Solar PV Stand Alone Design Project

1

Solar Energy: System Design II

Renewable Energy Technology and Systems

1

System Design System Design

o Produce a system within specified cost and power, choosing among trade-offs between availability, the fraction of solar used and system losses

o Trade-offs between tilt angle, battery capacity and array size arises from seasonal variability in load • The array or the battery must be over designed for (usually)

summer use to meet availability needs during low insolation periods, meaning substantial power is lost during high insolation periods

• Increasing battery size means less over design of PV system, and vice versa

Photovoltaic Systems Types of design procedures

o Several different types of design procedures, depending on availability of radiation data and time period over which calculations are performed 1. “Rule of Thumb”: Determine feasibility/select system

topology: rough calculations, no specific location dependent parameters, and usually no comparison, iteration or checking

2. Worst Month Calculations

3. Time-based simulations, usually hourly, but could also be daily, using detailed solar radiation data and suited to examining battery state of charge. These are usually computer-based

1. Rough Design Procedure No battery sizing or tilt angle calculations, just calculate rough estimate of array size

1. Calculate the total daily load, D, in Wh • Calculate D from appliance ratings or by comparing to

similar situations • If grid connected, can use utility bill energy use • Varies seasonally, should consider maximum daily load

2. Calculate average power need from array. • Increase load to account for electrical losses in inverter,

batteries, power controller, wiring losses, etc.

!"#$% &$$'$' () = +,-.//,0&1$%/$%,"/)$% where ,-.// ≈ 3.56,,0&1$%/$% ≈ 3.8, ,"/)$% ≈ 3.86

1. Rough Design Procedure 3. Calculate energy from X Watts of installed photovoltaic power: !"#$% &$'$%()$* +, = .×01',%×2)$34×2"4)×23503()6,

For latitudes 20º - 50º, average sunhr = 6.5 hrs

2)$34 » 0.9, 2"4) » 0.95, 23503()6,» 0.95. 4. Calculate amount of installed power needed: Power generated

must equal power needed by load !"#$% &$'$%()$* +, = !"#$% '$$* 7%"3 8"(* +,

.×01',%×2)$34×2"4)×23503()6,= 9

2:())25';$%)$%2"),$%

.(+) = 901',%×2)$342"4)23503()6,2:())25';$%)$%2"),$% ≈ 9(+,)?

The array size in watts needs approximately the total load per day in Wh divided by 4

1. Rough Design Procedure

• This approach can be tailored to a specific case by putting in known numbers for efficiency and sunhours. o In calculations here have used optimum numbers.

• Uses of rough design procedure o Get an answer quickly, minimal calculations o As this does not include losses due to oversizing to

accommodate lower insolation, it can be viewed as a minimum array size

• Disadvantages: o Not a “design” methodology – no trade-offs, no tilt angle

calculations, no battery calculations

Summary: PV System Design II • 3 general approaches: “Rule of Thumb”, Worst

Month Calculations, and time-based • Rule of thumb uses average daily load corrected for

system inefficiencies to size array; similar to using array load ratio (ALR) for sizing

• Simple approximations used for sun hours, and the optical/battery/inverter/other efficiencies

• Provides a minimum configuration for a given load application, implicitly assuming that storage allows the array energy production to be used 24-7

1

Solar Energy: System Design III

Renewable Energy Technology and Systems

1

2. Worst Month Calculations

• Worst month calculations use specific load and solar radiation data, but only use averages of solar radiation. This ignores the

day-to-day variability that determines battery size (and

availability), which must then be determined by other means

• Advantages: very simple calculations and short, simple input data – can calculate by hand, no need for large data sets or

computers

• Disadvantages: o No inherent inclusion of statistical analysis of battery

systems

o If only calculating for one worst month, then possibility exists for unexpected consequences for other months.

