Chapter 3 wind power systems feb 2011

Historical Development of Wind Power• First wind turbine outside of the US to generate electricity was built by Poul la Cour in 1891 in Denmark • Used electricity from his wind turbines

Green Energy Renewable Energy Systems

Course-Biên sọan: Nguyễn Hữu Phúc Khoa Điện- Điện Tử- Đại Học Bách Khoa TPHCM

Wind Power Systems

Photos taken near Moraine View State Park, IL

Historical Development of Wind Power

• The first known wind turbine for producing

electricity was by Charles F Brush turbine, in

Historical Development of Wind Power

• First wind turbine outside of the US to generate electricity was built by Poul la Cour in 1891 in Denmark

• Used electricity from

his wind turbines to

electrolyze water to

make hydrogen for

the gas lights at the

schoolhouse

http://www.windpower.org/en/pictures/lacour.htm

Historical Development of Wind Power

• In the US - first wind-electric systems built in the late

1890’s

• By 1930s and 1940s, hundreds of thousands were in use

in rural areas not yet served by the grid

• Interest in wind power declined as the utility grid

expanded and as reliable, inexpensive electricity could

be purchased

• Oil crisis in 1970s created a renewed interest in wind

until US government stopped giving tax credits

• Renewed interest again since the 1990s

Global Installed Wind Capacity

Global Wind Energy Council

http://www.gwec.net/fileadmin/documents/PressReleases/PR_stats_annex_table_2nd_feb _final_final.pdf

Annual Installed Wind Capacity

Global Wind Energy Council

http://www.gwec.net/fileadmin/documents/PressReleases/PR_stats_annex_table_2nd_feb _final_final.pdf

Growth in US Wind Power Capacity

With new installations of about 4000 MW in First Half 2009

Historical Change in Wind Economics,

Constant 2005 Dollars

Source: National Renewable Energy Lab (NREL), Energy Analysis Office

Top 10 Countries - Installed Wind Capacity

(as of the end of 2008)

Global Wind Energy Council

http://www.gwec.net/fileadmin/documents/PressReleases/PR_stats_annex_table_2nd_feb _final_final.pdf

Country MW Capacity % of Global Capacity

US Wind Resources

http://www.windpower.org/en/pictures/lacour.htm

http://www.windpoweringamerica.gov/pdfs/wind_maps/us_windmap.pdf

Wind Resource Atlas of SouthEast Asia

Vietnam is really going green

Researches in the field

of Green Energy related

to electric power really

attract undergraduate

and graduate students.

Worldwide Wind Resource Map

Source: www.ceoe.udel.edu/WindPower/ResourceMap/index-world.html

Types of Wind Turbines

• “Windmill”- used to grind grain into flour

• Many different names - “wind-driven

generator”, “wind generator”, “wind turbine”,

“wind-turbine generator (WTG)”, “wind energy conversion system (WECS)”

• Can have be horizontal axis wind turbines

(HAWT) or vertical axis wind turbines (VAWT)

• Groups of wind turbines are located in what is called either a “wind farm” or a “wind park”

Horizontal axis wind turbines (HAWT) are either upwind machines (a) or downwind

machines (b) Vertical axis wind turbines (VAWT) accept the wind from any direction (c).

Vertical Axis Wind Turbines

• Darrieus rotor - the only vertical axis machine with any

commercial success

• Wind hitting the vertical blades, called aerofoils, generates

lift to create rotation

http://www.reuk.co.uk/Darrieus-Wind-Turbines.htm

• No yaw (rotation about vertical axis)

control needed to keep them facing

into the wind

• Heavy machinery in the nacelle is

located on the ground

• Blades are closer to ground where

windspeeds are lower

http://www.absoluteastronomy.com/topics/Darrieus_wind_turbine

Horizontal Axis Wind Turbines

• “Downwind” HAWT – a turbine with the

blades behind (downwind from) the tower

• No yaw control needed- they naturally orient themselves in line with the wind

• Shadowing effect – when a blade swings

behind the tower, the wind it encounters is briefly reduced and the blade flexes

Horizontal Axis Wind Turbines

• “Upwind” HAWT – blades are in front of

(upwind of) the tower

• Most modern wind turbines are this type

• Blades are “upwind” of the tower

• Require somewhat complex yaw control to keep them facing into the wind

• Operate more smoothly and deliver more

power

Number of Rotating Blades

• Windmills have multiple blades

– need to provide high starting torque to overcome weight of the pumping rod

– must be able to operate at low windspeeds to provide nearly continuous water pumping

– a larger area of the rotor faces the wind

• Turbines with many blades operate at much lower

rotational speeds - as the speed increases, the turbulence caused by one blade impacts the other blades

• Most modern wind turbines have two or three blades

•Wind turbines with many blades operate with much lower rotational speed than

those with fewer blades As the rpm of the turbine increases, the turbulence caused

by one blade affects the efficiency of the blade that follows

•With fewer blades, the turbine can spin faster before this interference becomes

excessive

•And a faster spinning shaft means that generators can be physically smaller in size.

