Understanding wind energy

7 / 1 0 / 2 0 1 2

Uma Venkat Karanam

37204140

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Understanding Wind Energy.

Independent study(MAE 501).

Author: Uma Venkat Karanam

Instructor: Prof. Gary F Gardush.

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Table of Contents 1. Why wind energy? ................................................................................................................................ 4

1. Dutch windmills ................................................................................................................................ 4

2. Savonius rotors ................................................................................................................................. 4

3. Darrieus rotor .................................................................................................................................... 4

4. Modern wind turbines ...................................................................................................................... 5

5. Shrouded rotors ................................................................................................................................ 5

2. Introduction to Betz limit ...................................................................................................................... 9

3. Thrust principle vs. the lift principle. .................................................................................................. 11

4. Introduction to lift principle. ............................................................................................................... 13

Force diagram. ........................................................................................................................................ 13

5. The need to breakdown the blade into elements. ............................................................................. 14

6. Blade design ........................................................................................................................................ 14

7. Airfoil characteristics .......................................................................................................................... 15

8. Some wind turbine terminology ......................................................................................................... 17

1) Tip speed ratio (TSR) ....................................................................................................................... 17

2) Power coefficient ( ) .................................................................................................................... 17

3) Angle of attack ................................................................................................................................ 17

9. Taper and twist ................................................................................................................................... 17

1) Taper of the blade ....................................................................................................................... 17

2) Included twist .............................................................................................................................. 18

10. A word about the Darrieus rotor .................................................................................................... 19

Darrieus rotor vs. Modern WT. ............................................................................................................... 20

Water pumping and wind turbines ......................................................................................................... 20

11. A summary of working equations (from the force diagram). ......................................................... 22

12. A sample calculation ....................................................................................................................... 23

13. Aerodynamic Efficiency ................................................................................................................... 25

14. Rotor design. ................................................................................................................................... 26

How big should a WT be? ....................................................................................................................... 26

How many blades should a WT have? .................................................................................................... 27

How small should the solidity be? .......................................................................................................... 27

Chord distribution ................................................................................................................................... 27

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15. Tower design. .................................................................................................................................. 27

16. Power speed characteristics and Torque speed characteristics. ................................................... 28

17. Controlling and operating the wind turbine. .................................................................................. 31

So how can we control the WT ? ............................................................................................................ 32

1) Pitch control ................................................................................................................................ 32

2) Stall .............................................................................................................................................. 32

How do we control the pitch angle? ....................................................................................................... 33

How is a WT stopped? ............................................................................................................................ 33

18. Site selection and analysis. ............................................................................................................. 33

19. Anemometers ................................................................................................................................. 33

1. Robinson Cup Anemometer ........................................................................................................ 33

2. Pressure tube Anemometer ........................................................................................................ 34

3. Hot wire Anemometer ................................................................................................................ 34

20. Probability density distribution....................................................................................................... 37

21. Energy (power)distribution curve. .................................................................................................. 39

Rayleigh distribution function ................................................................................................................. 39

Weibull distribution ................................................................................................................................ 40

22. Electrical conversion of the mechanical power. ............................................................................. 45

23. Stability of the induction generator ................................................................................................ 51

24. Conclusion ....................................................................................................................................... 52

25. Personal note .................................................................................................................................. 52

26. Bibliography .................................................................................................................................... 53

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1. Why wind energy? The force of the wind can be very strong, as can be seen after the passage of a hurricane or a typhoon. Historically, people have harnessed this force peacefully, its most important usage probably being the propulsion of ships using sails before the invention of the steam engine and the internal combustion engine. Wind has also been used in windmills to grind grain or to pump water for irrigation or, as in The Netherlands, to prevent the ocean from flooding low-lying land. At the beginning of the twentieth century, electricity came into use and windmills gradually became wind turbines as the rotor was connected to an electric generator. The first electrical grids consisted of low-voltage DC cables with high losses. Electricity therefore had to be generated close to the site of use. On farms, small wind turbines were ideal for this purpose. Gradually, however, diesel engines and steam turbines took over the production of electricity and only during the two world wars, when the supply of fuel was scarce, did wind power flourish again. Wind is the most exploitable form of energy of the renewable sources of energy. Has been a popular choice since renaissance but became obsolete with advent of steam engine and cheap fuel prices. There are different types of windmills today. Some of the basic ones are:

1. Dutch windmills: Are high torque, low speed machines. And intended for water pumping and grain grinding purposes. These are mainly installed on farms as shown in fig 1. These windmills can be constructed on the site and are fairly straight forward in construction and are low maintenance.

2. Savonius rotors: These windmills are mainly used for water pumping. These are based on thrust principle as against lift principle. Two configurations of Savonius rotors are available. These can be constructed on site and is one of the popular DIY projects all over the world for green energy enthusiasts. The Savonius turbine is one of the simplest turbines. It consists of two or three scoops. Looking down on the rotor from above, a two-scoop machine would look like an "S" shape in cross section. Because of the curvature, the scoops experience less drag when moving against the wind than when moving with the wind. The differential drag causes the Savonius turbine to spin. Because they are drag-type devices, Savonius turbines extract much less of the wind's power than other similarly-sized lift-type turbines. Much of the swept area of a Savonius rotor may be near the ground, if it has a small mount without an extended post, making the overall energy extraction less effective due to the lower wind speeds found at lower heights. Refer to fig 3.

