= 250 rad/s = 2387.3 rpm

The rotor speed and the average frequency of the induced voltage are related by:

                   (Eq. 3.7)

Since a two-pole machine will be designed, the frequency is calculated using equation 3.9 to be 39.79 Hz.

3.6.2 Rotor and Stator Core

A cylindrically shaped rotor will be appropriate for this design as it allows maximum flux distribution over the armature surface as the field coils are spread over the periphery of the rotor. This type of design also accommodates the use of small cylindrical magnets [11].

A low carbon steel core with low permeability will be used in this design as it was found in the recyclable materials found in the village. This type of steel is cheap and mostly available. Compared with other better and expensive steel such as silicon, cobalt, etc. this type of steel has a very high core loss. The steel saturation flux density Bsat is estimated from the BH curve to be 1.5T.

3.6.3 Rotor Diameter (D)

The rotor diameter must be greater than the rotor yoke height (Hry), shaft radius (Rshaft) and the radial magnet length (Lm) [10].

D = 2 Hry + 2 Rshaft + 2Lm                                       (Eq. 3.8)

In this design, D is restricted by the magnet arc radius of 25mm. Therefore D will be 50mm.

3.6.4 Rotor and Stator Yoke heights

The minimum rotor yoke height Hry is the same as the stator yoke height Hsy. The height should be large enough to avoid saturation. This also has advantages of reducing core loss and reluctance.

The minimum yoke heights are given by [10]:

                                        (Eq. 3.9)

3.6.5 Airgap Length

The airgap length has a minimum value limited by the manufacturing tolerances; this value is typically in the range of 0.3mm to 1mm. In this design 0.5mm is chosen to be the airgap length.

3.6.6 Generator Length

The generator length is estimated to be 95mm; this is approximated from flux required to give the output voltage of the generator.

3.6.7 Airgap Flux Per Pole

In a radial machine, the flux per pole is given by:

                                              (Eq. 3.10)

where B is the average airgap flux density, D is the rotor inner diameter, L is the generator length, Kst is the lamination stacking factor and p is the pole pairs.

For this design the average flux density per pole Bgav is equal to the peak flux density Bg since the magnet arc is close to 180 degrees. Therefore the peak airgap flux is estimated to be 0.5T at the airgap and Kst is assumed to be 0.97.

The airgap flux and the lamination stacking factors were estimated from the following dimensions of the loudspeaker magnet:

·        Magnet arc = 180 mechanical degrees

·        Inner radius = 8mm

·        Arc radius = 25mm

·        Magnet radial length = 4mm

·        Area of one pole = 706.8 μm2

From the above magnet dimensions, the flux per pole in the machine is then estimated to be 1.16 mWb this value is calculated from equation 3.10.

3.6.8 Windings

The stators of most synchronous generators are wound with three distinct and independent windings to generate three-phase power [14]. A simple layer winding was used in this design. Slot per pole per phase was chosen to be 1 and the winding pitch was full pitch.

A.      Types of winding

The preferred type of winding is distributed winding as it reduces harmonics and makes better use of the stator or rotor structure. The mmf induced in the airgap is not sinusoidal, to get a pure sinusoidal mmf the number of slots have to be infinity. This means that the distributed winding is expected to have some harmonics.

Induced voltage for the distributed windings is:

                   (Eq. 3.11)

Kw is the winding factor and depends on the winding arrangements and has a value less than unity. Distribution factor Kd and a short pitch factor Kp reduces the winding voltage magnitudes but also reduces certain harmonics in EMF and MMF waveforms.

            (Eq. 3.12)

Distributed winding configuration has one slot per pole per phase and its winding factor is equal to 1.

B.      Winding arrangement

Single layer winding, where each slot contains one coil side, will be used in this design as it is economical to manufacture and has simpler end connection. Emf and mmf can be modified to reduce harmonics. In a three phase system even harmonics do not appear due to the winding symmetry, the only visible harmonics are the belt harmonics.

C.      Winding Pitch

Short pitch is the most commonly used type of winding pitch. It reduces the distorting harmonics and produces a truer sinusoidal wave. The length of the end connection is also reduced thereby saving copper and reducing copper loss in the coil.

The drawback of short pitch winding is that the induced emf in it is smaller than in a full-pitch coil. The reason is that the total flux linking the short-pitch coil is smaller than that of the full-pitch coil.

3.6.9 Number of turns

The number of turns per pole is estimated to be 60 turns from equation 3.11.

