Wind Energy Notes

Topic 7 - Wind Energy

Ravita Prasad

Historical Development of Wind Power

Brief History – Early Systems

• 1st Wind Energy Systems: Ancient Civilization in the Near East / Persia
• Vertical‐Axis Wind‐Mill: sails connected to a vertical shaft connected to a grinding stone for milling
• Middle ages: horizontal windmills used for pumping water and grinding grains
• Wind in 19th century: Wind‐rose horizontal-axis water-pumping wind-mills found throughout rural America
• Harvesting wind power isn’t exactly a new idea – sailing ships, wind‐mills, wind‐pumps

Brief History – Rise of wind power electricity

• 1888: Charles Brush builds first large-size wind electricity generation turbine (17 m diameter wind rose configuration, 12 kW generator)
• 1890s: Lewis Electric Company of New York sells generators to retro-fit onto existing wind mills
• 1920s-1950s: Propellor type 2&3 bladed horizontal-axis wind electricity conversion systems (WECS)
• 1940s – 1960s: Rural Electrification in US and Europe leads to decline in WECS use

Brief History – Modern Era

• Key attributes of this period:
  • Scale increase
  • Commercialization
  • Competitiveness
  • Grid integration
• Catalyst for progress: OPEC Crisis (1970s)
  • Economics
  • Energy independence
  • Environmental benefits
• Turbine Standardization:
  • 3-blade Upwind Horizontal-Axis on a monopole tower

Onshore and Offshore Wind Turbines

Comparison between Multi-blade and Few Bladed wind turbines

Wind Turbine

• Almost all electrical power on Earth is produced with a turbine of some type
• Turbine - converting rectilinear flow motion to shaft rotation through rotating airfoils

Turbine Types and Primary Electrical Conversion

Types of Wind Turbines

• Common terminology for wind turbines:
  • “Wind ‐driven generator,” “wind generator,” “wind turbine,” “wind ‐ turbine generator” (WTG), and “wind energy conversion system” (WECS)
• Classification of wind turbine
  • HAWT – horizontal axis wind turbine
  • VAWT – vertical axis wind turbine
• Horizontal axis wind turbines (HAWT) are either upwind machines or downwind machines. Vertical axis wind turbines (VAWT) accept the wind from any direction.

Parts of Horizontal-Axis and Vertical-Axis Wind Turbines

• Key components of wind turbines include rotor, blades, gearbox, generator, nacelle, tower, etc.

Wind Turbine Components

• Blades: Most turbines have three blades. The turning of the blades generates electricity.
• Hub: Centre of the rotor to which the rotor blades are attached.
• Rotor: Blades and hub referred to together.
• Low-speed shaft: Turned by the rotor at about 30 to 60 rotations per minute (rpm).
• Gears: Connects low-speed shaft to high-speed shaft and increases rotational speeds from about 30 to 60 rpm to about 1000 to 1800 rpm (the rotational speed required by most generators to produce electricity).
• Generator: Produces electricity.
• High-speed shaft: Drives generator.
• Controller: Starts up and shuts off the machine.
• Anemometer: Measures wind speed and transmits wind speed data to controller.
• Wind vane: Measures wind direction and communicates with yaw drive to orient the turbine.
• Yaw drive: Keeps rotor facing into the wind as wind direction changes.
• Yaw motor: Powers yaw drive.
• Nacelle: Contains gear box, low- and high-speed shafts, generator, controller, and brake.
• Tower: Made from tubular steel, concrete, or steel lattice. Taller towers generate more power.
• Pitch: Blades are turned, or pitched, to control the rotor speed.
• Brake: Stops rotor in emergencies.

