User:Gaiyos
Title: DESIGN OF A WIND TURBINE TO BE USED FOR ELECTRICITY GENERATION ON A REMOTE FARM IN CHIVHU (ZIMBABWE)
Author: Taruvinga Tawanda
Email address: gaiyos@yahoo.co.uk/gaiyos@hotmail.com
Cell Number: +263 11 452 924
ABSTRACT
The project seeks assess the economical feasibility of using a wind turbine as a source of power for a remote farm in Chivhu as compared to the ZESA electricity grid. This is because most farmers in these remote farms are depending on fossil fuels e.g coal and oil for power production. Since these resources are non-renewable resources and are expected to get used up in the next 50 to 100 years an alternative and more economic source of power is needed. The project is about the design of a 30 m tall horizontal axis wind turbine to be used on a farm in Chivhu. The wind turbine will meet all the farm power requirements that have been calculated to be 600 KW and it has been designed for an average operating wind speed of 12 m/s. The components of the machine are to be replaced after 20 years and light weight materials such as aluminium and fibre materials are considered for the design purposes. Costs calculations have also been made and a conclusion that investment in a wind turbine is feasible for long-term investments rather than short-term investment has been made.
KEYWORDS
Wind turbine, 600 KW, conceptual designs, detailed design, economical feasibility, maintenance/ reliability
INTRODUCTION
What is a wind turbine/generator? The wind turbine is a machine that converts wind energy into useful energy. Wind turbines are used to generate electricity. The components of a wind turbine for the electricity generation includede a two- or three-blade rotor to capture the wind. The rotor blades are slender with cross sections similar to those of aeroplane wings. The rotational speed of the blade tip depends on the machine size. Other components are: the gearbox, which transfers the aerodynamic torque from the rotor to the electric generator (AC or DC) and the tower (Frandsen, 1991). Mechanical power generated directly from wind by rotor blades is transferred to the transmission system through a low speed shaft. The gearbox transmits this power to a generator through a high-speed shaft. The most common specifications quoted by the manufacturers are the diameter and the rated power.
There are two types of wind turbines, horizontal axis wind turbines (HAWTs) and the vertical axis wind turbines (VAWTs). HAWTs generally have two or three blades. Their axis of rotation is horizontal. They are employed mainly to generate electricity. VAWTs have an axis of rotation that is vertical and therefore can harness winds from any direction.
1.3 JUSTIFICATION Chivhu is a farming area in region 2 with a lot of commercial farms surrounding the small town. Some commercial farms are however located in very remote areas outside the ZESA electricity grid and the farmers are heavily dependent on fossil fuels (coal and oil) for power generation besides the environmental unfriendliness of fossil fuels and also the fact that research says fossil fuels are expected to get used up in the next 50 to 100 years. This means that as the amounts of fossil fuels decrease, the cost of their energy will increase dramatically due to the increasing cost of coal and oil. This implies that there is a need to find an alternative source of power for such farms and the farmers can only look at the renewable resources like hydro, solar and wind or join the ZESA electricity grid for the power supply purposes.
Looking at the meteorological aspects of Chivhu, it is a place with relatively high wind speeds with an annual mean wind speed of 3.9 m/s and with the lowest mean monthly wind speed of 3.3 m/s. This would make wind energy a better and reliable source of power ahead of using solar energy since solar energy can only be harnessed during the day only but not at night. Wind energy source is also better than hydropower source because of the rainfall pattern of Chivhu that does not favour hydropower source as the town has low rainfall totals and is sometimes affected by severe droughts. Since wind energy is the best source of energy, a wind turbine can be used to convert the wind power into electrical power for the total farm power requirements hence a need for the project to design a wind turbine for a commercial farm in Chivhu and assessing the feasibility of its use for power generation on a farm i.e looking at the economical aspect of its use and comparing with the ZESA costs.
OBJECTIVES • To design a feasible wind turbine for the generation of electricity on a farm with lowest weight and volume. • Study the total cost of generation of power using a wind turbine. • Calculate the payback period of investing in a wind turbine • Compare the total costs of using a wind turbine with that of the ZESA power to assess the economic feasibility of using a wind turbine as a source of power.
