Wind turbines mechanism to produce electrical power is basically using the power of the wind to rotate an electrical generator

Wind turbines mechanism to produce electrical power is basically using the power of the wind to rotate an electrical generator. Wind moves through the blades, generating lift and exerting a turning force. The rotating blades turn a shaft inside the nacelle, which transferred into a gearbox. The gearbox has the ability to increase the rotational speed to that value which is optimum for the generator used, which uses magnetic fields to convert the rotational energy into electrical energy.
The power output moves to a transformer, which converts the electricity from the generator to the appropriate voltage for the power system. The basic components included in the representation of a typical wind turbine generator are shown in Figure below:

2.1 Power Output from an Ideal Turbine:
The kinetic energy in a parcel of air of mass, m, flowing at speed, vw in the x direction is:

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where, U is the kinetic energy in joule, A is the cross-sectional area in m2, ? is
the air density in kg/m3, and x is the thickness of the parcel in m. The kinetic energy increasing uniformly with x, because the mass is increasing uniformly.
The output power in the wind, Pw, is the time derivative of the kinetic energy:

2.2 Power Output from Practical Turbines:
The fraction of power extracted from the power in the wind by a practical wind turbine is represented by Cp, which stands for the coefficient of performance or power coefficient.
The actual mechanical power output can be written as:

where, R is the blade radius of the wind turbine (m), Vw is the wind speed (m/sec), and ? is the air density (kg/m3). The coefficient of performance is not constant, but varies with the wind speed, the rotational speed of the turbine, and turbine blade parameters such as angle of attack and pitch angle. Generally, it is said that power coefficient, Cp, is a function of tip speed ratio, ?, and blade pitch angle, ? (deg). The tip speed ratio is defined as:

where, ?R is the mechanical angular velocity of the turbine rotor in rad/s, and Vw is the wind speed in m/s. The angular velocity ?R calculated from the rotational speed, n (r/min) by the equation:

1. Fixed-speed Wind Turbine Models:
A fixed-speed wind turbine with a squirrel cage induction generator is the simplest type of wind turbine technology. It has a turbine that converts the kinetic energy of wind into mechanical energy. The generator, which is a squirrel cage induction Generator, then transforms the mechanical energy into electrical energy and delivers the energy directly to the grid.

Noted that the rotational speed of the generator, depending on the number of poles,
is relatively high (in the order of 1000 – 1500 rpm for a 50 Hz system frequency). Such a rotational speed is too high for the turbine rotor speed in respect to the turbine efficiency and mechanical stress. For this reason, the generator speed must be stepped down using a gearbox with an appropriate gear ratio.
The relation between pole pairs and rotational speed is as follows:

where, f is the frequency of the stator voltage, p is the number of pole pairs, and ?s is the generator rotor speed (rpm).
3.1 Fault Response of a Fixed-Speed Wind Turbine:
The fault response of a fixed-speed wind turbine is determined by drive-train and generator response. As long as the driving torque variations are supposed to be slower than a considered grid fault duration, the driving torque of the generator shaft is supposed to be constant. Generator models of different complications were evaluated and compared with measurements.
3.2 Fixed Speed Wind Turbine Characteristics:
The modeling of a wind turbine rotor is somewhat complicated. According to the blade element theory, shafts and blades modelling need complicated and lengthy calculations. Detailed and accurate information about rotor geometry are also needed. For that reason, taking into consideration only the electrical behavior of the system, a simplified method of modeling the wind turbine blade and shaft is normally applied. In general, for fixed speed wind turbine applications, the following Cp equations have been used:

2. Variable Speed wind Turbine:
One of the current investment directions of a wind generation is to use variable speed wind turbine (VSWT) driving a doubly fed induction generator (DFIG), wound field synchronous generator (WFSG) or permanent magnet synchronous generator (PMSG). The main benefit of variable speed operation is that more energy can be generated for a specific wind speed system depends on the generator.
However, the electrical efficiency drops due to the losses in the power electronic converters that are essential for variable speed operation, the aerodynamic efficiency increases due to variable speed operation. In addition, the mechanical stress is less because the rotor acts as a flywheel storage (storing energy temporarily), reducing the drive train torque variations.
In a semi-variable speed turbine, a winding type induction generator of which the rotor resistance can be changed by power electronics is used widely.

By changing the rotor resistance, the torque/speed behavior of the generator is shifted, and about a 10% rotor speed drop from the nominal rotor speed is possible. In this generating system, a limited variable speed capability is achieved at relatively low cost.
Other variations are a conventional synchronous generator and a squirrel cage induction generator connected to the wind turbine through a gearbox and to the grid by a power electronics converter of the full generator nominal rating.
4.1 Variable Speed Wind Turbine Characteristics:
To calculate Cp for the given values of ? and ?, the following numerical approximations have been used:

For a VSWT, generated active power depends on the power coefficient, Cp, which is related to the proportion of power extracted from the wind hitting the wind turbine blades.