Physics behind the power in the wind

• The kinetic energy of wind is captured by wind turbine to produce electrical energy.
• Kinetic energy for any mass ($m$) moving at velocity ($v$) is given by: $KE = \frac{1}{2}mv^2$

Fluid Dynamics and Power in the Wind

• Mass flow rate: $\dot{m} = \rho A v$ where $\rho$ = air density (kg/m3), $A$ is the cross‐sectional area (m2) and $v$ is wind speed in m/s
• Power in the wind is kinetic energy per unit time: $P_{wind} = \frac{KE}{t} = \frac{\frac{1}{2}mv^2}{t} = \frac{1}{2} \dot{m} v^2$
• Substituting mass flow rate: $P_{wind} = \frac{1}{2} (\rho A v) v^2 = \frac{1}{2} \rho A v^3$
• $P_{wind} = \frac{1}{2} \rho A v^3$ When wind speed doubles, the power in the wind increases by a factor of 8!
• The bigger the turbine blades, the higher the power output will be.

Maximum Rotor (wind turbine) Efficiency

• Approaching wind slows and expands as a portion of its kinetic energy is extracted by the wind turbine, forming the stream tube shown.

Mass Flow Rate and Swept Area

• Easiest way to calculate mass flow rate ($\rho A v$) is a place where we know the cross‐sectional area, so this happens to be at the blades.
• The swept area of the blades will be A

Wind Speed at Turbine Blades

• Assume that velocity at wind blades is average of the upwind and downwind speeds.

Defining Velocity Ratio

• Let's define $\lambda$ as the ratio of upstream to downstream speed: $\lambda = \frac{v_d}{v}$

Power Equations and Fraction Extracted

• $P = \frac{1}{2} \rho A (v + v<em>d) (v^2 - v</em>d^2)$
• $P = \frac{1}{4} \rho A v^3 (1 + \lambda) (1 - \lambda^2)$
• $P_{wind} = \frac{1}{2} \rho A v^3$
• Fraction extracted: $\frac{P}{P_{wind}} = \frac{1}{2}(1 + \lambda) (1 - \lambda^2)$

Rotor Efficiency and Power Coefficient

• $\eta = \frac{P}{P<em>{wind}} = \frac{1}{2} (1 + \lambda) (1 - \lambda^2) = C</em>p$
• Rotor Efficiency To find max possible Rotor eff we differentiate $c_p$ with respect to $\lambda$
• $P = \eta \frac{1}{2} \rho A v^3 = \frac{1}{2} \rho A v^3 C_p$

Differentiating $C_p$ to find maximum Rotor efficiency

• $\frac{dC<em>p}{d \lambda} = \frac{d}{d \lambda} [\frac{1}{2} (1 + \lambda) (1 - \lambda^2)] = 0$$\frac{dC</em>p}{d \lambda} = \frac{1}{2} [(1-\lambda^2) + (1+\lambda)(-2\lambda)] = 0$
  $\frac{dC<em>p}{d \lambda} = \frac{1}{2} [1 - \lambda^2 -2\lambda -2\lambda^2] = 0$$\frac{dC</em>p}{d \lambda} = \frac{1}{2} [1 - 3\lambda^2 -2\lambda] = 0$
  => divide by $\frac{1}{2}$ -> becomes -> $\frac{dC_p}{d \lambda} = [1 - 3\lambda^2 -2\lambda] = 0$

Solving for $\lambda$

• (1 + \lambda) = 0 => \lambda = -1 not possible because V 1-3\lambda = 0 -> \lambda^2 = \frac{1}{3} => \lambda = \frac{1}{\sqrt{3}}

Betz Coefficient

• At $\lambda = \frac{1}{3}$ we get max eff.
• Max eff of Rotor is
• $C<em>p = \frac{1}{2} (1 + \lambda) (1 - \lambda^2) = \frac{1}{2} (1 + \frac{1}{\sqrt{3}}) (1 - (\frac{1}{\sqrt{3}})^2)$$C</em>p = \frac{1}{2} (1 + \frac{1}{\sqrt{3}}) (1 - \frac{1}{3}) = \frac{1}{2} (\frac{\sqrt{3} + 1}{\sqrt{3}}) (\frac{2}{3}) = \frac{\sqrt{3} + 1}{3\sqrt{3}} = 0.5932$

Modern Wind Turbine Efficiency

• The obvious question is, how close to the Betz limit for rotor efficiency of 59.3 percent are modern wind turbine blades?
• Under the best operating conditions, they can approach 80 percent of that limit, which puts them in the range of about 45 to 50 percent efficiency in converting the power in the wind into the power of a rotating generator shaft.

