I and two others built a wind turbine capable of generating electricity. 100% renewable.
It was meant to be an affordable way for people in the third world to generate power without requiring an expensive grid connection. The goal was a 1 kW machine, mass producable for under $700 including a battery bank to store the energy and inverter to use it. The battery bank had to be sized so that it could run a modest load for at least 2 days, in case the weather wasn't suitable to generating wind electricity.
It was built out of used car parts scrounged from a junkyard, a set of very strong and dangerous Neodymium Iron Boron magnets, some enamled magnet wire, and a bunch of spare electronics.
A lot more went into this project than what you will read below, and I will have more pics and info to add later. Anyway, here is the appendix part of a paper we wrote describing the project:
======================
Appendix A (Calculated Blade Performance, Blade Parameter Selection)
Calculated Blade Performance:
The generator was designed to turn at a high speed so that it could produce a high enough voltage to charge a battery at low wind speeds(See Appendix C). This required a blade design with a high tip speed ratio.
Tip speed ratio is a ratio of the speed of the blades versus the wind speed.
TSR = (2 * pi * r * n) / (88 * V) Eq A.1
TSR = tip speed ratio of the blades
pi = 3.141592654…
r = radius of blade in feet
n = generator/rotor revolutions per minute
V = wind speed in mph
A tip speed ratio of 7 and a blade diameter of 8 feet was chosen, the first being the highest TSR a 3 blade design will operate at.
The chart below compares rotor efficiency and tip speed ratio:
Figure A.1 TSR versus Power Coefficient(% efficiency) for various blade types

This tip speed ratio gives an efficiency of 40% for a high speed 3 blade propeller. This will be used to calculate the amount of power that can be produced by the rotor. In practice, after all losses are considered and considering tip speed ratio is not constant, an efficiency of about 15% is more often realized. Thus, to get 1 kW from the generator, at least 3 kW or so must be theoretically producible from the blades. The speed at which the the most power is typically produced on small scale vertical axis wind turbines is about 30 mph; afterwards a speed limiter begins to reduce output. To meet the design constraints, an 8 foot diameter blade is thus ideal.
The swept area of the rotor now needs to be found.
A = pi * (r * 2)^2 / 4 Eq A.2
A = swept area of the blades (feet squared)
For an 8 foot diameter rotor:
A = 50.3 ft^2
Pr = .5 * Rho * 1.041 * A * V^3 * Reff Eq A.3
Pr = power extracted from wind by rotor (Watts)
Reff = rotor efficiency (%)
Rho = air density (m^3/kg), 1.25 m^3/kg a sea level
Using Eq A.1, Eq A.2, and Eq A.3, a chart plotting extracted wind power versus wind speed can be created:
Table A.1 (Wind Speed versus Extractable Rotor power)

Blade Parameter Selection:
When designing the blades that the turbine will use, the width needs to be calculated. The following equation is used to calculate blade width:
C = 2.44 * r / (TSR^2 * B) Eq A.4
C = blade width (m)
B = number of blades
The ideal blade width at the tip is thus .0664 m. The blades built measured .062 m at the tip, and an attempt was made to keep them as close to this spec as possible.
The ideal blade angle can be determined from Figure A.2 below:
Figure A.2 Ideal Blade angle versus Tip Speed Ratio

Thus the ideal blade angle is 2.5 degrees with a TSR of 7.
Wind turbine blades are commonly designed in 6 stations.
For a tip speed ratio of 7, the ideal station widths as a percentage of radius length are as follows:
Station 1(root): 12.5%
Station 2: 10%
Station 3: 8.3%
Station 4: 6.7%
Station 5: 5.8%
Station 6(tip): 5%
For a tip speed ratio of 7, the ideal drop from the trailing edge as a percentage of radius length are as follows:
Station 1(root): 3.1%
Station 2: 2.1%
Station 3: 1%
Station 4: 0.5%
Station 5: 0.3%
Station 6(tip): 0.2%
For a tip speed ratio of 7, the ideal blade thickness as a percentage of radius length are as follows:
Station 2: 2.1%
Station 3: 1.1%
Station 4: 0.8%
Station 5: 0.7%
Station 6(tip): 0.6%
Figure A.3 shows the carved blades.
Figure A.3 (Carved Blades)

Alternative Blade Parameter Selection:
Other designs were considered. A blade design with a 5.2:1 TSR was considered earlier when it was thought that the generator would produce power at lower wind speeds. This would be ideal for maximizing blade efficiency(see Figure A.1), theoretically obtaining a 47% efficiency.
B = 80 / (TSR)^2 Eq A.5
B = 3
Thus for 3 blades, the ideal tip speed ratio is 5.2 according to Eq A.5.
The ideal blade width of this design using Eq A.4:
C = .241 m
From Figure A.2, the ideal blade angle is 4 degrees.
This was impractical for two reasons. First, it would spin too slowly to generate the voltage needed to charge a battery at low speeds(~10 mph) without an expensive charge controller. Second, the wood obtained to carve the blades from was not thick enough to accommodate their construction.
If the stator coils were wound perfectly, this TSR value may have been practical for generating power at low speeds.
Appendix B (Generator Parameters)
The machine consists of 12 pole pairs of 2" diameter by 1/2" thick NdFeB magnets rated at 1.35 Tesla. The machine has 9 stator coils, each coil wound 64 turns of #14 AWG enamled magnet wire.
After the coils were wound, the synchronous impedance of a single coil was measured by an inductometer. The frequency at which this value was obtained was 60 Hz.
The synchronous impedance can be represented by the following equation:
Zs = Rs + j*Xs Eq B.1
Zs = synchronous impedance (Ohms)
Rs = synchronous resistance (Ohms)
Xs = synchronous reactance (Ohms)
The value obtained for Zs was the following:
Zs = .1203 Ohms + 1.38j Ohms
Since there are three stator coils per phase, the per phase value for Zs is as follows:
Zs = .3609 Ohms + 4.14j Ohms
Beforehand, the inductance values had been calculated. Though there are multiple ways to calculate inductance, we needed an equation that would find the inductance of a particular solenoid of thickness c and diameter of 2a.
Figure B.1 (Depiction of a Stator Coil)