3. Darrieus rotor: Is a VAWT class wind turbine. They are based on a very interesting troposkein geometry. It is a little complicated to construct but has a high value for shore based sites. Troposkein is a shape that a flexible string will take when rotated around its axis. Owing to this geometry the only forces induced in the WT operation are the tensile forces in the ends and no additional stresses are induced. This geometry has minimal chances for blade failure as will be discussed later when discussing the force diagram. In this configuration, the Darrieus design is theoretically less expensive than a conventional type, as most of the stress is in the blades which torque against the

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generator located at the bottom of the turbine. The only forces that need to be balanced out vertically are the compression load due to the blades flexing outward (thus attempting to "squeeze" the tower), and the wind force trying to blow the whole turbine over, half of which is transmitted to the bottom and the other half of which can easily be offset with guy wires as shown in fig 4. By contrast, a conventional design has all of the force of the wind attempting to push the tower over at the top, where the main bearing is located. Additionally, one cannot easily use guy wires to offset this load, because the propeller spins both above and below the top of the tower. Thus the conventional design requires a strong tower that grows dramatically with the size of the propeller. Modern designs can compensate most tower loads of that variable speed and variable pitch.

4. Modern wind turbines: Are based on the lift principle as against the thrust principle. These are typically low torque, high speed machines. These are extremely expensive to build and require careful design considerations. Their capacities range from 1MW to 7MW.

5. Shrouded rotors: A wind lens is a modification made to a wind turbine, as shown in fig 5,6,7, to make it a more efficient way to capture wind energy. The modification is a ring structure called a "brim" or "wind lens" which surrounds the blades, diverting air away from the exhaust outflow behind the blades. The turbulence created as a result of the new configuration creates a low pressure zone behind the turbine, causing greater wind to pass through the turbine, and this, in turn, increases blade rotation and energy output.

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Figure1. Dutch windmill

Figure 3. Savonius Rotor

Figure 2. Darrieus Rotor

Figure 4. Modern wind turbine

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Figure 5. Shrouded Rotor

Figure 6. Shrouded rotor

Figure 7. Shrouded rotor

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Wind is a low quality energy in its free flowing form. And wind turbines extract this and convert it into a more condensed state. However, like all low to high energy conversions there is an upper limit to the energy extraction.

We begin our discussion with how much energy is available and how much can be extracted and how much do we actually extract? The basic premise here is that the wind energy available for extraction is the energy contained in the air that flows through the virtual cylinder that contains the rotor as shown in fig 8,

So the power contained in the wind is :

Energy available at the rotor:

=

Where , = undisturbed wind speed, A= Area of the rotor, =density of the air 1.225 kg/ =velocity at the rotor.

Figure 8. Control volume of a WT rotor.

The implication here is that there is a cubical relationship between the power available and the wind velocity.

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This observation is very important and has a significant bearing on the design and selection of wind turbines. It can be seen that even the slightest of the changes in the wind speeds can result in a drastic change in the power output. Other concerns will be discussed later in the subsequent sections.

2. Introduction to Betz limit

Applying Bernoulli’s principle between sections A and B we have:

And between sections B and C,

Using equations 3 and 4 we get:

Thrust is defined as:

From equation 5 we have:

(

)

Thrust is also given by the change of momentum as:

Since equations 7 and 8 describe thrust they both should be equal. This gives us:

Introduction to axial interference factor. So at what wind speed does the maximum extraction of power occur? This is influenced by a factor called the axial interference factor. It is defined as :

{

Using equation 9 in 10 we get:

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Power extracted = drop in kinetic energy.

=

(

)

Using equations 10 and 11 we get:

To get the maximum extraction point we differentiate equation 13 and get:

3

Which gives us a=1,1/3. Now a=1 is not possible, hence, a=1/3.

This gives us

That is the maximum extraction happens when the blade sees the wind at two-thirds the undisturbed site wind velocity. So when we use this result in the equation 1, we get:

(

)

The leftmost term in the equation represents the power extracted at the rotor from the wind, the middle term is the available wind power and the rightmost term represents the maximum fraction that can be extracted. This is referred to as the Betz limit.

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3. Thrust principle vs. the lift principle.

Figure 9. Control volume of a WT rotor

Where, is the coefficient of force.

Now, if the rotor was receding at a velocity then the force would be

So the power extracted, , would be

It follows, naturally, that if =0 or = => = 0.

And to find the maximum power extracted:

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[ ]

Introduce

[ ]

]

This leaves us with

Using this result in 17 we get:

(

)

for ideal momentum transfer.

Equation 20 is the basis for discarding the thrust principle in favour of the lift principle for low torque, high speed wind turbines intended for electricity production.

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4. Introduction to lift principle.

Figure 10. Aerodynamic forces on an airfoil section.

Force diagram.

