Planning of mobile complete set for a rural wind generator
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Planning of mobile complete set for a rural wind generator
The aim of this thesis is to alleviate the chronic lack of electricity supply in the rural South African areas by designing a portable wind generator kit.
An extensive assessment on the rural village of Ga-Rampuru, in Limpopo Province, was conducted, to investigate the present needs, as well as the availability of resources both human and material that would be needed to construct and assemble the system. From the inventory of recyclable materials found during the investigation the author was more inclined to suggest the design of a wind turbine that could be assembled and maintained by the local artisans.
A two pole permanent magnet synchronous generator was designed using standard commercial magnets, which were later replaced by recyclable loudspeaker magnets that were found in the village. This was done to compare the output of the generator in both cases. All the designs were modelled in FEMM, a software package, to estimate the induced voltage and flux of the generators.
Using standard commercial magnets the simulated voltage and flux levels were 9.4, 5.1, 3.6V and 0.0489, 0.0186, 0.0175 Wb, respectively. Assuming a generator current rating of 1 amp this would yield 36 watts at the estimated average wind speed of 4 meters per second.
Then when these were substituted with recycled speaker magnets the generator yielded a voltage of 3.5V and a flux of 0.0171Wb. The estimated output power of the recycled generator was estimated to be 10.5W. This compared well with the power output from the commercial magnets generators.
From these preliminary results it is quite apparent that a viable generator can be designed from the recyclable magnetic components. The same design procedure as outlined in this thesis can be used to design larger recycled generators with larger outputs. The design of this wind turbine will obviously have a wide range of positive developmental benefits on the community of Ga-Rampuru.
The next stage was practical construction to validate of the simulation results. This however could not be realised in time.
Chapter 1. Introduction1.1 The subject of the reportThe aim of this thesis is to design a simple wind generator kit that can be easily assembled and installed by rural artisans. The kit will use recyclable materials that are found in the rural areas to ensure a cost effective and environmentally sustainable solution. 1.2 Background to research and investigation of rural electrification“Electricity brings immeasurable benefits to human life. With electricity, comes lighting and the ability to extend the daylight hours, to study and to improve education. With electricity come cooling and heating and the ability to store food and cooking. At its extended level, electricity facilitates communications, transportation and production and paves the way for the eradication of poverty, industrialisation and ultimately the growth of our country's economy”.Electricity is a basic necessity and access to it has a wide range of positive developmental benefits for communities , yet, in 2001 2.8 million South African households still had no access to electricity . The majority of these households are poor and live in remote places which are located far from the central business districts and the country's electricity grid. And this makes it very expensive to connect them to the country's electricity grid. As a national initiative to improve the quality of life in South Africa, National Electrification Programme (NEP) aims to provide universal access to all South Africans by 2012 . Hence, this has lead to the investigation of other safe, cost effective and environmentally friendly alternative methods of electrifying rural areas in South Africa. Renewable energy resources such as wind and solar, are the fastest growing alternative means of providing a reasonable amount of energy at the point of demand. The Government of South Africa is also determined that renewable resources will be a major complement to the national mix .1.2.1 Ga-Rampuru, a typical rural South African villageGa-Rampuru is a small village located in Limpopo Province in South Africa. The village is in a fairly rural mountainous area, which is situated some 58 odd kilometres from Polokwane, the provincial capital city. The area has sparsely populated households with some trading stores and schools. Most of the people in the village are unemployed and rely on agriculture for their subsistence.People in the village have to travel long distances to collect wood or to purchase fuels like liquid petroleum gas (LPG) and kerosene to meet their cooking, lighting, refrigeration, infotainment and other needs. Figure 1 illustrates a picture of an LPG refrigerator in one of the trading store in Ga-Rampuru. This picture and others that will follow in this thesis we taken by the author during a visit at Ga-Rampuru last June vacation.The supply of these fuels is both expensive and unpredictable. Additionally the problems related to the use of fuels such as kerosene are incidences concerning burned houses and respiratory problem for children who use kerosene candles for reading is well documented world wide .