METHODOLOGY After the literature review, the project methodology was carried out in four stages i.e calculation of the total farm power requirements, determination of operating conditions (height, rotor dimensions), conceptual design and detailed design.
STAGE 1: FARM POWER REQUIREMENTS
The wind turbine will meet all the farm power requirements. These power requirements include power for all household appliances, grinding mills and for the irrigation pump which draws water from a nearby dam. The total farm power requirements calculated are approximated to be 600KW.
STAGE 2: Operating conditions
CALCULATION OF THE ROTOR DIAMETER
Assuming the wind turbine will have an efficiency of 80% and designing the wind turbine to operate at a height of 30m, the power extracted from the turbine is given by:
where is the power required
is the efficiency of the wind turbine
is the density of air
is the area swept by the wind turbine blades
is velocity of the wind
From the above equation we need to calculate the velocity of the wind, , at the 30 m height of operation of the turbine.
The measurement height for Chivhu from the weather data is 1.8 m. This height will be used as the reference height in the above formula.
The obstruction factor varies from 0 to 0.9 and the obstruction factor for Zimbabwe is 0.78
The wind velocity at this height can be calculated using the formula:
where is the velocity at the wind turbine height
is the mean velocity at the reference height
is the obstruction factor
is the wind turbine operation height
is the reference height of measurements
Therefore
Therefore
Now using the formula
600 000 = 0,593 0,8 1.2
and Area =
Therefore
= 19.7 m which is approximately 20 m.
Therefore for the design, the rotor has a radius of 20 m.
STAGE 2: CONCEPTUAL DESIGNS
The design specifications are • Rotor blade of radius 20 m • Turbine should be 30 m tall • Wind turbine will have an efficiency of 80% • Turbine components to last for 20years
CONCEPT ONE : TWO BLADED CONCEPT
Fig 1: Diagram showing the two bladed concept
The design has two blades inclined at an angle of . The axis of rotation is horizontal. The rotor is keyed onto the shaft whist the blades and the hub are welded together. The design has less weight and is economical.
CONCEPT TWO : THREE BLADED CONCEPT
Fig 2: Diagram showing the three bladed concept
The design has three blades with an angle of between the blades. The axis of rotation is horizontal and the rotor is bolted onto the shaft by using bolts.
CONCEPT THREE : DARREUS WIND TURBINE DESIGN
Fig 3: Diagram showing the darreus wind turbine concept
The Darreus wind turbine design is a vertical axis wind turbine with two blades. It can harness winds from all directions. The disadvantage is that it is situated at the ground therefore it cannot experience high wind speeds.
CONCEPT SELECTION
Factors Weight Concept 1 Concept 2 Concept 3
Rank Score Rank Score Rank Score
No. of blades 0.12 6 0.72 7 0.84 6 0.72
Stability 0.18 6 1.08 8 1.44 6 1.08
Weight 0.13 8 1.04 7 0.91 7 0.91
Wind Speed 0.15 7 1.05 7 1.05 4 0.6
Efficiency 0.12 7 0.84 8 0.96 6 0.72
Wind direction 0.1 5 0.5 5 0.5 8 0.8
Method of joining blades to hub 0.1 5 0.5 6 0.6 5 0.5
Axis of rotation 0.1 6 0.6 6 0.6 8 0.8
Total 1 6.33 6.9 6.13
Table 1: Table showing the concept selection
Concept 2 has the highest score, hence the most suitable. I choose concept 2 for the design therefore the three bladed concept is used in the design.
STAGE 3: DETAILED DESIGNS
At this stage the design of the components of the wind turbine is carried out. These components include the blades, hub, tower, gearbox and the bearing selection.