The force diagram is the represntative diagram of the force vectors of the aerodynamic lift and drag arising in the WT operation. It is drawn perpendicular to the rotor plane. A parallelogram is drawn using the tip speed and the wind speed at the rotor to get the relative wind speed as the blade sees it. This generates the lift whose drag component is aligned along the relative velocity and the lift component iperpendicular to the drag component. The lift component has a projection in the direction of the blade rotation and it is this component that is the prime mover for all modern WT’s. Force diagram also shows the direction of the generated thrust and the moment as shown. The angle between the relative wind velocity and the tip linear velocity is called the angle of incidence and is related to the angle of attack as shown in equation 27.The idea is to increase the lift component and decrease the drag. It will be discussed later as how the drag component is influenced by the amount of the blade surface wind sees. There is direct proportionality between drag and the amount of area seen by the wind. This is where the the angle of attack and pitch angle enter the picture. The area can be minimized by including a twist in the design and also allowing pitch control of the blade.

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Figure 11. Force diagram

Based on the force diagram for the blade (element):

]

5. The need to breakdown the blade into elements.

When analysing the blade behaviour we cannot calculate the loads along the entire length of the blade. As is evident from the equation 23, the moment produced along the length of the blade as do the forces since the andle of inclination changes along the blade as well.Angle of inclination changes with the change of the linear velocity as we move along the blade as has been mentioned earlier. Due to these reasons, we take one element, fig 10, and draw the force diagram for it and repeat the process for each element.

6. Blade design:

How is a blade designed? Blade design is a complicated affair and out of scope this project. However, for those interested an introduction to propeller theory and a little structural design is recommended. We will only discuss the requirements of blade design briefly in this report. The blade of a WT is an extruded airfoil with an inbuilt twist and taper. The fuctionality of the taper and twist is to offset and balance out the induced moments and bending stresses over the span of the blade. We can take an airfoil and run simulations and introduce twist and taper as

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per the results and requirements. Alternatively, some designers also experiment with different airfoils for different sections(root, mid section and tip) of the blade. The NREL and NACA websites have a comprehensive catalogue of different airfoils that have been tested in the wind tunnels and have been compiled. Based on experimental data tested in wind tunnels through which the and are calculated. and are dependent on the shape of the blade roughness and geometry.

Figure 10. Blade elements

7. Airfoil characteristics

Airfoil characteristics are basically a compilation of the experimental data collected in wind tunnels. The data is about the generated coefficients of lift and and drag at each angle of attack. This is given in table format,table 1, and also in a graphical format as shown in figs

11,12,13 . The graphical format is a plot of

and is preferred owing to the ease of

use.These charateristics are specific to the particular airfoils.

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Figure 11. Coefficient of lift.

Figure 12 Coefficient of drag.

Figure 13. Combined airfoil characteristics.The graphical format.

Table 1. Tabular format for airfoil characteristics

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8. Some wind turbine terminology:

1) Tip speed ratio (TSR): Tip speed ratio is the tip velocity to the speed of the undisturbed air.

The typical TSR for water pumping WTs range from 1.5 to 2 whereas the typical TSR for electricity production WTs range from 6 to 9.

2) Power coefficient ( ): It is defined as the output power(mechanical) to the power

contained in the wind.

Maximum occurs at a specific TSR and hence TSR must be controlled at a constant

value or within a design range. It is obvious that wind speed fluctuates constantly and this needs the term to be varied correspondingly. That is the rotational speed of the WT has to be controlled (manually) at all times. This can be done by changing the pitch angle as shown in fig.

3) Angle of attack: It is angled at an angle called the pitch angle. Angle of attack , incident angle and pitch angle are related as :

It is obviously imperative that the angle of attack ( ) must be kept constant to maintain the optimum tip speed ratio(TSR). And this makes for an important consideration in the design of the blade. It has already been demosntrated in section how the angle of incidence ( ) changes along the length of the blade which highlights the importance included twist in the design and the pitch angle.

9. Taper and twist

From equation 24 it can be seen that the moment changes as we proceed along the blade length. The tip experiences greater moment than the root and flies faster than the root. Consequentially, there’s a shear force that tries to break the blade and is one the reasons for blade failure. Similarly, there is also a gradient in the experienced thrust force. This leads to a bending moment which can cause blade failure. This is addressed in two ways.

1) Taper of the blade: The taper of the blade controls the term in the in the and equations and thereby controls the amount of moment and the bending stresses produced at each section of the blade. Also, we want minimal drag which requires minimal exposure to the wind. So minimize the exposed to . This is also taken care by included twist.

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2) Included twist in the design: The pitch angle cannot be the same throughout the blade as can be seen from the force diagram. The ‘ ’ term changes leading to a continuous change in the angle of incidence along the blade and thus the pitch angle has to be varied correspondingly to maintain the angle of attack within the design range.

Figure 13. Taper in WT blade.

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10. A word about the Darrieus rotor

Figure 14. Force diagram of a Darrieus rotor.

Figure 14 represents the force diagram of the darrieus rotor at various blades at any given time of the operation. As we can see from the force diagram, there is a component of the lift force in moving direction,at all times, which rotates the rotor. Thus, the rotor experiences a positive torque at all positions of operations. And, as has been mentioned earlier this blade is safe from failure owing to induced stresses. Also, there is the inherent provision for stall should the wind speeds go beyond the operational range. However, if there is no that is the tip speed no rotation. Hence, the Darrieus rotor needs an external torque to start.

