For a given survivable wind speed, the mass of a turbine is approximately proportional to the cube of its blade-length. Wind power intercepted by the turbine is proportional to the square of its blade-length. The maximum blade-length of a turbine is limited by both the strength and stiffness of its material.

Labor and maintenance costs increase only gradually with increasing turbine size, so to minimize costs, wind farm turbines are basically limited by the strength of materials, and siting requirements.

Typical modern wind turbines have diameters of 40 to 90 metres (130 to 300 ft) and are rated between 500 kW and 2 MW. As of 2010 the most powerful turbine is rated at 7 MW.

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Typically, 2 types of towers exist: floating towers and land-based towers.

Tower height

Wind velocities increase at higher altitudes due to surface aerodynamic drag (by land or water surfaces) and the viscosity of the air. The variation in velocity with altitude, called wind shear, is most dramatic near the surface.

Typically, in daytime the variation follows the wind profile power law, which predicts that wind speed rises proportionally to the seventh root of altitude. Doubling the altitude of a turbine, then, increases the expected wind speeds by 10% and the expected power by 34%. To avoid buckling, doubling the tower height generally requires doubling the diameter of the tower as well, increasing the amount of material by a factor of at least four.

At night time, or when the atmosphere becomes stable, wind speed close to the ground usually subsides whereas at turbine hub altitude it does not decrease that much or may even increase. As a result the wind speed is higher and a turbine will produce more power than expected from the 1/7th power law: doubling the altitude may increase wind speed by 20% to 60%. A stable atmosphere is caused by radiative cooling of the surface and is common in a temperate climate: it usually occurs when there is a (partly) clear sky at night. When the (high altitude) wind is strong (a 10-meter (33 ft) wind speed higher than approximately 6 to 7 m/s (20–23 ft/s)) the stable atmosphere is disrupted because of friction turbulence and the atmosphere will turn neutral. A daytime atmosphere is either neutral (no net radiation; usually with strong winds and/or heavy clouding) or unstable (rising air because of ground heating — by the sun). Here again the 1/7th power law applies or is at least a good approximation of the wind profile. Indiana had been rated as having a wind capacity of 30,000 MW, but by raising the expected turbine height from 50 m to 70 m, the wind capacity estimate was raised to 40,000 MW, and could be double that at 100 m.^[13]

For HAWTs, tower heights approximately two to three times the blade length have been found to balance material costs of the tower against better utilisation of the more expensive active components.

Wind Turbine Blade design

The ratio between the speed of the blade tips and the speed of the wind is called tip speed ratio. High efficiency 3-blade-turbines have tip speed/wind speed ratios of 6 to 7.

Modern wind turbines are designed to spin at varying speeds (a consequence of their generator design, see above). Use of aluminum and composite materials in their blades has contributed to low rotational inertia, which means that newer wind turbines can accelerate quickly if the winds pick up, keeping the tip speed ratio more nearly constant. Operating closer to their optimal tip speed ratio during energetic gusts of wind allows wind turbines to improve energy capture from sudden gusts that are typical in urban settings.

In contrast, older style wind turbines were designed with heavier steel blades, which have higher inertia, and rotated at speeds governed by the AC frequency of the power lines. The high inertia buffered the changes in rotation speed and thus made power output more stable.

The speed and torque at which a wind turbine rotates must be controlled for several reasons:

• To optimize the aerodynamic efficiency of the rotor in light winds.
• To keep the generator within its speed and torque limits.
• To keep the rotor and hub within their centripetal force limits. The centripetal force from the spinning rotors increases as the square of the rotation speed, which makes this structure sensitive to overspeed.
• To keep the rotor and tower within their strength limits. Because the power of the wind increases as the cube of the wind speed, turbines have to be built to survive much higher wind loads (such as gusts of wind) than those from which they can practically generate power. Since the blades generate more downwind force (and thus put far greater stress on the tower) when they are producing torque, most wind turbines have ways of reducing torque in high winds.
• To enable maintenance; because it is dangerous to have people working on a wind turbine while it is active, it is sometimes necessary to bring a turbine to a full stop.
• To reduce noise; As a rule of thumb, the noise from a wind turbine increases with the fifth power of the relative wind speed (as seen from the moving tip of the blades). In noise-sensitive environments, the tip speed can be limited to approximately 60 m/s (200 ft/s).

More and more engineers realized that the scale of the today's wind turbine blades is now rendering the early trial-and-error intuition-based approaches outdated. Predictive computer tools which are fundamentally founded on mechanics principles are needed to analyze the blade structure in the early design process. Recently, VABS originally developed in helicopter industry, is introduced as a rigorous, engineering-friendly approach for modeling realistic, composite rotor blades. VABS can easily save orders of magnitude computational cost without sacrificing the accuracy. An critical assessment of computer tools for calculating composite wind turbine blade properties has shown that VABS is the best tool available for modeling composite wind turbine blades among all the other tools available in the wind industry.

Using composites adds a significant level of complexity into the engineering of modern wind turbines. One has to simultaneously consider the heterogeneity and anisotropy of the material in the design and analysis. Such characteristics of composites will introduce new deformation modes such as extension-twist or twist-bending couplings defying the conventional blade analysis. VABS is the only computational tool which can rigorously capture all the deformation modes including elastic couplings due to use of composites.

Wind Turbine Blade count

The determination of the number of blades involves design considerations of aerodynamic efficiency, component costs, system reliability, and aesthetics. Noise emissions are affected by the location of the blades upwind or downwind of the tower and the speed of the rotor. Given that the noise emissions from the blades' trailing edges and tips vary by the 5th power of blade speed, a small increase in tip speed can make a large difference.

