EE535: Renewable Energy:
Systems, Technology &
Economics
Session 6: Wind (1)
Global Wind Resource
Annual global mean wind power at 50m above the surface
Ref:
Conversion
• Wind energy – atmospheric kinetic energy –
determined by mass and motion speed of the air
• Utilising wind energy involves installation of a
device that converts kinetic energy in the
atmosphere to useful energy (mechanical,
electrical)
• Windmills have been used to convert wind
energy into mechanical energy for over
3000years
Basic Calculations: Power Density
• Kinetic Energy (KE) – ½
mV2
• For a constant wind
speed v, normal cross
sectional area A, and
given period of time, t,
and air density ρ,
v
A
– Air mass m = ρAVt
• So,
• KE = ½ ρAtV3
• Wind power density (per
unit area and per second)
is:
• Power = ½ ρ V3
Harvestable power scales with the cube of the wind speed
Power Density
• The atmosphere approximates an ideal gas
equation in which at the STP (T0 = 288.1K), (P0
= 100.325 Pa),
– ρ0 = 1.225kg/m3
Distribution of wind speed
• The strength of wind varies, and an average value for a given
location does not alone indicate the amount of energy a wind
turbine could produce there
• To assess the frequency of wind speeds at a particular location,
a probability distribution function is often fit to the observed data.
• Different locations will have different wind speed distributions.
• A statistical distribution function is often used to describe the
frequency of occurrence of the wind speed – a Weibull or
Rayleigh distribution is typically used
• The wind power density is modified by the inclusion of an energy
pattern factor (Epf)
• Where Va is the average wind speed
Distribution of Wind Speeds
• As the energy in the wind varies as the cube of the wind
speed, an understanding of wind characteristics is
essential for:
–
–
–
–
Identification of suitable sites
Predictions of economic viability of wind farm projects
Wind turbine design and selection
Effects of electricity distribution networks and consumers
• Temporal and spatial variation in the wind resource is
substantial
–
–
–
–
Latitude / Climate
Proportion of land and sea
Size and topography of land mass
Vegetation (absorption/reflection of light, surface temp, humidity
Distribution of Wind Speeds
• The amount of wind available at a site may vary from one year to the
next, with even larger scale variations over periods of decades or
more
• Synoptic Variations
– Time scale shorter than a year – seasonal variations
– Associated with passage of weather systems
• Diurnal Variations
– Predicable (ish) based on time of the day (depending on location)
– Important for integrating large amounts of wind-power into the grid
• Turbulence
–
–
–
–
Short-time-scale predictability (minutes or less)
Significant effect on design and performance of turbines
Effects quality of power delivered to the grid
Turbulence intensity is given by I = σ / V, where σ is the standard
deviation on the wind speed
Annual and Seasonal Variations
• It’s likely that wind-speed at any particular
location may be subject to slow long-term
variations
– Linked to changes in temperature, climate changes,
global warming
– Other changes related to sun-spot activity, volcanic
eruption (particulates),…
– Adds significantly to uncertainty in predicting energy
output from a wind farm
• Wind-speed during the year can be
characterised in terms of a probability
distribution
Weibull Distribution
• Weibull distribution gives a good
representation of hourly mean wind
speeds over a year
• F(V) = exp(-(V/c)k)
– Where F(V) is the fraction of time for which
the hourly mean wind speed exceeds V
– c is the ‘scale parameter’ and k is the ‘shape
parameter’ which describe the variability
about the mean
– Mean wind speed = V = cΓ(1 + 1/k)
Weibull Distribution
• The probability
distribution function :
F(U)
1.2
1
0.8
0.6
F(U)
0.4
0.2
24
22
20
18
16
14
12
8
10
6
4
2
0
0
• f(V) = -dF(V)/dV = k(Vk-1
/ ck) exp(-(V/c)k)
f(U)
24
22
20
18
16
14
12
10
8
6
4
f(U)
2
• V = ∫0∞ V f(V)dV
0
• Since mean wind
speed is given by:
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
