ISSN 1751-8660 Design and prototyping of an optimised ... generator considering practical...

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Published in IET Electric Power ApplicationsReceived on 2nd December 2012Revised on 3rd February 2013Accepted on 8th February 2013doi: 10.1049/iet-epa.2012.0377

38The Institution of Engineering and Technology 2013

ISSN 1751-8660

Design and prototyping of an optimised axial-fluxpermanent-magnet synchronous machineAmin Mahmoudi1, Solmaz Kahourzade1, Nasrudin Abd Rahim1, Hew Wooi Ping1,

Mohammad Nasir Uddin2

1UM Power Energy Dedicated Advanced Centre (UMPEDAC), University of Malaya, Kuala Lumpur, Malaysia2Department of Electrical Engineering, Lakehead University, Thunder Bay, Ontario, Canada P7B 5E1

E-mail: [email protected]

Abstract: This study presents the design and performance analysis of a prototype axial-flux permanent-magnet (AFPM)synchronous machine. First, the design of AFPM machine is optimised by genetic algorithm based sizing equation and finiteelement analysis. The design objectives of this machine are maximum power density, minimum total harmonic distortion(THD) of the sinusoidal back-electromotive force (back-EMF) waveform and low cogging torque. Based on the optimiseddesign of the machine a prototype 1 kW, three-phase, 50 Hz, four-pole AFPM synchronous machine is built. Then, theperformance of the prototype machine is tested to see the cogging torque, torque–speed characteristic, efficiency and the THDof the induced voltage. It is found that the prototype machine validates the design in terms of high-power density, lowestpossible THD of the back-EMF, low cogging torque while maintaining high efficiency.

Nomenclature

A
total electrical loading Bcr rotor-disc flux density Bcs stator-core flux density Bg air-gap flux density Bmax maximum flux density cf friction coefficient Dg average diameter of machine Di machine inner diameter Do machine outer diameter Ds slot depth Dtot machine outer diameter total e(t) phase-air-gap EMF Epk peak value of phase-air-gap EMF f electrical frequency fα angle frequency Gi gene value g air-gap length Gmax gene maximum value Gmin gene minimum value Gnormal normalised chromosome I current i(t) phase current Ipk peak value of phase current Irms phase current rms value Ke EMF factor ke eddy current constant kh hysteresis constant Ki current waveform factor KL aspect ratio coefficient
Kp

IET

electrical power waveform factor
Kw winding distribution factor Kφ electrical loading ratio l coil length Lcr rotor-core axial length Lcs stator-core axial length Le effective axial length of machine le end winding length Lpm permanent-magnet length Ltot machine axial length total m number of machine phases m1 number of phases for each stator n rotation speed Nph number of winding turns per phase Nph-p number of winding turns in parallel per phase Nph-s number of winding turns in series per phase Ns number of stator slots Nt number of winding turns per phase p number of machine pole pairs Pcor core loss Pcu copper loss Pden power density Pe eddy current loss Ph hysteresis loss Pi input power Pm mutation probability Pnom nominal power Pout output power Prot rotational loss Rs stator resistance scu cross-section area of wire T period of one EMF cycle
Electr. Power Appl., 2013, Vol. 7, Iss. 5, pp. 338–349doi: 10.1049/iet-epa.2012.0377

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VLL
IET Electr. P

doi: 10.1049

line-to-line voltage
Vnom nominal voltage Ws slot width γp pole pitch η motor efficiency λ diameter ratio ɛ fitness limit ρc density of core material ρr density of rotating part σT electric conductivity of wire tp permanent-magnet skew angle ζ hysteresis coefficient Ψ flux linkage coupled by per pole
1 Introduction

Recently, the permanent-magnet motors are gainingpopularity to the researchers because of their highefficiency, high-power density, high torque-to-inertia ratioand robustness [1]. The invent of high-energy permanentmagnets, semiconductor technology, modern controlalgorithms and digital signal processors prices enableresearchers to use permanent-magnet motors from domesticto high-performance industrial drive applications [2].Permanent-magnet motors come in different geometries,among which is a disc-type or axial-flux permanent-magnet(AFPM) motor available in various configurations [3–7].The AFPM motor’s high torque-to-volume ratio, excellentefficiency and flat structure are especially suited to militaryand transport applications, and motivate researchers todevelop new approaches for designing AFPM machines[8, 9]. The AFPM machines can be single- or double-sided,with or without armature slots/core, have internal/externalpermanent-magnet rotors, contain a surface-mounted orinterior permanent magnet, and are single- or multi-staged[10]. The AFPM motor cogging torque is normally muchhigher as compared with the conventional motors [11];however, they can still potentially be applied to high-torqueapplications such as ship propulsion or elevator direct drive[12, 13]. The double-sided AFPM motor type is the mostpromising and widely used as it needs less permanentmagnets and windings. Topologies for double-sided AFPMmachines are: one-stator-two-rotor, which is the type ofTORUS structure, and two-stator-one-rotor, which is calledaxial-flux interior rotor (AFIR) [14]; whereas either of thetwo arrangements (external stator or external rotor) ispractical. The external-stator arrangement uses fewerpermanent magnets but at the expense of winding.However, the external-rotor arrangement is consideredespecially advantageous where the space is limited,mechanical robustness is required and torque-to-volumeratio is crucial [15]. The double-sided slotted TORUSAFPM motors are the most frequently applied among theother configurations, as they are mechanically strongerand have higher power density than the other configurations[16]. So, the slotted TORUS AFPM motor is used herefor modelling and simulation. The genetic algorithm(GA) and finite element analysis (FEA) are used in thedesign process so that the machine’s power density ismaximised, the cogging torque is reduced and the undesiredback-electromagnetic force (back-EMF) harmonics areeliminated. Thus, the operational performance of the initialdesign is enhanced.Huang et al. [17] derived the general sizing and the power

