Wind Turbine Essay

CHAPTER 3

MODELLING OF WIND TURBINE AND WIND ENERGY

SYSTEM CONFIGURATIONS

3.1 OVERVIEW

Wind turbine model is required to design and implement controllers for wind energy conversion system. In this chapter, the mathematical analysis and modelling of wind turbine is presented. This chapter begins with the discussion of the wind source and its characteristics. Then the modelling of wind turbine is presented including the stream tube model of air flow for maximum power extraction by a wind turbine. The influence of number of turbine rotor blades is also discussed. Wind turbine power characteristics and different aerodynamic power control strategies namely passive/active stall control and pitch control are discussed. Finally, wind turbine configurations

3.1 Typical Wind Speed Curve and Corresponding Power Variation

3.3 MODELLING OF WIND TURBINE

Wind is the movement of air mass and it has kinetic energy. This kinetic energy of the wind can be converted mechanical energy using a wind turbine with rotor blades. This mechanical energy is then converted to electrical energy using a generator.

3.3.1 Power in the Wind

Consider an air mass m flowing through an area A with a speed of vw as shown in Fig. 3.2. The kinetic energy of wind is given by:

K.E.=1/2 mv_w^2 (3.1) where, m = air mass (kg) vw = wind speed (m/s)

The power is energy per unit time, the power represented by a mass of air moving with a velocity of vw through an area A for a duration of time T is given by: P_w=1/2×mass/time×v_w^2=1/2×m/T×v_w^2 (3.2)

Since mass flow rate (m/T) through area A is the product of air densityρ , air speed vw and cross.sectional area A, then equation (2.2) can be written as

P_w=1/2 ρ A v_w^3 (3.3) where, Pwind = power in the wind (W) ρ = air density (kg/m3) (at 150 C and 1 atm, ρ = 1.225 kg/m3)

A = cross.sectional area through which the wind passes (m2)

Fig. 3.2 Air Mass m Flowing Through an Area A with A Velocity

3.3 Power in the Wind (At 150C and 1 Atm)

A plot of equation (3.3) is shown in Fig.3.3. The power in the wind increases as the “cube” of the wind speed. This means that the doubling the wind speed increases the power by eight times. Equation (3.3) also suggests that the wind power is proportional to the swept area covered by the wind.

3.3.2 Power Captured by the Wind Turbine

A wind turbine converts the kinetic energy in the wind into mechanical energy using the rotor blades. The amount of energy which the wind transfers to the rotor depends on the density of the air, the rotor swept area, and the wind speed. The rotor blades of the wind turbine capture only part of the available wind power, and the actual power extracted by a wind turbine is given by : P_T=C_p×P_wind (3.4)

P_T=1/2 ρ A v_w^3×C_p (λ,β)