2. Worst Month Calculations

• Generally calculate system in Amp-hr (Ah) rather than Watt-hr (Wh): Most losses in the system are voltage losses

o De-rate current by ~10% to account for reductions in current due to dirt, etc.

o When converting from Wh to Ah, must use the same system voltage throughout

• Variations of worst-month approaches, related to how to pick battery. Approaches are:

o Size the array to meet load during worst month, and then pick battery size based on experience, availability curves, etc.

o Statistical design of battery size

2. Worst Month Calculations

Average monthly or worst month calculations: 1. Make initial choice about system topology

2. Calculate load for each month of the year in Ah

• The voltage used in these calculations must be the same as the system voltage

• Increase load by dividing by battery, inverter, power conditioning efficiency

3. Pick a tilt angle, or calculate for several tilt angles

• For initial guess, look at load and pick tilt angle that maximizes solar radiation on array during month in which load is highest

– Array = latitude gives overall maximum power: Constant load or slightly higher load in summer

– Array = Latitude + 15°: Suited towards winter loads – Array = Latitude – 15° : Suited towards summer loads

2. Worst Month Calculations 4. Get solar radiation data on chosen tilt angle

a) Find declination angle for mid-point of month (watch for radians vs degrees)

b) Find elevation angle at solar noon

c) Convert average monthly radiation on horizontal to solar radiation on module

Bsin5.23 !=d ( )81NDY 365 2

B - p

=

( )dfa -±°=90 Where the sign is positive and Φ is negative in the Southern Hemisphere and the sign is negative and the latitude is positive in the Northern Hemisphere.

2. Worst Month Calculations 5. Find total current needed from array

6. Find number of panels needed in parallel

• Current from panel is found by looking on manufacturers data sheet at maximum power point current and adjusting for incident radiation/standard

• Current from panel is at maximum power point and is derated (in this case 10%) to account for reduction in current due to dirt, etc.

Array current = Load (Ah)

Sun Hours (hr)

#Panels = Array Current (A)Current from panel ×0.9 (A)

2. Worst Month Calculations 7. Find total number of panels in series to meet system

voltage requirements

• Need to account for • Temperature drops due to operating temperature as

opposed room temperature, at which module power is usually specified

• Diode drops • Changes in battery voltages due to temperature

(unless maximum power tracker included)

• Battery voltage needs to be above 12V (should be ~14V) for a nominally 12V system

• Total number of panels in series= system voltage • Total number of panels = # series × # parallel

2. Worst Month Calculations

8. Find battery size

o Estimate number of days autonomy from statistical analysis of radiation data, existing systems, etc.

o Make a guess as to type of battery to be used o Determine depth of discharge (DOD) for battery from

manufacturers data sheets of estimate from type of battery

o Determine battery capacity in Ah

o The load in the above equation is the “corrected” load which takes into account battery, inverter inefficiencies

DOD Autonomy Days(Ah) Load

(Ah)Capacity Battery ´

=

2. Worst Month Calculations 8. Find battery size (con’t)

Find total number of batteries:

o Battery voltage and rated battery capacity are determined from manufacturer’s data

o Check and adjust if necessary battery capacity based on temperature, discharge rates, and also make sure make sure battery is used according to specifications.

Number Batteries = System Voltage (V)×Battery Capacity (Ah)Battery Voltage (V)× Rated Battery Capacity (Ah)

2. Worst Month Calculations 9. Specify other parameters.

o Charge controller: handle maximum current and power from array, suited to type of batteries

o Inverter: Rated power should be just under typical load Check possibility for peak load

o BOS components: meet specifications and standards. 10. Check that system makes sense or check for other options.

o Is stand-alone choice and type of power reasonable o Tracking: if more than one month has low solar radiation,

then tracking may prove useful, but if the month with the lowest insolation is used to calculate the tilt angle, then tracking does not provide a benefit

Summary: PV System Design III • Worst month calculations useful in trying to

estimate battery sizing in addition to array size • Assuming a fixed system voltage, the load and array

are specified in Ah (normal units for batteries) • Worst month used to optimize tilt and calculate

power from modules • Number of days days of autonomy and depth of

discharge used to calculate battery charge need • Total number of batteries estimated from voltage

and current needs based on battery charge need

1

Solar Energy: PV Systems Design IV

Renewable Energy Technology and

Systems

1

Battery Sizing & LOLP

• Loss of load probability (LOLP=1-A) for a system in which the

array can meet the load & battery charging loads is determined

by the number of days storage

• The number of days storage can be determined by examining

the probability of having a certain number of number of cloudy

days (< 50% radiation) in a row

o Example: probability of having 5 cloudy days in a row is

3%: If battery sized to give 5 days power for load, then

LOLP =3% or A = 97%

• Assumes that array will recharge battery to a full level

before another cloudy period comes (tends to

underestimate battery size needed)

• Ignores the power available to the array during the

cloudy days (tends to underestimate the power available

and overestimate battery size)