The design parameters discussed will be modelled in FEMM in the next chapter to induce the output voltage and flux of the generator.

Chapter 4. Modelling the design in FEMM

4.1 Introduction

The investigation that will follow focuses on the effect of substituting standard commercial magnets with recyclable speaker magnets that were collected from a dumpsite in the village, to compare the performance of the generator in either case.

In this chapter, the two pole generator geometry discussed in chapter 3 will be modelled in FEMM to analyse the output induced voltage and the flux of the generator. The lua-script in FEMM is run and the rotor is rotated 360 electrical degrees, for the lua-script refer to appendix C1.

Initially, a choice was made of three typical commercial magnet grades. Neodymium-iron-boron NdFeB was chosen from the rare-earth magnet group. Alnico6 was chosen from the Alnicos and the last type was barium ferrite from the ferrite or ceramic group. Then the machine will be modelled using different types of commercial magnets to investigate the performance of the generator.

The author then proceeded to investigate the magnetic properties of the loudspeaker magnet. This was done so that the parameters can be modelled in the finite element package.

Finally a design using the loudspeaker magnets was modelled to explore the recycled generator output.

4.2 Two pole geometry

Table 4.1 below summarizes the generator specifications that were discussed in chapter 3. These parameters will be modelled in FEMM to view the output induced rms voltage and the flux.

Table 4.1 Data of designed PM machine

The design is modelled in FEMM and is illustrated in figure 4.1 below.

Figure 4.1 The generator modelled in FEMM

4.3 Commercial magnets

To investigate the performance of the generator, the author began by modelling the generator with standard commercial magnets with the properties given in table 3.1. The output rms emf and flux of the generator is tabulated in table 4.2 with different magnets that were used in the design.

Refer to appendix B for the graphs of the outputs. Matlab soft ware was used to draw the output rms emf and the flux, matlab code included in appendix C2.

Table 4.2 Generator output with commercial magnets

4.4 Recyclable magnet found in the rural area

The magnet that was used in this section was from a loudspeaker that was found lying in one of the dumps at Ga-Rampuru village. To start with the magnet shape was not of concern. The author aimed to investigate the performance of the magnet on the speaker if used as it was found. The properties of this magnet were investigated and a design was modelled using these magnets. The magnet is shown below in figure 4.2.

4.4.1 Background on the characteristics of loudspeaker magnets

For speaker applications, the amount of permanent magnet required is directly proportional to the rated output power of the speaker. In other words high power speakers are often made using the high-grade magnetic types like the rare-earth. But since the speakers found in the dumpsite were from low power appliances their typical magnets are normally from the ceramic group type. In addition unlike Alnico magnets, ferrite or ceramic magnets are not easily demagnetised magnetized and hence find wide application in such appliances.

4.4.2 Properties of the loudspeaker magnet

According to its nameplate the speaker that used the magnet in figure 4.3 had a 0.5W rms and an impedance of 8 ohm. The magnet type on the loudspeaker is a ferrite [Refer to appendix D1]. The manufacturer of the magnet on the speaker is traced in order to find the B-H properties of the magnet on the speaker.

Appendix D2 indicates TDK datasheet for ferrite magnets FB series. These notes were used to find the magnetic, physical and mechanical characteristics of the magnet. The properties of the loudspeaker are summarized in table 4.3.

Table 4.3 Summarized properties of the magnet speaker

4.4.3 Output EMF and flux of the recyclable generator

The properties were modelled in FEMM, and the generator outputs are tabulated in table 4.4. Refer to appendix B2 for the graphs of the outputs.

Table 4.4 Generator output with the loudspeaker magnet

4.5 The estimated output power of the generators

The output electrical power of a generator is given by:

                                      (Eq. 4.1)

where V is the terminal voltage of the machine. The power factor is assumed to be unity for these calculations since all the simulations and investigations are done at no-load.

From the rated power of the generator which is 36W. If the rated voltage is assumed to be 12 V then the rated current of the generator can be calculated from equation 4.1 to be 1A.

Table 4.2 and 4.3 above gives the results of the simulated induced voltages and flux obtained from the generator with commercial and recycled magnets. Using the 1A above as the rated current, the output power of the generator using commercial magnets and recycled loudspeaker magnets is summarized in table 4.5 below. The output power in all the cases is calculated from equation 4.1.

