ELECTRICAL FAULT CONTROL FOR WIND TURBINES BASIC INFORMATION AND TUTORIALS

WIND TURBINE ELECTRICAL FAULT CONTROLS

How To Control Electrical Faults in Wind Turbines

One of the roles of a monitoring and control system in a turbine is that if some fault is detected, the proper action is taken. A fault can be any malfunctioning of a component, including damage and breakage; high or low operating temperature or pressure; or a value outside of the allowed tolerances for a mechanical or electrical parameter such as speed, voltage, current, and the like.

Depending on how serious the fault is, a turbine must be shut down if the fault cannot be corrected. If a turbine has to be shut down, a process of shutting down the turbine must be followed. Some faults may lead to a temporary action that must be checked a number of times to see if it persists.

Th e number of faults that can occur is large and it is not practical to list them, since faults can be diff erent from one machine to another. Some of the more important mechanical faults that can happen are mentioned here:

a. Excessive vibration in various parts of the turbine; this can be in any of the main bearings, in the nacelle, in the tower, and in the gearbox.

b. High temperatures of various fluids in the gearbox, bearings, oil cooling system, or any other hydraulic system.

c. Low level or low pressure of various liquids in various parts of the system.

Also, some faults are not detectable by a turbine controller, unless redundant systems are used. Redundant means that one parameter or variable is measured by two devices, so that if one fails the other shows a (diff erent) value. For instance, suppose that the anemometer malfunctions or freezes in a freezing rain. 

The reading from the anemometer then shows a zero speed for wind, whereas there is wind. In such a case, the controller interprets this as lack of wind and, thus, the turbine is put into halt and with the brakes on. Th is is a typical scenario that calls for a technician to act.

One of the major faults that can happen in a wind turbine and can lead to disastrous results is when a turbine speed increases beyond the allowed limit. Th is is called overspeed. When a turbine rotates, there are dynamic forces that act on blades and all the other related mechanical components.

The magnitude of these forces depends on the speed of rotation. If the speed goes up, the magnitudes of these forces increase as well, and can go beyond the values for which the components are designed. If this happens, these components can break. And if one component in a mechanical system breaks and the cause is still present, this can lead to other component failure and serious damage.

In particular, if the speed of a wind turbine increases beyond its designed value, the blades can fl y away and the whole turbine can fall apart in a short time. If during the normal operation of a wind turbine, the load is suddenly taken off the turbine, this can lead to overspeed. 

This can happen if the generator is disconnected from the grid, for instance, in the case of lightning tripping the overhead breakers and disconnecting the circuit. Even if the turbine controller starts shutting down the turbine in such a condition, the momentum in the rotor, as a result of its existing speed, can speed up the turbine to overspeed. 

In order to prevent this from happening to the turbine, modern turbines are equipped with a set of resistors that can connect to the generator and become a temporary load, until the situation is corrected, or the turbine has slowed down. 

These resistors, called crowbars, are not normally connected, but in the case when such a fault occurs they kick in and connect to generator stator. As a result of taking a large load from the generator, these resistors become hot and their heat must be taken from them as fast as possible. For this reason, they are placed outside of the nacelle where they can be cooled by fresh air.

Control Systems

As we have learned so far, many variables must be controlled in a wind turbine, such as blade pitch angle and nacelle yaw angle. Also, on the electrical side, there are voltage, current, frequency, and other variables that must be controlled to a desired value. Here, we elaborate on how an entity, in general, is controlled. The discussion here applies to any variable that needs to be controlled. But for sake of clarity, we may use the terms for blade pitch control, when necessary.

Suppose that the value of pitch angle for blades at a certain time during the operation of a turbine must be 35°. This value is from a reference point for measurement of blade angle that one may physically count 35°. Moreover, this value is not fixed, since a minute later, it could be altered to, say, 38°. But, for any given instant the figure defines the desired value.

A control action is normally taken in a control loop. In order for better control, feedback control is used and the value to be controlled is continuously checked and compared to the desired value, and corrections are made. In the control loop the desired value is the set point.

An action is taken on the difference between the actual value (that is, the measured value) and the set point. This difference is called error.

The action to be taken based upon the error is performed by the actuator. For a pitch control system, the actuator is an electric motor or a hydraulic piston that turns the blade. The command to the actuator for how much must it rotate the blade can be found by a control law. 

There are various control laws; but the most common and traditional ones are proportional control and PID control (PID stands for proportional, integral, and derivative). Each element in a PID control has a different role.