THE BLADES
The material used for construction is an aluminium alloy 2024-T81
Material properties
Density of 2024-T81 = 2770 kg/m3
Yield strength (y) = 230 MN/m2
Young’s modulus (E) = 69 GPa
Tensile strength = 390 MN/m2
Endurance limit (Se) = 69 MN/m2
TIP SPEED RATIO (TSR)
A suitable tip speed ratio (TSR) is selected. Tip speed ratio is given by :
= 28.6 rev/min
STARTING TORQUE
Starting torque can be estimated from the formula:
= 46.08 KNm
CALCULATING THE FATIGUE STRENGTH
Since light material is preferred in order to reduce the weight of the wind turbine, Aluminium is used in the design. The fatigue strength of Aluminium ranges between 30- 40% of the ultimate tensile strength depending upon whether the material is cast or wrought. The material does not have an endurance limit, and the fatigue strength is based on or of stress reversal.
The components of the blade are to be designed to last for 20 years,
20 years = 20 × 365 ×24 × 60 minutes
= 1.05 ×107 minutes The total number of cycles to failure = 1.05 107 28.6 = 3 108 cycles From the S-N graphs of aluminium, the endurance limit is 75 MPa.
Strength of the blades Consider the hub to have a radius of 88 mm as calculated in the next section, therefore the length of the blade = 20 000 – 88 = 19.912 mm
Lift,
Where Cl =lift coefficient and assuming Cl = 1
=38.79 m2 = 3351 N
Drag, Assuming drag coefficient, Cd = 0.01
= 33.51 N
Force per unit length, = 168.3 N/m
The force per unit length can be used to calculate the moments at different points of the shaft
= -33.66 KNm
Fig 4: Bending moment diagram for the blades
Fig 5: DIAGRAM SHOWING THE BLADE
= 238 kg Total mass of blades = mass of one blade total number of blades = 238 3
= 714 kg
Radius of gyration (k) = 1/3 blade length
= 6.67 m Angular velocity, =3.0 rad/s Centrifugal force on blade, = 714 32 6.67 = 42.9 KN Second moment of area, = 1.56 10-4 m4
A = (2.82 0.3) – (2.818 0.298) = 0.00624 m2
Values of maximum and minimum stresses are given by
Maximum stress = 32.45 MPa Minimum stress = 6.88 MPa a safety factor of 2 is used and the maximum stress tolerated = 34.5 MPa DESIGN OF THE HUB
Since the material used for the design is an Aluminium alloy, therefore the maximum stress the hub can experience is 34.5 MPa. After carrying out the design of the hub, I choose radius of 0.088 m. The radius of gyration is therefore 0.044 m. The volume of hub = πr2 x length = 0.0109 m2 The mass of hub = density volume = 30.3 kg Centrifugal force on hub = 12 N
GEARBOXES FOR WIND TURBINES
The power from the rotation of the wind turbine rotor is transferred to the generator through the power train, i.e. through the main shaft, the gearbox and the high speed shaft. With a gearbox one converts between slowly rotating, high torque power got from the wind turbine rotor - and high speed, low torque power, which is used for the generator. The gearbox in a wind turbine does not "change gears". It normally has a single gear ratio between the rotation of the rotor and the generator.
GEARBOX DESIGN
The gear connected to the rotor of the wind turbine will rotate at the angular velocity of the hub that is 3 rad/s. Since ,
= 28.65 rev/min
The gearbox is designed in such a way that it increases the speed from 28.65 rev/min rotor to the generator speed of 900 rev/min. The gear ratio is given by the formula:
= 1 : 31
The gear ratio of 31 is used in the design. This gear ratio is large and would result in a large gear transmitting power to a very small pinion therefore I will design a gear train of three gears. The pinion and the idler will have a gear ratio of 10 while the idler and the gear will have a gear ratio of 3.1.
STRENGTH OF THE GEARS
The strength of the gear is found by calculating the strength of the weaker gear. When the gear and the pinion are made of the same material, the pinion is always the weaker of the two because the teeth of the smallest gear have more undercutting. Assuming the gears are made of BS640M40 alloy steel heat-treated and to tensile strength (Sut) = 800 MPa and yield strength (Sy) = 580 MPa. The teeth are generated with a rack cutter.