Wind turbines developed over the last 50 years have almost universally used either two or three blades. Aerodynamic efficiency increases with number of blades but with diminishing return. Increasing the number of blades from one to two yields a six percent increase in aerodynamic efficiency, whereas increasing the blade count from two to three yields only an additional three percent in efficiency. Further increasing the blade count yields minimal improvements in aerodynamic efficiency and sacrifices too much in blade stiffness as the blades become thinner.

Component costs that are affected by blade count are primarily for materials and manufacturing of the turbine rotor and drive train. Generally, the fewer the number of blades, the lower the material and manufacturing costs will be. In addition, the fewer the number of blades, the higher the rotational speed can be. This is because blade stiffness requirements to avoid interference with the tower limit how thin the blades can be manufactured, but only for upwind machines; deflection of blades in a downwind machine results in increased tower clearance. Fewer blades with higher rotational speeds reduce peak torques in the drive train, resulting in lower gearbox and generator costs.

System reliability is affected by blade count primarily through the dynamic loading of the rotor into the drive train and tower systems. While aligning the wind turbine to changes in wind direction (yawing), each blade experiences a cyclic load at its root end depending on blade position. This is true of one, two, three blades or more. However, these cyclic loads when combined together at the drive train shaft are symmetrically balanced for three blades, yielding smoother operation during turbine yaw. Turbines with one or two blades can use a pivoting teetered hub to also nearly eliminate the cyclic loads into the drive shaft and system during yawing.

Finally, aesthetics can be considered a factor in that some people find that the three-bladed rotor is more pleasing to look at than a one- or two-bladed rotor.

Wind Turbine Blade materials

New generation wind turbine designs are pushing power generation from the single megawatt range to upwards of 10 megawatts. The common trend of these larger capacity designs are larger and larger wind turbine blades. Covering a larger area effectively increases the tip-speed ratio of a turbine at a given wind speed, thus increasing the energy extraction capability of a turbine system.

Current production wind turbine blades are manufactured as large as 100 meters in diameter with prototypes in the range of 110 to 120 meters. In 2001, an estimated 50 million kilograms of fiberglass laminate were used in wind turbine blades. New materials and manufacturing methods provide the opportunity to improve wind turbine efficiency by allowing for larger, stronger blades.

One of the most important goals when designing larger blade systems is to keep blade weight under control. Since blade mass scales as the cube of the turbine radius, loading due to gravity becomes a constraining design factor for systems with larger blades.

Current manufacturing methods for blades in the 40 to 50 meter range involve various proven fiberglass composite fabrication techniques. Manufactures such as Nordex and GE Wind use an infusion process for blade manufacture. Other manufacturers use variations on this technique, some including carbon and wood with fiberglass in an epoxy matrix. Options also include prepreg fiberglass and vacuum-assisted resin transfer molding. Essentially each of these options are variations on the same theme: a glass-fiber reinforced polymer composite constructed through various means with differing complexity. Perhaps the largest issue with more simplistic, open-mold, wet systems are the emissions associated with the volatile organics released into the atmosphere. Preimpregnated materials and resin infusion techniques avoid the release of volatiles by containing all reaction gases. However, these contained processes have their own challenges, namely the production of thick laminates necessary for structural components becomes more difficult. As the preform resin permeability dictates the maximum laminate thickness, bleeding is required to eliminate voids and insure proper resin distribution. A unique solution to resin distribution is the use of a partially preimpregnated fiberglass. During evacuation, the dry fabric provides a path for airflow and, once heat and pressure are applied, resin may flow into the dry region resulting in a thoroughly impregnated laminate structure.

Epoxy-based composites are of greatest interest to wind turbine manufacturers because they deliver a key combination of environmental, production, and cost advantages over other resin systems. Epoxies also improve wind turbine blade composite manufacture by allowing for shorter cure cycles, increased durability, and improved surface finish. Prepreg operations further improve cost-effective operations by reducing processing cycles, and therefore manufacturing time, over wet lay-up systems. As turbine blades are approaching 60 meters and greater, infusion techniques are becoming more prevalent as the traditional resin transfer moulding injection time is too long as compared to the resin set-up time, thus limiting laminate thickness. Injection forces resin through a thicker ply stack, thus depositing the resin where in the laminate structure before gelatin occurs. Specialized epoxy resins have been developed to customize lifetimes and viscosity to tune resin performance in injection applications.

Carbon fiber-reinforced load-bearing spars have recently been identified as a cost-effective means for reducing weight and increasing stiffness. The use of carbon fibers in 60 meter turbine blades is estimated to result in a 38% reduction in total blade mass and a 14% decrease in cost as compared to a 100% fiberglass design. The use of carbon fibers has the added benefit of reducing the thickness of fiberglass laminate sections, further addressing the problems associated with resin wetting of thick lay-up sections. Wind turbine applications of carbon fiber may also benefit from the general trend of increasing use and decreasing cost of carbon fiber materials.

Smaller blades can be made from light metals such as aluminum. Wood and canvas sails were originally used on early windmills due to their low price, availability, and ease of manufacture. These materials, however, require frequent maintenance during their lifetime. Also, wood and canvas have a relatively high drag (low aerodynamic efficiency) as compared to the force they capture. For these reasons they have been mostly replaced by solid airfoils.

For large, commercial size horizontal-axis wind turbines, the generator is mounted in a nacelle at the top of a tower, behind the hub of the turbine rotor. Typically wind turbines generate electricity through asynchronous machines that are directly connected with the electricity grid. Usually the rotational speed of the wind turbine is slower than the equivalent rotation speed of the electrical network - typical rotation speeds for a wind generators are 5-20 rpm while a directly connected machine will have an electrical speed between 750-3600 rpm. Therefore, a gearbox is inserted between the rotor hub and the generator. This also reduces the generator cost and weight.