The inductance formula that can approximate inductance of Figure 1.A is by the use of Wheeler’s equation:
L = 31.33(4π x 10e-7)N^2((a^2)/(8a + 11c)) Eq B.2
N = number of turns ≈ 64
a = .03175 m if d = 2.5 in.
c = .0381 m if d = 1.5 in.
L = 2.42 * 10^-4 H
Below are the measured results of the inductance parameters measured in series for a randomly selected stator coil:
Figure B.2 (Depiction of Stator coil Inductance)

Appendix C (Generator Testing)
After the generator was first assembled, it was tested. A wired phase was hooked up to a multimeter, the rotor spun until it reached 2V, and that voltage was kept reasonably constant by maintaining a steady speed. The amount of revolutions per minute to maintain that steady voltage was recorded. This was repeated for 4V and 6V.
We got the following data from the Agilent 33120A Digital Multimeter:
Table C.1 (Measured Voltage versus generator RPM)

It was determined that roughly 1V was produced for every 30 rpm. Permanent magnet AC generators are supposed to have a voltage that varies linearly with speed, and this one has that same characteristic.
The 3 generator phases were then wired in the delta configuration so that the generator could be tested under loaded conditions. It was spun at a constant speed, and an oscilloscope printout was taken from an Agilent 54622D Oscilloscope of the line to line delta voltage. The printout is Figure C.1.
Figure C.1 (Measured Generator output to Oscilloscope under load)

The current was measured at the same time the printout was taken with an Agilent 33120A Digital Multimeter. It was found to be 1.03A.
Appendix D (Generator Selection and Performance Calculations)
Permanent Magnet AC alternator- These have the advantage of being low cost per watt of output and are very efficient. The disadvantage is that small AC alternators suitable for wind turbines are difficult to obtain in low volume which usually means that one must be built from scratch. Building a design from scratch often means that it can be designed so that a gearbox is not needed.
AC Induction motor- AC induction motors have a low cost per installed watt and perform well at low speeds, but they lose efficiency at high speeds and are prone to overheating.
Permanent Magnet DC generator- While widely available and capable of producing usable amounts of power at low speed, these require a control system which may be difficult or expensive to obtain, require a DC to DC converter to give a steady output voltage suitable for charging a battery, and maintenance for these systems is increased.
Decision: Due to a desire for a system that requires minimal maintenance and offers a high amount of power per unit of cost, it was decided that a permanent magnet AC alternator would be the best choice for our design. If one can't be found for an affordable price, it will have to be built.
The equivalent circuit for a single phase of a permanent magnet AC generator is as follows:
Figure D.1 (Equivalent circuit of Permanent Magnet AC Alternator)

From this, equations for the stator voltage, current, and ideal power produced can be derived.
Ea = k*w Eq D.1
MAG[Ia] = MAG[Ea] / ((Rs + Ra)^2 + Xs^2)^.5 Eq D.2
Pe = (Ea^2 * Ra) / ((Rs + Ra)^2 + Xs) Eq D.3
Ea = stator voltage (V)
k = constant determined by number of poles and other factors
w = angular electrical speed (radians/s)
Ia = armature load current (A)
Rs = synchronous resistance (Ohms) = .3609 Ohms (See Appendix A)
Ra = armature load resistance (Ohms)
Xs = synchronous reactance (Ohms)
Pe = ideal power generated without losses (W)
MAG stands for magnitude, found by taking the square root of the quantity of the real component squared added to the imaginary component squared.
From the above,
w = 2*pi*f Eq D.4
f = electrical frequency (Hz)
It is known that the machine has 12 poles(See Appendix A). From this, angular mechanical speed can be found:
wm = 2*w / P Eq D.5
wm = angular mechanical speed
P = number of magnetic poles
Thus,
n = (wm * 30) / pi Eq D.6
Xs = w*Ls Eq D.7
Ls = synchronous inductance of stator coil (H)
Since the value of Xs varies with the angular electrical speed of the stator, the value for Ls should be solved first. Xs per phase is 4.14 at an electrical frequency of 60 Hz(See Appendix A). From Eq D.7:
Ls = .01098 H
A datapoint was taken of the generator’s 3 phases connected in the delta configuration so that the value of Ra under load could be found. This datapoint had the following information:
MAG[Ea] = 2.45V (See Appendix A)
MAG[Ia] = 1.03A (See Appendix A)
f = 3.39 Hz (See Appendix A)
From Eq D.2:
Ra = 2.01 Ohms
The stator voltage varies linearly with RPM, by a constant k. From the above datapoint and from Eq D.1:
k = .115
The generator is not 100% efficient, however. There are copper losses, core losses, mechanical losses, and stray losses to account for.
Copper losses can be found with the following equation:
Pcu = MAG[Ia]^2 * (Rs + Ra) Eq D.8
Pcu = copper losses (W)
It is assumed that core losses are 10% of the ideal power output. There was no available means to accurately measure core losses on hand.
Pcr = .10 * Pe Eq D.9
Pcr = core losses (W)
Friction losses also couldn’t be measured. It is assumed that friction losses are 1% of the ideal power output.
Pfr = .02 * Pfr Eq D.10
Stray losses are assumed to be 20% of core losses:
Ps = .2 * Pcr Eq D.11
Ps = stray losses (W)
Since Pe is the ideal power per phase, the power output per phase including losses can be found from the equation below:
Pp = Pe – Pcu – Pcr – Pfr – Ps Eq D.12
Now the total power output for the generator can be solved by multiplying the power per phase times the number of phases:
Ptot = 3*Pe Eq D.13
Ptot = total power produced by all three phases (W)
Thus from Eq A.1 and all equations listed in Appendix D, the following chart is obtained:
Table D.1 (Generator Performance chart)

