Wind Power & Factors Affecting It. Wind Speed is Key Probably need a site with at least 9 (4 m/s) mph average @ 30 meters for small wind turbines & 15.

Wind Power & Factors Affecting It

Wind Speed is Key• Probably need a site with at

least 9 (4 m/s) mph average @ 30 meters for small wind turbines & 15 mph (6.5 m/s) for large

• These sites are not widespread in southeast

• But there are some great sites on the coast and in the mountains

• Assessing your wind resource is essential

1 m/s = 2.24 mph

Annual Average Wind Speeds & Energy OutputMarginal site vs. Good site

Example: Bergey XL.1 ($6500 system)

• 4 m/s* avg. wind site• “Marginal” Site

– AEO=1920 kWh/year– Lower output– $/kWh/20yr = $0.17– Higher cost per KWH

• 7 m/s avg. wind site• “Good” Site

– AEO=4800 kWh/year– 2.5x higher output– $/kwh/20yrs = $0.07– Lower cost of energy

240% difference in cost/kWh between good and marginal sites * 1 m/s = 2.24 mph

Power in the Wind• Wind is air in motion• Air has mass

– Air density = 1.225 kg/m3 at sea level & 59 F • Mass of moving air contains kinetic energy• The amount of power in the wind is a function of

speed & mass• Power in wind is described as Wind Power Density

in Watts per m2 (P/A) • (P/A in Watts/m2) =

½ (air density in kg/m3) x (V in m/s)3

Wind Power Example

• How much power per square meter is there in a 5 m/s wind at sea level and 59 F?

• Wind Power = 1.225/2 x 5 m/s 3

• Wind Power = .6125 x 125• Wind Power = 76.56 watts/m2

Impact of Temperature & Elevation

• Air density is inversely related to Temperature & Elevation

• Air density decreases with increasing temperature & elevation

• Cold and low places have higher air densities

• Temperature is typically less significant and often ignored (10 – 15 % yearly variation)

• Elevation can be significant and a constant (density @ 5,000’ is 15 % lower than sea level)

Air Density Changes with Elevation

Density Change with Elevation

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

70 75 80 85 90 95 100

Density Change Compared to Sea Level, %

Ele

vati

on

, ft

Air Density Changes with Temperature

Air Density Change with Temperature

-40-30-20-10

0102030405060708090

100110

90 95 100 105 110 115 120 125

Density Change Compared to 59 F, %

Te

mp

era

ture

, F

Air Density @ 4,000’ and 0o F

• Elevation Correction– 1.225 kg/m3 x .88 = 1.078 kg/m3

• Temperature Correction– 1.078 kg/m3 x 1.13 = 1.218 kg/m3

1.218 kg/m3 at 4,000’ & 0o F

Wind Power Intercepted by Turbine at Specific Location

• How much power would be intercepted by a wind turbine with a 20’ (6.09 m) rotor diameter if it was located at 4,000’ and the temperature was 0 F when the wind was blowing 20 mph (8.9 m/s)?

• Power = ½ density X swept area (m2) x v3

Area of a Circle = Swept Area

• Area of circle = ∏ x R 2

• Area of 20’ (6.09 m) diameter rotor = ∏3.042

• Area = 29 m2

1 meter = 3.28 feet

Power Intercepted by 20’ Diameter Turbine on a 4,000’ mountain when the temperature is 0 F and wind is blowing 20

mph

• Power = ½ air density x area x V3

• Power = 1.218/2 x 29m2 x 8.9 m/s• Power = .609 x 29m2 x 8.93m/s• Power = 12,450 watts = 12.45 KW

Starting with Useful Data

• Shot-in-the-dark: “It’s always windy here. I can’t wait to put up a wind turbine and tell the power company to go to you-know-where.”

VS.

• Informed Estimates: “At my site, the average annual wind speed at 30 meters is 7 m/s. I’m researching a turbine that, according to my math, should give me about 6,000 kWh a year.”

Wind – What is it?• Differences in temperature and pressure!

– The atmosphere is a huge, solar-fired engine that transfers heat from one part of the globe to another.

Temperature Differences Pressure Differences Wind

Wind – What is it?