Commercial size generators have a rotor carrying a field winding so that a rotating magnetic field is produced inside a set of windings called the stator. While the rotating field winding consumes a fraction of a percent of the generator output, adjustment of the field current allows good control over the generator output voltage. Enercon has produced gearless wind turbines with separately excited generators for many years, and Siemens produces a gearless "inverted generator" 3MW model while developing a 6MW model. This gives better reliability and performance than gear based systems.

Older style wind generators rotate at a constant speed, to match power line frequency, which allowed the use of less costly induction generators. Newer wind turbines often turn at whatever speed generates electricity most efficiently. This can be solved using multiple technologies such as doubly fed induction generators or full-effect converters where the variable frequency current produced is converted to DC and then back to AC, matching the line frequency and voltage. Although such alternatives require costly equipment and cause power loss, the turbine can capture a significantly larger fraction of the wind energy. In some cases, especially when turbines are sited offshore, the DC energy will be transmitted from the turbine to a central (onshore) inverter for connection to the grid.

A wind turbine is designed to produce a maximum of power at wide spectrum of wind speeds. All wind turbines are designed for a maximum wind speed, called the survival speed, above which they do not survive. The survival speed of commercial wind turbines is in the range of 40 m/s (144 km/h) to 72 m/s (259 km/h). The most common survival speed is 60 m/s (216 km/h). The wind turbines have three modes of operation:

• Below rated wind speed operation
• Around rated wind speed operation (usually at nameplate capacity)
• Above rated wind speed operation

If the rated wind speed is exceeded the power has to be limited. There are various ways to achieve this.

Stall

Stalling works by increasing the angle at which the relative wind strikes the blades (angle of attack), and it reduces the induced drag (drag associated with lift). Stalling is simple because it can be made to happen passively (it increases automatically when the winds speed up), but it increases the cross-section of the blade face-on to the wind, and thus the ordinary drag. A fully stalled turbine blade, when stopped, has the flat side of the blade facing directly into the wind.

A fixed-speed HAWT inherently increases its angle of attack at higher wind speed as the blades speed up. A natural strategy, then, is to allow the blade to stall when the wind speed increases. This technique was successfully used on many early HAWTs. However, on some of these blade sets, it was observed that the degree of blade pitch tended to increase audible noise levels.

Vortex generators may be used to control the lift characteristics of the blade. The VGs are placed on the airfoil to enhance the lift if they are placed on the lower (flatter) surface or limit the maximum lift if placed on the upper (higher camber) surface.

Pitch control

Furling works by decreasing the angle of attack, which reduces the induced drag from the lift of the rotor, as well as the cross-section. One major problem in designing wind turbines is getting the blades to stall or furl quickly enough should a gust of wind cause sudden acceleration. A fully furled turbine blade, when stopped, has the edge of the blade facing into the wind.

Standard modern turbines all pitch the blades in high winds. Since pitching requires acting against the torque on the blade, it requires some form of pitch angle control, which is achieved with a slewing drive. This drive precisely angles the blade while withstanding high torque loads. In addition, many turbines use hydraulic systems. These systems are usually spring loaded, so that if hydraulic power fails, the blades automatically furl. Other turbines use an electric servomotor for every rotor blade. They have a small battery-reserve in case of an electric-grid breakdown. Small wind turbines (under 50 kW) with variable-pitching generally use systems operated by centrifugal force, either by flyweights or geometric design, and employ no electric or hydraulic controls.

Other controls

Yawing

Modern large wind turbines are typically actively controlled to face the wind direction measured by a wind vane situated on the back of the nacelle. By minimizing the yaw angle (the misalignment between wind and turbine pointing direction), the power output is maximized and non-symmetrical loads minimized. However, since the wind direction varies quickly the turbine will not strictly follow the direction and will have a small yaw angle on average. The power output losses can simply be approximated to fall with cos³(yaw angle).

Electrical braking

Braking of a small wind turbine can also be done by dumping energy from the generator into a resistor bank, converting the kinetic energy of the turbine rotation into heat. This method is useful if the kinetic load on the generator is suddenly reduced or is too small to keep the turbine speed within its allowed limit.

Cyclically braking causes the blades to slow down, which increases the stalling effect, reducing the efficiency of the blades. This way, the turbine's rotation can be kept at a safe speed in faster winds while maintaining (nominal) power output. This method is usually not applied on large grid-connected wind turbines.

Mechanical braking

A mechanical drum brake or disk brake is used to hold the turbine at rest for maintenance. Such brakes are usually applied only after blade furling and electromagnetic braking have reduced the turbine speed, as the mechanical brakes would wear quickly if used to stop the turbine from full speed. There can also be a stick brake.

The wind turbine aerodynamics of a horizontal-axis wind turbine (HAWT) are not straightforward. The air flow at the blades is not the same as the airflow further away from the turbine. The very nature of the way in which energy is extracted from the air also causes air to be deflected by the turbine. In addition the aerodynamics of a wind turbine at the rotor surface exhibit phenomena that are rarely seen in other aerodynamic fields.

Axial momentum and the Betz limit

Energy in fluid is contained in four different forms: gravitational potential energy, thermodynamic pressure, kinetic energy from the velocity and finally thermal energy. Gravitational and thermal energy have a negligible effect on the energy extraction process. From a macroscopic point of view, the air flow about the wind turbine is at atmospheric pressure. If pressure is constant then only kinetic energy is extracted. However up close near the rotor itself the air velocity is constant as it passes through the rotor plane. This is because of conservation of mass. The air that passes through the rotor cannot slow down because it needs to stay out of the way of the air behind it. So at the rotor the energy is extracted by a pressure drop. The air directly behind the wind turbine is at sub-atmospheric pressure; the air in front is under greater than atmospheric pressure. It is this high pressure in front of the wind turbine that deflects some of the upstream air around the turbine.