At 30 mph, this machine should theoretically produce about 500W based on what could be calculated from experimental data.
If a capacitor were added in series with the armature, sized so that capacitance and inductance were equal at the resonant frequency of the circuit, the generator would be able to produce more power and extract more power from the rotor. Power output from the generator could potentially increase two-fold or more. However, in order to find this value, actual data points on voltage, current, and frequency along with the angles of voltage and current would be needed from high wind speed levels. These were not obtainable without the machine set up outdoors.
So long as the generator power output at a given speed is more than the wind power available from the rotor, it will be stalled. Thus from Table A.1 and Table D.1, the machine will spin at greater than 14 mph. With a properly sized capacitor in series with the armature, it would produce power at any speed where Ea is at least as high as the battery voltage. With a charge controller and this capacitor, it would produce usable power and spin at near stall condition.
Figure D.2 shows the completed generator.
Figure D.2 (Assembled generator)

Appendix E (Rectifiers)
Figure E.1 (Assembled Rectifier Block)

With the rectifiers connected to the circuit, a stable 3 phase DC voltage output was verified with an Agilent 54622D Oscilloscope.
Figure E.2 (Rectifier Output as Generator is turned from Oscilloscope)

Appendix F (Battery Selection and Calculations)
An energy storage medium will be needed to store the energy generated by the wind turbine for later use, so that it can be harnessed to run a water pump or other electric-powered device. To run a modest 50W load for 24 hours would require at least 1.2 kWh of energy storage, not factoring in efficiency losses. The following options were considered below.
Storage Medium Selection:
Pumped Water Storage- Retrieving energy from stored water is roughly 75% efficient. At a mass of 1000 kilograms per cubic meter, the potential energy of 1 cubic meter of stored water at 10 meters height is only 27.2 watt-hours. This is not feasible for this application.
Hydrogen Fuel Cell- Inefficient, costly, short-lived, and cumbersome, this would be a poor choice for this application at this time.
Flooded Lead Acid Battery- Flooded lead acid batteries are easy to maintain, inexpensive, and widely available. The require no regulation system for charging, making them ideal for wind turbine applications where the power going to them is not constant. Their downsides are that they typically have a shelf life under 5 years and last about 300-500 cycles to 100% discharge, require periodic watering with distilled water, and are heavy. In cold weather, they rapidly lose their ability to store energy. Keeping the batteries chronically discharged can cause permanent damage.
Sealed Lead Acid Battery- These are slightly more expensive than flooded lead acid batteries, widely available, and maintenance free. Their shelf life is about the same as flooded lead acid batteries, but they typically last fewer cycles, and require a battery management system to prevent overcharging. In cold weather, they rapidly lose their ability to store energy. Keeping the batteries chronically discharged can cause permanent damage.
Flooded Nickel Cadmium Battery- Far more expensive than any lead acid battery up front. However, their long shelf life of over 20 years, cycle life over 1,000 full discharge cycles, and ability to operate in cold weather without any loss in capacity makes them ideal for a small wind turbine application. However, they require a functioning battery management system to prevent overcharging and periodic watering. Cadmium is toxic and poses a serious environmental hazard.
Nickel Metal Hydride Battery- Large NiMH battery sizes for stationary applications are technologically feasible and have been built before, but are currently not available. They have similar shelf life and cycle life to flooded NiCd batteries, but don't require periodic watering and do not have toxic cadmium for their electrolyte. They require a battery management system.
Lithium Ion Battery- Lightweight and cycle life similar to lead acid batteries, but increased shelf life. In order to build a pack suitable for a wind turbine, a large array of cells would have to be assembled into a battery pack, requiring an extremely complicated battery management system to actively monitor each cell on charge and discharge. For this application, they are extremely cost prohibitive. Without a proper charging algorithm, serious safety concerns would arise.
Decision- Either the flooded or sealed lead acid battery would be the best choice for the application given the constraints outlined in the project description. While floodeds require periodic maintenance, they are more forgiving of abuse than sealed lead acid batteries, and therefore may be the better choice. The Trojan T105 flooded lead acid battery was selected for its large size, wide availability, low price, and long cycle life. The manufacturer and various distributors claim 300-500 cycles to 100% discharge, 225 AH at the 20 hour rate, 6V nominal. One battery can be had for less than $100 per unit from most retailers, making a set of two 6V batteries less than $200, for a total of 2.7 kWh of storage at the 20 hour rate. This is more than sufficient to power a 25W load for more than 2 days straight, which may be needed for days where the weather is unsuitable for generating power. Competitors included US Battery, Exide, and Interstate. Later in this report are calculations determining how long various appliances could run off of a fully charged battery bank with no new power being generated.
Battery Run Time:
Since the wind generator will not be making power 100% of the time, a battery bank and inverter will be needed so that an electronic appliance can be used. The battery run time will be determined by the power demand of the appliance being used.
It will be assumed that the Inverter averages 85% efficient.
Lead Acid batteries have a capacity that varies with the amount of amps drawn from them. The higher the amp draw, the less capacity they will deliver. Likewise, the lower the amp draw, the more capacity will be delivered. This is known as Peukert's effect.
At the 20 hour rate, the Trojan T105s have 225 AH of capacity, rated at 6V nominal. They have 115 minutes of reserve capacity at 75 amps, meaning they deliver a 75 amp draw for 115 minutes before running out. We can solve for the two Peukert's numbers with these figures.
Ex = (LOG10(20) - LOG10(RC / 60)) / (LOG10(75) - LOG10(RA / 20)) Eq F.1
X = Peukert’s exponent
K = Peukert’s capacity
RC = reserve capacity (Minutes)
RA = battery capacity at 20 hour rate (AH)
K = (RA / 20)^(X) * 20 Eq F.2
From this, we get 1.236 for Peukert's Exponent and 399 for Peukert's Capacity.
The Trojan T105s have .004 ohms internal impedance as well. So as current draw increases, battery pack voltage decreases.
Pb = Battery Power demanded (W)
S = Number of Batteries in String
O = Impedance of each Battery (Ohms)
R = Total Impedance of Battery String (Ohms)
Vn = Nominal Battery Pack Potential (V)
I = Battery Current Draw
K = Peukert's Capacity
X = Peukert's Exponent
Ti = Run Time (hours)
Ni = inverter efficiency (%)
Pa = Appliance power consumption (W)
We are using two batteries connected in 1 series string for 12 V nominal. The internal resistance of the pack can be found as follows:
R = S * O Eq F.3
R is therefore .008 ohms.
Next, we can calculate the current demanded from the pack for a given load.
I = (Vn - (Vn^2 - 4 * R * Pb)^.5) / (2 * R) Eq F.4
Pb = Pa / Ni Eq F.5
The run time in hours of the battery pack for a given current draw is as follows:
Ti = K / (I^X) Eq F.6
Below is a chart showing the power demands of various appliances.
Table F.1 (Average Power consumption of common appliances)