Battery Sizing & LOLP

• By using such a statistical analysis of the solar radiation, an

estimate of the LOLP probability can be included in worst month

calculations without requiring daily or hourly system

performance calculations

• Result of analysis are plots that give LOLP as a function of the

number of days of storage

Battery Sizing & LOLP

• If the plots of days storage and LOLP need to be calculated for each

location, then it reduces the utility of simple worst-month calculations

• However, for a given latitude range, the average number of peak sun

hours is correlated to the number of cloudy periods. These in turn

tend to have similarly shaped probability functions

• This means that many locations will behave similarly, and hence plots

relating LOLP, average sun hours, and battery storage can be

determined

• If a location has a weather

pattern in which # cloudy days

not well correlated to average

radiation (e.g., monsoon), cannot

necessarily use generalized plot,

but need to calculate LOLP

based on analysis of the radiation

for that type of climate

3. Hourly based PV simulation

Computer-based calculations

o Computer allow daily/hourly variations in radiation data, and

hence allow impact of variation on system design

o Accuracy of design in general limited by statistical nature of

radiation and inability to predict relevant parameters

o Accuracy of computer simulations does not typically limit the

system performance, and hence many programs have simple

models for temperature dependence, matching and losses that

depend on the operating point of the array or batteries

o Programs generally restricted to battery/array/tilt trade-offs, and

sometimes life cycle costing (LCC) – the specification of other

system components, temperature effects, etc. still needs to be

done and checked.

o Should perform sensitivity, LCC on system

3. Hourly based PV simulation

• Daily simulations require larger set of input specifications and more detailed

output specifications

• Inputs into design process

o Location (solar radiation data, including potentially temperature, wind, etc.)

o Load profiles (including potential effects of small load, surge currents, etc.)

o Specifications of components (battery efficiency, impact of temperature on

battery specs, inverter efficiency curves)

o Design goals: Specify whether goal is to have maximum availability, low cost,

etc. These are ‘constraints’ in terms of design optimization

• Outputs

o Array size and tilt angle, type of solar panel, average operating temperature

o Other components: battery charger, maximum power tracking, inverter,

wiring, generator, etc.

o Numerical specification of system according to design goal

o Documentation, maintenance schedules etc.

3. Hourly based PV simulation

• Calculations generally follow similar approach to worst month calculations,

but on an hourly basis

o Calculate solar radiation

o Calculate radiation on tilted surface and power generated by array

o Determine where energy from array goes: battery, load, lost

o Determine where load draws power from: array, battery, or load not

powered

o Determine BSOC (battery state of charge)

o Calculation system performance indicators (availability, solar fraction

used, cost, etc.)

o Vary tilt angle, array size, battery capacity until optimum reached

• In addition, must calculate life cycle costs, temperature effects, sensitivity

to design parameters, and other features as required by specifications

Summary: PV System Design IV

• Battery sizing determined by Loss of Load

Probability (LOLP)= 1- Availability (A)

• Statistical data in terms of number of cloudy days

used to determine LOLP, as well as sun hours at

location

• Most accurate approach is computer simulation

based on daily or hourly solar radiation data as well

as load data

• System optimization performed by variation of

parameters

1

Wind Energy: Overview and Wind Resource

Renewable Energy Technology and

Systems

1

Wind Energy and Wind Generators

• Used for thousands of years for sailing, milling, and

pumping water

• Use of wind for generating electricity relatively recent,

James Blyth at Strathclyde University built the first

wind generators in 1887

• Only since the 1980’s that wind generators became

cost effective for large scale production of electricity

Wind Power

• Many types and shapes of wind

turbines

• Wind farms are utility scale

deployments of hundreds of

wind turbines

• Two major types: Offshore and

onshore

Wind Power

• Wind power now the most deployed and cheapest source of

renewable energy

Wind Power

• Wind power now the most deployed and cheapest source of

renewable energy

Section 4: Wind Energy

• Wind Resource

o Source of wind resource

o Global and local resources

o Measured wind resources

• Power from wind turbines

o Power curve

o Measured resource data

• Operation of wind turbines

o Blades: Aerodynamics

o Wind turbine components

Source of Wind Energy

• Wind affected by:

o Pressure differentials due to local heating of air

o Balance between forces acting on a mass of air, including Coriolis

force (due to rotation of the Earth), gradient and inertial forces.

o Frictional forces at the Earth’s surface.