Endurance limit (Se) =0.45 Sut
= 360 MPa
If a safety factor of 3 is used, then the maximum permissible bending stress is given by Permissible bending stress (p) = Sy/3
=120 MPa
Assuming a safety factor of 3 and calculating the pitch diameter, pitch line velocity, the transmitted load, the velocity factor, the face width and the maximum and minimum face width for different trial values of module in order to come up with the pinion diameter.
Formulas Let m be the module, then pitch line diameter d is given by Pitch line velocity v, is given by
Where P is Power in watts, the transmitted load Wt, is given by
The velocity factor kv, is given by
If p is permissible bending stress and Y = 0.29327, the face width F, is given by
The minimum and maximum face widths are 3p and 5p respectively.
The power per unit area for a wind speed of 12 m/s is 1100 W/m2. The area covered by the blade At = r2 = 202 = 1257 m2
Power = 1257 1100
= 1.38 106 Watts
The Pitch (p) is given by the formula :
Module, m 5 4.5 4 3.5 3 2 1 0.5
Diameter, d 0.1425 0.129 0.115 0.1 0.086 0.0573 0.029 0.0143
Velocity, v 0.215 0.1934 0.173 0.15 0.129 0.086 0.043 0.0215
Transmitted load, Wt (106) 6.43 7 8 9.22 10.7 16 32.1 64.3
Velocity factor, kv 0.965 0.969 0.97 0.976 0.979 0.986 0.993 0.996
Face width 0.038 0.046 0.059 0.077 0.1035 0.23 0.92 3.67
Fmin, 3p 0.075 0.067 0.06 0.052 0.045 0.03 0.015 0.007
Fmax, 5p 0.125 0.113 0.1 0.087 0.07 0.05 0.025 0.012
DESIGN OF THE SHAFT
CALCULATION OF FORCES
FIG 6: DIAGRAM SHOWING FORCES ACTING ON THE SHAFT
The total centrifugal force on the gears as calculated before Fc2 = 57.5 KN, and it will be acting upwards. The total weight of the gears is given by: total weight = total mass × gravity W2 = 4305 × 9.81 = 42.232 KN (downwards) Resultant force acting on gears, F2 = 57.5 – 42.232 = 15.27 KN (upwards) The total centrifugal force on the other end of the shaft given by: Total centrifugal force = centrifugal force on blades + centrifugal force on hub Fc1 = 12 + 42 900 = 42.912 KN Total weight of hub and blades = (238 + 30.3) × 9.81 W1 = 2632 N Resultant force acting on the end, F1 = 42 912 – 2632 = 40.28 KN (upwards) Calculating the reaction R1 and R2 Taking moments about the point of R2, (40.28 2) + (R1 1) + (15.27 0.5) = 0 R1 = 88.2 KN (downwards) R2 = 88.2 - (40.28 + 15.27) = 32.65 KN (upwards)
FIG 7:DIAGRAM OF FORCES ACTING ON THE SHAFT
FIG 8: SHEAR FORCE DIAGRAM
BENDING MOMENT DIAGRAM CALCULATIONS MA = 0 MB = 40.28 1 = 40.28 KNm MC = (40.28 1.5) –(88.2 0.5) = -16.32 KNm MD = (40.28 2) – (88.2 1) + (15.2 0.5) = 0
FIG 9: BENDING MOMENT DIAGRAM
Using o safety factor (n) of 2 for the shaft,
Use a diameter of 0.144 m or 144mm.
= 0.107 m or 107 mm
BEARING SELECTION At point B, consider a bearing that would withstand a force of 88.2 KN A spherical roller bearing with designation number 23944 CC/W33 Diameter (d) = 220 mm Dynamic load rating = 552 KN Mass (m) =13 kg The same bearing is also used on point D.
WIND TURBINE TOWERS From the three tower types above, the most suitable for this design is the tubular steel tower, on the basis of stability and strength since the tower will be used on a very large machine. The tower was designed to determine the dimensions.The overall design was as follows: The Tower is to have a height of 30 m. From the literature review, on the types of towers to be used, the chosen type is tubular steel tower with varying wall thickness and diameter. The tower is to carry a maximum load equal to the sum of masses of the blades, the gears, the hub and the bolts, which is 5080 kg. For carbon steel material, E = 207 GPa.