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Darrieus rotor vs. Modern WT.

How does the Darrieus rotor compare against the modern WT?

Darrieus rotor

Has access to relatively lower wind speeds in inland sites and therefore has lesser available energy.

More suitable for shore based sites which have access to higher wind speeds directly from the ocean.

Doesn’t have any induced stresses and therefore mitigates the chances of blade failure.

There is no specific design required for the tower design and everything is located at the base. Hence the chance of tower failure is also mitigated.

Maintenance is easy. Doesn’t need a continuous yaw or

pitch control since there are present inherently in the design.

There is lesser wastage of land due to spacing problem.

Can be erected on buildings. Typical sizes:

Modern WT

Has access to higher wind velocities,

therefore, higher available energy.

More suitable for inland sites.

High investments required in blade design ,

the tower design, assembly and

maintenance

Many causes of failure

Has induced stresses

Everything (generators and gearbox) in the

turbine is located in the nacelle and hence

the maintenance is very difficult.

Blade configuration and performance may

change due to accumulated dust and

corrosion of the blade surface.

Needs continuous yaw control and pitch

control.

There is huge wastage of land, per se, due to

spacing requirements.

Water pumping and wind turbines

These are low speed, high torque machines and have a large number of blades for the production of a large torque. An additional rim is mounted on the blades to add to the

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structural strength of the blades. The shaft runs through the tower. These WTs can be constructed on site with relatively ease and the yaw control can be included in design by means of a tail vane as shown in fig 16. Inherent safety mechanism, fig 15, is present for extreme winds. High speeds orient the vane in line with the wind direction whereas extreme winds will produce a large thrust and will disorient the WT. However, in HAWTs we need certain control mechanisms. For example, the rotor can only start after a certain velocity, cut-in velocity, is reached. The rotor can be run only up to a certain wind velocity until the rated power of the WT’s generator is reached and then it can be allowed to operate for a while until a speed after which the WT cannot be allowed to be operational absolutely else the WT blades and the generator will be destroyed.

Figure 15. Included safety mechanism in yaw control.

Figure 16. Yaw control mechanism

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Figure 17. WT characteristics

11. A summary of working equations (from the force diagram).

1)

2)

3) 4) 5) ] 6)

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12. A sample calculation

A sample calculation to illustrate what we have discussed.

A 3 blade wind turbine operating at 9 m/s with a rotor diameter of 9 m and a rotational speed of 100 rpm and a TSR of 5.23. The chord length is 0.45 m and the distance from the shaft to inner edge is 0.5 m. The pitch angle is 5 . The airfoil section is NACA 23018.

Figure 18. Blade elements

From the Betz theory we know,

= 6m/s. 0.45 N= 100 rpm = 1.66rps

For element 1

(

) (

) (

)

Similarly, for elements 2,3 and 4

(

) (

)

(

) (

)

(

) (

)

And we know from equation 25

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And the corresponding values for the coefficients of lift and drag are then read from the airfoil characteristic table.

Table 2. Calculated airfoil characteristics.

And from equations 23 and 24 we get:

]

]

Using:

In equation 28 ,we get:

]

This gives us:

watts watts watts watts

This is the power extracted by one blade. The total power extctracted by the wind turbine is then:

watts KW

Thrust force on tower:

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By each blade:

N N N N

Hence, the total thrust on the tower:

Comparing the power and thrust experienced by the innermost and the outermost elements we can see that the outer elements experience quite a large thrust and extract more power as compared to the innermost elements. This leads to a bending moment that can cause blade failure. Hence, the blades are tapered to even out the forces. However, it is not sufficient by itself to modulate the area and is coupled with twist and also reinforcing the structural strength of the blade.

13. Aerodynamic Efficiency

Aerodynamic efficiency is defined as the ratio of the mechiancal power extracted from the wind to the power contained in the

]

]

Divide N/D by :

]

]

,

=

To maximize the , we will need to minimize .

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Figure 19. Method 1

Figure 20. Method 2

We can do this in two methods. In method 1, we can plot vs and choose the point of tangency at which ‘ holds the minimum value. However, this is very difficult since & have

very close values. Alternatively, we can also plot

and choose the at which the ratio is

minimum.

14. Rotor design.

How big should a WT be?

To begin designing a WT , we will need an idea as to the size of the WT as a rough draft basis. General idea of the WT size can be calculated as:

Given the requirement of the power extraction, wind speeds, using equation 32 we can calculate an initial size of the WT rotor. The tower is generally about the same size as the rotor diameter or slightly larger.

Alternatively, we can also get an intial assessment as:

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How many blades should a WT have?

This is a general idea that we can have either 2 or 3 blade WT rotors but the reasoning lies in the concept of solidity. Solidity is defined as the ratio of the blade area to the swept area. Low speed, high torque WTs like water pumping ones require high solidity whereas high speed , low torque WTs like the modern ones have low solidity.

How small should the solidity be?