• Pressure Differentials

o Atmospheric pressure due to weight of column of air over a

particular location

o Heating causes the

density of the air to

decrease, making it

lighter and hence the

air rises

o Regions with this

effects will have a

low pressure

Source of Wind Energy

• Coriolis Effect

o Inertial force caused by a

rotating reference frame.

o Causes a right directed

force relative to direction of

travel in northern hemi.

o Combination of pressure

differences between two

regions and Coriolis effect

gives rise to global or

geostrophic winds

• Pressure Effects

o As it rises, air cools and also expands

o Cooler heavier air (high pressure) sinks back down to earth.

fUF C  )sin(2 f

where  is the angular rotation

of the earth and  is the latitude

Source of Wind Energy

o Geostrophic wind

• Geostrophic winds tend to be parallel to pressure

isobars

• Friction due to the earth’s surface

o Depends strongly on Earth’ surface

o Surface winds are the geostrophic winds taking into

account friction

o Roughness and obstacles

• Roughness determines by types of land surface:

• Obstacles reduce power density and introduce

turbulence

Summary: Wind

• Wind energy is one of the oldest forms of energy

used by society

• Wind generators and wind turbines refer specifically

to electricity produced by wind

• Wind energy conversion is the largest deployed

renewable energy technology and least expensive

• The wind resource is due the rotation of the earth

and inertial forces acting on the atmosphere as well

as local heating

• Its locally affected by the roughness of the ground

and topological features

1

Wind Energy: Source of Wind Energy

Renewable Energy Technology and

Systems

1

Source of Wind Energy

• Local winds includes smaller scale atmospheric circulation,

called secondary and tertiary winds

• Secondary circulation

o Occurs due to heating

or cooling of the

lower atmosphere

o Example: hurricanes,

monsoons, cyclones

• Tertiary winds

o Local circulations

caused by local winds

o Not considered in

large scale resource selection, but considered for site

assessment

o Examples: land and sea breezes, valley and mountain

winds, other pass or mountain winds, thunderstorms, etc

Source of Wind Energy

• Tertiary winds

o Valley/mountain, sea/land and other mountain winds can

give predictable wind patterns

Frequency of Wind Patterns

• The changes in wind speed give rise to a frequency pattern.

T Bruton, Wind Energy Handbook

Wind Resource

• Surface features have a major impact on local wind, and can

increase or decrease in wind power and speed and cause

turbulence

• Flat terrain with obstacles: causes turbulence and decrease in

wind power and speed for a significant distance from object

Wind Resource

• A gently sloping hill can increase the power if the slope of the

hill does not cause turbulence

Wind Resource versus Height

• Surface Roughness or friction between the Earth and the wind

cause the wind speed to be lower closer to the surface.

• Based on the roughness of the terrain, the wind speed at one

height can be extrapolated to another.

   

o

r

o

z

z

z z

r zv

zv

ln

ln

)(

)(  Where zr is a reference height and z0 is a

measure of surface roughness

Wind Resource versus Height

o Another empirical formula for wind speed with height is

the power law equation



  

   

 

rr z

z

zv

zv

)(

)( Where  is a measured or estimated parameter.

Since the power

produced is

proportional to the

cube of the wind

speed, strong

incentive to increase

tower height

Summary: Wind Resource and Speed

• In addition to global forces leading to large general

wind patterns globally, there are secondary and

tertiary wind patterns

• Surface topology can have a large impact on local

wind patterns

• The wind speed has a strong dependence in terms

of height depending on the degree of surface

roughness

• Increasing the height of wind towers for increased

wind velocity a major consideration in new designs

1

Wind Energy: Power from Wind Energy

Renewable Energy Technology and

Systems

1

Power of Wind Energy

• Energy in wind is associated with the kinetic energy of moving

air

• Calculate the power density (W/m²)

where m/t is the mass of air flowing across a surface for a

given amount of time, t

• Can determine the equation for m/t from fluid dynamics as

2

2 1 mvE 

2

2

1 v

t

m

t

E P



 

Av dt

dm 

Power of Wind Energy

• Derivation of equation for m/t

o Need to calculate the mass of air flowing across a surface

for a given amount of time, say t

o Volume of cylinder determines the mass of air

o In time t, air entering surface with a velocity of v travels a

distance l = vt

• So volume of cylinder

V= r²vt =Avt

• Mass of air = V

Av t

Avt

dt

dm 

 

where  is density of air and other

parameters are defined on diagram

Power of Wind Energy

• So the power and power density of wind is

• Density of air is 1.225 kg/m³ (sea level, 15 °C).