Tip-Speed Ratio (TSR)

• 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 present it 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:
  • $TSR = \frac{rpm * D}{v}$
  • where rpm is the rotor speed, revolutions per minute; D is the rotor diameter (m); and v is the wind speed (m/s) upwind of the turbine.

Wind Turbine Example

• A 40-m, three-bladed wind turbine produces 600 kW at a windspeed of 14 m/s. Air density is the standard 1.225 kg/m3.
• a) At what rpm does the rotor turn when it operates with a TSR of 4.0?
• b) What is the tip speed of the rotor?
• c) If the generator needs to turn at 1800 rpm, what gear ratio is needed to match the rotor speed to the generator speed?
• d) What is the efficiency of the complete wind turbine (blades, gear box, generator) under these conditions?

Wind Turbine Example continued

• a) $\text{TSR} = \frac{\text{Rotor tip speed (m/s)}}{\text{Wind speed (m/s)}}$
  $4 = \frac{\text{Rotor tip speed (m/s)}}{14}$
• Rotor tip speed = 4 x 14 = 56 m/s

Solutions to Wind Turbine Example

• $\frac{56 \text{m}}{\text{s}} \times \frac{60 \text{s}}{1 \text{min}} \times \frac{1 \text{rev}}{\pi (40 \text{m})} = 26.7 \text{ rev/min}$

• The blade tip speed is 56m/s

Gear Ratio Calculation

• $\text{Gear Ratio} = \frac{\text{Generator rpm}}{\text{Rotor rpm}} = \frac{1800}{26.7} = 67.4$

• Gear box Increases the rotor shaft Speed by a factor of 67.4

Typical Values for Large Wind Turbines

• The answers derived in the above example are fairly typical for large wind turbines.
  • A large turbine will spin at about 20–30 rpm
  • The gear box will speed that up by roughly a factor of 50–70
  • The overall efficiency of the machine is usually in the vicinity of 25–30%.

Power Curve of a Wind Turbine

• The power curve of a wind turbine is a graph that indicates how large the electrical power output will be for the turbine at different wind speeds.
• $v_c$ – cut‐in wind speed (m/s) (wind speed needed to overcome the friction of blades to make them spin and generate power.
• $v_R$ – rate wind speed (m/s) [wind speed at which the output power from the wind turbine is maximum or to its rated value).
• $v_f$ – furling wind speed (m/s) [the wind turbine stops generation at this specific wind speed for safety reasons].

Equations for Power Output from Wind Turbine

• $C_{op}$ is the overall power coefficient of the wind turbine.
• It is the product of mechanical efficiency (gear box), electricity efficiency (generator) and aerodynamic efficiency (Betz coefficient).
• Typical values ranges from 25‐45%.

Annual Energy output from wind turbine

• $E = P t$
• t is number of hours that particular wind speed occurs in a year.
• For this you have to know the wind speed distribution for your site for at least a year.

Wind Speed Frequency Curve

• Wind speed frequency curve is a curve that indicates the number of hours per year that specific wind speeds occur

Capacity Factor of a Wind Turbine

• The capacity factor CF is a convenient, dimensionless quantity between 0 and 1 that connects rated power to energy delivered:

Example 2

• Suppose that the wind speed distribution for a site is given in the table on the right.
  • (a) Draw the wind speed distribution curve
  • (b) If the site is installed with a 25kW wind turbine with cut-in wind speed of 3 m/s, rated wind speed of 12 m/s and furling wind speed of 16 m/s, calculate the energy output from the turbine. [diameter of turbine blades is 10m and overall power coefficient is 30%]
    *Solution
    *Refer to excel sheet