Implement model of variable pitch wind turbine

Renewables/Wind Generation

The model is based on the steady-state power characteristics of the turbine. The stiffness of the drive train is infinite and the friction factor and the inertia of the turbine must be combined with those of the generator coupled to the turbine. The output power of the turbine is given by the following equation.

$${P}_{m}={c}_{p}(\lambda ,\beta )\frac{\rho A}{2}{v}_{\text{wind}}^{3},$$ | (1-1) |

where

P | Mechanical output power of the turbine (W) |

c | Performance coefficient of the turbine |

ρ | Air density (kg/m |

A | Turbine swept area (m |

v | Wind speed (m/s) |

λ | Tip speed ratio of the rotor blade tip speed to wind speed |

β | Blade pitch angle (deg) |

Equation 1-1 can be normalized. In the per unit (pu) system we have:

$${P}_{m\text{\_pu}}={k}_{p}{c}_{p\text{\_pu}}{v}_{\text{wind\_pu}}^{3},$$ | (1-2) |

where

P | Power in pu of nominal power for particular values of
ρ and |

c | Performance coefficient in pu of the maximum value of
c |

v | Wind speed in pu of the base wind speed. The base wind speed is the mean value of the expected wind speed in m/s. |

k | Power gain for |

A generic equation is used to model c_{p}(λ,β).
This equation, based on the modeling turbine characteristics of [1],
is:

$${c}_{p}(\lambda ,\beta )={c}_{1}\left({c}_{2}/{\lambda}_{i}-{c}_{3}\beta -{c}_{4}\right){e}^{-{c}_{5}/{\lambda}_{i}}+{c}_{6}\lambda ,$$ | (1-3) |

with

$$\frac{1}{{\lambda}_{i}}=\frac{1}{\lambda +0.08\beta}-\frac{0.035}{{\beta}^{3}+1}.$$ | (1-4) |

The coefficients *c*_{1} to *c*_{6} are: *c*_{1 }= 0.5176, *c*_{2 }= 116, *c*_{3 }= 0.4, *c*_{4 }= 5, *c*_{5 }= 21 and *c*_{6 }= 0.0068. The *c*_{p}*-*λ characteristics,
for different values of the pitch angle β, are illustrated below.
The maximum value of *c*_{p }(*c*_{pmax }= 0.48) is achieved for β = 0
degree and for λ = 8.1. This particular value of λ is
defined as the nominal value (λ_{_nom}).

The Simulink^{®} model of the turbine is illustrated in the
following figure. The three inputs are the generator speed (ωr_pu)
in pu of the nominal speed of the generator, the pitch angle in degrees
and the wind speed in m/s. The tip speed ratio λ in pu of λ_{_nom} is
obtained by the division of the rational speed in pu of the base rotational
speed (defined below) and the wind speed in pu of the base wind speed.
The output is the torque applied to the generator shaft.

**Nominal mechanical output power**The nominal output power in watts (W).

**Base power of the electrical generator**The nominal power of the electrical generator coupled to the wind turbine, in VA. This parameter is used to compute the output torque in pu of the nominal torque of the generator.

**Base wind speed**The base value of the wind speed, in m/s, used in the per unit system. The base wind speed is the mean value of the expected wind speed. This base wind speed produces a mechanical power which is usually lower than the turbine nominal power.

**Maximum power at base wind speed**The maximum power at base wind speed in pu of the nominal mechanical power. This parameter is the power gain

*k*_{p }already defined.**Base rotational speed**The rotational speed at maximum power for the base wind speed. The base rotational speed is in pu of the base generator speed. For a synchronous or asynchronous generator, the base speed is the synchronous speed. For a permanent-magnet generator, the base speed is defined as the speed producing nominal voltage at no load.

**Pitch angle beta to display wind turbine power characteristics**The pitch angle beta, in degrees, used to display the power characteristics. Beta must be greater than or equal to zero.

**Display wind turbine power characteristics**Click to plot the turbine power characteristics for different wind speeds and for the specified pitch angle beta.

`Generator speed (pu)`

Simulink input of the generator speed in pu based on the nominal speed of the generator.

`Pitch angle (deg)`

Simulink input of the pitch angle.

`Wind speed (m/s)`

Simulink input of the wind speed in m/s.

`Tm (pu)`

Simulink output of the mechanical torque of the wind turbine, in pu of the nominal generator torque. The nominal torque of the generator is based on the nominal generator power and speed.

The mechanical power *P*_{m} as
a function of generator speed, for different wind speeds and for blade
pitch angle β = 0 degree, is illustrated below. This figure
is obtained with the default parameters (base wind speed = 12 m/s,
maximum power at base wind speed = 0.73 pu (*k*_{p} = 0.73) and base rotational speed = 1.2
pu).

[1] Siegfried Heier, "Grid Integration of Wind Energy Conversion Systems," John Wiley & Sons Ltd, 1998, ISBN 0-471-97143-X

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