Table F.2 shows how long certain appliances could operate on a full battery charge if the wind turbine quit generating power, solved with all equations present in Appendix F:
Table F.2 (How long batteries can run an appliance from a full charge)

Appendix G (System Block Diagram)
Figure G.1 (Block diagram of Entire proof of Concept System)

Appendix H (Budget Analysis):
Table H.1 (Breakdown of costs for each item)

* The batteries were purchased used and would generally cost more at the mass production level. Trojan T105s can be found retailing for as low as $70 each.
A pricing formula was obtained and modified. It took on the following form(per turbine):
material cost + (overhead)/(x * n) + labor / 1 unit = price Eq H.1
x = lot size = 1000
n = number of lots(in one thousand units) per year = 20
overhead = $150,000
labor = $20/hr., total 10 hr. construction,
It is a generally accepted tule of thumb that at a manufacturing level, items can be purchased at a 45.7% industry discount over retail costs giving a $549 material cost.
The total consumer cost assuming $150 profit is $699.50, under $700.
Appendix I (Speed control)
A governor is not essential for a functioning wind turbine, however it can prevent damage from occurring to the turbine in dangerous weather conditions There are different ways to control the speed that the turbine rotates.
Electronic Speed Control- This method of speed control often requires the use of an anemometer and wind vane to determine the wind speed and direction that the wind is blowing it. If these two parameters become suitable for causing damage to the turbine, an electronic governor can shut the turbine off to prevent damage. However, this design greatly adds complexity and cost to a wind turbine.
Pitch Control- This method of speed control involves changing the pitch of the blades with wind speed so that rotor and generator speed are regulated with changing weather conditions. This is best suited to large scale applications.
Stall Control- Stall speed control involves shifting the rotor axis to an optimized direction based on wind conditions. Blades can be shifted to produce no lift, essentially shutting them off in unfavorable wind conditions. Once the machine is stalled, it needs to be restarted manually.
Yaw and Tilt The direction of the rotor can be changed to match the direction of the wind. This is known to reduce noise and allow the design to operate more safely at higher speeds.
Decision: Stall control is too labor intensive in fluctuating weather conditions, pitch control is ill suited for small turbine applications, and electronic speed control adds to cost and complexity. Given the relatively low power output of this design and a premium placed on efficiency, Yaw and Tilt control is optimal for this design.
The aforementioned generator design contains a furling system that will allow the turbine to turn out of high wind speeds and turn with lower wind speeds. If time permits, an electronic PWM governor may be added to the design.
Below is a schematic of the generator's yaw and tilt control furling system, designed by and credited to otherpower.com:
Figure I.1 (Furling System for Generator)

