Source : Wind/1 Wind Power

This Worksheet contains

• How wind turbines work (in detail in the Appendix)• Advantages and disadvantages of wind farms• Comparison of offshore and onshore wind• Land area required to provide 10% of the average UK person’s energy use• Case study of Scroby Sands offshore wind farm

Where does wind come from?

• Wind is a result of large convection currents driven by heat energy from the sun.• The sun heats the air, causing it to expand and rise creating an area of low pressure.• Air from the surrounding area then moves in to fill this space; this movement is wind.

How do wind turbines work?

• Wind turbines usually have three large blades on top of a tall tower.• A typical modern wind turbine has rotor radius of 25-30m (about thelength of a basketball court).• The kinetic energy of the wind rotates the blades thereby beingconverted to mechanical energy. *• The mechanical energy drives a generator in the centre of theblades and is converted into electrical energy.• A transformer is used to deliver the electricity to the national grid.• Wind farms are made up of many wind turbines, spaced out so that the air flows through the turbines do not interfere with one another.

* See Appendix for more details on the Physics of Wind Turbines

Source: Wind/2 Wind Power

Advantages

• Wind is renewable and free.• Wind turbines cause no pollution, except noise.• A wind turbine can pay back the energy required to build it in less than one year.(see Sources: Energy Payback for details)

Disadvantages

• Wind generation is variable.• Large wind turbines have a typical capacity of 1MW –1000s of turbines are required to replace a single large coal-fired power station (capacity over 1GW): large wind farms are therefore needed (onshore or offshore)

Capacity factor, and variable power output:

• Wind turbines do not generate power all of the time – there is no power when the wind doesn’t blow, and they are also shut down in very high winds to avoid damage.

• A wind turbine has a nominal power rating, when it is running under optimum conditions. The ratio of the actual energy produced (averaged over a year) to the nominal energy capacity of the machine, running continuously, is called the capacity factor (typically around 30-40%).

• Grid systems help to balance the variation in wind power from day-to-day and place to place. Backup generation systems are of course needed – but the overall demand on the backup is reduced by the wind power generated.

• Strategies for smoothing the variable output of wind farms are: (a) integration with energy storage systems (e.g. pumped storage hydroelectric power, hydrogen storage) to store energy when there is high wind generation; (see Sources: Energy Storage)(b) “smart” domestic and industrial devices that are designed to run preferentially when there is plenty of power being generated.

Source: Wind/3 Wind Power

Are wind farms a danger to wildlife?

People are concerned that wind turbines kill birds and endanger fish. Consider these numbers to put this in context.

In Denmark:• approximately 30,000 birds a year are killed by wind turbines (which provide 9% of Danish electricity).• 1 million birds are killed a year by traffic.

In the UK:• 55 million birds are killed a year by cats.

And what about fish? It is proposed that offshore wind farms may in fact provide a sanctuary for fish spawning, and protection from intensive fishing activities.

What do you think?

Source: Wind/4 Wind Power

Comparison of onshore and offshore wind:

Cost

• Offshore wind farms are more expensive to maintain and install compared to onshore wind farms.

• Onshore wind turbines require cheaper foundations, are easier to access for maintenance, and are cheaper to integrate with the national grid.

Power generated

• The wind is faster and less variable offshore, leading to a higher capacity factor.

• For a small non-grid installation, onshore wind turbines are the better choice, with a wide range of power ratings; offshore wind farms are most efficient with many large turbines.

Community

• Some people object to the sight of wind farms, particularly in wild landscapes, and the noise they create in more built-up areas.

• Onshore wind farms can provide revenue for rural communities and income for farmers in the form of rent – and the land below the turbines can still be used for agriculture.

Source: Wind/5 Wind Power

Shallow and deep offshore wind

The figure on the right shows the conventional way of distinguishing between shallow and deep offshore wind in the UK territorial water.

The yellow (light grey in black and white) is the shallow waters of depth less than 25m.

The purple (dark grey in black and white) is the deep waters of depth between 25m and 50m.

Source: Wind/6 Wind Power

How much land or sea do we need to provide 10% of our current energy use? (see Sources: Power Density for details of calculation)

* the Power Density is the total average power output of an installation divided by the area it occupies.

Onshore Wind Offshore Wind

Current Total Energy Use in UK 125kWh/day/person 125kWh/day/person

Typical Power Density * of a Wind Turbine 2 W/m² 3 W/m²

Total area of wind farms needed, for 10% of total UK energy 15,750km² 10,500km²

Total area available in UK 240,000km²(area of UK)

40,000km² (shallow)80,000km² (deep)

Population of UK 60 million 60 million

Area required (per person) for 10% of UK energy use 263m² 175m²

Source: Wind/7 Wind Power

Onshore Wind• 263m² of land per person• 6.6% of total land area of UK

Offshore Wind• 175m² of sea per person• 26% of shallow UK territorial waters

13% of deep UK territorial water• equivalent to 4.4% of the land area of UK

Area of land or sea needed to provide 10% of UK energy use?