Proportional control introduces an action proportional to the value of the error. Its role is for stabilization of a system. The integral action is intended to take care of a drift in the controlled value. 

This drift is called offset or steady-state error. If not taken care of, by integral control, the value reached can be slightly different from the desired value. Derivative control has the effect of looking forward and predicting what can be expected to happen, and adding the necessary action.

WIND TURBINE BLADE CONSTRUCTION BASIC INFORMATION AND TUTORIALS

Blade construction of wind turbine defined.

Wind turbine blades are hollow; otherwise their weight would be tremendous, even with a lightweight material, and their use would be impossible. They might not even start to move the rotor. 

It is, however, necessary that they have a sturdy structure to withstand all the stress from various loads, and work for the useful life of a turbine.

The blades of a turbine spinning at 14 rpm must go through 175 million cycles in 25 years. Blade shells are made from composite material that is light and strong.

Inside, they must have structural support for the shell. The internal structure can be made from wood or a similar lightweight material. 

The shape of blades, their construction, and the other related subjects are to be determined based on careful and extensive studies, and experiments if needed.

One of the important issues in new blades is the integration of a lightning rod in the blade structure. The lightning rod is a strip of copper along the blade.

At some point at the tip of a blade it is exposed to the outside by a small disk. At the other end, it is connected to a metallic counterpart in the hub. Through a number of metal connectors, the strip in the blade ultimately makes a connection to the ground through the tower.

If a blade becomes damaged in operation, it must be repaired. Normally the broken parts must be cut, replaced by pieces of the same size, and glued together by the proper material. Depending on the severity of damage, this can be done while the blade is in the air, or it may have to be brought down to the ground. 

Any repair work on the blades is a costly job and involves loss of production.

WIND TURBINE FAULT CONTROL BASIC INFORMATION AND TUTORIALS

Monitoring and Preventing Faults of the Wind Turbine



One of the roles of a monitoring and control system in a turbine is that if some fault is detected, the proper action is taken. A fault can be any malfunctioning of a component, including damage and breakage; high or low operating temperature or pressure; or a value outside of the allowed tolerances for a mechanical or electrical parameter such as speed, voltage, current, and the like.

Depending on how serious the fault is, a turbine must be shut down if the fault cannot be corrected. If a turbine has to be shut down, a process of shutting down the turbine must be followed. Some faults may lead to a temporary action that must be checked a number of times to see if it persists.

The number of faults that can occur is large and it is not practical to list them, since faults can be diff erent from one machine to another. Some of the more important mechanical faults that can happen are mentioned here:

a. Excessive vibration in various parts of the turbine; this can be in any of the main bearings, in the nacelle, in the tower, and in the gearbox.

b. High temperatures of various fl uids in the gearbox, bearings, oil cooling system, or any other hydraulic system.

c. Low level or low pressure of various liquids in various parts of the system.

Also, some faults are not detectable by a turbine controller, unless redundant systems are used. Redundant means that one parameter or variable is measured by two devices, so that if one fails the other shows a (different) value. For instance, suppose that the anemometer malfunctions or freezes in a freezing rain.

The reading from the anemometer then shows a zero speed for wind, whereas there is wind. In such a case, the controller interprets this as lack of wind and, thus, the turbine is put into halt and with the brakes on. This is a typical scenario that calls for a technician to act.

One of the major faults that can happen in a wind turbine and can lead to disastrous results is when a turbine speed increases beyond the allowed limit. This is called overspeed. When a turbine rotates, there are dynamic forces that act on blades and all the other related mechanical components.

The magnitude of these forces depends on the speed of rotation. If the speed goes up, the magnitudes of these forces increase as well, and can go beyond the values for which the components are designed. If this happens, these components can break. And if one component in a mechanical system breaks and the cause is still present, this can lead to other component failure and serious damage.

In particular, if the speed of a wind turbine increases beyond its designed value, the blades can fl y away and the whole turbine can fall apart in a short time. If during the normal operation of a wind turbine, the load is suddenly taken off the turbine, this can lead to overspeed.

This can happen if the generator is disconnected from the grid, for instance, in the case of lightning tripping the overhead breakers and disconnecting the circuit. Even if the turbine controller starts shutting down the turbine in such a condition, the momentum in the rotor, as a result of its existing speed, can speed up the turbine to overspeed.