• This process repeats itself daily everywhere, working cyclically like the crankshaft in a car.

• Sometimes this daily effect is overshadowed by large-scale low and high pressure events (fronts and storms)

• Most of the wind we feel is caused by a pressure differential of only 1%

• The strength of air movement can be accelerated or slowed by several key factors...

Factors that Affect the Wind• Elevation• Obstructions• Surface Roughness• Shape and Direction of

Mountains Ridges• Water / Land Connections• Time of day• Time of Year

Elevation• The greater the distance above the surface the

faster the wind blows • Wind data almost always includes the height

at which it was measured • Wind Shear is the change in speed with height

Wind shear formula: S/S0 = (H/H0)α

• In terms of decision making for wind installations, this can be very useful to us in 2 ways...

Elevation & Wind Velocity in Western NC

66.6

7.38.16

6.597.2

89

0123456789

10

3600'class 2

4000' class 3

4418' class 4

4690' class 5

M/S @ 50 mM/S @ 80

Wind Speed and Power Increase with Height Above the Ground

25

50

75

100

125

150

1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75

Increase Compared to 30 ft

To

wer

Heig

ht,

ft

Wind Speed Increase

Wind Power Increase

Wind Shear Extrapolating a measured wind speed

up HIGHER Useful for modeling a turbine to see

how well it will perform at that hub-height

We can use the math to “synthesize” wind speeds at this new height

We can get better performance at higher hub-height, but towers are expensive, and we can make informed decisions with the math

Wind Shear Formula

• S/S0 = (H/H0)α

– S0 – wind speed we’ve measured

– H0- height where we obtained our measurement– H – height we want to extrapolate to– S – wind speed we want to obtain

– α = surface roughness 1) .14 smooth terrain2) .20 trees, buildings, corn fields3) .25 or higher with more trees, buildings

Shear Example• If the wind was measured at 30 meters with an annual average speed of

8 m/s, what would be the speed at 50 meters, if the wind shear was .25 ?

» S/So= (H/Ho)α

» S/8 = (50/30) .25

» S/8 = 1.14

» S = 8 x 1.14

» S = 9.12

» Wind speed at 50 m = 9.12 m/s

Wind Shear• We can also find the wind shear (α) value specific

to our property

Wind Shear Exponent (α) describes the uniformity of how the wind speed “stacks up” vertically at our site. This depends on surface roughness.

• Low α (low effect) over water and in the great plains

• High α (high effect) in rough terrain and developed areas

• We can find α at our site by plugging in 20m WS for So

and 30m WS for S

Example S/So= (H/Ho)α α = LN(S/So)/LN(H/Ho )

• If we measure WS to be 8.7 m/s and 9.2 m/s at two heights (20m and 30m respectively), what is the wind shear value at our site?

• α = LN(S/So)/LN(H/Ho )• α = LN(9.2/8.7)/LN(30/20)• α = LN (1.057)/LN(1.5)• α = .14 (consistent with “smooth terrain”)

Example

WIND SHEAR 20/30M = .14

α= .14

• Now we know that our site has a wind shear exponent of about .14

• We can use that to get a more accurate extrapolation up to 50m

• Remember, we measured 9.2m/s at 30m

S/So= (H/Ho)α

S/9.2 = (50/30).14

S/9.2 = 1.074

WS at 50m = 9.9 m/s

Factors that Affect the Wind• Elevation• Obstructions• Surface Roughness• Shape and Direction of

Mountains Ridges• Temperature Inversions• Water / Land Connections• Time of day• Time of Year

Obstructions and wind speed

• Buildings, thick forests, and other manmade and natural obstructions create significant obstacles to the wind.

• We can’t see it, but the region of disturbed flow downwind of an obstacle is twice the height of that obstacle and quite long.

• For example, a 30-ft tall house creates a region of turbulence that is 60 ft high and 600 ft long (2 football fields!).