• For wind turbines, the area depends on the area swept by the

rotor (A= r²) where r is the radius of the rotor.

• Power density depends chiefly on wind velocity, and goes up

as cube of the wind velocity

322

2

1

2

1

2

1 Avv

t

Avt v

t

m P 

 



 

3

2

1 v

A

P 

Power of Wind Energy

• Energy densities for various wind speeds

• Average yearly power densities

o P/A < 100 W/m² poor

o P/A  400 W/m² good

o P/A > 700 W/m² very good

Wind Speed

(m/sec)

Wind Speed

(miles/hr)

Power density

(W/m²)

5 1.9 80

7 4.2 210

10 6.0 610

12 7.2 1058

15 9.0 2070

Coefficient of Performance

• Only a part of the power contained in the moving

air, 𝑷𝒘𝒊𝒏𝒅, can be converted into useful power extracted by a wind turbine, 𝑷𝒂𝒆𝒓𝒐, which is given by the coefficient of performance

𝑪𝒑 = 𝑷𝒂𝒆𝒓𝒐 𝑷𝒘𝒊𝒏𝒅

= 𝑷𝒂𝒆𝒓𝒐

𝟏/𝟐𝝆𝝅𝒓𝟐𝒗𝟑

• The theoretical maximum turbine efficiency is given

by the Betz limit (after Albert Betz) as

𝑪𝒑 = 𝟏𝟔

𝟐𝟕 ≈ 𝟎.𝟓𝟗 = 𝑩𝒆𝒕𝒛 𝒍𝒊𝒎𝒊𝒕

• Additionally, 𝑪𝒑 𝐢s a function of the how fast the tips

of the WT blades move relative to the wind speed

𝑻𝒖𝒓𝒃𝒊𝒏𝒆 𝒕𝒊𝒑 𝒔𝒑𝒆𝒆𝒅 𝒓𝒂𝒕𝒊𝒐 = 𝝎𝒓

𝒗 ,𝝎 = 𝐭𝐮𝐫𝐛𝐢𝐧𝐞 𝐫𝐨𝐭.𝐟𝐫𝐞𝐪,𝐫𝐚𝐝/𝐦𝐢𝐧

Coefficient of Performance

Summary: Power from Wind Energy

• The available power from wind is related to the

kinetic energy of the moving mass of air and the

area captured by the area of the wind turbine

• The wind power goes as the cube of the wind

velocity

• The coefficient of performance, 𝑪𝒑, is the ratio of

the extracted power to the wind power

• The Betz limit predicts that 𝑪𝒑 cannot be higher than

59%

• 𝑪𝒑 also depends on the angular rotation frequency

of the turbine

1

Wind Energy: Variability of Wind Resource

Renewable Energy Technology and Systems

1

Measured Resource • Measured wind resources include average wind speed data

(including as a function of direction and as it varies with height) and data of on the statistical variation of the resource

• Below: Average wind resource maps at 60 m elevation (NREL)

Variability of Wind Resource • Power from a wind turbine depends on the distribution of wind

speeds, not just average • In absence of detailed statistical data, can estimate wind

distribution by fitting to a probability curve • Rayleigh distribution requires only average wind speed for

fitting, and matches well to some sites

Insert Manwell, fif 2.28 p 57

2

2 ( ) exp

2 4 v v

p v v v

p pé ùæ ö æ ö = -ê úç ÷ ç ÷

è ø è øê úë û

where p(v) is the probability density function, v is velocity and v is the average velocity

Weibull Distribution • Weibull distribution function depends on two parameters, k=

shape factor and c=scale factor, which depend on average wind speed and wind distribution

• Rayleigh is a special case of the Weibull distribution (k=2) and the scale factor c=average wind speed

where p(v) is the probability density function, and k and c are fitting parameters

1

( ) exp k k

k v v p v

c c c

- é ùæ ö æ ö = -ê úç ÷ ç ÷

è ø è øê úë û

Properties of Weibull • Shape factor, k, describes the variability around the mean, with

a higher number indicating a site where the variation of the hourly mean is small compared to the annual mean speed and low vales of k indicate greater variability around the mean o Sites with trade winds can have high k

T Bruton, Wind Energy Handbook

Properties of Weibull • The mean wind speed is determined by:

• Scale parameter, c, is related to the annual mean wind speed by:

Where G() is the gamma function 1

1v c k

æ ö = G +ç ÷

è ø

0 ( )v vp v dv

¥ = ò

Where p() is the probability distribution function

( ) ( )xxx G=+G 1

G() is typically determined from tabulated values, in the range of 1 to 2.