The author paid a visit to the Provincial ESKOM office to enquire about any plans to extend the grid to Ga-Rampuru village; and the Electrification Manager guaranteed that ESKOM has plans to ultimately electrify the whole country by 2012. However, further discussions with people from Ga-Rampuru dismissed the ESKOM Manager's promises as empty. They contended that they had heard similar promises but they still lived in darkness.
It was the conclusion of the author that an alternative solution to the problem had to be devised. Some means of generating electric power to meet loads such as the refrigerator in figure 1, if only it could be an affordable design. The best design would clearly be one that uses local material and human resources.1.2.2 Resource assessmentThe author spent the next three weeks exploring the resources available in Ga-Rampuru that would support the design and sustainable construction of electricity generators. To begin with Ga-Rampuru has two schools, namely Rampuru primary school and Seokeng secondary school, all which constitute a total population of roughly 1400 pupils. On average 30% of school leavers will continue to tertiary education, some will migrate to urban centres in search for jobs and a substantial number will remain in the village. This village is endowed with adequate human capacity with intermediate levels of education. These would constitute a source of trainable technicians and potential consumers of locally manufactured products. There are also local mechanics who fix cars and some electrical appliances. These people will be easily trained as they have hands on experience.Some of the people who left the village for jobs in the cities come back to settle down in the village and build big houses like the one indicated in Fig 2. This clearly indicates that this people can afford the electricity tariffs if they were to be supplied with power.Moving further around the village there was evidence of old windmills used for pumping water. Figure 3 shows one of the windmills. These windmills operate satisfactorily providing enough water to the villagers. The presence of these windmills in this area is evidence that there is some wind resource in the area.Further investigations took the author to various waste-dump sites and a range of disused old gadgets that could potentially be re-used, as shown in appendix A, were discovered. These included cables from an old car, loudspeaker magnets, drums and old machines that were used for grinding grain.The other natural resource in the area (of course) is the sun but from the inventory of recyclable materials found during the investigation it is more inclined to suggest the design of a wind turbine.1.3 Objectives of the reportIn light of the above background, the main objective of this thesis is to design a small wind generator for Ga-Rampuru village using recyclable materials found in this village. The idea is to build an easily assembled and manufactured machine that can be build by the rural artisans. This wind generator must of course be cost effective.The resource assessment of Ga-Rampuru village is conducted in order to investigate the present needs, as well as the availability of resources both human and material that would be needed to construct and assemble the wind turbine using recyclable materials. Furthermore, the resource assessment analyses lead to an appropriate wind generator design specifically for Ga-Rampuru village.1.4 Method of investigationThe investigations were conducted in July 2006 at Ga-Ramrupu village in Limpopo province. The author collected information regarding this village in the following manner: 1. The author grew up in Ga-Rampuru village and therefore knows the problems and challenges that the villagers face on a day-to-day basis living without electricity. This was an advantage in terms of moving around the village doing the resource assessment analysis.2. One of the store owners in the village, Mr Morifi was interviewed regarding the issues he faces in supplying power to his store, especially to the refrigerator he has in store. The store owner mentioned that he has to refill the petroleum gas (LPG) in his store every two weeks. He also added that this is very expensive as there are also transport costs involved. 3. Face to face interviews were conducted with some of the villagers where many concerns and challenges were raised. Most of the villagers said that it has been several years since they have been promised to be electrified and nothing has been done to date. 4. The author paid a visit to the Provincial ESKOM office in Pretoria to enquire about any plans to extend the grid to Ga-Rampuru village. The ESKOM Electrification Manager, Jack Bandile was interviewed in this regard. 1.5 Plan of developmentThe report begins with a brief background of the thesis and introduction of the rural area for which the wind generator will be designed for. Then, the remaining project researches are outlined as follows:· Chapter 2 reviews the design of a small wind generator and after that a wind generator suitable for Ga-Rampuru village is designed using recyclable materials that where found in this village.