Obstructions and Wind Speed

30’ above obstructions within 300 – 500’

Wind Roses

Wind Frequency Rose0°

22.5°

45°

67.5°

90°

112.5°

135°

157.5°

180°

202.5°

225°

247.5°

270°

292.5°

315°

337.5°0% calm

6%

12%

18%

Total Wind Energy (50 m)0°

22.5°

45°

67.5°

90°

112.5°

135°

157.5°

180°

202.5°

225°

247.5°

270°

292.5°

315°

337.5°

6%

12%

18%

Surface Roughness (as we saw in the different wind shear values) effects the vertical behavior, wind turbulence, and ultimately, the speed of the wind.

Surface Roughness and wind speed• Frictional effects caused by surface roughness

decrease as you get away from them (get higher)• And… the rate at which the wind speed increases

(α) varies directly with how rough the surface is. • Flat and smooth = 1/7 or .14 (the amount of

friction applied to the wind by open ground)• Grass, crops, hedges, trees, buildings all impede

moving air (through friction) as it interacts with the ground

Surface Roughness and Wind SpeedTerrain Wind Shear ExponentIce .07Snow on flat ground .09Calm Sea .09Coast with onshore winds .11Snow covered crop-stubble .12Cut grass .14Short prairie grass .16Tall prairie, crops .19Scattered trees and hedges .24Trees, hedges, a few buildings .29Suburbs .31Woodlands .43

*Aspliden and Frost

Factors that Affect the Wind• Elevation• Obstructions• Surface Roughness• Shape and Direction of

Mountains Ridges• Water / Land Connections• Time of day• Time of Year

Factors Affecting Wind Speed

• There is an increase in wind speed over a ridge

Topo USA & True Winds4500’ siteRidge runs NE/SW

Topographic Effects• The length and orientation of topographic features

can serve to accelerate wind speeds• Topographic Funneling Effect

Accelerated wind speeds through tight passes, canyons, etc.Columbia River Gorge: 45.59156, -120.6975

• Wind Deflection EffectMountain ridge redirects wind until it can

accelerate into open spacesKahuku Point, HI: 21.404, -157.8168

Funneling: Columbia River Gorge, OR/WA

Wind Deflection: Kahuku Point, HI

Land/Water Interactions• During the day, the sun warms

the land much quicker than water (1). Warm air above the land rises (2) , allowing cold air from the sea to move inland (3).

• At night, the flow reverses as the land cools more quickly than the water.

• These coastal exchanges can push winds of 10-15mph on average

• This effect decreases greatly more than 2mi from the body of water

Altamont Pass: 37.7170, -121.6494

Altamont Pass, CA

Factors that Affect the Wind• Elevation• Obstructions• Surface Roughness• Shape and Direction of

Mountains Ridges• Temperature Inversions• Water / Land Connections• Time of day• Time of Year

Time of Day/Time of Year and Wind

• Average annual wind speed is important, but not very descriptive. Wind varies greatly through the year and through the day.

• Monthly Pattern: Generally, summer and fall winds are light (driven mostly by convection cycle) and increase in winter and spring (storms and fronts).

• Diurnal (daily) Pattern: Wind speeds often increase in the morning and late evening after convective circulation has been set in motion.

Daily Average Wind Speeds

0 6 12 18 240

4

8

12

16

Mea

n W

ind

Sp

eed

(m

/s)

Mean Daily Profile

Hour of Day

50WS HI40WS30WS

Monthly Average Wind Speeds

2003 2004Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

8

10

12

14

16

1850

WS

HI (

m/s

)50WS HI40WS30WS

Monthly AveragesAverage

SpeedPower Density

(W/M2)March 2003 8.32 M/S 450.1

April 2003 7.11 M/S 442.3

May 2003 8.17 M/S 489.0

June 2003 6.30 M/S 232.8

July 2003 15.4 276.1

August 2003 10.38 257.4

September 2003 13.85 89.9

October 2003 17.10 403.9

November 2003 18.58 517.8

December 2003 12.22 473.3

January 2004 19.69 756.3

February 2004 13.40 577.1

Annual Average

15.6 413.8

Review• Elevation• Obstructions• Surface Roughness• Shape and Direction of Mountains Ridges• Water / Land Connections• Time of day• Time of Year• Local factors (above) supplement global

convective wind cycles• These can serve to accelerate or

decrease wind speeds