EE535: Renewable Energy: Systems, Technology & Economics

1. EE535: Renewable Energy: Systems, Technology & Economics Session 6: Wind (1)

2. Global Wind Resource Annual global mean wind power at 50m above the surface Ref:

3. 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

4. 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, Air mass m = ρAVt So, KE = ½ ρAtV3 Wind power density (per unit area and per second) is: Power = ½ ρV3 Basic Calculations: Power Density v A Harvestable power scales with the cube of the wind speed

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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)

11. Weibull Distribution • The probability distribution function : • f(V) = -dF(V)/dV = k(Vk-1 / ck) exp(-(V/c)k) • Since mean wind speed is given by: • V = ∫0∞ V f(V)dV

12. 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 Vertical Axis Wind -> Mechanical energy -> Electricity

13. 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 • Runs at 1 speed, regardless of windspeed • Cheap and robust • Prone to noise and mechanical stress • Variable speed double feed induction generator • 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

14. Power Output • Power output from a wind turbine is given by: • P = ½ Cpρ 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

15. Energy Extracting Mechanism Actuator disk / Turbine Blades Stream tube V∞ velocity p+d Vd Vw velocity p ∞ pressure p ∞ pressure p-d

16. 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

17. 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 (iii) • = overall change in velocity x mass flow rate • 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)

18. 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)

19. Axial Speed Loss • Upstream: • ½ ρ∞V∞2 + p∞ + ρ∞g h∞ = ½ ρd Vd2 + p+d + ρdghd (vi) • Assuming ρ∞=ρd andh∞ = 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) (ix) • Vw = (1 -2a)V∞ (x)

20. 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

21. 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

22. 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)

23. Variation of Cp and CT with Axial Induction Factor a

24. 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

25. 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

26. Variation of windspeed with Height Typical Surface Roughness Lengths (from Wind Energy Handbook, pg 10

27. 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

28. 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

29. 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

30. 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?

31. 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

32. 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 Resource & Market Status

33. 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