· Chapter 3 details the procedure undertaken to design a permanent magnet synchronous generator for Ga-Rampuru village wind turbine.· Chapter 4, the generator geometry discussed in chapter 3 is modelled in FEMN using recyclable and commercial magnets to analyse and estimate both machine designs.· Chapter 5 discusses the results found in chapter 4.· Chapter 6 details all the steps that were taken in an attempt to assemble a prototype of the wind generator.· Chapter 7 & 8 concludes the discussion based on the analyses and finally presents recommendations.Chapter 2. Design of the wind turbine prototype 2.1 Background on wind energyWind powered systems have been widely used since the tenth century for water pumping, grinding grain and other low power applications . Since then, this has lead to an investigation and attempt to build large wind energy systems to generate electricity.Wind energy has proven to be cost effective and reliable in the past years. The main development of this technology has been with large wind turbines in the industrialized world, but there is scope to deliver decentralized energy service in the rural areas of developing countries . Furthermore, wind energy is an attractive option to generate electricity since it does not consume fossil fuels nor emit greenhouse gases. The land on which the wind generators are build may also be used for agricultural purposes such as ploughing the land or domestic animal gazing. During its transition from the earlier day's wind `mills' to the modern electric generators, the wind energy conversion systems (WECS) have transformed to various sizes, shapes and designs, to suit the applications for which they are intended for . In this chapter, the main components of a simple small wind generator will be investigated and a wind generator suitable for Ga-Rampuru village will be designed using recyclable materials found in the area. The available wind resource is governed by the climatology of the region concerned and has a large variability from one location to the other and also from season to season at any fixed location . Hence, it is important that the wind generator is designed for a specific area; this will ensure that the wind energy in that specific area is exploited to generate maximum power from the wind. 2.2 Wind turbine basic principles The wind generators are specially designed and build to extract power from turning blades with the maximum efficiency and minimum complexity . The magnet rotor disk rotates as a result of the force of the wind on the turbine's blades. A typical small wind generator consisting of blades, tower, PM generator and the cabling is illustrated in figure 2.1. The main components, which are common to most wind generators, will be discussed below.Fig 2.1 Basic features of a typical small wind generator 2.2.1 The bladesModern wind turbine rotors usually have two or three wooden blades. A larger number of blades would create more turning force (torque), but would not be capable of driving the PM generator fast enough to generate the required voltage, because the rotor would turn more slowly . The rotor blades are designed in such a way that they extract the maximum power from the wind.Power supplied by the blades to the generator is : (Eq 2.1)whereis the air density (Kg/m3), C is the dimensionless power coefficient and A the area swept by the blades in m3. In equation 2.1 above, the power drawn from the wind is proportional to the cube of the wind speed. This means that if the wind speed doubles, there is 8 times as much power available from it . A further important parameter is the tip speed ratio. The tip speed ratio is defined as the ratio of the tip of the blade to that of the undisturbed wind velocity entering the blades . The ratio is given by : (Eq 2.2)where R is the radius of the blades, щr is the rotor speed in rad/s and W the wind speed (m/s). Multi bladed rotors operate at low tip speed ratios of 1 or 2, where else, one, two or three bladed rotors operate at higher tip speeds of 6 to 10. The power coefficient in equation 2.1 depends on tip speed ratio as shown in figure 2.2. For a particular wind rotor design there exists a tip speed ratio which will produce the maximum value of power coefficient .Fig. 2.2 Power coefficient Cp versus tip speed ratio 2.2.2 Permanent magnet generatorUsing permanent-magnet generators for small wind turbines is very commonly used world wide. Usually an AC generator with many poles operates between 10-100 Hz. Many configurations use surface mounted three phase permanent magnet synchronous generators with a rectifier connected to the generator terminals. A simple PM generator consists of the stator, magnet rotor disk and a shaft. The magnet rotor disk is mounted on a bearing hub so that it can rotate on the shaft due to the rotating blades of the wind generator. The stator has coils of copper wire wound around them, which are accommodated in the slots. Electricity is then generated when the magnets on the rotor disks rotate past the coils embedded in the stator. The magnetic field that is created induces a voltage in the coils .2.2.3 Rotor designThere are two types of rotor configurations commonly used world wide, these are the disk and the cup as shown in figure 2.3 below . Fig. 2.3 Disk and cup rotor designsThe radius of the rotor primarily depends on the power expected from the turbine and the strength of the wind regime in which it operates . 