In order to prevent this from happening to the turbine, modern turbines are equipped with a set of resistors that can connect to the generator and become a temporary load, until the situation is corrected, or the turbine has slowed down.

These resistors, called crowbars, are not normally connected, but in the case when such a fault occurs they kick in and connect to generator stator. As a result of taking a large load from the generator, these resistors become hot and their heat must be taken from them as fast as possible. For this reason, they are placed outside of the nacelle where they can be cooled by fresh air.

WIND TURBINE OPERATING POWER CURVE BASIC INFORMATION AND TUTORIALS

What is the operating power curve of wind turbine?

The power curve of a turbine is built by connecting the maximum points of individual characteristic curves at various blade pitch angles, taking into account the maximum capacity of the turbine generator.

A curve specific to a wind turbine that determines the output power versus the wind speed. This curve is used by the wind turbine controller during operation to adjust the blade pitch.

Illustrates a typical characteristic curve of wind turbines based on which a turbine is to adjust its parameters and set points for the operation at various wind speed conditions. It is interesting to understand how this curve has been generated.

The performance (power coefficient and power capture) of a turbine changes with the tip speed ratio and that for a specific rpm of a turbine the tip speed ratio depends on the wind speed. On the other hand, we would like a turbine to always work, as much as possible, with maximum power coefficient, that is, around the peak of its characteristic curve at each wind speed.

If the maximum points of the characteristic curves for each wind speed are connected together, the resulting curve shows the desired points of operation of a turbine at various speeds. This curve, when blended with a cap for the maximum capacity of the turbine generator, defines a curve based on which a turbine is scheduled and controlled. That is the curve introduced in figure 10.3; it is referred to as a wind turbine power curve.

WIND MACHINE BUYING GUIDE - WIND MACHINE BASICS

What to Look for When Buying a Wind Machine?

While there are many turbines on the market, careful load and site analysis will narrow the field considerably. Once you have determined your average monthly electrical load and the average wind speed on your site, you can select a wind turbine  that will produce enough electricity to meet your demands.

Manufacturers provide a plethora of technical data on their wind machines that can be used to make comparisons. Unfortunately, most of it is useless. Further complicating matters,

“There can be a big difference in reliability, ruggedness, and life expectancy from one brand to the next,” according to Mike Bergey, president of Bergey Windpower.

So how do you go about selecting a wind machine?
Although wind turbines can be compared using many criteria, there are only a
handful that really matter: (1) swept area, (2) durability, (3) annual energy output,
(4) governing mechanism, (5) shut-down mechanism, and (6) sound.

Swept Area 
Swept area is the area of the circle described by the spinning blades of a turbine. Because the blades of a wind turbine convert wind energy into electrical energy, the swept area is the collector area of the turbine. The greater the swept area, the greater the collector area.

The bigger the swept area, the more energy you’ll be able to capture from the wind. To get the most out of a wind turbine — to produce the most electricity at the lowest cost — select a wind turbine with the greatest swept area.

Swept area allows for easy comparison of different models. Swept area is determined by rotor diameter. The rotor diameter is the distance from one side of the circle created by the spinning blades to a point on the opposite side or about twice the length of the blades.

When comparing wind turbines, then, the rotor diameter is a pretty good measure of how much electricity a turbine will generate. Although other features such as the efficiency of the generator and the design of the blades influence energy production, for most turbines they pale in comparison to the influence of rotor diameter and, hence, swept area.

Manufacturers list the rotor diameter in feet or meters — often both. The greater the blade length, the greater the rotor diameter and the greater the swept area. Most manufacturers also list the swept area of the rotor. Swept area is presented in square feet or square meters — sometimes both.

Annual Energy Output 
 Another, even more useful, measure is the annual energy output (AEO) or annual energy production (AEP) at various wind speeds. The AEO of a given wind turbine is presented as kilowatt-hours of electricity produced at various average wind speeds.

Like the US EPA’s estimated gas mileage for vehicles, AEO gives buyers a convenient way to compare models. As in the estimated gas mileage rating, however, AEOs won’t tell you exactly how much electricity a wind machine will produce  at a site. Performance varies depending on a number of factors such as turbulence and the density of the air.

Durability: Tower Top Weight 
Another extremely important criterion is durability. The most important measure of durability is tower top weight — how much a wind turbine weighs.

Four turbines that produce about the same amount of electricity are for example, the Proven WT2500 (419 pounds), the ARE110 (315 pounds), the Skystream 3.7 (170 pounds) and the Whisper 500 (155 pounds). The weight differences are in some cases substantial.