This is dependent on the fact that once the blade of a rotor sweeps through the space the air is disturbed and the ambient air is at a considerably lower speed than what the blades are designed to see. So, it becomes imperative that the ambient air regain the design speed before the next blade comes to the space. This limits the modern WTs to 3 blades for the ones that are exclusively used for electricity prodcution. Another advantage 3 bladed WTs have is that they feel a much more mitigated torque pulsation. Torque pulsation is the reduction in torque due to the disturbed air in front of the tower and regaining of it. These WTs also are more stable structurally as against 2 bladed ones.

Time taken by the disturbed wind to pass:

.

Time taken by the blade to move to the preceding blade’s position:

.

We ideally want .

Chord distribution:

Chord distribution directly ties with the taper and twist requirements of the WT blade.How we determine chord is directly related to the term which controls the drag force. The process of blade design begins with an apriori design with an assumed design as discussed earlier. Then, we determine the bending stress and design a taper for the highest operational wind velocity. The taper is also dictated by the strength of the blade. The twist is desgined as discussed earlier and additionally pitch control is also provided for in the mounting hub for the rotor.

15. Tower design.

The tower is generally the same size as the rotor or slightly bigger. It needs to be strong to withstand the stresses as shown in the example earlier and also has to contend with the naturally occuring frequencies form the gearbox, generator which have to be different from the tower’s natural frequency.

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Figure 21. Height vs. Rotor Diameter.

16. Power speed characteristics and Torque speed characteristics.

Power speed characteristics is the graph plotted between the coefficient of power versus TSR and mechanical power exctracted versus the rotational speed of the turbine as shown in fig 22. The cubical dependence of power on speed can be seen by the behaviour of the peaks at different wind speeds as is shown by the bold line.

And for a given wind velocity the power extracted in terms of TSR is:

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So at the optimum TSR, , power extracted :

And we see the relation :

Figure 22. Power speed characteristics.

And aerodynamic torque becomes:

So we see a relation :

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When the power is fed by the generator to the grid, the WT will experience a back torque due to loading. Back torque (loading) is given as:

Figure 23. Torque- speed characteristics

As shown in the fig the loading torque must equal the aerodynamic torque for optimum performance of the WT. In either case of the loading torque exceeding or falling short of the aerodynamic torque, the WT performs sub-optimally.

Equation 37 has an important bearing on the design of the WT as it shows the cubical dependency of the optimal power extraction on the rotational speed. This consequentially makes the torque produced squaredly dependent on the rotational speed of the rotor. This requires that the back torque fom the generator equal the aerodynamic torque for optimal performance. This requires a careful selection of the coefficient of back torque, for the generator. This is why along with the pitch angle, the characteristics of the generator also have to be controlled to maintain and optimal TSR.

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17. Controlling and operating the wind turbine.

The wind turbine operation can be understood better in the graphical format. These graphs are called the WT characteristics and form an important aspect when it comes to selecting a WT for a particular site. It will be discussed how coupling these characterstics with the site characteristics will give us the sense of the which WT will be ideal for a given site.

Figure 24. WT characteristics. The top curve shows the extended operational characteristic for some generators that can exceed the design rated power.

The WT characteristics are power output versus wind speed plots as shown in fig.The WT becomes operational only after the wind attains a threshold speed. This is called the cut in speed. The power extcracted then rises cubically as has been shown by equation 2. This goes on until the power extracted reaches the maximum capacity of the generator installed. This speed is called rated power speed. Certain generator configurations allow production of electricity for upto 40% of the rated power. After this point the WT can still be operated by certain methods by means of which the optimum TSR is maintained for the maximum power extraction until we

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reach speeds after which the WTs should not be operated as this will cause WT failure. This speed is called the cut out or furling velocity.

So how can we control the WT ?

1) The mechanical methods primarily deals with :

1) Pitch control: Turning the blades in the wrong direction to induce a stall as shown in fig 25.

2) Stall: In stall there are two methods. 1) Active stall: in which pitch angle is controlled in such a manner that there is no lift

produced and consequentually the WT stalls. 2) Passive stall: In this method the blade pitch angle is imbibed in the design such that

the Wt automatically stalls after the furling speed is reached.

2) The electrical method of controlling the WT deals with how the power is taken out of the system. That is done by altering the generator characteristics such that it applies a larger back torque and the WT is forced to work at sub-optimal TSR as was discussed while discussing torque-speed characteristics.

3) Yaw control: In this method we totally turn the WT to face a wrong direction such that no lift is produced. However, this method is not really preferred because it consumes a lot of power and causes a lot of noise.

Figure 25. Variable pitch control mechanism.

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How do we control the pitch angle?

One of the methods to monitor the pitch angle is to calculate the TSR by placing a sensor at the tip of the blade and make a comparision against the optimum TSR and have a mechanism to automatically regulate the WT.

Another method of controlling the pitch angle is to control of power taken out of the generator and thus use the feedback to control the pitch. Mathematically, it can be shown as:

∫

How is a WT stopped?

To completely stop the WT from operating. This is done by changing the pitch angle so much that no torque is created and the rotor stalls or mechanical brakes are used to stop the WT(elaborate further).

