241 | 2.7 |

9 | Denmark | 3.180 | 2.6 |

10 | Portugal | 2.862 | 2.4 |

Rest of the world | 16.693 | 13.8 | |

Total of the 10 first | 104.104 | 86.2 | |

Total | 120.798 | 100.0 |

**Table 2.**World market share in 2008 for the world largest manufacturers (published in [4]) (composed using the data from the manufacturers catalogs).

Manufacture | Country | negotiated MW in 2008 | % | Electrical Generator |
---|---|---|---|---|

Vestas | Denmark | 5.647 | 19.0 | DFIG |

GE Energy | USA | 5.350 | 18.0 | DFIG |

Gamesa | Spain | 3.270 | 11.0 | DFIG |

Enercon | Germany | 2.675 | 9.0 | EESG |

Suzlon | India | 2.080 | 7.0 | VRRIG |

Siemens | Germany | 2.080 | 7.0 | DFIG |

Sinovel | China | 1.486 | 5.0 | DFIG |

Goldwind | China | 1.189 | 4.0 | PMSG |

Acciona WP | Spain | 1.189 | 4.0 | DFIG |

Nordex | Germany | 1.189 | 4.0 | DFIG |

Total by others manufacturers | 3.569 | 12.0 | ||

Total | 29.724 | 100.0 |

## 2. Dynamic Model of Wind Turbines Based on the Doubly Fed Induction Generator (DFIG)

#### 2.1. Aerodynamic Model

- T
_{m}= Mechanical torque (N.m) - P
_{m}= Mechanical power (W) - A = Swept area by the turbine rotor (m
^{2}) - R = Turbine rotor radius (m)
- ρ = Air density (kg/m
^{3}) - V = Wind speed (m/s)
- C
_{p}= Power coefficient (or performance coefficient) - λ = Tip speed ratio (ω
_{m}.R/V) - ω
_{m}= Angular speed of the wind turbine (rad/s) - β = Blade pitch angle (degree)

_{p}) indicates how efficiently the conversion of wind power to rotational mechanical power is performed by the wind turbine. The Betz limit is the maximum theoretic value reached by the power coefficient which is 0.59 for three blades horizontal axis wind turbine (a more complete discussion can be find in [12]). The C

_{p}curves are obtained experimentally by the manufactures following international rules. In more generic analysis, the Equations (3) and (4) can be used to model the dynamics of the C

_{p}. The values of c1–c9 presented in Table 3 were suggested by Slootweg to represent the aerodynamics of modern wind turbines [13].

c1 | c2 | c3 | c4 | c5 | c6 | c7 | c8 | c9 |
---|---|---|---|---|---|---|---|---|

0.73 | 151 | 0.58 | 0.002 | 2.14 | 13.2 | 18.4 | –0.02 | –0.003 |

#### 2.2. Electrical Model

- Disconnection of the rotor windings from the RSC.
- Insertion of the three-phase resistance in series to the rotor windings (crowbar system).
- Disconnection of the crowbar system from the rotor windings.
- Reconnection of the RSC to the rotor windings.

## 3. The Induction Generators Stability and the Critical Rotor Speed

_{crit}), it is the maximum duration of a grid fault supported by the generator without losing the stability. The T

_{crit}is related to the critical rotor speed (ω

_{CR}), which in fact indicates the same information, however, in a way to better represent the interest of a specific study.

_{f}) before achieving the critical rotor speed, the electrical torque returns to the operation point C. In this situation, the electrical torque is higher than the mechanical torque. Therefore, the generator speed decelerates and returns to a stable operation in point A, as shown in Figure 5.

_{f}) after achieving the critical rotor speed, the electrical torque returns to the operation point C. In this situation, the electrical torque is lower than the mechanical torque, therefore, the generator speed accelerates and does not return to a stable operation (Figure 6).

_{CR}) in a more efficiently way than the limited action of the crowbar system.

_{E}) is also enlarged, however, the maximum torque for motor operation (positive T

_{E}) is diminished.

_{E}) and for motor operation (positive T

_{E}) is enlarged. The maximum torque for generator and for motor operation is diminished when the applied voltage is enlarging in the positive direction.

**Figure 7.**Electromagnetic torque curve vs. slip of wound rotor induction machine for different values of V

_{dR}.

**Figure 8.**Electromagnetic torque curve vs. slip of wound rotor induction machine for different values of V

_{qR}.

_{E}during the short circuit (or immediately after its elimination, depends on the grid requirements) to a value that enlarges the critical rotor speed and forces T

_{E}to be equal (or higher) to T

_{M}much more faster than in the case of the SCIG despite the higher rotor speed operation of the DFIG.

## 4. The Dynamic Analysis of the Crowbar System Actuation during Grid Faults

#### 4.1. Influence of the Crowbar Resistance Value (R_{crow})

_{crow}are analyzed (2, 5 and 10 times the original rotor resistance R

_{R}). This is the most common operation mode during faults for countries with no reactive current injection requirement.

_{crow}equal to 10

^{.}R

_{R}is used. In Figure 9b, the lower consumption of reactive power during the fault can explain the lower value of rotor speed shown in Figure 9c. Considering the stability of the machine the desired rotor speed should be as closer as possible to the normal operation speed in order to avoid the critical rotor speed, as described in Section 3. The active power injected by the DFIG is also increased for high values of the R

_{crow}, as shown in Figure 9d.

**Figure 9.**Dynamic analysis of the DFIG for different crowbar resistance value during a fault eliminated in 150 ms at B5.

_{crow}do not contribute in a different way from each other. However, the crowbar system is still important to guarantee a fast reconnection of the RSC to reestablish normal operation and to protect the power electronics of the RSC from damage. If the fault is not eliminated before the critical rotor speed is achieved the rotor may accelerate and loose the stability. The period of time that the wind turbines must remain connected to the network depends on the TSO requirements of the region and of the country (for some countries these times can be found in [8,10,22]).

**Figure 10.**Dynamic analysis of the DFIG for different crowbar resistance value during a fault eliminated in 150 ms at B7.

#### 4.2. Influence of the Crowbar System Operation Time

_{crow}is considered equal to 2

^{.}R

_{R}for the following analysis.

**Figure 11.**Dynamic analysis of the DFIG for different crowbar operation time during a fault at B5 eliminated in 150 ms.

**Figure 12.**Dynamic analysis of the DFIG for different crowbar operation time during a fault at B7 eliminated in 150 ms.

## 5. Conclusions

## Acknowledgements

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## Share and Cite

**MDPI and ACS Style**

Salles, M.B.C.; Hameyer, K.; Cardoso, J.R.; Grilo, A.P.; Rahmann, C.
Crowbar System in Doubly Fed Induction Wind Generators. *Energies* **2010**, *3*, 738-753.
https://doi.org/10.3390/en3040738

**AMA Style**

Salles MBC, Hameyer K, Cardoso JR, Grilo AP, Rahmann C.
Crowbar System in Doubly Fed Induction Wind Generators. *Energies*. 2010; 3(4):738-753.
https://doi.org/10.3390/en3040738

**Chicago/Turabian Style**

Salles, Maurício B. C., Kay Hameyer, José R. Cardoso, Ahda. P. Grilo, and Claudia Rahmann.
2010. "Crowbar System in Doubly Fed Induction Wind Generators" *Energies* 3, no. 4: 738-753.
https://doi.org/10.3390/en3040738