Wind Energy

Question 1

Why is there wind?

Answer 1

• Movement of air on appreciable scales is caused by temperature differentials
• Higher temperature air is less dense than cold air
• Temperature gradients are predominately caused
  by uneven solar heating
• (Wind is another form of solar energy)

Question 2

What factors does wind speed depend on?

Answer 2

– Geographic location
– Climate
– Height above ground
– Terrain

Question 3

What are the three types of distribution and give a brief explanation

Answer 3

• Synoptic Variations
  – Time scale shorter than a year – (seasonal variations)
  – Associated with passage of weather systems
• Diurnal Variations
  – Predicable based on time of the day (depending on location)
• Turbulence
  – Short-time-scale (minutes or less)
  – Significant effect on design and performance of turbines
  – Effects quality of power delivered to the grid

Question 4

What does the Weibull distribution show?

Answer 4

The Weibull distribution gives a good representation of hourly
mean wind speeds over a year

Question 5

What is the Weibull Distribution equation for probability of having a given wind speed (x) during the year?

Answer 5

p(x) = (k/C) * (x/C)^-1 * exp^[-(x/C)^k]

Where,
k= shape factor
C= scale factor

Side note:
k >1, usually 1.5
C >0 usually 1

Question 6

What is the modal value of the Weibull Distribution

Answer 6

5.5 m/s

Question 7

What is the mean value of the Weibull Distribution?

Answer 7

6.6 m/s

Question 8

What is the equation for the variation of windspeed with height?

Answer 8

v(z) = Vref * (Z/Zref)^alpha

Alpha usually around 1/7
Vref is speed at height Zref

Included in formula sheet

Question 9

What is the monkey’s rule of thumb for Variation of windspeed with height?

Answer 9

doubling the height, z, increases windspeed by 10% and thus increases power density by >30%

Question 10

What is the wind shear formula which includes roughness length?

Answer 10

v(z) = Vref log(Z/Zo) / log(Zref/Zo)

Zo is surface roughness length

Included in formula sheet

Question 11

What is the equation for wind power density?
(i.e. energy per unit area, per second)

Answer 11

Pd = 1/2 * density *v^3

Question 12

What is the equation for mass of air?

Answer 12

m = density * A * t * v

Question 13

What is the equation for kinetic energy of wind?

Answer 13

KE = 1/2 m v^2

using mass of air

Question 14

What is the equation for power output from a wind turbine

Answer 14

-P = 1/2 Cp p A v^3

Cp is the turbine power coefficient
A is the rotor swept area

Question 15

What is the beta limit? describe and state the value.

Answer 15

The maximum efficiency a turbine is capable of.
Derived as 59.3%
Typical efficiencies are around 30-40%

Question 16

Example question:
A wind turbine has a diameter d = 25m. The power coefficient is 40%. What is the power density of the facility when the windspeed is 6 m/s? What is the power produced by the wind turbine if it harvests the wind?

Answer 16

Power density of the wind
= ½ ρv3 = ½ x 1.3kg/m3 x (6m/s)3
= 140 W/m2

Power of the wind turbine
= Cp x power density x area
= 40% x ½ ρv3 x π x (½ d)2
= 40% x 140 W/m2 x π x (½ x 25)2 = 28 kW

Question 17

Decribe what wind turbine packing density is and what effect does it have?

Answer 17

While extracting energy, turbines will leave characterised air in its wake, which has reduced speeds and increase levels of turbulence.

A turbine operating in the wake of another turbine will produce less energy and may suffer greater structural loading

Question 18

What is the monkey’s rule of thumb for Wind turbine Packing density?

Answer 18

Turbines cannot be spaced closer than 5 times their diameter without losing significant power.

Question 19

What is the equation for power per unit land area ( including packing density)

Answer 19

Power / unit land area = (Cp * 1/2 p v^3 * Pi r^2) / (5d)^2

Question 20

Example question:
A wind farm utilizes the same wind turbines as before (with a
diameter, d = 25 m, & efficiency factor of 40%). What is the power
per unit area harvested by the wind farm if the windspeed is 6
m/s?

Answer 20

• = 40% x ½ ρv3 x π x (½ d)2 / (5d)2
• = 40% x 140 W/m2 x π x (½ x 25)2 / (5 x 25)2
• = 27,489 / 15,625
• = 1.8 W/m2

Question 21

What is the capacity factor

Answer 21

CF = Actual productivity / theoretical maximum

Question 22

What are advantages and disadvantages of vertical axis win turbines?

Answer 22

1.Do not have to face the wind to harness energy
2.Generator is located at the base which has mechanical advantages

1.They are more expensive
2.They don’t tend to be so efficient

Question 23

What is the purpose of the yaw. drive in a horizontal wind turbine?

Answer 23

To allow the turbine to rotate towards the direction of the win flow, in order to ensure maximum efficiency.

Question 24

What is the purpose of the gear box in a horizontal wind turbine?

Answer 24

To convert low speed, high torque power received from rotor to high speed and low torque required for generator.

Question 25

Why is offshore wind usually favourable?

Answer 25

• Close to load centers
  (avoids long-distance transmission)
  – Better wind resource
  – Available shallow water

Question 26

What are some issues with offshore wind?

Answer 26

– Installation challenges
– More expensive
– Maintenance
– Blocking shipping lanes
– Eyesore