The proposed but unimplemented PWM governor has the following block diagram:
Figure I.2 (Block diagram of PWM Speed control)
It was meant to be an affordable way for people in the third world to generate power without requiring an expensive grid connection. The goal was a 1 kW machine, mass producable for under $700 including a battery bank to store the energy and inverter to use it. The battery bank had to be sized so that it could run a modest load for at least 2 days, in case the weather wasn't suitable to generating wind electricity.
It was built out of used car parts scrounged from a junkyard, a set of very strong and dangerous Neodymium Iron Boron magnets, some enamled magnet wire, and a bunch of spare electronics.
A lot more went into this project than what you will read below, and I will have more pics and info to add later. Anyway, here is the appendix part of a paper we wrote describing the project:
======================
Appendix A (Calculated Blade Performance, Blade Parameter Selection)
Calculated Blade Performance:
The generator was designed to turn at a high speed so that it could produce a high enough voltage to charge a battery at low wind speeds(See Appendix C). This required a blade design with a high tip speed ratio.
Tip speed ratio is a ratio of the speed of the blades versus the wind speed.
TSR = (2 * pi * r * n) / (88 * V) Eq A.1
TSR = tip speed ratio of the blades
pi = 3.141592654…
r = radius of blade in feet
n = generator/rotor revolutions per minute
V = wind speed in mph
A tip speed ratio of 7 and a blade diameter of 8 feet was chosen, the first being the highest TSR a 3 blade design will operate at.
The chart below compares rotor efficiency and tip speed ratio:
Figure A.1 TSR versus Power Coefficient(% efficiency) for various blade types

This tip speed ratio gives an efficiency of 40% for a high speed 3 blade propeller. This will be used to calculate the amount of power that can be produced by the rotor. In practice, after all losses are considered and considering tip speed ratio is not constant, an efficiency of about 15% is more often realized. Thus, to get 1 kW from the generator, at least 3 kW or so must be theoretically producible from the blades. The speed at which the the most power is typically produced on small scale vertical axis wind turbines is about 30 mph; afterwards a speed limiter begins to reduce output. To meet the design constraints, an 8 foot diameter blade is thus ideal.
The swept area of the rotor now needs to be found.
A = pi * (r * 2)^2 / 4 Eq A.2
A = swept area of the blades (feet squared)
For an 8 foot diameter rotor:
A = 50.3 ft^2
Pr = .5 * Rho * 1.041 * A * V^3 * Reff Eq A.3
Pr = power extracted from wind by rotor (Watts)
Reff = rotor efficiency (%)
Rho = air density (m^3/kg), 1.25 m^3/kg a sea level
Using Eq A.1, Eq A.2, and Eq A.3, a chart plotting extracted wind power versus wind speed can be created:
Table A.1 (Wind Speed versus Extractable Rotor power)

Blade Parameter Selection:
When designing the blades that the turbine will use, the width needs to be calculated. The following equation is used to calculate blade width:
C = 2.44 * r / (TSR^2 * B) Eq A.4
C = blade width (m)
B = number of blades
The ideal blade width at the tip is thus .0664 m. The blades built measured .062 m at the tip, and an attempt was made to keep them as close to this spec as possible.
The ideal blade angle can be determined from Figure A.2 below:
Figure A.2 Ideal Blade angle versus Tip Speed Ratio

Thus the ideal blade angle is 2.5 degrees with a TSR of 7.
Wind turbine blades are commonly designed in 6 stations.
For a tip speed ratio of 7, the ideal station widths as a percentage of radius length are as follows:
Station 1(root): 12.5%
Station 2: 10%
Station 3: 8.3%
Station 4: 6.7%
Station 5: 5.8%
Station 6(tip): 5%
For a tip speed ratio of 7, the ideal drop from the trailing edge as a percentage of radius length are as follows:
Station 1(root): 3.1%
Station 2: 2.1%
Station 3: 1%
Station 4: 0.5%
Station 5: 0.3%
Station 6(tip): 0.2%
For a tip speed ratio of 7, the ideal blade thickness as a percentage of radius length are as follows:
Station 2: 2.1%
Station 3: 1.1%
Station 4: 0.8%
Station 5: 0.7%
Station 6(tip): 0.6%
Figure A.3 shows the carved blades.
Figure A.3 (Carved Blades)

Alternative Blade Parameter Selection:
Other designs were considered. A blade design with a 5.2:1 TSR was considered earlier when it was thought that the generator would produce power at lower wind speeds. This would be ideal for maximizing blade efficiency(see Figure A.1), theoretically obtaining a 47% efficiency.
B = 80 / (TSR)^2 Eq A.5
B = 3
Thus for 3 blades, the ideal tip speed ratio is 5.2 according to Eq A.5.
The ideal blade width of this design using Eq A.4:
C = .241 m
From Figure A.2, the ideal blade angle is 4 degrees.
This was impractical for two reasons. First, it would spin too slowly to generate the voltage needed to charge a battery at low speeds(~10 mph) without an expensive charge controller. Second, the wood obtained to carve the blades from was not thick enough to accommodate their construction.
If the stator coils were wound perfectly, this TSR value may have been practical for generating power at low speeds.
Appendix B (Generator Parameters)
The machine consists of 12 pole pairs of 2" diameter by 1/2" thick NdFeB magnets rated at 1.35 Tesla. The machine has 9 stator coils, each coil wound 64 turns of #14 AWG enamled magnet wire.
After the coils were wound, the synchronous impedance of a single coil was measured by an inductometer. The frequency at which this value was obtained was 60 Hz.
The synchronous impedance can be represented by the following equation:
Zs = Rs + j*Xs Eq B.1
Zs = synchronous impedance (Ohms)
Rs = synchronous resistance (Ohms)
Xs = synchronous reactance (Ohms)
The value obtained for Zs was the following:
Zs = .1203 Ohms + 1.38j Ohms
Since there are three stator coils per phase, the per phase value for Zs is as follows:
Zs = .3609 Ohms + 4.14j Ohms
Beforehand, the inductance values had been calculated. Though there are multiple ways to calculate inductance, we needed an equation that would find the inductance of a particular solenoid of thickness c and diameter of 2a.
Figure B.1 (Depiction of a Stator Coil)