Albert Betz and Frederick W. Lanchester were the first to study this phenomenon. Betz notably determined the maximum limit to wind turbine performance. The limit is now referred to as the Betz limit. This is derived by looking at the axial momentum of the air passing through the wind turbine. As stated above some of the air is deflected away from the turbine. This causes the air passing through the rotor plane to have a smaller velocity than the free stream velocity. The ratio of this reduction to that of the air velocity far away from the wind turbine is called the axial induction factor. It is defined as below:

where: a is the axial induction factor, U1 is the wind speed far away upstream from the rotor, and U2 is the wind speed at the rotor.

The first step to deriving the Betz limit is applying conservation of axial momentum. As stated above the wind loses speed after the wind turbine compared to the speed far away from the turbine. This would violate the conservation of momentum if the wind turbine was not applying a thrust force on the flow. This thrust force manifests itself through the pressure drop across the rotor. The front operates at high pressure while the back operates at low pressure. The pressure difference from the front to back causes the thrust force. The momentum lost in the turbine is balanced by the thrust force.

Another equation is needed to relate the pressure difference to the velocity of the flow near the turbine. Here the Bernoulli equation is used between the field flow and the flow near the wind turbine. There is one limitation to the Bernoulli equation: the equation cannot be applied to fluid passing through the wind turbine. Instead conservation of mass is used to relate the incoming air to the outlet air. Betz used these equations and managed to solve the velocities of the flow in the far wake and near the wind turbine in terms of the far field flow and the axial induction factor. The velocities are given below as:

U₂ = U₁(1 − a)

U₄ = U₁(1 − 2a)

U4 is introduced here as the wind velocity in the far wake. This is important because the power extracted from the turbine is defined by the following equation. However the Betz limit is given in terms of the coefficient of power. The coefficient of power is similar to efficiency but not the same. The formula for the coefficient of power is given beneath the formula for power:

Betz was able to develop an expression for Cp in terms of the induction factors. This is done by the velocity relations being substituted into power and power is substituted into the coefficient of power definition. The relationship Betz developed is given below:

C_p = 4a(1 − a)²

The Betz limit is defined by the maximum value that can be given by the above formula. This is found by taking the derivative with respect to the axial induction factor, setting it to zero and solving for the axial induction factor. Betz was able to show that the optimum axial induction factor is one third. The optimum axial induction factor was then used to find the maximum coefficient of power. This maximum coefficient is the Betz limit. Betz was able to show that the maximum coefficient of power of a wind turbine is 16/27. Airflow operating at higher thrust will cause the axial induction factor to rise above the optimum value. Higher thrust cause more air to be deflected away from the turbine. When the axial induction factor falls below the optimum value the wind turbine is not extracting all the energy it can. This reduces pressure around the turbine and allows more air to pass through the turbine, but not enough to account for lack of energy being extracted.

The derivation of the Betz limit shows a simple analysis of wind turbine aerodynamics. In reality there is a lot more. A more rigorous analysis would include wake rotation, the effect of variable geometry. The effect of air foils on the flow is a major component of wind turbine aerodynamics. Within airfoils alone, the wind turbine aerodynamicist has to consider the effect of surface roughness, dynamic stall tip losses, solidity, among other problems.

Angular momentum and wake rotation

The wind turbine described by Betz does not actually exist. It is merely an idealized wind turbine described as an actuator disk. It's a disk in space where fluid energy is simply extracted from the air. In the Betz turbine the energy extraction manifests itself through thrust. The equivalent turbine described by Betz would be a horizontal propeller type operating with infinite blades at infinite tip speed ratios and no losses. The tip speed ratio is ratio of the speed of the tip relative to the free stream flow. This turbine is not too far from actual wind turbines. Actual turbines are rotating blades. They typically operate at high tip speed ratios. At high tip speed ratios three blades are sufficient to interact with all the air passing through the rotor plane. Actual turbines still produce considerable thrust forces.

One key difference between actual turbines and the actuator disk, is that the energy is extracted through torque. The wind imparts a torque on the wind turbine, thrust is a necessary by-product of torque. Newtonian physics dictates that for every action there is an equal and opposite reaction. If the wind imparts a torque on the blades then the blades must be imparting a torque on the wind. This torque would then cause the flow to rotate. Thus the flow in the wake has two components, axial and tangential. This tangential flow is referred to as wake rotation.

Torque is necessary for energy extraction. However wake rotation is considered a loss. Accelerating the flow in the tangential direction increases the absolute velocity. This in turn increases the amount of kinetic energy in the near wake. This rotational energy is not dissipated in any form that would allow for a greater pressure drop (Energy extraction). Thus any rotational energy in the wake is energy that is lost and unavailable.

This loss is minimized by allowing the rotor to rotate very quickly. To the observer it may seem like the rotor is not moving fast; however, it is common for the tips to be moving through the air at 6 times the speed of the free stream. Newtonian mechanics defines power as torque multiplied by the rotational speed. The same amount of power can be extracted by allowing the rotor to rotate faster and produce less torque. Less torque means that there is less wake rotation. Less wake rotation means there is more energy available to extract.

Blade Element and Momentum Theory

The simplest model for horizontal axis wind turbine (HAWT) aerodynamics is Blade Element Momentum (BEM) theory. The theory is based on the assumption that the flow at a given annulus does not affect the flow at adjacent annuli. This allows the rotor blade to be analyzed in sections, where the resulting forces are summed over all sections to get the overall forces of the rotor. The theory uses both axial and angular momentum balances to determine the flow and the resulting forces at the blade.