18. Site selection and analysis.

How do we know if the site is suitable for production of wind energy extraction? This is done by plotting the site characteristics. To do this various anemometers are deployed in the site to log wind speeds for the required durations and wind data is logged continuously in the systems as shown in fig 29. This data is further run through probability density distribution and other distribution functions to obtain a useful form of the site charactersitics which lets us understand how much power is available from the site throught out the year and then coupling this with various WT characteristics will give us an idea of the most suited WT for the site. It will become clear ,in a later section, that a WT that may be suit one site may not suit another site. This process of identifying the most suitable WT is very specific to the site.

19. Anemometers:

Anemometers are the devices that measure and log wind data. Three types of anemometers will be discussed here.

1. Robinson Cup Anemometer:

Robinson cup anemometer is essentially like a savonius rotor. A simple type of anemometer, it consists of four hemispherical cups each mounted on one end of four horizontal arms, which in turn were mounted at equal angles to each other on a vertical shaft. The air flow past the cups in any horizontal direction turned the cups in a manner that was proportional to the wind speed. Therefore, counting the turns of the cups over a set time period produced the average wind speed for a wide range of speeds. On an anemometer with four cups it is easy to see that since the cups are arranged

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symmetrically on the end of the arms, the wind always has the hollow of one cup presented to it and is blowing on the back of the cup on the opposite end of the cross. It relies on the thrust force and is used as an analog data logging device. Alternatively , it is also used as a digital device when coupled with a taco generator. The problem with this device is the presence of a back torque due to friction due to which low speed winds are not captured efficiently. Another factor is the inertia which reduces the sensitivity of the device to low speed winds.

2. Pressure tube Anemometer:

These devices are used in places where there is no electrical supply. consisted simply of a glass U tube containing a liquid manometer (pressure gauge), with one end bent in a horizontal direction to face the wind and the other vertical end remains parallel to the wind flow If the wind blows into the mouth of a tube it causes an increase of pressure on one side of the manometer. The wind over the open end of a vertical tube causes little change in pressure on the other side of the manometer. The resulting liquid change in the U tube is an indication of the wind speed. Small departures from the true direction of the wind causes large variations in the magnitude. Another kind of pressure tube anemometer uses the same pressure difference between the open mouth of a straight tube facing the wind and a ring of small holes in a vertical tube which is closed at the upper end. Both are mounted at the same height. The pressure differences on which the action depends are very small, and special means are required to register them. The recorder consists of a float in a sealed chamber partially filled with water. The pipe from the straight tube is connected to the top of the sealed chamber and the pipe from the small tubes is directed into the bottom inside the float. Since the pressure difference determines the vertical position of the float this is a measured of the wind speed. In the tube anemometer the pressure is measured, although the scale is usually graduated as a velocity scale. In cases where the density of the air is significantly different from the calibration value (as on a high mountain, or with an exceptionally low barometer) an allowance must be made This device also has issues with sensitivity to low wind speeds.

3. Hot wire Anemometer:

Hot wire anemometers use a very fine wire (on the order of several micrometers) electrically heated up to some temperature above the ambient. Air flowing past the wire has a cooling effect on the wire. As the electrical resistance of most metals is dependent upon the temperature of the metal (tungsten is a popular choice for hot-wires), a relationship can be obtained between the resistance of the wire and the flow speed. Several ways of implementing this exist, and hot-wire devices can be further classified as CCA (Constant-Current Anemometer), CVA (Constant-Voltage Anemometer) and CTA (Constant-Temperature Anemometer). The voltage output from these

35

anemometers is thus the result of some sort of circuit within the device trying to maintain the specific variable (current, voltage or temperature) constant. Additionally, PWM (pulse-width modulation) anemometers are also used, wherein the velocity is inferred by the time length of a repeating pulse of current that brings the wire up to a specified resistance and then stops until a threshold "floor" is reached, at which time the pulse is sent again. Hot-wire anemometers, while extremely delicate, have extremely high frequency-response and fine spatial resolution compared to other measurement methods, and as such are almost universally employed for the detailed study of turbulent flows, or any flow in which rapid velocity fluctuations are of interest. These devices can measure low speeds very accurately.

√

Most favoured is the robinson cup anemometer.

Figure 26. Robinson Cup Anemometer

36

Figure 27. Pressure Tube Anemometer

Figure 28. Hot Wire Anemometer

37

Calculation of the average wind speed, :

∫

∑

20. Probability density distribution.

Probability density distribution function can be derived from the data logged by the anemometers as wind speed distribution function to give us a number of hours per annum versus wind speed plot to give us a picture of how many hours of a particular wind speed can be expected over a year as shown in fig 29.

Figure 29. Original data logged by the anemometers at the wind site.

38

Figure 30. Factoring the logged data.

Figure 31. Probability density distribution. This plot gives the number of hours a partcular wind speed sustains over a year.

39

21. Energy (power)distribution curve.

This distribution can be built from the wind speed distribution and gives us the suitable rated power of the WT for the site.

Figure 32. Probability density distribution for energy. This plot gives the number of hours a partcular energy sustains over a year.

Rayleigh distribution function:

Rayleigh distribution is a continuous probability distribution. A Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. The Rayleigh distribution naturally arises when wind speed is analyzed into its orthogonal 2-dimensional vector components. Assuming that the magnitude of each component is uncorrelated and normally distributed with equal variance, then the overall wind speed (vector magnitude) will be characterized by a Rayleigh distribution. However, this method can be used only for the sites satisfying the Rayleigh distribution.