In our experience, heavyweight wind turbines tend to survive the longest sometimes many years longer than medium or lightweight turbines. Weight is usually reflected in the price. Remember, however, that you get what you pay for.

Producing electricity on a precarious perch 80 to 165 feet above the ground isn’t a job you want to relegate to the lowest bidder, which is invariably the lightest turbine.

Balance of System Cost 
Before you buy a machine, consider the total system cost. You’ll need to purchase a tower and pay for installation, unless, of course, you install the tower yourself. Even then, you’ll need to pay for concrete, rebar and equipment to excavate the foundation and anchors.

You’ll also need to run electrical wire from the turbine to the house and purchase an inverter (although they’re included in most batteryless grid-tie wind turbines). If you’re going off-grid or want battery backup for your gridconnected system, you’ll also need to buy batteries.

All of this will add to the cost. The cost of the turbine itself may range from 10 to 40 percent of the total system cost. Governing Systems

Found in all wind generators worth buying, governing, or overspeed control, systems are designed to prevent a wind generator from burning out or breaking apart in high winds. They do this by slowing down the rotor when the wind reaches a certain speed, known as the governing wind speed. Why is this necessary?

As wind speed increases, the rotor of a wind turbine spins more rapidly. The increase in the revolutions per minute (rpm) increases electrical output. Although electrical output is a desirable goal, if it exceeds the machine’s rated output, the generator could overheat and burn out.

In addition, centrifugal forces in high wind speeds exert incredible forces on wind turbines that can tear them apart if the rotor speed is not governed.

A governing system is essential because it allows the turbine to shed extra energy when the winds are really strong. Not all wind turbines come with governing mechanisms, however. Many of the smallest wind turbines, the micro-turbines, with rated outputs of around 400 watts, for example, have no governing mechanisms.

(These turbines are too small to produce a significant amount of electricity for most applications.) Larger wind turbines, those with swept areas over 38 square feet, however, come with overspeed controls. Two types are commonly found: furling and blade pitch.

WIND TURBINE AERODYNAMIC BLADES BASIC INFORMATION AND TUTORIALS

Aerodynamic Blade Wind Turbines

Each blade of a turbine is subject to aerodynamic forces from the wind. The airstream has a relatively fixed direction for the area swept by the blades, at an instant, but since blades are twisted the relative direction of wind with respect to a blade is not the same for various segments of the blade. 

Moreover, whereas the windstream has a constant speed (for a short period under consideration), the speed of air as a result of the blade rotation is smaller for the segments of the blade closer to the hub than the segments closer to the tip of the blade.

Consequently, the relative motion of air with respect to the blade as a result of wind and blade motion varies along the length of a blade. The resulting aerodynamic force, thus, varies in both magnitude and direction along the blade span. The typical force for a segment is shown in figure below (a blade can be assumed to be made of any arbitrary number of segments).

The force on each blade segment consists of two components: one component along the direction of wind (the drag force, almost in the horizontal direction) and one perpendicular to wind (the lift component, in a near vertical plane). These forces are depicted for a two-blade turbine in figure below.

A two blade-turbine is more appropriate to demonstrate the fact that all the components along the wind direction have the same force direction in the two blades, whereas the forces normal to the wind have opposite directions in the two blades, since the blades are symmetric to each other. 

The forces shown correspond to when the blade is feathered and does not catch much energy (the lift components are smaller than the drag components). This is just for the sake of clarity of the figure. This implies, also, the fact that the horizontal force on the blades is greater when a turbine is parked than when it is working.

It is easy to verify that the resultant of the two sets of forces is a push on both blades in the wind direction and a torque about the turbine shaft axis. In other words, all those force components along the wind direction contribute to a backward push on the blades, and do not generate any rotational motion.

However, those force components that are in the opposite direction in a (near) vertical plane are the only ones that generate a torque that makes the turbine rotate.

Note that the just mentioned aerodynamic forces are functions of wind speed, rotational speed, and pitch angle. Therefore, they are not the same for different operating conditions and for when the turbine is parked. 

A blade must be able to withstand these forces in the harshest condition; that is, when these forces are at their highest.

All the forces on a turbine must ultimately be transferred to the ground through the tower.

SAFETY ON WIND TURBINE OPERATION BASIC INFORMATION AND TUTORIALS

WIND TURBINE SAFETY OPERATION
How to stay safe in operating wind turbines?