The momentum equations for the far field flow dictate that the thrust and torque will induce a secondary flow in the approaching wind. This in turn affects the flow geometry at the blade. The blade itself is the source of these thrust and torque forces. The force response of the blades is governed by the geometry of the flow, or better known as the angle of attack. Refer to the Airfoil article for more information on how airfoils create lift and drag forces at various angles of attack. This interplay between the far field momentum balances and the local blade forces requires one to solve the momentum equations and the airfoil equations simultaneously. Typically computers and numerical methods are employed to solve these models.

There is a lot of variation between different version of BEM theory. First, one can consider the effect of wake rotation or not. Second, one can go further and consider the pressure drop induced in wake rotation. Third, the tangential induction factors can be solved with a momentum equation, an energy balance or orthognal geometric constraint; the latter a result of Biot-Savart law in vortex methods. These all lead to different set of equations that need to be solved. The simplest and most widely used equations are those that consider wake rotation with the momentum equation but ignore the pressure drop from wake rotation. Those equations are given below. a is the axial component of the induced flow, a' is the tangential component of the induced flow. σ is the solidity of the rotor, φ is the local inflow angle. C_n and C_t are the coefficient of normal force and the coefficient of tangential force respectively. Both these coefficients are defined with the resulting lift and drag coefficients of the airfoil:

Corrections to Blade Element Momentum theory

Blade Element Momentum (BEM) theory alone fails to accurately represent the true physics of real wind turbines. Two major shortcomings are the effect of discrete number of blades and far field effects when the turbine is heavily loaded. Secondary short-comings come from dealing with transient effects like dynamic stall, rotational effects like coriolis and centrifugal pumping, finally geometric effects that arise from coned and yawed rotors. The current state of the art in BEM uses corrections to deal with the major shortcoming. These corrections are discussed below. There is as yet no accepted treatment for the secondary shortcomings. These areas remain a highly active area of research in wind turbine aerodynamics.

The effect of the discrete number of blades is dealt with by applying the Prandtl tip loss factor. The most common form of this factor is given below where B is the number of blades, R is the outer radius and r is the local radius. The definition of F is based on actuator disk models and not directly applicable to BEM. However the most common application multiplies induced velocity term by F in the momentum equations. As in the momentum equation there are many variations for applying F, some argue that the mass flow should be corrected in either the axial equation, or both axial and tangential equations. Others have suggested a second tip loss term to account for the reduced blade forces at the tip. Shown below are the above momentum equations with the most common application of 'F':

The typical momentum theory applied in BEM is only effective for axial induction factors up to 0.4 (thrust coefficient of 0.96). Beyond this point the wake collapses and turbulent mixing occurs. This state is highly transient and largely unpredictable by theoretical means. Accordingly, several empirical relations have been developed. As the usual case there are several version, however a simple one that is commonly used is a linear curve fit given below, with a_c = 0.2. The turbulent wake function given excludes the tip loss function, however the tip loss is applied simply by multiplying the resulting axial induction by the tip loss function.

when a > a_c

Please note the following: do not confuse C_T and C_t, the first one is the thrust coefficient of the rotor, which is the one which should be corrected for high rotor loading (i.e. for high values of a), whilst the second one (c_t) is the tangential aerodynamic coefficient of an individual blade element, which is given by the aerodynamic lift and drag coefficients.

Other Methods of Aerodynamic Modeling

BEM is widely used due to its simplicity and overall accuracy, but its originating assumptions limit its use when the rotor disk is yawed, or when other non-axisymmetric effects (like the rotor wake) influence the flow. Limited success at improving predictive accuracy has been made using computational fluid dynamics (CFD) solvers based on Reynolds Averaged Navier Stokes (RANS) and other similar three-dimensional models such as free vortex methods. These are very computationally-intensive simulations to perform for several reasons. First, the solver must accurately model the far-field flow conditions, which can extend several rotor diameters up- and down-stream and include atmospheric boundary layer turbulence, while at the same time resolving the small-scale boundary-layer flow conditions at the blades' surface (necessary to capture blade stall). In addition, many CFD solvers have difficulty meshing parts that move and deform, such as the rotor blades. Finally, there are many dynamic flow phenomena that are not easily modelled by RANS, such as dynamic stall and tower shadow. Due to the computational complexity, it is not currently practical to use these advanced methods for wind turbine design, though research continues in these and other areas related to helicopter and wind turbine aerodynamics.

Free vortex models (FVM) and Lagrangian particle vortex methods (LPVM) are both active areas of research that seek to increase modelling accuracy by accounting for more of the three-dimensional and unsteady flow effects than either BEM or RANS. FVM is similar to lifting line theory in that it assumes that the wind turbine rotor is shedding either a continuous vortex filament from the blade tips (and often the root), or a continuous vortex sheet from the blades' trailing edges. LPVM can use a variety of methods to introduce vorticity into the wake. Biot-Savart summation is used to determine the induced flow field of these wake vorticies' circulations, allowing for better approximations of the local flow over the rotor blades. These methods have largely confirmed much of the applicability of BEM and shed insight into the structure of wind turbine wakes. FVM has limitations due to its origin in potential flow theory, such as not explicitly modelling model viscous behavior, though LPVM is a fully viscous method. LPVM is more computationally intensive than either FVM or RANS, and FVM still relies on blade element theory for the blade forces.

The design specification for a wind-turbine will contain a power curve and guaranteed availability. With the data from the wind resource assessment it is possible to calculate commercial viability. The typical operating temperature range is -20 to 40 °C (-4 to 104 °F). In areas with extreme climate like Inner Mongolia or Rajasthan, specific cold and hot weather versions are required.