(

)

40

Figure 33. The probability density fucntion using Rayleigh distribution

Weibull distribution:

The Weibull distribution is a continuous probability distribution and is one of the most commonly used distributions in reliability. It is commonly used to model time to fail, time to repair and material strength. The shape parameter is what gives the Weibull distribution its flexibility. By changing the value of the shape parameter, the Weibull distribution can model a wide variety of data. The scale parameter determines the range of the distribution.

(

) (

)

[ (

)

]

Effects of and :

For weibull distribution behaves like the rayleigh distribution.

(

∫

)

41

(∑

)

Figure 34. The probability density fucntion using Weibull distribution

Equations 50 and 51 tell us how suitable a site is for extraction for wind energy, and equations 52 and 53 give us the power that can be extracted on an average from the site. is the site characteristics derived from Rayleigh and Weibull distributions from equations 48 and 49.

The graphical method:

This is the general preferred method for reasons that will become obvious when we see them. It is so much more convenient than taking up the statistical data described above. In this method we take the site characteristics and mark the regions corresponding to the cut-in speed , the rated speed and the cut-off speed to get an area as shown in fig 37. This area corresponds to the amount of power extractable from a wind site by a specific WT. These characteristics are specific to the WT being analyzed. The WT that gives the largest area for these plots is the one that’s best suited to that particular site. It becomes obvious that the WT that’s suitable for a site may not be suited to another site with different site characteristics and vice versa.

42

.

Figure35. WT characteristics

The final WT-Site characteristics follow the sequence of fig 35 - fig 36 - fig 37. It can be seen how the meaningless wind data measured by the anemometers can be run through suitable distribution functions to get a meaningful form to evaluate a site-WT combination.

43

Figure 36. Final form of site characteristics. This plot gives us the number of hours a given wind speed has been exceeded in a year.

Figure 37. Site-WT characteristics.

44

Figure 38. WT-site characteristics.

Area under ABCD, fig 38, is the case where the WT is run at the maximum rated power all through the year.

The WT can also be chosen based on the capacity factor. The WT that exhibits the best capacity factor is the most suitable one.

{

∫

∫ ∫

However, this is done by graphical methods which are again more convenient for the obvious reasons.

45

22. Electrical conversion of the mechanical power.

So far we have discussed the extraction of power into the mechanical domain from wind energy. What types of generators do we install to convert this to the electrical domain?

We can use three types of machines:

1) DC machines 2) Synchronous machines 3) Induction machines

DC machines are not very suitable for the WT setup being very cumbersome in design and accident prone. Unless there is a specific requirement DC machines are not favoured.

Synchronous machines are generally used as standalone systems which operate independently of the grid, like sites in remote locations or independent houses. These are the ones used in do-it-yourself projects.

Induction machines are farthest most suitable for WT farms connected to a grid. One of the important aspects of the machine is the suitability to variable speed constant frequency requirement of the grid. This is apparent since the WT almost always work under variable speed scenario, however, the supply to the grid must remain constant. Most favoured is the squirrel cage rotors which are very inexpensive and are rugged in design.

Figure 39. Induction motor

46

If the rotor in the squirrel cage machine is held fixed then it behaves like a transformer. So we can draw a circuit for a transformer and develop it for the induction machine. The circuit for the transformer is as shown in the fig 40.

Figure 40. Initial motor-transformer analogue circuit

In the circuit the leftmost part is the stator circuit and the right most part is the rotor circuit. The impedance on the stator side is the magnetizing component of the induction machine and its corresponding represents the loss component. On the rotor side the ends are shorted since there is no output current from that end. The input voltage is supplied from the grid and is set to the grid frequency. The and terms are before the trans-ratios are introduced. Once the trans ratios are introduced they are represented as

and implying the transfer.

The induced voltage on the rotor side is the slip voltage and hence has a slip factor as shown in the fig 40. For convenience, we can alter the resistance and the reactance terms such that the voltage can be equaled to the stator side of the circuit and the circuit then can be redrawn as shown in fig 41.

47

Figure 41. Circuit after the voltage equalization.

The current flowing in the rotor side has to supply the rotor copper losses and the remaining

flows out as the electrical component to the grid. The rotor copper losses is given by . To

get this term we can split the resistance on the rotor as shown in the fig 42 to get the rotor copper losses and the other component is the power that gets converted into the electrical domain from the mechanical domain. The total electromagnetic power that flows from the

rotor to the stator, however, is given by ⁄ .

Stator copper loss:

Figure 42. Circuit after splitting the rotor resistances.

48

Figure 43. Circuit after joining the stator and rotor parts.

Further, we can now assume that the amount of electricity flowing through the magnetizing component is very less and redraw the circuit as shown in fig 43. This does lead to some error. However, it is about 10 percent and not really significant. This gives us an approximate equivalent circuit of the induction machine for the WT setup as shown in fig 44.