• When working on wind turbines, technicians and workers are subject to a number of hazards. These hazards are mainly due to the height, the confined environment, the electrical equipment, and the possibility of turbine motion.

• Falling from a height is the most serious hazard. The number of workrelated fatal occupational injuries in 2008 in the United States due to falls from height was 700.

• Human error or lack of knowledge and ignoring safety rules are among the other causes of accidents.

• It is necessary that technicians learn about safety rules and follow them carefully. Training for safety and rescue is provided to workers by employers.

• It is the responsibility of an employer to provide a safe environment for the workers. Because of the hazardous nature of work on wind turbines, moreover, it is a worker’s responsibility to care for his or her safety as well as the safety of other workers.

• Safety regulations are set and monitored by authorities in each country. In the United States, these regulations are set by the Occupational Safety and Health Administration (OSHA).

• A mindset for a good technician is that “safety is rule number 1, always.”

• For any job that involves hazards, personal protection equipment (PPE) is to be used in order to reduce the risk of having accidents. PPE is not the same for all jobs and depends on the nature of a hazard(s) involved in a job and the work environment.

• For working on wind turbines, PPE comprises climbing gear, a hard hat, and fall arrest equipment. In the simplest version, climbing gear includes a harness to wear, a cable grip, and a locking carabiner. The fall arrest gear is a lanyard with which a worker can hook himself or herself to a secure point during work.

• Long-sleeve shirts and pants, with no jewelry or unnecessary items on the body (or in the pockets) are part of the proper clothing that a wind turbine worker must bear in mind. A pair of gloves is often very useful when climbing a ladder.

• PPE must always be checked before each use to make sure it is in perfect order. A periodic professional inspection, for instance, a yearly inspection, may also become necessary, depending on the frequency of usage.

• A good safe action is to respect tagout and lockout practice at work. Tagout implies putting a note on a device or equipment, notifying others about a hazard or danger. Lockout implies that equipment or a device, or a place containing such a device, be physically locked to prevent it from being accessed.

• In addition to training for safety, a technician working on wind turbines receives training for self-rescue in case it becomes necessary to escape from a turbine without using the ladder inside the tower.

• It is also essential that a worker learns how to rescue a colleague who might get involved in an accident. A fi rst rule to follow is that one must never put his or her safety at risk in such a rescue mission.

NACELLE OF WIND TURBINES BASIC INFORMATION AND TUTORIALS

What is a nacelle?

The rotating part of a turbine is the rotor (the blades and the hub). Th e intermediate part between the rotor and the tower is the nacelle.

The nacelle does not rotate with the rotor, but it must rotate with respect to the tower. This rotating motion, called yaw, is necessary for directing the turbine to the wind stream, as the direction of wind is not fixed. This motion is provided by the yaw system, which comprises a number of yaw motors and a yaw gear.

The output shaft from the rotating rotor goes inside the nacelle. The shaft transfers the mechanical energy to a generator, to be converted to electrical energy.

In most of today’s turbines this transfer is not direct and there is a gearbox between the main shaft (rotor output) and the high-speed shaft (the generator input). Thus, various equipment are housed inside the nacelle.

Figure below shows the inside of a generic nacelle, indicating the main shaft , the gearbox, the generator, and other components. An overhead crane, also shown, makes lifting and displacement of heavy objects easier during maintenance works.

The nacelle is a compartment not fixed to the tower and not fixed to the hub. “Not fixed” here implies that there are bearings between the two that allow them to move with respect to each other; that is, the assembly of hub and blades rotate with respect to the nacelle, and the nacelle rotates about the tower axis.

The nacelle serves the following purposes:

1. Houses the gearbox, generator, coolers for the gearbox oil, heaters for winter time, turbine brake system, motors and gear for yaw system, the wind direction and speed measurement systems, the transformer for turbine energy supply, and other equipment based on the turbine design.

2. Allows yawing of the turbine; that is, adjusting the turbine orientation to the wind direction.

3. Provides counterweight for the hub and blades’ weight.

WIND TURBINE CLASSIFICATIONS BASIC INFORMATION AND TUTORIALS

What's the difference between HAWT and VAWT?

When air flows around an object, two forces act on the object, drag and lift . Accordingly, we have turbines that work based on either of these forces. Th us, in general, we have lift -based (or lift -type) turbines and drag-based (or drag-type) turbines.