Low temperature

Utility-scale wind turbine generators have minimum temperature operating limits which apply in areas that experience temperatures below –20 °C. Wind turbines must be protected from ice accumulation, which can make anemometer readings inaccurate and which can cause high structure loads and damage. Some turbine manufacturers offer low-temperature packages at a few percent extra cost, which include internal heaters, different lubricants, and different alloys for structural elements. If the low-temperature interval is combined with a low-wind condition, the wind turbine will require an external supply of power, equivalent to a few percent of its rated power, for internal heating. For example, the St. Leon, Manitoba project has a total rating of 99 MW and is estimated to need up to 3 MW (around 3% of capacity) of station service power a few days a year for temperatures down to –30 °C. This factor affects the economics of wind turbine operation in cold climates.

Wind turbines are designed to exploit the wind energy that exists at a location. Aerodynamic modeling is used to determine the optimum tower height, control systems, number of blades and blade shape.

Wind turbine designs are utilized to create wind turbines that exploit wind energy. A wind turbine installation consists of the necessary systems needed to capture the wind's energy, point the turbine into the wind, convert mechanical rotation into electrical power, and other systems to start, stop, and control the turbine.

Wind turbines convert wind energy to electricity for distribution. Conventional horizontal axis turbines can be divided into three components.

• The rotor component, which is approximately 20% of the wind turbine cost, includes the blades for converting wind energy to low speed rotational energy.
• The generator component, which is approximately 34% of the wind turbine cost, includes the electrical generator, the control electronics, and most likely a gearbox (e.g. planetary gearbox, adjustable-speed drive or continuously variable transmission) component for converting the low speed incoming rotation to high speed rotation suitable for generating electricity.
• The structural support component, which is approximately 15% of the wind turbine cost, includes the tower and rotor yaw mechanism.

A 1.5 MW wind turbine of a type frequently seen in the United States has a tower 80 meters high. The rotor assembly (blades and hub) weighs 48,000 pounds (22,000 kg). The nacelle, which contains the generator component, weighs 115,000 pounds (52,000 kg). The concrete base for the tower is constructed using 58,000 pounds (26,000 kg) of reinforcing steel and contains 250 cubic yards of concrete. The base is 50 feet (15 m) in diameter and 8 feet (2.4 m) thick near the center.

A wind turbine is a device that converts kinetic energy from the wind into mechanical energy. If the mechanical energy is used to produce electricity, the device may be called a wind generator or wind charger. If the mechanical energy is used to drive machinery, such as for grinding grain or pumping water, the device is called a windmill or wind pump.

Wind turbines can rotate about either a horizontal or a vertical axis, the former being both older and more common.

Horizontal axis

Horizontal-axis wind turbines (HAWT) have the main rotor shaft and electrical generator at the top of a tower, and must be pointed into the wind. Small turbines are pointed by a simple wind vane, while large turbines generally use a wind sensor coupled with a servo motor. Most have a gearbox, which turns the slow rotation of the blades into a quicker rotation that is more suitable to drive an electrical generator.

Since a tower produces turbulence behind it, the turbine is usually positioned upwind of its supporting tower. Turbine blades are made stiff to prevent the blades from being pushed into the tower by high winds. Additionally, the blades are placed a considerable distance in front of the tower and are sometimes tilted forward into the wind a small amount.

Downwind machines have been built, despite the problem of turbulence (mast wake), because they don't need an additional mechanism for keeping them in line with the wind, and because in high winds the blades can be allowed to bend which reduces their swept area and thus their wind resistance. Since cyclical (that is repetitive) turbulence may lead to fatigue failures, most HAWTs are of upwind design.

Modern wind turbines

Turbines used in wind farms for commercial production of electric power are usually three-bladed and pointed into the wind by computer-controlled motors. These have high tip speeds of over 320 kilometres per hour (200 mph), high efficiency, and low torque ripple, which contribute to good reliability. The blades are usually colored light gray to blend in with the clouds and range in length from 20 to 40 metres (66 to 130 ft) or more. The tubular steel towers range from 60 to 90 metres (200 to 300 ft) tall. The blades rotate at 10-22 revolutions per minute. At 22 rotations per minute the tip speed exceeds 300 feet per second (91 m/s). A gear box is commonly used for stepping up the speed of the generator, although designs may also use direct drive of an annular generator. Some models operate at constant speed, but more energy can be collected by variable-speed turbines which use a solid-state power converter to interface to the transmission system. All turbines are equipped with protective features to avoid damage at high wind speeds, by feathering the blades into the wind which ceases their rotation, supplemented by brakes.

Vertical axis design

Vertical-axis wind turbines (or VAWTs) have the main rotor shaft arranged vertically. Key advantages of this arrangement are that the turbine does not need to be pointed into the wind to be effective. This is an advantage on sites where the wind direction is highly variable.

With a vertical axis, the generator and gearbox can be placed near the ground, so the tower doesn't need to support it, and it is more accessible for maintenance. Drawbacks are that some designs produce pulsating torque.

It is difficult to mount vertical-axis turbines on towers, meaning they are often installed nearer to the base on which they rest, such as the ground or a building rooftop. The wind speed is slower at a lower altitude, so less wind energy is available for a given size turbine. Air flow near the ground and other objects can create turbulent flow, which can introduce issues of vibration, including noise and bearing wear which may increase the maintenance or shorten the service life. However, when a turbine is mounted on a rooftop, the building generally redirects wind over the roof and this can double the wind speed at the turbine. If the height of the rooftop mounted turbine tower is approximately 50% of the building height, this is near the optimum for maximum wind energy and minimum wind turbulence.

