Investigation of alternative energy

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Introduction
Wind power is one of the recently growing sources of green power which is subsidizing other sources of power such as hydroelectric power, solar power etc. This report is analyzing the constraints which are experienced in the use of wind power that limits maximum extraction of power by the turbines from the wind. The factors which are taken into consideration in this case is the power regulation applied on wind turbines, speed regulation which is directly related to noise produced by the turbine in the running mode and load mitigation which dictates the load limit of the wind turbine to ensure long lasting of the turbine component parts. Achievement of these investigations has been done through simulation of a wind turbine in Matlab Simulink.
Power regulation.
This is always achieved through the application of a constant torque to the generator. The maintenance of the turbine rotational speed at a desired value is done through blade pitching for the variable speed turbines and control of the pitch angle of the blades for the generated power should be as close as possible to the rated one for fixed-speed wind turbines.
Because not all power can be extracted by the turbine, there is definition of a power coefficient Cp which is basically the ratio of power extracted by the wind turbine to the total power available in the wind and that for a wind turbine, the maximum power that can be extracted from the wind is given by:
Cpmax=16/27 or 0.593 which is known as the Betz limit and that wind turbine cannot extract more than 59% of power from the air stream.
Speed regulation
During the rotation of a wind turbine, there is always an aerodynamic noise associated with the rotation which is approximately proportional to the fifth power of the tip speed of that particular turbine. This leads to the restriction of the rotational speed of the turbine especially when the wind speed is high which leads to increased ambient noise. The tip speeds of the turbines to be erected in normal sites on land is always limited to about 65m/s by the manufactures but in the case of offshore sitting wind turbines, the tip speed goes to even 120m/s because they are not subject to noise constraints due to the designers’ need for realization of savings in drive train costs.
Load mitigation
Due to high demand of power in recent years, there has been a necessity of higher production power plants which has resulted in numerous challenges in the design of wind turbines (Burton, 2001). The lifetime of the wind turbine components should be made to last through proper mitigation of loads in the system. A standard wind turbine experience the following loads which must be taken into consideration in its design: aerodynamics loads, gravitational loads, inertial loads which may include both the centrifugal and gyroscopic effects and finally the operational loads which arise from the control system action such as the generator disconnection, braking and blade-pitch control. Load mitigation can always be tackled at both the design, operational control and the level of dynamic control.
Model of the wind turbine.
This specific model is always based upon the turbine’s steady-state characteristics and the conditions for its simulation are that the torque exerted on the mechanical shaft must certify the equation below.
Tturbine=Pm/t Where
And, =density of air(kg/m)
S=turbine sweeping area.
Cp=turbine performance coefficient
V=speed of wind(m/s) β =pitch angle of the blades t=turbine’s mechanical speed.
Wind turbine is a combination of different component parts which include the aerodynamic subsystem, drive train subsystem, tower subsystem, generator subsystem and the pitch actuator subsystem.
Aerodynamic subsystem
This involves the description of the forces that acts on the rotor blades which are generated by the wind in the process of wind power transformation into electrical power. The equations representing both the aerodynamic torque (Ta) involved and the thrust force (Ft) which acts perpendicularly on the rotor blade are shown below.
Ta=ρ.π.R2.V3r.Cpβ,λ2ѡr
Ft=0.5.ρ.π.R2.V2r.Ctβ,λ
Whereby,
ρ =density of air Ct=coefficient of thrust Cp=coefficient of power β =pitch angle of the blades Vr=speed of wind λ=ratio of the tip speed R=radius of the rotor of the generator.
Generator subsystem
The generator torque can always be modelled and controlled using the first order differential equation which is shown below through the variation of the torque of the generator. Where Pref=reference power output, τg=time constant, wg=generator speed, Tg=generator torque Control subsystem This subsystem is basically the pitch actuator subsystem as it controls the movement of gears, motors and hydraulic systems so as to obtain the optimum power output of the wind turbine. The modelling of the pitch actuator subsystem can be done by use of first order differential equation as shown below. Whereby β is the actual pitch angle, τβ=time constant and finally βref is the input to the model which corresponds to the desired pitch angle. Block diagram of the wind turbine

Fig 1: Dynamic model of a wind turbine.
The figure 1 above represents a dynamic model of a wind turbine generator built in Matlab Simulink.
Input 1- This represents the speed of the generator that is used in the production of electricity when in motion. This speed is fed back to the turbine model so as to maintain it at optimal energy generation point.
Input 2- This is the blade pitch angle which is always in degrees. This angle is always fed to the turbine model through a pitch controller scheme that is always implemented by the use of a PI controller that tracks the error signal as long as there is a difference between the reference power and the generator output power.
Wind speed- This is the third input which compares the speed of the wind that is present and the minimum and maximum set speeds for the control of the generator speed to maintain the output power at the required range.
The power generated by the wind turbine can then be represented by the equation below.
P = 1/2 ρ A v3 where
P is the power generated in watts (W), ρ is the density of air in kg/m3,A is the area that the wind is passing through perpendicular to the wind in m2 and finally v is the wind velocity in m/s.
Simulation output of the wind turbine

Fig 2.Turbine power characteristics
The figure 2 above is showing that with the increase in the base wind speed, the speed of the wind turbine rotation also increases resulting to concurrent increase in the power generated by the wind turbine. It also evident from the graph that for all the base wind speeds for example 21m/s, the maximum power is achieved at a turbine speed of 1.2 pu after which the turbine output power starts to reduce. The control of pitch angle, the generator speed and the appropriate base wind speed is what is used in the simulation of the behavior of the wind turbine output characteristics. It is also important to note that the above model can be used in the simulation of different turbines to determine optimum operation conditions which results in maximum possible power output.
Conclusion
From the simulation results, it is obvious that a lot of factors are taken into consideration by the designers of wind turbines so as to produce turbines with the ability to produce maximum possible power without taking the lifespan and the environmental impact for granted. In this case, designer should take into consideration factors such as the load limit of the wind turbine, the speed regulation and the maximum possible power that can be produced from the turbine.

Reference list
Burton, T. (2001). Wind energy. Chichester: J. Wiley.