2.2.4 TowerThe main function of the tower is to raise the blades and the generator to a height where the wind is stronger and smoother than the ground level. The wind speed increases with height because of the earth surface . The tower should be high enough to avoid any obstacles such as trees, building, etc. Practical considerations such as expense, safety and maintenance limit the tower to between 10m to 20m  above ground level.2.3 Design of a wind turbine for Ga-Rampuru villageIn this section a wind generator that is designed specifically for Ga-Rampuru village will be discussed. The generator will be designed using recyclable materials such as car brake plates, cables and drums found in the village [See appendix A]; this will clearly ensure a cost effective design. The wind turbine will be designed in such a way that the local people can easily assemble and manufacture it themselves.All the recyclable materials that will be used in this design will be discussed below and an artist impression of the wind generator will be sketched.2.3.1 The drumThe output of the wind generator depend on the amount of wind swept by the blades, therefore the wind extracting materials in a wind generator are very significant. A plastic drum will be used in this design to extract the wind since it can be easily shaped and carefully balanced to run smoothly. Also, it is resistant to fatigue braking and has a very light weight.The drum will be assembled as follows:1. The top and the bottom part of the drum will be cut carefully by using a knife or pair of scissors to make a cylinder with open ends.2. The cylindrical drum is then cut length-wise into two equal halves.3. The two halves are then glued together similar to the drum shown in figure 2.4.Figure 2.4 An S-shaped drumTo prevent the over speeding of the drum, the permanent magnet generator should always be connected to a battery or other electrical load. If this is not done the wind turbine will become noisy and may vibrate so much that some parts come loose and fall to the ground . 2.3.2 Magnet rotor disk After a tour around the village neighbourhood dumpsites it was discovered that there are many discarded loud-speakers that are no longer in use in the village. These loud-speakers have permanents mounted to their back. Since the PM generator requires magnets, these loud-speakers will be recycled and the magnets on them will be used in this design. Figure 2.5 shows one such magnet that was found in the village.There are many factors such as heat, radiation and strong electrical currents that can affect the strength of a magnet , especially in such discarded state. These factors will be discussed later to investigate exactly how much surface magnetic flux density these magnets loose in the dumpsites. And later on in this thesis the performance of a PM wind generator designed using standard commercial magnets will be compared to a generator using the recycled loudspeaker magnets as substitutes. Designing a generator using the speaker magnets will pose the following challenges due to their shape and strength:· How does one design a machine with these magnets?· Do they have to be smashed and aligned to work?· Or should they be used the way they are?· How much flux density do these magnets have, in other word, can they give out any power when used in the generator design?· Can different magnet types be used on one machine? As this magnets are picked randomly in the rural area.2.3.3 Rotor Disk A cylindrically shaped rotor is preferred as it allows the proper distribution of flux over the armature surface as the field coils are spread over the periphery of the cylindrical rotor. Hence, a brake plate from an old car like the one in figure 2.6 will be used as the rotor in this design to hold and house the magnets.2.3.4 Distribution cablesAll the cabling that will be required in the construction of the wind generator was found in an old car in the village [See figure 2.7].2.3.5 Artist impression of the wind turbine
Figure 2.8 below shows the artist impression of the wind generator designed exclusively for Ga-Rampuru village.
Figure 2.8 Ga-Rampuru wind generator
The following chapters describe the steps taken by the author to investigate the performance of a synchronous permanent magnet machine constructed using recyclable loudspeaker magnets.Chapter 3. Generator Design3.1 A brief background
This chapter will detail a simple procedure undertaken to design the wind generator from recyclable materials. Permanent magnet machines are preferred for this application as they reduce the excitation losses significantly and hence a substantial increase in the efficiency of the machine. In addition, permanent magnet machines are simple to construct and maintain .
The most common wind turbine systems are three blades rotating on a horizontal axis coupled to an alternator to generate electricity, which could be used to for battery charging. For a picture of a typical basic wind turbine system refer to figure 2.1 in chapter 2.