Table 4.5 The output power of the generator

Chapter 5. Analysis of the generator outputs

In this chapter the author first began by analysing the output power of the generator designed with commercial magnets and the one with recycled loudspeaker magnets. The author then explored the factors that may have affected the outputs from the recycled generator.

The terminal voltage induced from the recycled generator is also explored to view if it can be used in any applications in the rural village. This is done so that the voltage can be evaluated if it is useful or not

Lastly the loudspeaker magnets are investigated to view how they can be used in the recycled generator design; whether they should be smashed and aligned to be re-used in the generator design or if they should be used the way they are without being smashed.

5.1 The estimated output power of the generators

The output power of the generators is estimated from the output induced voltages of the generators. Consequently, this means that the higher the terminal voltage of the generator the larger the output power.

From the theory of magnets it is clear that the induced voltage is directly proportional to the remanent magnetic flux density Br of a magnet. In other words it is expected that rare-earth magnets which posses higher Br will always induce high voltage when used in generators. Therefore it can be said that the type of magnet used in a generator is very important as it determines the output power of the generator.

As can be seen from the results, the induced voltage of the generator with NdFeB magnets from the rare-earth magnet family is higher than that with the AlNiCo and ferrite magnets. This was expected because of the different B-H properties of these magnets.

The recycled generator in this thesis was designed using loudspeaker magnet that is from the ferrite family. These types of magnets are cheap and readily available, but their disadvantage is that they posses low surface flux density. The induced voltage was therefore expected to be much lower than the voltage induced in a generator with NdFeD magnets.

5.2 The rms output flux of the generator

The magnetic flux density in the gap of PM generators is limited by the remanent magnetic flux density of PMs and saturation magnetic flux density of ferromagnetic core. Hence, the simulated value of output flux is directly proportional to the remanent magnetic flux. In addition, permanent magnet machine cannot normally produce the high flux density of a wound pole rotor.

5.3 Factors that may have affected the recycled generator outputs

There are many factors that should be taken in consideration with regards to the induced voltage from the recycled generator. Some magnetic deterioration may have occurred after the magnets were thrown into the dump. But, due to the magnet’s magnetic permanent properties, these magnets are expected to still have some surface flux density when found in the dumpsites.

This is evidence that any permanent magnet that is found in the dumpsites can be reused in a generator design to induce some voltage, of course depending on their B-H properties.

The estimated properties of the speaker magnets that were used in this thesis were found from the loudspeaker manufacture, clearly these properties will not be the same as the properties of recycled magnets that were found in the rural area of Ga-Rampuru. These recycled magnets have been affected by different conditions such as temperatures, climates, etc.

The exact properties of the recycled magnets can only be found by testing these magnets in the laboratory. For this thesis the author was unable to take the loudspeaker magnets found in the rural area of Ga-Rampuru to the laboratory.

5.4 Applications of voltage from the wind turbine

The induced voltage of the generator will vary with the wind speeds experienced in this village. The generator can be connected to a battery to store the power which can be utilized when there is little or no wind.

If more power is required, the voltage can be boosted by using any economical booster that can convert the output of the recycled generator to at least a minimum of 12V. The voltage from the booster can then be put through a cheap electronic regulator that will only charge the battery if the boosted voltage from the wind generator is sufficient to produce at least 12V direct current.

To power the refrigerator in chapter 1, the store owner in the village will have to purchase an inverter that will convert the DC voltage to AC voltage. The inverter will convert the low-voltage from the battery (12V) into mains-type 230V alternating current.

5.5 Design using speaker magnets

Finally, the author investigated how speaker magnets can be used in the generator design, if they have to be smashed or used as they are.

As already investigated, loudspeaker magnets are commonly from the ferrite magnets family. Ferrite and rare-earth magnets are by nature very hard and brittle. Although they can be cut, drilled and machined this should only be done by individuals who are experienced with ceramics. If the magnets get over about 300 deg F, they will lose their magnetism permanently [17].

Therefore, it will be very difficult for rural artisans to cut these magnets and use them. Due to limited time the author could not investigate if these magnets can be used as they are in the machine.

In the next chapter the author attempts to assemble the wind generator in the laboratory.

Chapter 6. Practical comparison of the generators

6.1 Introduction

The following chapter outlines the steps that were taken in order to assemble the permanent magnet generator discussed in the previous chapters. This is done in order to compare the practical outputs of the generator with the simulated ones. The other reason is to investigate the performance of recyclable magnets with irregular shapes.