Variability of Resource • The power probability

function and machine power curve together give the total power from the wind generator

• For more accurate analysis should use measured data for both

• Equation for total power:

dvvpvPP mò ¥

= 0

)()(

Variability of Resource • Velocity and power duration curves from data are a useful way

to compare different wind sites • Total power available from wind is area under the curve • Based on machine power curve, can then get power duration

from wind generator

Manwel 2.26 and 2.27, p 54, 55)

Wind Rose Diagram • Wind rose diagram gives

information on direction, power and percent of wind

• Useful for siting wind turbines. • Center gives no wind conditions. • Gives frequency, power or wind

speed (red bars) at each wind direction

• Can show more than one variable at each wind direction

Summary: Wind Resource Variability • Wind is a variable resource defined statistically in

terms of a probability distribution • The mean of the distribution is the average velocity;

wind resource maps show !" at different elevations • Raleigh and Weibull distributions commonly used • The power is found by averaging # " over the wind

velocity distribution • Wind Rose diagram provides directional information

as well as velocity distribution useful for site selection

1

Wind Energy: Wind Turbines

Renewable Energy Technology and Systems

1

Wind Turbines Multiple types of wind turbines, primarily differentiated by: • Drag or lift: drag are older, less efficient types

Wind Turbines • Multiple types of wind turbines, primarily differentiated by:

o Horizontal or vertical axis o Upwind or down wind o Number of blades and

rotors. • Most wind turbines are

horizontal axis, use lift rather than drag, with one rotor and one to three blades (called HAWT)

Aerodynamics • Wind turbine uses an airfoil to achieve lift and turn the blade. • Airflow over an object causes both lift and drag

• In order to make an efficient wind turbine, lift should be greater than drag

Aerodynamics • Lift created by Bernoulli

effect: the faster the air movement, the lower the pressure. o Air movement on the

upper edge of an airfoil moves faster as it has further to go

Apparent Wind • The motion of an object alters the wind seen by the object, or

the apparent wind • The apparent wind is the vector addition of the undisturbed

wind velocity, v0, and the velocity of the object, U • The faster the object is moving, the more the apparent wind

shifts towards the direction in which the object is traveling

Aerodynamics • Airfoil parameters

o The airfoil shape and its position to the wind determine the lift and drag components of the airfoil

o Important parameters are angle of attack (angle between apparent wind and chord line), chord length, area

Aerodynamics • Lift and drag forces are perpendicular to the apparent or relative wind • The wind is perpendicular

to the plane of the rotor • For an angular rotation

frequency ! (rad/s), the velocity of the blade is " = !$ along the axis

• The apparent wind is the vector sum

% = " − '( • '( = ( − ) '*; '* is the

undisturbed wind velocity, ) is the axial interference factor

• The net force in the plane of rotation is + = ,sin0 − 1cos0

Aerodynamics • Lift and drag coefficients for airfoils with blade area !" = $×&

o Lift coefficient

o Drag coefficient

o Both lift and drag depend on angle of attack, '

o Optimum ' maximizes (/* ratio, maximum efficiency

21 2

l b

L C

v Ar =

21 2

d b

D C

v Ar =

Aerodynamics • Angle of attack: several different regimes of operation

o Attached flow: for low angles of attack, lift increases with attack angle

o High lift/stall • Lift coefficient peaks • Beyond peak, separation of the boundary layer from

the airfoil, decreasing lift and increasing drag (stall) • Performance of wind turbine degrades past this point • ed

Summary: Wind Turbines • Wind turbines are generally either horizontal

(HAWT) or vertical (VAWT) in design • In a HAWT, the apparent angle of wind on the blade

is the vector sum of the external wind and the wind due to the rotation in the plane

• The torque generated is due to the difference of the lift and drag forces (Bernoulli’s principle)

• The ratio of !/# has a peak for an optimum angle of attack

• As the angle of attack is increased too far, turbulent forces lead to stall conditions, which can be used ot regulate the turbine speed