The inductance formula that can approximate inductance of Figure 1.A is by the use of Wheeler’s equation:
L = 31.33(4π x 10e-7)N^2((a^2)/(8a + 11c)) Eq B.2
N = number of turns ≈ 64
a = .03175 m if d = 2.5 in.
c = .0381 m if d = 1.5 in.
L = 2.42 * 10^-4 H
Below are the measured results of the inductance parameters measured in series for a randomly selected stator coil:
Figure B.2 (Depiction of Stator coil Inductance)

Appendix C (Generator Testing)
After the generator was first assembled, it was tested. A wired phase was hooked up to a multimeter, the rotor spun until it reached 2V, and that voltage was kept reasonably constant by maintaining a steady speed. The amount of revolutions per minute to maintain that steady voltage was recorded. This was repeated for 4V and 6V.
We got the following data from the Agilent 33120A Digital Multimeter:
Table C.1 (Measured Voltage versus generator RPM)

It was determined that roughly 1V was produced for every 30 rpm. Permanent magnet AC generators are supposed to have a voltage that varies linearly with speed, and this one has that same characteristic.
The 3 generator phases were then wired in the delta configuration so that the generator could be tested under loaded conditions. It was spun at a constant speed, and an oscilloscope printout was taken from an Agilent 54622D Oscilloscope of the line to line delta voltage. The printout is Figure C.1.
Figure C.1 (Measured Generator output to Oscilloscope under load)

The current was measured at the same time the printout was taken with an Agilent 33120A Digital Multimeter. It was found to be 1.03A.
Appendix D (Generator Selection and Performance Calculations)
Permanent Magnet AC alternator- These have the advantage of being low cost per watt of output and are very efficient. The disadvantage is that small AC alternators suitable for wind turbines are difficult to obtain in low volume which usually means that one must be built from scratch. Building a design from scratch often means that it can be designed so that a gearbox is not needed.
AC Induction motor- AC induction motors have a low cost per installed watt and perform well at low speeds, but they lose efficiency at high speeds and are prone to overheating.
Permanent Magnet DC generator- While widely available and capable of producing usable amounts of power at low speed, these require a control system which may be difficult or expensive to obtain, require a DC to DC converter to give a steady output voltage suitable for charging a battery, and maintenance for these systems is increased.
Decision: Due to a desire for a system that requires minimal maintenance and offers a high amount of power per unit of cost, it was decided that a permanent magnet AC alternator would be the best choice for our design. If one can't be found for an affordable price, it will have to be built.
The equivalent circuit for a single phase of a permanent magnet AC generator is as follows:
Figure D.1 (Equivalent circuit of Permanent Magnet AC Alternator)

From this, equations for the stator voltage, current, and ideal power produced can be derived.
Ea = k*w Eq D.1
MAG[Ia] = MAG[Ea] / ((Rs + Ra)^2 + Xs^2)^.5 Eq D.2
Pe = (Ea^2 * Ra) / ((Rs + Ra)^2 + Xs) Eq D.3
Ea = stator voltage (V)
k = constant determined by number of poles and other factors
w = angular electrical speed (radians/s)
Ia = armature load current (A)
Rs = synchronous resistance (Ohms) = .3609 Ohms (See Appendix A)
Ra = armature load resistance (Ohms)
Xs = synchronous reactance (Ohms)
Pe = ideal power generated without losses (W)
MAG stands for magnitude, found by taking the square root of the quantity of the real component squared added to the imaginary component squared.
From the above,
w = 2*pi*f Eq D.4
f = electrical frequency (Hz)
It is known that the machine has 12 poles(See Appendix A). From this, angular mechanical speed can be found:
wm = 2*w / P Eq D.5
wm = angular mechanical speed
P = number of magnetic poles
Thus,
n = (wm * 30) / pi Eq D.6
Xs = w*Ls Eq D.7
Ls = synchronous inductance of stator coil (H)
Since the value of Xs varies with the angular electrical speed of the stator, the value for Ls should be solved first. Xs per phase is 4.14 at an electrical frequency of 60 Hz(See Appendix A). From Eq D.7:
Ls = .01098 H
A datapoint was taken of the generator’s 3 phases connected in the delta configuration so that the value of Ra under load could be found. This datapoint had the following information:
MAG[Ea] = 2.45V (See Appendix A)
MAG[Ia] = 1.03A (See Appendix A)
f = 3.39 Hz (See Appendix A)
From Eq D.2:
Ra = 2.01 Ohms
The stator voltage varies linearly with RPM, by a constant k. From the above datapoint and from Eq D.1:
k = .115
The generator is not 100% efficient, however. There are copper losses, core losses, mechanical losses, and stray losses to account for.
Copper losses can be found with the following equation:
Pcu = MAG[Ia]^2 * (Rs + Ra) Eq D.8
Pcu = copper losses (W)
It is assumed that core losses are 10% of the ideal power output. There was no available means to accurately measure core losses on hand.
Pcr = .10 * Pe Eq D.9
Pcr = core losses (W)
Friction losses also couldn’t be measured. It is assumed that friction losses are 1% of the ideal power output.
Pfr = .02 * Pfr Eq D.10
Stray losses are assumed to be 20% of core losses:
Ps = .2 * Pcr Eq D.11
Ps = stray losses (W)
Since Pe is the ideal power per phase, the power output per phase including losses can be found from the equation below:
Pp = Pe – Pcu – Pcr – Pfr – Ps Eq D.12
Now the total power output for the generator can be solved by multiplying the power per phase times the number of phases:
Ptot = 3*Pe Eq D.13
Ptot = total power produced by all three phases (W)
Thus from Eq A.1 and all equations listed in Appendix D, the following chart is obtained:
Table D.1 (Generator Performance chart)