Th is categorization is based on the type of active force that makes the turbines turn. Turbines can also be classifi ed based on their axis, whether it is horizontal or vertical. Axis here refers to their main shaft about which the rotating parts revolve.

Certain turbine types can work only with a horizontal axis, while others can work with a horizontal axis or a vertical axis, and even they can be installed with their axis at an angle. In this sense, a wind turbine can be classifi ed as a horizontal-axis wind turbine (HAWT) or a vertical-axis wind turbine (VAWT).

Even without more details about any particular turbine, one can see a major diff erence between a horizontal-axis wind turbine and a vertical-axis wind turbine. Since in most cases wind blows horizontally, a wind turbine whose axis is horizontal (HAWT) is sensitive to the direction of wind.

Th is is not true for a turbine with vertical axis (VAWT), because no matter what the direction of wind, such a turbine can catch the wind.

Another advantage of a vertical-axis turbine is the fact that all the other equipment such as generator and gearbox do not need to be on the top of the tower, as is usually the case for a HAWT. So, they are easier to access when necessary.

Tip: A horizontal-axis wind turbine is sensitive to wind direction.

BELTZ LIMIT - WIND TURBINE ENERGY ABSORPTION

Any moving object has energy. This type of energy is called kinetic energy. For example, a car, a bicycle, or a ball, when moving, all have kinetic energy. If they stop, that energy is gone. The same is true for moving air, that is, the wind.

The amount of energy of a moving object depends on two factors, its mass and its speed. Using the proper units for measuring mass and speed, the relationship to determine the energy of a moving object is as follows:

Energy ½ (mass)(speed)2.

This equation implies that, for example, if mass is doubled (that is, if you have two objects the mass of one of which is two times the mass of the other, boTh having the same speed), the energy doubles.

But, if the speed is doubled (if you have two objects of the same mass, but one has a speed two times that of the other), then the energy is four times more. It is very important to understand the relationship given by an equation similar to that in.

This energy can be converted to work. In other words, it can be used to do work (see the text on energy and power in this chapter for the technical meaning of work).

As was mentioned earlier, for wind or any other moving fl uid it is more practical to fi nd the power rather than the energy. In this sense, in equation we can substitute for the mass of the air that fl ows in 1 sec, and that gives the power in the wind.

Note that
Mass (Density)(Volume) (2.2)

The power in a tunnel of wind is proportional to the air density, the cross-sectional area of the tunnel of wind, and the cubic power of the wind speed.

The cross-sectional area in this equation refers to the size of a turbine.

The following conclusions can be derived from equation:
1. For the same turbine and at the same time, if the wind speed doubles, the power in the wind increases by a factor of 8.

2. For the same turbine and the same wind speed, if the weather is cold (higher density), more power exists in the wind available for the turbine.

3. In the same weather conditions and for the same wind speed, a turbine that is two times larger in cross sectional area than a smaller one has twice as much wind power available to it.

From item 2 above it can also be concluded that a turbine at a given wind speed can produce more power in the winter than in the summer because the weather is colder. The same conclusion can be extended from day to night if the temperature diff erence is signifi cant. This diff erence due to temperature change is, nevertheless, not very much.

Power absorption by a turbine
In the previous section the available power in a stream of wind was defined in terms of the wind speed, turbine size, and the air density. This power, however, is the power that exists in the wind when it is blowing.

A turbine cannot necessarily capture all of this power; it can only absorb a portion of it. This depends on the type of turbine, the efficiency, and other conditions in the operation of a turbine.

In order to show the fraction of power in the wind that a particular wind turbine can harness from wind (i.e., wind harnessing), a coeffi cient is used in equation (2.4). Thus, we can say that

Power of a wind turbine (A coeffi cient)(Power in the wind) This coeffi cient must, obviously, be smaller than 1. It is called power coeffi cient.

Wind turbine power ½ (Power coeffi cient)(Density)(Cross–sectional area)(Speed)3 .The power coeffi cient depends on how good a turbine is in design and how well it can grasp the wind energy.

Thus, its value can be small or large. Nevertheless, there is a maximum value that no turbine in its best performance can exceed. It can be theoretically determined and is called the Betz limit. The value for Betz limit is =16/27 = 0.59.

Betz limit = 16/27 = 0.59 The power coeffi cients for certain turbines can reach values near the Betz limit. A value of 0.50 for a good design is acceptable. For others, this number can be smaller, say 0.25 or even 0.20. Any claim for coeffi cients greater than the Betz limit are groundless and can be rejected.