Subtypes

Darrieus wind turbine

"Eggbeater" turbines, or Darrieus turbines, were named after the French inventor, Georges Darrieus. They have good efficiency, but produce large torque ripple and cyclical stress on the tower, which contributes to poor reliability. They also generally require some external power source, or an additional Savonius rotor to start turning, because the starting torque is very low. The torque ripple is reduced by using three or more blades which results in a higher solidity for the rotor. Solidity is measured by blade area divided by the rotor area. Newer Darrieus type turbines are not held up by guy-wires but have an external superstructure connected to the top bearing.

Giromill

A subtype of Darrieus turbine with straight, as opposed to curved, blades. The cycloturbine variety has variable pitch to reduce the torque pulsation and is self-starting.^[18] The advantages of variable pitch are: high starting torque; a wide, relatively flat torque curve; a lower blade speed ratio; a higher coefficient of performance; more efficient operation in turbulent winds; and a lower blade speed ratio which lowers blade bending stresses. Straight, V, or curved blades may be used.

Savonius wind turbine

These are drag-type devices with two (or more) scoops that are used in anemometers, Flettner vents (commonly seen on bus and van roofs), and in some high-reliability low-efficiency power turbines. They are always self-starting if there are at least three scoops. They sometimes have long helical scoops to give a smooth torque.

The White Creek Wind Farm is an electricity generating wind farm facility in Klickitat County, Washington, United States. It is owned by Last Mile Electric Cooperative and began operations in 2007. The facility has a generating capacity of 205 megawatts.

Four Washington consumer-owned utilities ― Cowlitz PUD, Klickitat PUD, Lakeview Light & Power and Tanner Electric Co-op developed the White Creek Wind Project in Klickitat County, WA. It is the largest public power initiated wind project in the U.S.

Location
White Creek is located in the Columbia River Gorge on 9,500 acres of ranchland, 21 miles east of Goldendale, WA. It is just northwest of Roosevelt, WA, which is across the Columbia River from Arlington, OR. The photo below was taken from I-84 in Oregon, just west of Arlington, OR.

Equipment
Siemens Power Generation supplied, installed and commissioned the 89, 2.3-MW wind turbines and associated towers and other equipment at the project.

Shipping and Delivery
Siemens shipped towers, blades and other components to the Port of Longview (WA) from May to September 2007. The cargo was trucked to the project site.

Power production capability

• Installed capacity of 205 megawatts (MW)
• Based on a one-third capacity factor the projected
• annual output is 68 average MW
• Will power an estimated 38,000 residences or
• about 427 residences per wind turbine.

Power output shares

• 46% ― Cowlitz PUD
• 26% ― Klickitat PUD (Goldendale, WA)
• 26% ― Lakeview Light & Power (Lakewood, WA)
• 2% ― Tanner Electric Cooperative (North Bend, WA)

I-937 (Renewable Portfolio Standards passed by WA voters in November ‘06)

• Cowlitz PUD is the only one of the White Creek utilities with I-937 requirements in the foreseeable future.
• The new law calls for utilities to use non-hydro renewable energy sources for at least three percent of power resources in 2012, nine percent in 2016 and 15
• percent by 2020.
• Based on future load forecasts, Cowlitz PUD’s White Creek share will help it meet the 2012 requirement and most of the 2016 level.

BPA Allocation

• BPA will not be able to meet the load growth of the region post-2011.
• BPA customers have developed a regional plan to “allocate” the output of the
• Columbia River system.
• Each customer will get a share of BPA power based on its electric demand and
• BPA’s generation capability.
• All four White Creek partners will count on White Creek power to meet load
• growth needs post-2011.

Cost comparison: Cowlitz PUD wholesale power options post-2011

• White Creek: $50 per MWh.
• Power market: $60+ per MWh.
• BPA and other hydro sources now utilized by Cowlitz PUD cost $29-$35 per MWh, but unfortunately no additional cheap hydro is available.
• White Creek is the lowest cost alternative

Project cost and financing

• In December 2006 the White Creek Wind Project was sold to White Creek Wind I ― an investment group comprised of affiliates of Prudential Capital Group, Lehman Brothers and Summit Power.
• White Creek Wind I is providing equity capital and utilizing the Federal Production Tax Credits (PTCs) that are available to renewable wind projects.
• Utilizing PTCs will help keep the wholesale production costs about 11% lower than if more conventional tax-free bonds had been utilized for financing. That’s a major benefit to our customers.
• Total project cost was about $360 million (in the end it came in 1% less than projected) ― which includes the acquisition and installation of the wind turbine generators, and all other construction and development costs.
• The four utilities have entered into 20-year power purchase agreements with White Creek Wind I. At closing, the utilities paid for the power assured to be delivered during the contract term.
• Cowlitz PUD’s investment in White Creek is $120 million for the amount of power it is assured ― plus smaller charges for any additional power that can be generated and annual operating and maintenance expenses.
• The four utilities have the option to repurchase the project after 10 years.

Possibility of expansion
Wind studies have shown that as much as another 100 MW project is feasible.
Next phase is being discussed.

source:http://www.cowlitzpud.org/pdf/WC_Q&A_07.pdf

The New Mexico Wind Energy Center officially opened on October 1, 2003. Located 170 miles southeast of Albuquerque and 20 miles northeast of Fort Sumner, the wind farm is well suited for eastern New Mexico's windy landscape.

The New Mexico Wind Energy Center consists of 136 wind turbines, each standing 210 feet high. The facility can produce up to 200 megawatts of power, which is enough electricity to power 94,000 average New Mexico homes. Electricity production does not require water, produce emissions, or generate solid waste.

FPL Energy owns and manages the facility, while PNM purchases all of its output.