Figure 44. Final equivalent circuit for an induction generator for a WT

It should be understood that if rotor speed is greater than the stator speed the slip becomes a negative factor and this changes the sign of the generated current on the rotor side as shown in the equation 67. This then makes it the input current. And this is how an induction motor becomes a generator. It should be noted that the rotor circuit is not connected to the input point of the circuit and hence the frequency does not change for the WT. the only factor that remains variable in the circuit is the slip. And the frequency remains at the grid value. What

does the

term denote? It represents the generated power, the electrical

equivalent of the mechanical power converted per phase. This also supplies the iron losses, the

49

rotor couple losses, stator loss and the remaining flows out to the grid. The back torque is calculated as per equation. It’s an interesting observation that the back torque can simply be defined as the ratio of the power transmitted across the air gap to the angular synchronous speed.

[

(

)]

Using equations 61 and 62:

The effect of the variation of input voltage and the rotor resistance on the generated back torque is of significance here and can be seen in the fig 45. The torque vs. slip plots are called the slip characteristics and determine the suitability of the induction generator to the WT.

Figure 45. Torque-SlIp characteristics.

50

If, ,

(

)

, which means that generated power is negative. Hence, it means the motor

instead of converting electricity into mechanical power reverses the process and becomes a generator.

But the frequency remains constant which satisfies the requirement of variable speed constant frequency as only the term varies.

It is usual practice to have big capacitor at the wind farm installations for the generation of reactive power. Feedback of the power utilization is done through the back torque felt by the mechanical component. The back toque is generated by the load as mentioned earlier.

Since the generator is the operational diametric of the motor, the slip characteristics also follow the suit. So, we can draw the generator characteristics in the opposite quadrant of the motor characteristics as shown in fig 46.

In further discussion, we shall draw the generator mode characteristics in the first quadrant for the sake of convenience.

Figure 46. Motor-Generator characteristics.

51

23. Stability of the induction generator

On studying the behaviour of the back torque in the generator characteristics, fig 47, it can be seen that in the left zone before the peak when the slip increases for any reason the back torque also increases accordingly and therefore the WT is forced to compensate and slow down and come back to the normal mode of operation thereby keeping the operation at the optimal TSR and consequentially at maximum . However, on the right hand side of the slip curve it

can be observed that the back torque weakens as the slip increases and the WT compensates by running faster and the starts performing sub-optimally. Slip control is a little tricky subject and is out of the scope of this report. However, we can surmise that better the machine narrower the stable region. But this contradicts the main requirement that is to maintain the

in the optimum TSR zone we need to have a wide range of slip, , variation. And this happens to be one of the areas of research interest. Despite this severe disadvantage, induction generators remain a popular choice due to its rugged design and cost factor.

Figure 47. Regions of operation for an induction generator.

52

24. Conclusion

Wind energy and its potential has been studied and an initial assessment method has been established. A comprehensive detail has been covered into what goes from site selection to selection of the WT for the site and the operational requirements of a WT and the subsequent conversion of energy from the mechanical domain into electrical domain.

25. Personal note:

There are many radical designs available to WT and should be explored. The advantage is obvious in the light of the geo-political crisis concerning energy. Energy independence is of paramount importance both at an individual level and at the national level.

At the undergraduate level it would be a great idea to introduce the students to the wind energy sector through hands on projects that involves every step from the start to finish including the electrical extraction and using this to power a device. When we come to think of it, wind turbines have been a favourite do it yourself topic and it is really not that difficult to manufacture and sometimes can cost as less as $200. It would be a great exposure to the students to learn with hands on approach to design a small scale WT as semester long project or a yearlong project from the very basic design process to manufacture to procuring the wind data for selected sites on UB’s sprawling acreage. In a windy city like Buffalo it would be a shame not to tap such a great reserve of energy. Some WTs like the Darrieus rotors can even be installed on the rooftops of the buildings where the space is generally left unused. The design of a WT blade can be challenging and out of scope at some UG level but can be surmounted with some assistance from the department. It would help to arrange lectures from professionals working in this field on a regular basis. It could alternatively be arranged so a willing professional could mentor a student group in their endeavours to manufacture a WT and also help with blade design.

This report can be further utilized in conjunction with propeller theory and aerodynamics of wind turbines to further expand the student’s knowledge of wind energy and wind turbines. By no means can it be considered that justification has been done to the topics covered in this report. Each topic covered in this report requires further attention for the student to understand and fully exploit this form of energy. Students should also understand that studying WTs does not limit them to a certain sector of energy but also adds to their resume since WTs entail a lot more disciplines than just energy conversion. It would be a great exposure if the students are also encouraged to build their own WT in their garage or in the school workshops either as a part of the semester requirement or as a competition.

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26. Bibliography:

First and foremost: Google. And Wikipedia. (Education is a world different now than when I was in high school.)

NPTEL lectures. http://nptel.iitm.ac.in/. (‘when the student is ready the teacher appears’).

Aerodynamics of Wind turbines. Martin O.L. Hansen

Wind turbine technology.(Author unknown but the pdf version can be found online.)

Energy from Offshore Wind. W. Musial and S. Butterfield (National Renewable Energy Laboratory ),B. Ram (Energetics, Inc) Advanced Wind Technology: New Challenges for a New Century (R. Thresher and A. Laxson). Wind energy potential assessment in Uttara Kannada district of Karanataka, India. (T V ramachandra, D. K. Subramaniam and N. V. Joshi) NREL websites.