A normal two- pole synchronous permanent magnet generator will be designed and its performance will be analysed. Then recyclable loudspeaker magnets found in the rural area of Ga-Rampuru village will be used to substitute the standard commercial magnets in the generator. The performance of the new generator will be analysed to understand the effect of the loudspeaker magnets on the generator performance.
For this investigation, matching the refrigerator load in chapter 1 will not be a priority.
This chapter will start with outlining the desired generator specification and then the generator will be designed thereafter. To design the generator the permanent magnet properties will be discussed to understand their effect on the generator performance and losses due to these magnetic materials will also be investigated. And then, all the variables that are necessary to construct and design a generator geometry will also be discussed.
Throughout this thesis the generator performance will be tested under no-load conditions.3.2 Generator specificationsIn this thesis, a generator with the following specifications will be designed and modelled in FEMM, a finite element package:· Output power = 36W @ 12V· Number of phases = 3· Number of poles = 2The choice of the above dimensions of the generator was influenced by the following consideration:· Induced output voltage, 12V is standard voltage that is used in many applications. For example it is suitable to charge a battery. Batteries are suitable to power a wide range of rural appliances and instruments especially in remote areas of South Africa . · The generator must be easily assembled and manufactured so that the rural artisans with little training can be able to assemble this generator. The following design procedure will be followed:1. A simple two-pole synchronous permanent magnet generator will be designed using available standard commercial magnets such as ceramics, alnicos and rare-earth magnets.2. The effects of the above magnets on the performance of the generator will be investigated.3. The magnets from a loudspeaker that was randomly picked in the village will then be used in the design and the performance will also be investigated. The designs above will be modelled using FEMM, a finite element package. The main reason for using FEMM is to observe the output induced voltage of the generator. This will be the method of how the performance of the generator will be monitored.3.3 Generator basic principleThe main function of a generator is to supply power to the load, in order to do so; voltage has to be generated at the terminals. The generator principle is based on Faraday's law of induction : (Eq. 3.1)where e is the instantaneous voltage, is the flux linkage and t is the time.The law states that for voltage to be induced in a winding, the magnetic flux has to change relative to the winding. This means that the flux linkage is changing and the conductor is fixed or stationary. The flux linkage is the total flux,, linking all conductors in a winding with N turns. Therefore the flux linkage is given by: (Eq. 3.2)To generate voltage in practice, a mechanical motion and a source of magnetic flux must be present. The mechanical motion can be linear or rotational, in this thesis the motion is rotational and provided by the wind turbine. The source of flux is permanent magnets.3.4 Properties of permanent magnetsThe use of permanent magnets in the construction of electrical machines has lots of benefits. A PM can produce magnetic flux in the airgap with no exciting winding and no dissipation of electric power . Permanent magnets are known for their large hysteresis loop and B-H curves. These curves are in the second quadrant of the loop called the demagnetization curve; this is where the magnets operate. Demagnetization curves of the PM materials are given is Fig 3.1 In all machines using permanent magnets to set up the required magnetic flux, it is desirable that the material used for permanent magnets have the following characteristics :a) A large retentivity (residual flux density) so that the magnet is “strong” and provides the needed fluxb) A large coercivity so that it cannot be easily demagnetized by armature reaction fields and temperature.For analysis purpose, the magnet properties have to be known, the remanence flux density Br and coercivity Hc. The magnets are characterised by a large B-H loop, high Br and Hc. Table 3.1 summarizes the properties of some of the standard commercial magnets, these were estimated from figure 3.2 which indicate the demagnetization curves of different permanent magnet materials.
Diameter of Rotor
Air gap length
Turns per phase
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 speaker4.4.3 Output EMF and flux of the recyclable generatorThe 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.
