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 mV 2 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 ρAtV 3 A v Wind power density (per unit area and per second) is: Power = ½ ρ V 3 Harvestable power scales with the cube of the wind speed

Power Density The atmosphere approximates an ideal gas equation in which at the STP (T 0 = 288.1K), (P 0 = Pa), – ρ 0 = 1.225kg/m 3

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 V a 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(V) = -dF(V)/dV = k(V k-1 / c k ) exp(-(V/c) k ) Since mean wind speed is given by: V = ∫ 0 ∞ V f(V)dV

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) Wind -> Mechanical energy -> Electricity Horizontal AxisVertical 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 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

Power Output Power output from a wind turbine is given by: –P = ½ C p ρ A V 3 Where C p is the power coefficient ρ is the air density A is the rotor swept area V is the wind speed C p describes the fraction of the power in the wind that may be converted by the turbine into mechanical work

Energy Extracting Mechanism velocity pressure velocity V∞V∞ VwVw p ∞ VdVd p-dp-d p+dp+d Actuator disk / Turbine Blades Stream tube

Mass Flow Mass flow rate must be the same everywhere along the tube so, ρ A ∞ V ∞ = ρ A d V d = ρ A w V w (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: V d = 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 ∞ - V w ), Rate of change of momentum dP dP= (V ∞ - V w )ρA d V d (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 )A d = (V ∞ - V w )ρA d V ∞ ( 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 ρV 2 + p + ρgh = constant(v)

Axial Speed Loss Upstream: ½ ρ ∞ V ∞ 2 + p ∞ + ρ ∞ g h ∞ = ½ ρ d V d 2 + p + d + ρ d gh d (vi) Assuming ρ ∞ = ρ d and h ∞ = h d ½ ρ ∞ V ∞ 2 + p ∞ = ½ ρ d V d 2 + p + d (vii) Similarly downstream ½ ρ ∞ V ∞ 2 + p ∞ = ½ ρ d V d 2 + p - d (viii) Subtracting, (p + d – p - d ) = ½ ρ (V ∞ 2 - V w 2 ) From (iv), ½ ρ (V ∞ 2 - V w 2 ) A d = (V ∞ - V w )ρA d V ∞ ( 1-a)(ix) V w = (1 -2a)V ∞ (x)

Power Coefficient From earlier, Force F F = (p + d – p - d )A d = 2ρA d V 2 ∞ ( 1-a) Rate of work done by the force at the turbine = FV d Power = FV d = 2ρA d V 3 ∞ ( 1-a) 2 C p (Power Coefficient) = ratio of power harvested to power available in the air C p = (2ρA d V 3 ∞ ( 1-a) 2 ) / (½ ρA d V 3 ∞ ) C p = 4a(1 – a) 2

The Betz Limit The maximum value of C p occurs when dC p /da = 4(1-a)(1-3a) = 0 Which gives : a = 1/3 Therefore, C Pmax = 16/27 = This is the maximum achievable value of C p 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 C T, the coefficient of Thrust C T = Power / (½ ρ A d V 2 ∞ ) C T = 4a(1-a)

Variation of C p and C T with Axial Induction Factor a

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) = v 10 (z / 10m) α Where v 10 is the speed at 10m, α typically around Wind shear formula from the Danish Wind Energy Association: v(z) = v ref log(z/z o ) / log(z ref /z 0 ) Where z 0 is a parameter called the roughness length, v ref is the speed at a reference height z ref

Variation of windspeed with Height 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 m 2 ½ ρv 3 = ½ 1.3kg/m 3 x (6m/s) 3 = 140W/m 2 Power of the windmill = C p x power per unit area x area = 50% x ½ ρv 3 x (π/4)d 2 = 50% x 140W/m 2 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 ρv 3 x (π/4)d 2 ) / (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