At days the ocean is cool and the air is warm. At nights this is the opposite. When we have different temperatures – wind is created. We capture the wind by wind turbines. The story is similar with hills and valleys.

Wind has kinetic energy which is energy – energy that a body possesses when in motion. Wind – moving air consists of particles. When we refer to wind, we mean the sum of these particles (bodies).

Wind turbines harness the wind’s kinetic energy and turn it into rotary motion. This rotary motion drives a generator that produces electricity.

2 Main Types of Wind Turbines

  • Vertical Axis Design:
    • Savonious Design
    • Darrieus Desing
  • Horizontal Axis Design
Savonious Wind Turbine

Fig 1: Savonious Wind Turbine

Darrieus Wind Turbine

Fig 2: Darrieus Wind Turbine

Horizontal Axis Wind Turbine

Fig 3: Horizontal Axis Wind Turbine

Vertical Axis Design:

  • The rotary motion that the wind’s kinetic energy produces is in a form of a rotating shaft. This shaft is perpendicular to the surface of the earth, therefore, we refer to it as vertical axis design
  • All the heavy machinery that turns the rotational energy into electrical energy can be placed on the ground at the bottom of the turbine.
  • These turbines are not meant to be high up the ground, therefore, they are not very efficient. This is because wind is slower and turbulent closer to the ground.
  • They are also not very efficient due to slow tip speed – causes wake rotation losses (see below). The Savonious turbine has the slowest tip speed as it can rotate only as fast as the wind blows. Darrieus design has a faster tip speed.

Horizontal Axis Design:

  • The rotating shaft is in parallel to the surface of the earth.
  • All the heavy machinery (gear box) has to be up on top of the turbine.
  • Can be built higher above ground at remote locations.
  • More efficient due to high winds with no turbulence at greater heights.
    • Wind speed is important as the power generated has a cubic dependence on wind speed – see calculation below.
  • Fastest tip speed out of the 3 designs.
  • Difficult maintenance – need to climb to great heights.

Wind Power Calculation

  • The wind has kinetic energy, and the wind turbine harvests some of it.
    • m: mass of air
    • v: velocity of wind
Kinetic Energy Formula
  • The turbine obviously harvests the energy with its blades. As the blades rotate, they draw a circle with are A.
  • A is the surface the turbine captures the energy with.
  • d is a random distance in our example. The distance the wind travels from the blades behind the turbine.
  • ρ is a constant. It is the density of air.

The area and the distance d resemble a cylinder.

Now, let’s calculate the mass of the air that travels through the blades (left side of cylinder):

Calculation: Mass of Air through Wind Turbine
  • Substituting to the Kinetic Energy formula:
Calculation: Mass equation substituted in Kinetic Energy Formula
  • We know that Power is Energy over time
  • So, to get the power we have to differentiate.
  • All the ‘d’ in the differentiation says is: the change in E over the change in t.
Calculation: Power of Wind Turbine

For the differentiation we used one of the simplest differentiation formulas (below). First, move the constants in front and only differentiate the t, as we are differentiating with respect to t.

Formula: Differentiation

From the Wind Power equation: the turbine’s power depends on the cube of the wind speed.

Efficiency of Wind Turbines

A conventional power station generates 2000 MW power.

  • Power = Current x Voltage
  • So this power measurement is dependent on the current & voltage generated by generator at a given time.

A large format Wind Turbine’s rated power is 5 MW.

The mean output of a wind turbine is much lower than 5 MW due to varying wind speeds. So we need a lot of turbines to match the conventional power station!

Wind Turbines can’t collect all the power from the wind. This would mean that there would be no wind blowing behind the turbine. No movement of air.

Bet’z Law states that the maximum theoretical efficiency of a wind turbine is 59.3%. In real life the efficiency is more like 45%.

Wake Rotation Losses

As the turban rotates, the edge of the blades push the air molecules, thus, causing the wind to spin. This reduces efficiency.

It has been proven by experiment that the faster the tip of the blades spin, the less wake rotation there is, thus, the more efficient the turbine is.

Wind Turbine Power Curve

Wind Turbines are designed for a rated output power based on the conditions of the usual winds at their given location. This rated power is achieved at a rated wind speed.

So, if the wind blows at the rated speed, the turbine generates the power that it was designed for. If there is a stronger wind, they rotate the turbine off axis to reduce efficiency, thus, maintaining the rated power.

The Power Curve below describes 3 regions divided based on wind speed:

  1. Cut In Speed: This is where the turbine starts to generate power.
  2. Rated Speed: Where the turbine produces the rated power.
  3. Cut out Speed: Where the wind is too strong. To protect the turbine it is stopped – brought to a standstill.
Graph: Power Curve of Wind Turbine

Fig 4: Power Curve of Wind Turbines

The duty cycle of wind turbines is approx 30%. This is the average actually generated power compared to the rated power.

Calculation of Revenue

Let’s calculate how much money a 5 GW turbine generates in 1 year.

All we have to do is to multiply together the 5 GW rated power, the 30% duty cycle, the hours in a day, number of days in a year and feed-in tariff per kWh.

Essentially, what we do is multiplying the mean (average) power the turbine generates with the number of hours in a year and with the tariff.

5000 kW x 0.3 x 24h x 365.25 x 0.055 = £723.195