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262             Renewable Energy Devices and Systems with Simulations in MATLAB  and ANSYS ®
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                                  Lines of constant            Locus of maximum
                                                                 power delivery
                           Turbine torque                 Turbine torque/speed curves
                                     power

                                                           for increasing wind speed






                                      Turbine rotational speed

            FIGURE 10.7  Family of a typical wind turbine torque versus their rotational speed for variable wind velocities.


            wind turbine generators are usually based on inexpensive permanent magnet generators. Chapter 7
            discusses a PMSG wind turbine controller with maximum power optimization and a back-to-back
            PWM grid-connected inverter in Figure 7.13.
              Figure 10.7 shows a family of a typical wind turbine torque versus their rotational speed for vari-
            able wind velocity, where a change in the maximum power point can be observed when the wind
            velocity changes.
              Large-scale wind turbines have built-in optimized speed and/or pitch control. However, the  market
            for small-scale wind turbines does not accommodate expensive solutions. Gearboxes are often used
            in high-power wind turbines, but they significantly impact low-power wind turbines for two reasons:
            (1) they have low efficiency, since the viscous loss (1% of rated power per gearbox stage, which is
            proportional to the mechanical speed), and (2) they are the major factor (at least 19%) in the down-
            time in wind turbine generation due to their maintenance needs. Therefore, an optimized electric
            generator should be designed in order to have the best efficiency for a low wind velocity operating
            range, without a gearbox and a direct-drive system would be preferable. Small wind turbines have
            considerable cost constraints in order to be competitive in rural systems and applications for farms
            and villages. Typically, small turbine generators are made of permanent magnet machines, which are
            not optimized for capturing wind energy at the low wind speed range (up to about 7 m/s).

            10.6.1  Mechanical Control

            A pitch controller is used in the wind turbine to control the mechanical power extraction from the
            turbine. As wind is intermittent and stochastic, there will be cases when the wind speed is higher
            than the rated wind speed for nominal power, and the wind generator will generate higher than
            power the rated conditions. This may lead to damages to the generator winding and/or may cause
            system instability. Therefore, the mechanical power extraction is limited from the turbine side using
            a pitch controller. A conventional pitch controller is shown in Figure 10.8, first the error signal



                               e                 1         x s 0            90
                    P gen         Controller                                      β
                         +   –                 1+T d s                 0
                    P ref                    Pitch servo  Rate limiter  Hard limiter


            FIGURE 10.8  Block diagram of a pitch controller.
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