At 30 mph, this machine should theoretically produce about 500W based on what could be calculated from experimental data.
If a capacitor were added in series with the armature, sized so that capacitance and inductance were equal at the resonant frequency of the circuit, the generator would be able to produce more power and extract more power from the rotor. Power output from the generator could potentially increase two-fold or more. However, in order to find this value, actual data points on voltage, current, and frequency along with the angles of voltage and current would be needed from high wind speed levels. These were not obtainable without the machine set up outdoors.
So long as the generator power output at a given speed is more than the wind power available from the rotor, it will be stalled. Thus from Table A.1 and Table D.1, the machine will spin at greater than 14 mph. With a properly sized capacitor in series with the armature, it would produce power at any speed where Ea is at least as high as the battery voltage. With a charge controller and this capacitor, it would produce usable power and spin at near stall condition.
Figure D.2 shows the completed generator.
Figure D.2 (Assembled generator)

Appendix E (Rectifiers)
Figure E.1 (Assembled Rectifier Block)

With the rectifiers connected to the circuit, a stable 3 phase DC voltage output was verified with an Agilent 54622D Oscilloscope.
Figure E.2 (Rectifier Output as Generator is turned from Oscilloscope)

Appendix F (Battery Selection and Calculations)
An energy storage medium will be needed to store the energy generated by the wind turbine for later use, so that it can be harnessed to run a water pump or other electric-powered device. To run a modest 50W load for 24 hours would require at least 1.2 kWh of energy storage, not factoring in efficiency losses. The following options were considered below.
Storage Medium Selection:
Pumped Water Storage- Retrieving energy from stored water is roughly 75% efficient. At a mass of 1000 kilograms per cubic meter, the potential energy of 1 cubic meter of stored water at 10 meters height is only 27.2 watt-hours. This is not feasible for this application.
Hydrogen Fuel Cell- Inefficient, costly, short-lived, and cumbersome, this would be a poor choice for this application at this time.
Flooded Lead Acid Battery- Flooded lead acid batteries are easy to maintain, inexpensive, and widely available. The require no regulation system for charging, making them ideal for wind turbine applications where the power going to them is not constant. Their downsides are that they typically have a shelf life under 5 years and last about 300-500 cycles to 100% discharge, require periodic watering with distilled water, and are heavy. In cold weather, they rapidly lose their ability to store energy. Keeping the batteries chronically discharged can cause permanent damage.
Sealed Lead Acid Battery- These are slightly more expensive than flooded lead acid batteries, widely available, and maintenance free. Their shelf life is about the same as flooded lead acid batteries, but they typically last fewer cycles, and require a battery management system to prevent overcharging. In cold weather, they rapidly lose their ability to store energy. Keeping the batteries chronically discharged can cause permanent damage.
Flooded Nickel Cadmium Battery- Far more expensive than any lead acid battery up front. However, their long shelf life of over 20 years, cycle life over 1,000 full discharge cycles, and ability to operate in cold weather without any loss in capacity makes them ideal for a small wind turbine application. However, they require a functioning battery management system to prevent overcharging and periodic watering. Cadmium is toxic and poses a serious environmental hazard.
Nickel Metal Hydride Battery- Large NiMH battery sizes for stationary applications are technologically feasible and have been built before, but are currently not available. They have similar shelf life and cycle life to flooded NiCd batteries, but don't require periodic watering and do not have toxic cadmium for their electrolyte. They require a battery management system.
Lithium Ion Battery- Lightweight and cycle life similar to lead acid batteries, but increased shelf life. In order to build a pack suitable for a wind turbine, a large array of cells would have to be assembled into a battery pack, requiring an extremely complicated battery management system to actively monitor each cell on charge and discharge. For this application, they are extremely cost prohibitive. Without a proper charging algorithm, serious safety concerns would arise.
Decision- Either the flooded or sealed lead acid battery would be the best choice for the application given the constraints outlined in the project description. While floodeds require periodic maintenance, they are more forgiving of abuse than sealed lead acid batteries, and therefore may be the better choice. The Trojan T105 flooded lead acid battery was selected for its large size, wide availability, low price, and long cycle life. The manufacturer and various distributors claim 300-500 cycles to 100% discharge, 225 AH at the 20 hour rate, 6V nominal. One battery can be had for less than $100 per unit from most retailers, making a set of two 6V batteries less than $200, for a total of 2.7 kWh of storage at the 20 hour rate. This is more than sufficient to power a 25W load for more than 2 days straight, which may be needed for days where the weather is unsuitable for generating power. Competitors included US Battery, Exide, and Interstate. Later in this report are calculations determining how long various appliances could run off of a fully charged battery bank with no new power being generated.
Battery Run Time:
Since the wind generator will not be making power 100% of the time, a battery bank and inverter will be needed so that an electronic appliance can be used. The battery run time will be determined by the power demand of the appliance being used.
It will be assumed that the Inverter averages 85% efficient.
Lead Acid batteries have a capacity that varies with the amount of amps drawn from them. The higher the amp draw, the less capacity they will deliver. Likewise, the lower the amp draw, the more capacity will be delivered. This is known as Peukert's effect.
At the 20 hour rate, the Trojan T105s have 225 AH of capacity, rated at 6V nominal. They have 115 minutes of reserve capacity at 75 amps, meaning they deliver a 75 amp draw for 115 minutes before running out. We can solve for the two Peukert's numbers with these figures.
Ex = (LOG10(20) - LOG10(RC / 60)) / (LOG10(75) - LOG10(RA / 20)) Eq F.1
X = Peukert’s exponent
K = Peukert’s capacity
RC = reserve capacity (Minutes)
RA = battery capacity at 20 hour rate (AH)
K = (RA / 20)^(X) * 20 Eq F.2
From this, we get 1.236 for Peukert's Exponent and 399 for Peukert's Capacity.
The Trojan T105s have .004 ohms internal impedance as well. So as current draw increases, battery pack voltage decreases.
Pb = Battery Power demanded (W)
S = Number of Batteries in String
O = Impedance of each Battery (Ohms)
R = Total Impedance of Battery String (Ohms)
Vn = Nominal Battery Pack Potential (V)
I = Battery Current Draw
K = Peukert's Capacity
X = Peukert's Exponent
Ti = Run Time (hours)
Ni = inverter efficiency (%)
Pa = Appliance power consumption (W)
We are using two batteries connected in 1 series string for 12 V nominal. The internal resistance of the pack can be found as follows:
R = S * O Eq F.3
R is therefore .008 ohms.
Next, we can calculate the current demanded from the pack for a given load.
I = (Vn - (Vn^2 - 4 * R * Pb)^.5) / (2 * R) Eq F.4
Pb = Pa / Ni Eq F.5
The run time in hours of the battery pack for a given current draw is as follows:
Ti = K / (I^X) Eq F.6
Below is a chart showing the power demands of various appliances.
Table F.1 (Average Power consumption of common appliances)