The Fenton Wind Power Plant is a 205.5 megawatt wind energy project built by enXco, that became operational in the second half of 2007. The $385-million project is in Chandler, Minnesota on a site that encompasses Murray and Nobles counties and consists of 137 GE 1.5 MW wind turbines.

Power generated by the Fenton Wind Energy project will be sold to Northern States Power, a subsidiary of Minneapolis-based Xcel Energy.

The land was and is subject to archeological surveys as it is situated in culturally sensitive area previously inhabited by the Dakota.

Glacier Wind Farm is wind power plant in Montana. It is a growing industry. At a nameplate capacity of 210 megawatts (MW), the $500 million Glacier Wind Farm, which is located in Toole and Glacier counties,^[1] became Montana's largest in October 2009, surpassing the 135 MW Judith Gap Wind Farm in Wheatland County.

Rim Rock Wind Farm is a proposed wind farm about 25 miles due north of the Glacier project. The $800 million Rim Rock project will have 206 turbines generating 309 megawatts of power.

In 1994, a Minnesota legislative mandate increased the demand for wind power in Minnesota. Buffalo Ridge's geography is well suited for wind power and it has been heavily developed for this purpose. The history of modern wind power activity on Buffalo Ridge can be split into four phases of construction.

In 1994 the first wind farm cluster was built on Buffalo Ridge, northwest of the town of Lake Benton. This first cluster was built by the Kenetech Corporation and runs northwest to Lake Shaokatan; it consists of seventy-three wind turbines.

The second phase occurred in 1998 when Zond Energy Systems built the next wind farm cluster near Hendricks, Minnesota. This farm consists of 143 Zond Z-750 wind turbines with each turbine standing 257 feet (78 m) high and weighing about 196,000 pounds (89,000 kg). Each 750 kW turbine can deliver the annual electricity needs of approximately 250 homes.

The third phase occurred in mid 1999 and added an additional one hundred megawatts of power to the existing output.

In 2006 PPM Energy and Xcel Energy began construction of a one hundred and fifty megawatt project called the MinnDakota Wind Power Project. Buffalo Ridge Wind Power Plant project adds sixty-seven more wind turbines to the Buffalo Ridge wind farm. It also adds turbines to the portion of Buffalo Ridge that is in Brookings County, South Dakota.

The land where the wind farm resides is privately owned farm land. To acquire a piece of this land for the use of wind turbines the wind developer rents or leases the plot of land from the farmer who owns the land. Small projects, less than two megawatts in size, are offered subsidies of 1.5 cents per kilowatt-hour for power sold to utilities.

Xcel has contracted an additional 300 megawatts of wind energy by 2010 and must obtain ten percent of its own electricity from renewable sources by 2015. Xcel is expected to increase its wind power contracts from 302 megawatts to one 1125 megawatts by 2010.

Blue Canyon Wind Farm is the largest wind power plant in Oklahoma, United States. The project, located in the Slick Hills north of Lawton, consists of three phases.

The first phase consists of 45 NEG Micon 1.65 MW wind turbines, with a collective nameplate capacity of 74.25 MW. Blue Canyon Wind Farm began commercial operations in December 2003. The second phase consists of 84 Vestas V80-1.8 MW wind turbines, with a collective nameplate capacity of an additional 151.2 MW. Owned and operated by Horizon Wind Energy, a subsidiary of Energias de Portugal, a world leading Portuguese utility, it began commercial operations in December 2005.

As of 2008^[update], Blue Canyon Wind Farm remains Oklahoma's largest wind farm; however, several organizations including Oklahoma Gas & Electric plan to greatly increase Oklahoma's wind power capacity, and future projects may be larger.

The Blue Canyon Wind Farm is visible from the access road of nearby Mount Scott.

The Wild Horse Wind Farm is a 229-megawatt wind farm built by Puget Sound Energy that consists of one hundred twenty-seven 1.8-megawatt Vestas V80 turbines on a 8,600-acre (3,500 ha) site in Kittitas County, Washington, 15 miles (24 km) east of Ellensburg, Washington. The turbines are placed on the high open ridge tops of Whiskey Dick Mountain, which was chosen for its energetic wind resource, remote location, and access to nearby power transmission lines. The towers are 221 feet (67 m) tall, and each rotor is 129 feet (39 m) long, with a total rotor diameter of 264 feet (80 m), larger than the wingspan of a Boeing 747. The turbines can begin producing electricity with wind speeds as low as 9 mph (14 km/h) and reach full production at 31 mph (50 km/h). They shut down at sustained wind speeds of 56 mph (90 km/h). Average annual output is about 642,000 MW·h.

The Wild Horse Wind Farm was built by Horizon Wind Energy, a subsidiary of Energias de Portugal S.A. (EDP), a world leading Portuguese utility. Construction began in October 2005 and was completed in December 2006. There has been an application from Puget Sound Energy to add an additional 25 turbines. If approved these are planned to be active in 2010.

The Wild Horse Wind Farm also has a Renewable Energy Center that is open to the public everyday April 1 thru November 30 from 9:00-5:30.

The Smoky Hills Wind Power Plant (Phase I) is a 100.8 megawatt (MW) wind farm in Lincoln and Ellsworth Counties, 140 miles west of Topeka in Kansas, north of Ellsworth. The Smoky Hills Wind Power Plant is operated by Enel Green Power. Highway K-14 and Interstate 70 pass through parts of the wind farm, with clear views of many of the wind turbines. The project uses 56 Vestas V80 1.8 MW wind turbines and produces enough electricity to power some 37,000 average Kansas homes annually. As of 19 November 2008 (2008 -11-19)^[update], phase II is under construction with 99 GE 1.5 MW wind turbines for an additional 148.5 MW, to bring the total nameplate capacity to 249.3 MW.