•Most modern European wind turbines have three rotor blades, while American

machines have tended to have just two

•Three-bladed turbines show smoother operation since impacts of tower interference and variation of windspeed with height are more evenly transferred from rotors to drive shaft They also tend to be quieter The third blade, however, does add

considerably to the weight and cost of the turbine

•A three-bladed rotor also is somewhat more difficult to hoist up to the nacelle

during construction or blade replacement

Power in the Wind

• Consider the kinetic energy of a “packet” of air with

mass m moving at velocity v

• Divide by time and get power

• The mass flow rate is (r is air density)

2

m

v t

Power in the Wind

Combining (6.2) and (6.3),

1 Power through area A A

2  v v

 3

1

P A (6.4)

2

W   v Power in the wind

PW (Watts) = power in the wind

ρ (kg/m3)= air density (1.225kg/m3 at 15˚C and 1 atm)

A (m2)= the cross-sectional area that wind passes through

v (m/s)= windspeed normal to A (1 m/s = 2.237 mph)

Power in the Wind (for reference solar is

about 600 w/m^2 in summer)

• Power increases like

the cube of wind

speed

• Doubling the wind

speed increases the

Power in the Wind

• Power in the wind is also proportional to A

• For a conventional HAWT, A = (π/4)D 2 , so wind power

is proportional to the blade diameter squared

• Cost is roughly proportional to blade diameter

• This explains why larger wind turbines are more cost effective

Example 01 – Energy in 1 m2 of Wind

2  v t

1 Energy 1.225 kg/m (1m ) 6 m/s 100 h=13,230 Wh

2



1 Energy (3 m/s) 1.225 kg/m (1m ) 3 m/s 50 h=827 Wh

2



1 Energy (9 m/s) 1.225 kg/m (1m ) 9 m/s 50 h=22,326 Wh

Air Density for Different Temperatures

and Pressures

• M.W = molecular weight of air (g/mol) = 28.97 g/mol

• R = ideal gas constant = 8.2056·10-5·m3·atm·K-1·mol-1

• Air density is greater at lower temperatures

3 M.W 10

Air Density Altitude Correction

Air Density Correction Factors

• Can correct air density for temperature and altitude using scale factors

• Temperature correction factors KT and

altitude correction factors KA are in Tables 6.1 and 6.2 respectively

1.225K K T A (6.14)

 

Impact of Elevation and Earth’s

Roughness on Windspeed

• Since power increases like the cube of windspeed, we can expect a significant economic impact from even a

moderate increase in windspeed

• There is a lot of friction in the first few hundred meters above ground – smooth surfaces (like water) are better

• Windspeeds are greater at higher elevations – tall towers are better

• Forests and buildings slow the wind down a lot

• Can characterize the impact of rough surfaces and height

on wind speed

Impact of Elevation and Earth’s

Roughness on Windspeed

• α = friction coefficient – given in Table 6.3

• v0 = windspeed at height H0 (H0 is usually 10 m)

• Typical value of α in open terrain is 1/7

• For a large city, α = 0.4; for calm water, α = 0.1

Impact of Elevation and Earth’s

Roughness on Windspeed

• Alternative formulation (used in Europe)

• Note that both equations are just approximations

of the variation in windspeed due to elevation and roughness– the best thing is to have actual

measurements

ln( / )

(6.16) ln( / )

Impact of Elevation and Earth’s Roughness on Power in the Wind

0

1

2 1

2

Av P

Impact of Elevation and Earth’s

Roughness on Windspeed

Figure 6.8

For a small town, windspeed at 100 m is twice that at 10 mAreas with smoother surfaces have less variation with height

• Find the ratio of power in

the wind at highest point to

lowest point

• Power in the wind at the

top of the blades is 45%

higher!

Ex 02- Rotor Stress

• Wind turbine with hub at 50-m and a 30-m

Maximum Rotor Efficiency

• Two extreme cases, and neither makes

sense-• Downwind velocity is zero – turbine extracted all of the power

• Downwind velocity is the same as the upwind

velocity – turbine extracted no power

• Albert Betz 1919 - There must be some ideal slowing

of the wind so that the turbine extracts the maximum power

Maximum Rotor Efficiency

• Constraint on the ability of a wind turbine to

convert kinetic energy in the wind into mechanical power

• Think about wind passing though a turbine- it slows down and the pressure is reduced so it expands

Figure 6.9

Power Extracted by The Blades

• vd = downwind windspeed

• From the difference in kinetic energy between

upwind and downwind air flows and (6.2)

1

(6.18) 2

P  m v  v

Determining Mass Flow Rate

• Easiest to determine at the plane of the rotor because we know the cross sectional area A

• Then, the mass flow rate from (6.3) is

• Assume the velocity through the rotor vb is the

average of upwind velocity v and downwind velocity vd:

Power Extracted by the Blades

Power Extracted by the Blades

PW = Power in the wind

Maximum Rotor Efficiency

• Find the speed windspeed ratio λ which

maximizes the rotor efficiency, CP

• From the previous slide

 

maximizes rotor efficiency Set the derivative of rotor efficiency to zero and solve for λ:

Maximum Rotor Efficiency

• Plug the optimal value for λ back into CP to

find the maximum rotor efficiency:

• The maximum efficiency of 59.3% occurs when

air is slowed to 1/3 of its upstream rate

• Called the “Betz efficiency” or “Betz’ law”

Maximum Rotor Efficiency

Figure 6.10

Rotor efficiency

C P vs windspeed

ratio λ

• For a given windspeed, rotor efficiency is a function of the rate at which the rotor turns

• If the rotor turns too slowly, the efficiency drops off since the

blades are letting too much wind pass by unaffected

• If the rotor turns too fast, efficiency is reduced as the turbulence caused by one blade increasingly affects the blade that follows

• The usual way to illustrate rotor efficiency is to presentit as a

function of its tip-speed ratio (TSR)

•The tip-speed-ratio is the speed at which the outer tip of the blade

is moving divided by the windspeed.

Tip-Speed Ratio (TSR)

• Efficiency is a function of how fast the rotor turns

• Tip-Speed Ratio (TSR) is the speed of the outer tip of the

blade divided by windspeed

Rotor tip speed rpm D Tip-Speed-Ratio (TSR) = (6.27)

• v = upwind undisturbed windspeed (m/s)

• rpm = rotor speed, (revolutions/min)

Tip-Speed Ratio (TSR)

• TSR for various

rotor types

• Rotors with fewer

blades reach their

maximum

efficiency at higher

tip-speed ratios

Figure 6.11

Example 03

• 40-m wind turbine, three-blades, 600 kW, windspeed is

14 m/s, air density is 1.225 kg/m3

a Find the rpm of the rotor if it operates at a TSR of 4.0

b Find the tip speed of the rotor

c What gear ratio is needed to match the rotor speed to the generator speed if the generator must turn at 1800 rpm?

d What is the efficiency of the wind turbine under these

conditions?

60 sec/min



Rotor rpm 26.7

Synchronous Machines

• Spin at a rotational speed determined by the number

of poles and by the frequency

• The magnetic field is created on their rotors

• Create the magnetic field by running DC through

windings around the core

• A gear box is needed between the blades and the

generator

• 2 complications – need to provide DC, need to have slip rings on the rotor shaft and brushes

Asynchronous Induction Machines

• Do not turn at a fixed speed

• Acts as a motor during start up as well as a generator

• Do not require exciter, brushes, and slip rings

• The magnetic field is created on the stator instead of the rotor

• Less expensive, require less maintanence

• Most wind turbines are induction machines

Rotating Magnetic Field

Figure 6.13

• Imagine coils in the stator of this 3-phase generator

• Positive current i A flows from A to A’

• Magnetic fields from positive currents are shown

by the bold arrows

Rotating Magnetic Field

Figure 6.14 (a)

• Three-phase currents are flowing in the stator

• At ωt = 0, i A is at the maximum positive value and

i B =i C are both negative

Resultant magnetic flux points

vertically down

Rotating Magnetic Field

Figure 6.14 (b)

• Three-phase currents are flowing in the stator

• At ωt = π/3, i C is at the maximum negative value

and i A =i B are both positive

Resultant magnetic flux moves

clockwise by 60 degrees

Squirrel Cage Rotor

• The rotor of many induction generators has copper

or aluminum bars shorted together at the ends,

looks like a cage

Figure 6.15

• Can be thought of as a

pair of magnets

spinning around a cage

• Rotor current i R flows

easily through the thick

conductor bars

Squirrel Cage Rotor

Figure 6.16

• Instead of thinking of a rotating stator field, you can think of a stationary stator field and the rotor moving counterclockwise

• The conductor experiences a clockwise force

The Inductance Machine as a Motor

• The rotating magnetic field in the stator causes the rotor to spin in the same direction

• As rotor approaches synchronous speed of the

rotating magnetic field, the relative motion becomes less and less

• If the rotor could move at synchronous speed, there would be no relative motion, no current, and no force

to keep the rotor going

• Thus, an induction machine as a motor always spins somewhat slower than synchronous speed



The Induction Machine as a Motor

• As load on motor increases, rotor slows down

• When rotor slows down, slip increases

• “Breakdown torque” increasing slip no longer satisfies the load and rotor stops

• Braking- rotor is forced to operate in the

opposite direction to the stator field

Torque- slip curve for an induction motor, Figure 6.17

The Induction Machine as a Generator

• The stator requires excitation current

– from the grid if it is grid-connected or

– by incorporating external capacitors

• Windspeed forces generator shaft to exceed

synchronous speed

Figure 6.18 Single-phase, self-excited, induction generator

The Induction Machine as a Generator

• Slip is negative because the rotor spins faster than synchronous speed

• Slip is normally less than 1% for grid-connected

• Typical rotor speed

(1 ) [1 ( 0.01)] 3600 3636 rpm

Wind Farms

• The study in Figure 6.28 considered square

arrays, but square arrays don’t make much

sense

• Rectangular arrays with only a few long rows are better

• Recommended spacing is 3-5 rotor diameters

between towers in a row and 5-9 diameters

between rows

• Offsetting or staggering the rows is common