1. Socio-economic rights project, “The right to affordable electricity” copyright @ community law centre 2002
2. IDASA, https://www.idasa.org.za
3. Department of Minerals and Energy, White Paper on the Renewable Energy Policy of the Republic of South Africa. August 2002
4. Department of Minerals and Energy, White Paper on the Renewable Energy Policy of the Republic of South Africa. November 2003
5. Sathyajith Mathew, “Wind Energy-Fundamentals, Resource Analysis and Economics ” © Springer- Verlag Berlin Heidelberg 2006
6. Smail Khennas, Simon Dunnett and Hugh Piggott, “Small wind systems for rural energy services”. ITDG Publishing 2003
7. Kevin Reeves, “The design and Implementation of a 6kW wind turbine simulator” University Of Cape Town, South Africa, Oct 2004
8. FrequentlyAskedQuestions https://www.magnetsales.com/Design/FAQs_frames/FAQs_2.htm © 2000 Magnet Sales & Manufacturing Company, Inc
9. R.C. Bansal, T.S. Bhatti, D.P. Kothari, “On some of the design aspect of wind energy conversion systems” Birla Institute of technology and science, Pilani, September 2002
10. Jacek F. Gieras, Mitchell Wing, “Permanent magnet motor technology-Design and Applications” 1st edition. Marcei Dekker, Inc. 1997
11. Prof E. J. Odendal, “Design, construction and testing of a small wind generator with electronic controller for domestic use”. University of Natal, Durban
12. Jacek F. Gieras, Mitchell Wing, “Permanent magnet motor technology-Design and Applications” 2nd edition. Marcei Dekker, Inc. 1997
13. P.C. Sen, “Principles of electric machines and power electronics” 2nd edition. John Wiley & Sons
14. Bhag S. Guru, Huseyin R. Hiziroglu, “Electric Machinery and Transformers” 3rd edition. Oxford University Press, Inc. 2001
15. Dr. James Livingston, “Magnetic Materials Overview”
16. E. Muljadi, C.P. Butterfield, Yih-Huei Wan, “Axial flux, Modulator, Permanent-Magnet with a Toroidal winding for wind turbine applications”. Cole Boulevard, Nov 1998
17. Magfag, 2003 by Force Field
18. M.A. Khan, P. Pillay, “Design of a PM wind generator, optimised for energy capture over a wide operating range”
19. Joe Naylor, “Speakers with Alnico magnets vs. speakers with ceramic magnets”
20. Hybrid (Wind/Solar/LP Gas) Systems for Rural Community Development, “Electrifying South Africa for prosperity and development”. Upper Maphaphethe by Mike Wintherden
21. Danish Wind Industry Association, `Guided Tour' online htt://windpower.org/en/tour/wres/betz.htm
22. Lysen, E.H., `Introduction to Wind Energy' CWD,2nd edition, p.p 51-73
23. Ripinga Nonkululeko, “Comparison of grid and off-grid rural electrification, based on the actual installation in Limpopo Province”. University of Cape Town, Oct. 2005
24. Alfred Still & Charles S. Siskind, “Elements of electrical machine design”. 3rd edition. McGraw-Hill Book company,inc. 1954
Graphs of output rms induced voltage and flux of the generator
1. Commercial Standard Magnets
a) Ceramic FLux_RMS = 0.0175
EMF_RMS = 3.6075
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
Matlab code for sketching the output emf and flux of the generators
% EMF calculation from FEMM
%By Maribini Manyage
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);
for k = 1:hgt
AA(k,:) = polyder(pp_flux_A.coefs(k,:));
dpp_flux_A = MKPP(time,AA)
[hgt,wdth] = size(pp_flux_B.coefs);
for k = 1:hgt
AA(k,:) = polyder(pp_flux_B.coefs(k,:));
dpp_flux_B = MKPP(time,AA);
[hgt,wdth] = size(pp_flux_C.coefs);
for k = 1:hgt
AA(k,:) = polyder(pp_flux_C.coefs(k,:));
dpp_flux_C = MKPP(time,AA);
emf_A = ppval(time,dpp_flux_A);
emf_B = ppval(time,dpp_flux_B);
emf_C = ppval(time,dpp_flux_C);
title('Flux linkage - under noload');
xlabel('Time [ms]'),ylabel('Flux linkage [WbT]')
title('Back Emf - under noload');
xlabel('Time [ms]'),ylabel('Back EMF [V]')
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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|Учебники по дисциплине: Физика и энергетика|
курсовая работа по предмету Физика и энергетика на тему: Planning of mobile complete set for a rural wind generator - понятие и виды, структура и классификация, 2017, 2018-2019 год.
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