We can put these areas into perspective with a map of the UK

Onshore wind 6.6% UK land area

Offshore wind 4.4% UK land area

Source: Wind/8 Wind Power

Wind power in the news:

Friday 8 January 2010 – expansion in UK offshore wind farms

The UK prime minister launched a £100 billion programme for deep offshore wind farms in UK waters. There are nine areas, shown in the picture on the right, which companies are bidding for.

The process is lengthy, so construction will begin in 2014 at the earliest but it is hoped that by 2020 about a third of the country’s energy will be provided by these wind farms.

The areas will have a range of capacities with Dogger Bank providing the most power of 9GW (9 times larger than an average, medium sized coal power station).

Source: Wind/9 Wind Power

CASE STUDY: SCROBY SANDS

Scroby Sands is an offshore wind farm situated 1.6 miles off the coast of Great Yarmouth, Norfolk, in the North Sea.

Why site a farm at Scroby Sands?

• High mean wind speeds of 7.5 to 9 m/s.• Low wave forces• Shallow waters (13-20m)• Close to major ports

Turbine Details

• Model: Vesta V80, power rating 2 MW• 3 x 40m fibre composite blades• Steel towers are 4.5m diameter hollow tubes, with rotor mounted 60m above mean sea level• Foundations up to 30m under sea bed to give stability in the shifting sands which move up to 3m each day

Other Details

• Constructed from November 2003 to December 2004• Total project cost: £75 million• Typical annual operating cost £1.6million• Wind farm provides up to 60MW of power, supplying over 30,000 homes• 35,000 people go to the visitors centre each year• Typical lifetime of the turbines in a wind farm of this type is 20–25 years

Sources

MacKay DJC, Sustainable Energy – without the hot air, UIT Cambridge, 2009. Also available online from www.withouthotair.comA. Typical wind turbine dataB. Wildlife statisticsC. Data for land area calculations

DTI Atlas of Renewable Marine Resources.A. Shallow and deep water map

http://www.berr.gov.uk/files/file46398.pdfhttp://www.eon-uk.com/generation/scrobysands.aspxhttp://www.power-technology.com/projects/scrobysands/

A. Scroby Sands case study data

Source: Wind/10 Wind Power

How much kinetic energy can we extract from the wind?Wind turbines extract kinetic energy from the wind, which must therefore slows down as it interacts with the blades. But we can’t remove all of the energy – the air must keep moving to get out of the way! So how much can be extracted? To answer this question, consider the following schematic of air flow around a wind turbine:

The air can’t be compressed, and the volume of air flowing in and out must be the same (this is called flow continuity). Consider the path taken by the air that goes through the circular disk swept out by the blades – at this point it has an area A, and a velocity U. Upstream, the flow is faster with velocity V, and occupies a smaller area Ao; downstream the velocity falls to a lower value U1, occupying an area A1. This flowing volume fills a streamtube, illustrated by the separating solid lines in the figure. Streamlines track the path an individual air particle would take in a flow – so the streamtube is the boundary containing all streamlines that pass through the turbine.

The analysis of the fluid flow through the turbine (below) makes a number of assumptions: (i) laminar, inviscid flow (i.e. smooth, non-viscous flow); (ii) constant wind speed and direction (i.e. no variation with height).

Source: Wind/11 Appendix : Physics of wind turbines

Source: Wind/12 Appendix : Physics of wind turbines

The key equation relating the pressures and velocity along streamlines in steadily moving fluids is Bernoulli’s equation:

where P is the pressure, v is the wind velocity, ρ is the air density, g is the acceleration due to gravity, and z is the height. The change in height along a streamline is small, so we can neglect the change in the potential energy term when compared to the changes in velocity and pressure.

Initially, consider the flow between points A and B (equation 1):

and between points C and D (equation 2):

Now subtract equation 2 from equation 1 his gives:

The difference in pressure across the turbine generates a thrust force T upon it:

From continuity, there is the same mass flow rate dm/dt at inlet and outlet to the streamtube. Consider the momentum of this air flow over the system: the rate of change in momentum = thrust force:

Rearranging gives:

The mass flow rate through the turbine area A at velocity U must be the same as everywhere else:

Hence as the mass flow rate is constant:

So the velocity at the position of the turbine is the average of the incoming and outgoing velocities. But we don’t yet know what the outgoing velocity might be, and this determines how much power is being extracted.