For the top most section of the tower, Consider d1 = 0.1 m, t = 20 mm, D1 = 0.12 m, L = 5 Area 1, = 3.46 10-3 m2 Volume 1, = 1.73 10-2 m3. Mass 1, m1= 7800 1.73 10-2 = 134.8 kg Total mass mt1 = 134.8 + 5080 = 5214.8 kg Force F1 = 5214.8 9.81 = 51.16 KN
For columns with one end fixed and the other freely supported n = 0.25
0.04 = 107.8 KN
The load experienced by the tower is less than the critical load therefore the dimensions are suitable. Consider d2 = 0.14 m, t2 = 10 mm, D2 = 0.15 m, L2 = 11
M2 =7800 0.0137 = 106.6 kg Mt2 =106.6 + 5214.8 =5321.4 kg F2 = 5321.4 9.81 = 52.2 KN
= 25.3 KN
Since the load experienced by the tower is greater than the critical load, the dimensions are unsuitable.
Consider d2 = 0.18, t2 = 20 mm, D2 = 0.2 m, L2 = 11
M2 = 7800 0.0358 = 279 kg Mt2 = 279 + 5214.8 =5494.2 kg F2 = 5494.2 9.81 = 53.9 KN
= 112.7 KN
The result is good therefore dimensions are correct.
Consider d3 = 0.225, t3= 25 mm, D3 =0.25, L3 = 19 m
M3 = 0.103 7800 = 800 kg Mt3 =800 + 5494.2 = 6294.4 kg F3 = 6294.4 9.81 = 61.75 KN
= 90.03 KN
The result is satisfactory therefore the dimensions are correct.
Consider d4 = 0.25 m, t4 =50 mm, D4 = 0.3 m, L = 30
M4 =0.238 7800 = 1853 kg
Mt4 =1853 + 6294.4 = 8147.5 kg
F4 = 8147.5 9.81 = 79.93 KN
The result is good therefore the dimensions are correct.
FIG 10; DIAGRAM SHOWING THE TOWER
OVERALL SPECIFICATIONS OF THE DESIGN
General specifications Rotor diameter 20 m Rotor speed 28 – 50 rpm Nominal power 600 KW Rated wind speed 12 m/s Survival wind speed 25 m/s Rotor speed control Full span pitch, mechanical passive pitching Control Microprocessor main function Transmission
Type Integrated gear type Gearbox type Helical
Generator
Type Asynchronous Grid connection AC – DC – AC inverter
Tower Type Conical, tubular steel tower Height 30 m
Safety System Yawing out of the wind, followed by passive blade pitching
COST CALCULATIONS Cost calculations are carried out in order to determine the economical feasibility of using a wind turbine for the generation of electricity in order to carry out a comparison with the current costs of power using the ZESA electricity grid. The costs include capital investment (components costs, transportation costs, installation costs, operation maintenance costs). The prices are quoted in United States dollars and are based on cost per unit mass of material used. The costs are the current costs researched on the Internet. Some of the materials are not manufactured in Zimbabwe, therefore since they are imported, transportation costs will play a significant part in the capital costs of a wind turbine.