This investigation will only concentrate on assembling the generator part of the wind turbine system.

For the construction of the PM generator in this thesis two options were considered, the first was to collect readily available off-shelf materials to assemble a small generator. And the second was to convert an AC induction motor to a PM generator. Both options are discussed in this chapter.

6.2 Materials required to assemble a PM generator

The main idea is to build a portable generator that is easily assembled and constructed in the laboratory. The author first begins with highlighting all the materials that are needed in the construction of this generator. Figure 6.1 gives the schematic of how the generator will look like.

Figure 6.1 Basic wind generator design

From the generator illustrated above it is clear that the following materials will be required in the construction of the generator:

·        Magnets

·        Stator and rotor

·        Rotor mounted on a rotating structure

·        Structure mound

In the following sections the author will outline steps taken and the challenges faced in collecting these materials.

6.2.1 Magnets used in the generator

In the investigation of the performance of the generator, the author was to begin by designing the generator using standard commercial magnets, which were to be later substituted with recyclable magnets. The recyclable magnets are picked randomly in the dumpsites of Ga-Rampuru village.

Finding commercial magnets for this investigation was a major challenge since for this two-pole generator the author needed to purchase two NdFeb32 magnets, two Alnico5 magnets and two ceramic8 magnets.

6.2.2 Stator and rotor

The rotor rotates with the structure mount while the stator is fixed and mounted to a support structure. Since all these investigations were to be carried out under controlled laboratory conditions a drive and a frequency inverter which are readily available in the laboratory will be used to rotate the rotor at the desired speeds.

The drive will rotate the rotor and the induced voltage from the coils on the stator will be monitored by a voltmeter in the laboratory. Figure 6.2 illustrated this type of drive.

The size of the rotor in this thesis was constrained by the diameter of the recyclable speaker magnets. Therefore steel with this shape had to be found or cut to this shape. After finding the relevant steel, the cylindrical steel has to be drilled at the center.

6.3 Converting an induction motor into a PM generator

Due to the challenges faced in gathering the materials needed to assemble the generator the author then decided to find an alternative method to investigate the performance of the generator using recyclable magnets. A company called Magnetag that supplies motors and generators was approached and after some negotiations the company was willing to donate an AC induction motor to the author.

The idea was to convert this AC induction motor into a permanent magnet generator. This was going to be done by stripping the motor down and replacing the wound rotor with recyclable magnets. This looked like an attractive option since recyclable magnets with any shape can be used in the generator to explore its performance

The author was unable to complete investigating this option in detail. This is strongly recommended for further work most probably at MSc level.

6.4 Challenges faced during the construction of the PM generator

The main challenge in the construction of this wind generator was cost. For the laboratory investigation of the PM generator, a lot of materials, like the magnets and coils on the stator were found to be very expensive. This inadvertently gives more support for the use of recycled materials.

There was a lot of machining needed for this project, the rotor and the stator needed to be cut and shaped to the desired diameter and drilled in the centre to fit on the mount structure. Time was the major constrained since a lot of things were required to be done in the limited time given for this thesis.

However the framework of how to proceed in constructing and assembling the wind generator is already well laid out in this thesis.

Chapter 7. Conclusions

Based on the findings of the report, the following analyses and conclusions were drawn:

7.1 There is an urgent need of electricity

Due to the number of people living without electricity in rural South Africa it is clear that alternative means of supplying these areas is essential. According to ESKOM, all house holds will eventually be electrified, but the problem is, what is happening in the meantime? Where are children’s medicines being stored? Therefore this makes the electrification process extremely urgent.

7.2 Resource assessment

7.2.1Recyclable materials in the village

An extensive assessment on the rural village of Ga-Rampuru was conducted. There are plenty of recyclable materials including old milling machines that are not in use. These materials can be recycled to clean Ga-Rampuru village.

7.2.2 Rural artisans who can assemble the wind turbine

Since there are many local artisans who fix cars, electrical appliances and do some mechanical work in this village, manpower should not a problem. An engineer from the government or Non-governmental organization could educate these local artisans on assembling the wind generator. This will have a positive impact on Ga-Rampuru village as it will encourage people to work and be creative. There are many old wind mills used for pumping water in Ga-Rampuru village, most of these wind mills are working perfectly well supplying sufficient water. This is a clear indication that there is a reliable supply of wind in the village.