To proceed further, we introduce an induction factor (a) defined by:

constant zgvP 2

2

1

constant 22

2

1

2

11 UPVPo

constant)( 22

2

1

2

111 UPPUPo

)( 221

2

1VUP

)( 221

2

1UVAAPT

)( 2211

2

1UVATUmVm

)( 12

1UVAm

UAm

)( 12

1UVU

)( aVU 1

Source: Wind/13 Appendix : Physics of wind turbines

We can now re-write the relationship between the inlet and outlet velocities in terms of the induction factor:

Since we can write

Now we can calculate the power extracted – it is the difference between the rates of incoming and outgoing kinetic energy of the air (energy = ½ m v2, so to find the power we replace m with the expression for , from above):

Re-expressed in terms of the induction factor:

The power flow in the air across the area A, at the position where it reaches the turbine, is:

We define the power coefficient Cp as the ratio of the extracted power to the power available:

So the fraction of the power extracted depends on the induction factor. We can find a theoretical maximum for this fraction by differentiating the expression for the power coefficient to find the maximum turning point:

From , we find: so a = 1, or a = 1/3.

The solution a = 1 is a minimum, and is not physically possible as the air stops before it reaches the turbine!

The solution a = 1/3 is a maximum – substituting this value into the equation we find: Cp = 16/27 = 59%. So the maximum theoretical fraction of the energy that can be extracted from the wind is 59%.

The graph below shows the variation of Cp with a.

m

)( 12

1UVU )( aVU 211

UUVAP )( 221

2

1

)(1))(1(1 2 aaVAP 22

1 3

2)(1 aaVAP 42

1 3

32

2

1

2

1VAVmPref

2)(1 aaP

PC

refp 4

0 da

dCp )()(2 aaaa 3110341

The graph shows the maximum fraction of 59% that can be extracted –this theoretical upper limit is referred to as the Betz limit.

Source: Wind/14 Appendix : Physics of wind turbines

There is also the issue of the capacity factor. The wind will not blow at a constant speed all of the time, and the nominal power varies with the cube of the wind speed. But during high winds the turbine will be shut down (to avoid serious damage, or even catastrophic failure). The machine will also have scheduled downtime for maintenance.

All of these factors combine to give a total extracted power of less than the design rating of the turbine, which is the maximum electrical power output of the machine operating under optimum conditions. The capacity factor is the ratio of the total energy extracted to that nominally available at the design rating of the turbine over the same given time period. The capacity factor is the usual measure of the efficiency of the installation. Typical values are 20-40%.

The Betz limit gives a good idea of the best efficiency we could expect from a wind turbine. In practice, the fraction extracted depends on many factors, e.g. how fast the blades are allowed to rotate, or the variation in wind speed with height above the ground:

What makes the rotor spin?The rotor blades of a wind turbine share many similarities with propeller blades and aerofoils of plane wings. Figure 1 shows a typical blade in cross-section; Figure 2 shows schematic streamlines past the blade.

The air is forced to change speed and direction as it flows past the blade – this produces a pressure difference across the blade and thus a net force. The component normal to the incoming flow is called the lift, that parallel to the flow is the drag. Another way to think of the same effect is that the blade forces the air to change direction (i.e. change its momentum, round curved paths) – this requires a force on the air, and the equal and opposite reaction is the force on the blade.

The situation for a wind turbine blade is somewhat more complicated since the blade is also rotating about an axis parallel to the airflow – and its rotational velocity increases with distance from the hub. The local direction of air flow with respect to the blade thus combines the incoming air velocity and the rotational velocity – for this reason, the orientation of the aerofoil changes along the blade (i.e. they look twisted – just like a propeller).

The net effect of the air flow through the rotating blade is a force all along the blade in the circumferential direction of rotation – this distributed force leads to the overall torque turning the blades and driving the electrical generator.

Source: Wind/15 Appendix : Physics of wind turbines

How is the rotation turned into electricity?The top of the wind turbine is called the nacelle and this houses an electrical generator. This generator allows the conversion of the rotors’ rotational kinetic energy to electrical energy.

The rotor of the wind turbine is attached via a shaft and a gearbox to the electrical generator. As the shaft spins it creates a rotating magnetic field by rotating magnets attached to it. These can either be permanent magnets or electromagnets supplied by an external source. Faraday’s law states that when a conductor moves relative to a magnetic field, an emf is induced. So wind turbine generators convert rotational kinetic energy to electrical energy in the same way as many other energy sources – stream turbines, hydroelectric turbines etc.

The coupling between the wind turbine and the generator usually requires a gearbox. The gearbox allows the speed of rotation of the generator to be higher than that of the blades, which has two advantages.

1. The physical size of the generator can be reduced. The volume of a generator of given power capability scales with its speed of rotation.

2. The size of the park brake can be reduced. The power required to stop a wind turbine is equal to that extracted from the wind. Since power = torque x rotational speed, a larger torque is needed (for a given power) when rotating slowly, compared to when rotating quickly. The size of he torque dictates how strong / large the brake needs to be. With a higher generator speed, a smaller brake can be used and significant cost savings can be made.

Source: Wind/16 Appendix : Physics of wind turbines