Components costs COST OF THE BLADES The blades are made of aluminium The cost of aluminium is $1.75/kg The total mass of the blades was calculated to be = 714 kg Cost of aluminium for the blades = 714 ´ $1.75 = $1 250 Cost of manufacturing = $293 Total cost of the blades = $293 + $1 250 = $1 543
COST OF THE HUB The hub is made of aluminium with the cost of $1.75/kg The total mass of the hub is 34 kg Total cost of the hub = 34 ´ $1.75 = $60 The cost of manufacturing = $4 Total cost of the hub = $60 + $4 = $64 COST OF THE GEARS The gears are made of steel The cost of steel is $3.80/kg The total mass of the gear train was calculated to be 4 305 kg Cost of steel for the gears = 4305 $3.80 = $1 636 Cost of manufacturing the gears = $207 Total cost of the gears = $207 + $1 636 = $1 843
COST OF THE SHAFT The shaft is made of steel, with a radius of 350 mm and 2 m long Volume of the shaft = Mass of shaft = 0.192 7800 = 1500 kg Steel costs $3.80/kg Cost of steel used on shaft = $3.80 1500 =$5 700 Cost of manufacturing the shaft = $317 Total cost of the shaft = $317 + $5 700 = $5 617
COST OF THE TOWER The tower is made of tubular steel which costs $1 500 per meter The tower height is 30m Total tower cost = 30 $1 500 = $45 000
OTHER COSTS Cost of the 600 KW generator is $14 000 Cost of the bearing and the housing is $300 Miscellaneous costs are estimated to be $100 Transportation and installation costs of the components are estimated to be $15 000
Capital costs = $100 + $300 + $14 000 + $45 000 +$5 617 + $1 843 + $64 + $1 543 + $15 000 = $83 467 The major turbine components are designed to last for 20 years before they are replaced. Therefore assuming that all the turbine components will last for 20 years, it means that the above capital will be an investment for the next 20 years. However maintenance work will also be carried out on the moving parts that require lubrication and other small operations. Maintenance costs Maintenance costs are 2 % per year of the original investment Total maintenance cost = 0.02 $83 467 20 = $33 387 Total cost of wind turbine in 20 year period = Capital costs + maintenance costs = $83 467 + $33 387 = $116 853.80 COST OF USING THE ZESA ELECTRICITY GRID (US$) Using the current ZESA rates and the fixed costs, the total cost per year for a setup being supplied with 600 KW is approximately $11 226.
RESULTS Investing in a wind turbine has proved to be cheaper than utilizing the ZESA electricity grid since the $ 116 853.80 is an investment which covers about 20 years according to the design (i.e when the components are replaced) as compared to $ 11 226 which is for one year.
DISCUSSION/ ANALYSIS The wind turbine proved to be more expensive as compared to the ZESA electricity grid over a short period of time but it is cheaper for longer periods of time. This is because if an investment is made for a period of more than 20 years, the installation costs, transportation costs, and some other costs will not be there as there will only be replacements of the components that are expected to fail after 20 years e.g the blades, whilst the tower, generator and shafts will not be replaced and will continue working. This will reduce the cost of investment in the wind turbine for a long period of time.
The two main disadvantages of the ZESA electricity grid are on the reccuring power cuts experienced during load shading which inconveniences the customers and also that the cost of electricity of the ZESA electricity grid is very much affected by the high annual inflation rate of Zimbabwe which is above 100 %. This means that the cost of electricity will increase every year whilst for a wind turbine, the capital cost is enough for the next 20 years hence will not be affected by the annual rate of inflation.
The capital investment for a wind turbine is so much that many farmers cannot afford it and would therefore be forced to resort to the ZESA electricity grid alternative even if the wind turbine proves suitable. This means that implementation of the wind turbine will greatly depend on whether the farmer has the capital or not but not on whether the turbine is economically sensible or not. This might end up in a situation where there can be wind turbines in state owned farms only since the government might have the capital whilst individual farmers cannot afford the capital even if wind turbines are the best option. However there will not be as many cases of cables theft in using wind turbines unlike in using the ZESA electricity grid where theft cases of cable are common.
RECOMMENDATIONS AND CONCLUSION In conclusion, where the capital is available for a farm in Chivhu and a long term investment is required on a farm, a wind turbine can be used but for a short investment, the ZESA electricity grid is better. Therefore where there is a ZESA electricity grid there is little benefit in using the wind turbine since the government is carrying out a rural electrification programme, therefore wind turbine investments will be reduced to short term investments.
ACKNOWLEDGEMENTS
I would like to acknowledge the following personnel for their contributions:
Mr W. Mungwena Mr M. T Hlambelo Mr Tapiwa Gaiyos Mr Prosper Taruvinga Mr Martin Munyanyi Mrs J. Gaiyos It would have been difficult to write the project without the financial support from my mother Mrs J Gaiyos and Mr Tapiwa Gaiyos. Special thanks go to Mr W Mungwena for the literature he provided and his supervisory role.
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