JNTU B.Tech IV WIND, SOLAR AND HYBRID ENERGY SYSTEMS Previous Question Paper (July/August - 2022 - R16)

The power curve of a wind turbine is a graphical representation that shows the relationship between the wind speed at the hub height and the electrical power output of the turbine. It defines the operational range and efficiency of the wind energy conversion system.

The typical power curve is characterized by four distinct regions:

1. Cut-in Speed: The minimum wind speed at which the turbine begins to generate usable power. Below this speed, the turbine remains stationary or idles.
2. Region of Increasing Power: As wind speed increases beyond the cut-in speed, the power output rises, typically following a cubic relationship with wind speed, until it reaches the rated power.
3. Rated Power/Constant Region: Once the turbine reaches its rated wind speed, the power output is capped at the rated capacity through control mechanisms like pitch regulation or stall control to protect the generator and components.
4. Cut-out Speed: The maximum safe operating wind speed. If wind speeds exceed this limit, the turbine is shut down or feathered to prevent mechanical damage or structural failure.

Wind speed is inherently stochastic and varies due to complex atmospheric and geographical factors.

Temporal Variation: Wind speed varies with time due to solar radiation, which causes uneven heating of the Earth's surface. This creates pressure gradients that drive air movement. These variations occur on multiple scales: diurnal (day-night cycles), seasonal, and short-term turbulence caused by local terrain features, thermal plumes, and weather fronts.

Variation with Height: Wind speed increases with height due to the reduction of surface friction. As air moves over the Earth's surface, obstacles like trees, buildings, and hills create drag, slowing the wind near the ground. This is mathematically described by the wind shear profile, often modeled using the power law:

where v is the wind speed at height h, v_0 is the speed at reference height h_0, and α is the Hellmann exponent (surface roughness coefficient). Higher altitudes experience less surface roughness, resulting in higher, more consistent wind speeds.