Wind Turbines
• Wind energy systems
convert kinetic energy in
the atmosphere into
electricity (or for pumping
fluid)
• Two basic categories
– Horizontal axis wind turbine
(rotating axis horizontal to
ground)
– Vertical axis wind turbine
(rotating axis vertical to
ground)
Horizontal Axis
Wind -> Mechanical energy -> Electricity
Vertical Axis
Horizontal axis wind turbine
•
•
•
Most common type of turbine in use
Power ratings typically 750kW to 3.5MW (rotor diameters 48m – 80m)
Usually with 3 aerofoil type rotor blades
–
–
•
•
Creates aerodynamic lift when wind passes over them
Ideal operating conditions : circa 12 – 14m/s
Rotating shaft connected to gearing box to set suitable speed to drive a generator
3 types:
–
Constant Speed Turbine
•
•
•
–
Variable speed double feed induction generator
•
•
•
–
Runs at 1 speed, regardless of windspeed
Cheap and robust
Prone to noise and mechanical stress
Runs at variable speeds
Greater dynamic efficiency
Reduced mechanical stress and noise generation
Variable speed direct drive turbine
•
•
Runs without gearbox
Most expensive capital equipment costs
Power Output
• Power output from a wind turbine is given
by:
– P = ½ Cp ρ A V3
•
•
•
•
Where Cp is the power coefficient
ρ is the air density
A is the rotor swept area
V is the wind speed
• Cp describes the fraction of the power in
the wind that may be converted by the
turbine into mechanical work
Energy Extracting Mechanism
Actuator disk /
Turbine Blades
Stream tube
V∞
velocity
p+d
Vd
velocity
p∞
pressure
Vw
p∞
pressure
p-d
Mass Flow
• Mass flow rate must be the same everywhere
along the tube so,
•
•
•
•
ρ A∞ V∞ = ρ Ad Vd = ρ Aw Vw (i)
∞ refers to conditions far upstream/downstream
d refers to conditions at the disk
w refers to conditions in the far wake
• The turbine induces a velocity variation which is
superimposed on the free stream velocity, so:
• Vd = V∞(1 – a)
(ii)
• Where a is known as the axial flow induction factor, or the
inflow factor
Momentum
• The air that passes through the disk undergoes
an overall change in velocity (V∞ - Vw),
• Rate of change of momentum dP
• dP= (V∞ - Vw)ρAdVd
• = overall change in velocity x mass flow rate
(iii)
• The force causing this change in momentum is
due to pressure difference across turbine so,
• (p+d – p-d)Ad = (V∞ - Vw)ρAdV∞( 1-a)
(iv)
Bernoulli’s Equation
• Bernoulli’s equation states that, under
steady state conditions, the total energy in
a flow, comprising kinetic energy, static
pressure energy, and gravitational
potential, remains the same provided no
work is done on or by the fluid
• So, for a volume of air,
• ½ ρV2 + p + ρgh = constant
(v)
Axial Speed Loss
• Upstream:
• ½ ρ∞V∞2 + p∞ + ρ∞g h∞ = ½ ρd Vd2 + p+d + ρdghd (vi)
• Assuming ρ∞ = ρd and h∞ = hd
• ½ ρ∞V∞2 + p∞ = ½ ρd Vd2 + p+d
(vii)
• Similarly downstream
• ½ ρ∞V∞2 + p∞ = ½ ρd Vd2 + p-d
(viii)
• Subtracting,
• (p+d – p-d) = ½ ρ (V∞2 - Vw2)
• From (iv),
• ½ ρ (V∞2 - Vw2) Ad = (V∞ - Vw)ρAdV∞( 1-a)
• Vw = (1 -2a)V∞
(ix)
(x)
Power Coefficient
• From earlier, Force F
• F = (p+d – p-d)Ad = 2ρAdV2∞( 1-a)
• Rate of work done by the force at the
turbine = FVd
• Power = FVd = 2ρAdV3∞( 1-a)2
• Cp (Power Coefficient) = ratio of power
harvested to power available in the air
• Cp = (2ρAdV3∞( 1-a)2 ) / (½ ρAdV3∞)
• Cp = 4a(1 – a)2
The Betz Limit
• The maximum value of Cp occurs when
dCp/da = 4(1-a)(1-3a) = 0
• Which gives : a = 1/3
• Therefore, CPmax = 16/27 = 0.593
• This is the maximum achievable value of Cp
• No turbine has been designed which is
capable of exceeding this limit
The Thrust Coefficient
• The force on the turbine caused by the
pressure drop can be expressed as CT, the
coefficient of Thrust
• CT = Power / (½ ρ AdV2∞)
• CT = 4a(1-a)
Variation of Cp and CT with Axial
Induction Factor a
1.2
1
0.8
CT
0.6
Cp
0.4
0.2
0
a
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Variation of windspeed with Height
• Principal effects governing the properties of wind
close to the surface (the boundary layer)
include:
–
–
–
–
The strength of the geostrophic wind
The surface topography / roughness