Table F.2 shows how long certain appliances could operate on a full battery charge if the wind turbine quit generating power, solved with all equations present in Appendix F:
Table F.2 (How long batteries can run an appliance from a full charge)

Appendix G (System Block Diagram)
Figure G.1 (Block diagram of Entire proof of Concept System)

Appendix H (Budget Analysis):
Table H.1 (Breakdown of costs for each item)

* The batteries were purchased used and would generally cost more at the mass production level. Trojan T105s can be found retailing for as low as $70 each.
A pricing formula was obtained and modified. It took on the following form(per turbine):
material cost + (overhead)/(x * n) + labor / 1 unit = price Eq H.1
x = lot size = 1000
n = number of lots(in one thousand units) per year = 20
overhead = $150,000
labor = $20/hr., total 10 hr. construction,
It is a generally accepted tule of thumb that at a manufacturing level, items can be purchased at a 45.7% industry discount over retail costs giving a $549 material cost.
The total consumer cost assuming $150 profit is $699.50, under $700.
Appendix I (Speed control)
A governor is not essential for a functioning wind turbine, however it can prevent damage from occurring to the turbine in dangerous weather conditions There are different ways to control the speed that the turbine rotates.
Electronic Speed Control- This method of speed control often requires the use of an anemometer and wind vane to determine the wind speed and direction that the wind is blowing it. If these two parameters become suitable for causing damage to the turbine, an electronic governor can shut the turbine off to prevent damage. However, this design greatly adds complexity and cost to a wind turbine.
Pitch Control- This method of speed control involves changing the pitch of the blades with wind speed so that rotor and generator speed are regulated with changing weather conditions. This is best suited to large scale applications.
Stall Control- Stall speed control involves shifting the rotor axis to an optimized direction based on wind conditions. Blades can be shifted to produce no lift, essentially shutting them off in unfavorable wind conditions. Once the machine is stalled, it needs to be restarted manually.
Yaw and Tilt The direction of the rotor can be changed to match the direction of the wind. This is known to reduce noise and allow the design to operate more safely at higher speeds.
Decision: Stall control is too labor intensive in fluctuating weather conditions, pitch control is ill suited for small turbine applications, and electronic speed control adds to cost and complexity. Given the relatively low power output of this design and a premium placed on efficiency, Yaw and Tilt control is optimal for this design.
The aforementioned generator design contains a furling system that will allow the turbine to turn out of high wind speeds and turn with lower wind speeds. If time permits, an electronic PWM governor may be added to the design.
Below is a schematic of the generator's yaw and tilt control furling system, designed by and credited to otherpower.com:
Figure I.1 (Furling System for Generator)

The proposed but unimplemented PWM governor has the following block diagram:
Figure I.2 (Block diagram of PWM Speed control)


Comment