Wind turbine merits and output: 5.5 m blade

Electricity generation from a wind turbine

The moving air turns the rotor blades; the rotor converts the kinetic energy of wind into mechanical torque on a shaft. A gearbox steps up the speed, and the generator converts it to electricity, which is fed to the grid through a converter and transformer (or stored in batteries for stand-alone systems).

 Wind -> Blades/hub -> Low-speed shaft -> Gearbox
                                           |
 Grid <- Transformer <- Converter <- Generator
 (yaw drive, pitch control and brake on the nacelle)

Merits of wind energy

• Renewable, free fuel, no emissions during operation.
• Low running and maintenance cost.
• Modular; quick installation; land below can still be used for farming.
• Suitable for remote areas and hybrid systems with solar and hydro.

Power output

$$P = \frac{1}{2}\rho A v^3 C_p, \qquad A = \pi r^2$$

Given: $r = 5.5$ m (blade length), $v = 25$ m/s, $\rho = 1.23$ kg/m³, $C_p = 0.4$.

$$\begin{aligned} A &= \pi \times 5.5^2 = 95.03\ \text{m}^2 \\ P_w &= 0.5 \times 1.23 \times 95.03 \times 25^3 \\ &= 0.5 \times 1.23 \times 95.03 \times 15625 = 913{,}209\ \text{W} \\ P &= 0.4 \times 913{,}209 = 365{,}284\ \text{W} \end{aligned}$$

Answer: Power output $\approx 365.3$ kW.

Note: 25 m/s is near the usual cut-out speed of large turbines, so in practice the output would be limited to the rated value by pitch control.