Coriolis effects due to the earth’s rotation
Thermal effects
• Most interesting for us is that the boundary layer
properties are strongly influenced by surface
roughness – therefore site selection is critical
Variation of windspeed with Height
• Taller windmills see higher wind speeds
• Ballpark: doubling the height increases windspeed by
10% and thus increases power density by 30%
• Wind shear formula from NERL (National Renewable
Energy Laboratory):
• v(z) = v10(z / 10m)α
• Where v10 is the speed at 10m, α typically around 0.143
• Wind shear formula from the Danish Wind Energy
Association:
• v(z) = vref log(z/zo) / log(zref/z0)
• Where z0 is a parameter called the roughness length, vref is the
speed at a reference height zref
Variation of windspeed with Height
Type of Terrain
Cities, forests
suburbs, wooded countryside
Villages, countryside with trees and hedges
Open farmland, few trees and buildings
Flat grassy plains
Flat desert, rough sea
Roughness Length z0 (m)
0.7
0.3
0.1
0.03
0.01
0.001
Typical Surface Roughness Lengths
(from Wind Energy Handbook, pg 10
Example – Windmill Power
• A windmill has a diameter d = 25m, and a hub
height of 32m. The efficiency factor is 50%.
What is the power produced by the windmill if
the windspeed is 6m/s?
• Power of the wind per m2
• ½ ρv3 = ½ 1.3kg/m3 x (6m/s)3 = 140W/m2
• Power of the windmill = Cp x power per unit area
x area
• = 50% x ½ ρv3 x (π/4)d2
• = 50% x 140W/m2 x (π/4)(25m)2
• = 34kW
Windmill Packing Density
• As it extracts energy from the wind, the turbine
leaves behind it a wake characterised by
reduced wind speeds and increased levels of
turbuence
• A turbine operating in the wake of a turbine will
produce less energy and suffer greater structural
loading
• Rule of thumb is that windmills cannot be
spaced closer than 5 times their diameter
without losing significant power
Windmill Packing Density
• Power that a
windmill can
generate per unit
land area =
• Power per windmill
/ land area per
windmill
• = (Cp x ½ ρv3 x
(π/4)d2) / (5d)2
d
5d
Example – Power per unit land area
• A wind farm utilizes windmills with a
diameter d = 25m, and a hub height of
32m. The efficiency factor is 50%. What is
the power per unit area harvested by the
wind farm if the windspeed is 6m/s?
Capacity Factor
• Since wind speed is not constant, a wind farm's annual
energy production is never as much as the sum of the
generator nameplate ratings multiplied by the total hours
in a year
• Capacity factor = actual productivity / theoretical
maximum
• Typical capacity factors are 20–40%, with values at the
upper end of the range in particularly favourable sites
• Unlike fueled generating plants, the capacity factor is
limited by the inherent properties of wind. Capacity
factors of other types of power plant are based mostly on
fuel cost, with a small amount of downtime for
maintenance
Resource & Market Status
•
•
•
•
Ireland has an exceptional wind
energy resource, with an
estimated technical resource of
613 TWh / year
Wind is intermittent &
unpredictable – challenging
integration into the national grid
Back-up and storage solutions
necessary
Wind energy resource in Ireland is
4x European average
•
•
•
•
As of 2007, Ireland had circa
800MW installed wind capacity : 1
offshore and 35 on-shore wind
energy sites
Market has become larger and
more stable
Current cost of wind generated
electricity is approximately on a
par with fossil fuel generated
electricity (5.7 cent per kHh –
large wind energy >5MW),
(5.9cent per kWh – small wind
energy < 5MW)
Cost of wind electricity generation
is dependant on many factors
including: location, wind speeds,
electrical grid connections
Barriers
• Major issues restricting the development of wind
energy include:
– Lack of robust technical information has lead to
opposition to wind farms being developed in certain
areas
– Environmental concerns including noise, shadows,
flickering, wildlife (birds), visual impact,
electromagnetic interference
– Financial incentives and taxation from government
are inadequate
– Grid connection and axis not fairly provided