7.3 Simulation results

It has been shown that a reasonable amount of power can be realised from a generator using recycled magnets from the dumpsites

7.4 Cost involved in the design

The overall cost of assembling this wind generator system will be very cost effective since all the materials are recycled from the village, and the entire system will be assembled by local artisans.

7.5 Validity of this thesis

Small power that can turn on small lamps will really be appreciated in this village as children will be able to study after sunset. This will clearly have a wide range of positive developmental benefits on this community.

Chapter 8. Recommendations

Based on the above conclusions, the following recommendations were drawn:

1.       For a more accurate recyclable wind turbine design, all its components such as the drum, the tower, rotor disk and cables must be explored in depth. The following must be considered:

·        Investigate how to extract maximum power from the wind using the drum, and how to prevent the drum from over spinning.

·        How to use other irregular recyclable magnets in the village in the generator design.

2.       Investigate how a permanent magnet generator topology can be changed or re-designed to accommodate the design of a generator with the shape of the loudspeaker magnets.

3.       Look in to how the magnets can be removed from the speakers, since very strong clue is used to mount them, how this can be done in a cost effective way.

4.       The axial flux permanent magnet topology should also be looked into to compare it to the radial flux type.

5.       The exact costs of assembling and maintaining the recycled wind turbine should also be incorporated in the design procedure.

6.       With the little output power generated in this thesis, this project must definitely be taken further to alleviate the electricity problems in South Africa.

References

1.       Socio-economic rights project, “The right to affordable electricity” copyright @ community law centre 2002

2.       IDASA, <#"1.files/image027.gif">

b)       Alnico FLux_RMS =0.0168

EMF_RMS = 5.1619

c)      
NdFeB FLux_RMS = 0.0459

EMF_RMS = 9.4262

2. Loud Speaker Magnet

FLux_RMS = 0.0171

EMF_RMS = 3.4987

Appendix B

Matlab code for sketching the output emf and flux of the generators

% EMF calculation from FEMM

%By Maribini Manyage

clc

clear all; close all;

P = 2;

w = 1912; %mechanical speed in rpm

freq = (w*pi/30)*P/(4*pi); %frequency

XA = load('flux_link_A.txt');

XB = load('flux_link_B.txt');

XC = load('flux_link_C.txt');

beta = XA(:,1); % angle between Is_r and d-axis [elec degrees]

alpha = beta - beta(1,1); % Rotor position in [elec degrees] from Zero

time = alpha*(pi/180)/(2*pi*freq);%*1000; %time

flux_link_A = 2*XA(:,2);

flux_link_B = 2*XB(:,2);

flux_link_C = 2*XC(:,2);

% Perform spline in order to differentiate flux linkage vs time

pp_flux_A = spline(time,flux_link_A);

pp_flux_B = spline(time,flux_link_B);

pp_flux_C = spline(time,flux_link_C);

% extracting piecewise polynomial coefficients and derivation

[hgt,wdth] = size(pp_flux_A.coefs);

clear AA;

for k = 1:hgt

AA(k,:) = polyder(pp_flux_A.coefs(k,:));

end

dpp_flux_A = MKPP(time,AA)

[hgt,wdth] = size(pp_flux_B.coefs);

clear AA;

for k = 1:hgt

AA(k,:) = polyder(pp_flux_B.coefs(k,:));

end

dpp_flux_B = MKPP(time,AA);

[hgt,wdth] = size(pp_flux_C.coefs);

clear AA;

for k = 1:hgt

AA(k,:) = polyder(pp_flux_C.coefs(k,:));

end

dpp_flux_C = MKPP(time,AA);

%back emf

emf_A = ppval(time,dpp_flux_A);

emf_B = ppval(time,dpp_flux_B);

emf_C = ppval(time,dpp_flux_C);

figure(1);

plot(time*1000,flux_link_A,'r-');

hold on;

plot(time*1000, flux_link_B,'b-');

plot(time*1000, flux_link_C,'g-');

title('Flux linkage - under noload');

xlabel('Time [ms]'),ylabel('Flux linkage [WbT]')

grid;

figure(2);

plot(time*1000,emf_A,'r-');

hold on;

plot(time*1000, emf_B,'b-');

plot(time*1000, emf_C,'g-');

title('Back Emf - under noload');

xlabel('Time [ms]'),ylabel('Back EMF [V]')

grid;

x = length(flux_link_A);

FLux_RMS = norm(flux_link_A)/sqrt(x)

y = length(emf_A);

EMF_RMS = norm(emf_A)/sqrt(y)

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