density equations for radial-flux permanent-magnet machines,

ower Appl., 2013, Vol. 7, Iss. 5, pp. 338–349/iet-epa.2012.0377

which was a systematic method comparing the capabilities ofvarious machine topologies. In another work, they developedthe sizing equation for AFPM machines but did not presentthe machines’ optimised size [18]. A general optimisationprocess for an AFPM machine is possible with shapemodification, via geometrical parameters, deterministicmethods or soft computing methods. Aydin et al. [19, 20]has developed optimum-sized AFPM machines for bothTORUS and AFIR topologies, but only two parameters(diameter ratio and air-gap flux density) were considered asoptimisation variables, and the optimisation was donethrough the shape modification. In all shape-modificationmethods, there are trade-offs among the performanceparameters, and the methods are not applicable to themulti-objective optimisation problems. In some studies theoptimised value of 1/√3≃0.58 for the ratio (λ) of innerdiameter to the outer diameter was chosen in order tomaximise the output power in AFPM machines [21, 22].In [23], a method to reduce the free design parameters, inorder to make a simple parametric study and to obtain animproved design for an AFPM machine equipped withconcentrated winding was proposed and the most relevantfigures of merit were theoretically analysed by means ofsome parametric analysis. In [24], Rostami et al. provided adesign based on GA method for variable speed AFPMsynchronous generator considering practical limitations.However, the design methodology is not clear and theanalysis of the designed machine is very limited as they didnot provide any results on power density, efficiency andtotal harmonic distortion (THD) of the induced voltage.Moreover, the prototype machine was not built to verify thedesign.Therefore in this paper a clear design methodology based

on GA and FEA is developed for the double-sided AFPMsynchronous machine. The GA is used as an optimisationtool to minimise the machine size considering practicallimitations and various parameters such as winding turns,winding coefficient, electrical loading, air-gap length,diameter ratio, air-gap flux density, stator-slot number andpermanent-magnet skew. The design objectives of themachine are maximum power density, minimum THD ofthe sinusoidal back-EMF waveform and low coggingtorque. In order to verify the design, a prototype 1 kW,three-phase, 50 Hz, four-pole synchronous machine is built.It is found from the experimental results that the optimisedprototype machine exhibits low cogging torque, high-powerdensity, low THD of the induced voltage which verifies theanalytical results based on FEA.

2 Specific GA-based design optimisation

This section presents the key elements of GA-based designoptimisation incorporating practical limitations and theoptimised dimensions of the machine.

2.1 Design restrictions and requirements

Optimally, a design would include maximum power densityincorporated with desired sinusoidal back-EMF and wouldbe maintained within design restrictions and requirements.Table 1 lists all the practical limitations and requirementsfor the design. The limitations are based on the typical 1kW AFPM synchronous machine applied to scooter or anylow-power application with similar rating, considering thematerials available in the lab.

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Table 1 Design restrictions and requirements

Dimensional constraintsmachine outer diameter (Do) Do ≤ 300 mminner to outer diameter ratio (λ) 0.4 ≤ λ ≤ 0.75effective axial-length of the motor (Le) Le ≤ 500 mmair-gap length (g) 0.5 mm ≤ g ≤ 2.5 mmMaterial limitationsstator and rotor core flux density(Bcs, Bcr)

Bcs, Bcr ≤ Bmax = 1.5 T

permanent remanence 1.3 TRequirementsrated line-to-line voltage (rms) VLL ≤ 100 Vinput phase current (rms) Irms ≤ 20 Aair-gap flux density (Bg) 0.35 T ≤ Bg ≤ 0.95 Telectrical loading (A) 1000 ≤ A ≤ 30 000nominal power (Pnom) Pnom = 1 kWpole pairs (p) p = 2motor efficiency (η) η ≥ 80%Frequency ( f ) f = 50 Hznumber of phases (m) m = 3

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It is to be mentioned that in high-speed, high-torque andlow-supply-voltage applications, sine-wave machines offermany advantages [25]. Mostly for small machines, thenumber of poles is limited because of the reduced spaceavailable for the windings. Nevertheless, the mostrestricting limitation for the number of poles is the motoroperation speed. If the speed is high, a large number ofpoles will bring an increase in the frequency, whichdirectly leads to higher stator core losses and higherconvertor losses. In addition, the cost of permanentmagnets increases. Therefore the final decision is made infavour of the four-pole machine, with the frequencylimited to 50 Hz.

2.2 Key sizing equation

The main dimensions of each electrical machine aredetermined by the electrical-machine-output powerequation. Assuming negligible leakage inductance andresistance, the machine output power is expressed as [17]

Pout = hm

T

∫T0e(t) · i(t) dt = mKphEpkIpk (1)

where e(t) is the phase air-gap EMF, i(t) is the phase current,η is the machine efficiency, m is the number of machinephases and T is the period of one EMF cycle. Epk andIpk are peaks of phase air-gap EMF and current,respectively. Kp is the electrical power waveform factor. Ageneral-purpose sizing equation for AFPM machines is thenextracted as [18]

Pout =1

1+ Kf

m

m1

p

2KeKiKpKLhBgA

f

p1− l2( )

× 1+ l

2

( )D2

oLe (2)

where Le is the machine’s effective axial length; Kφ is theelectrical loading ratio on rotor and stator; Ki is thecurrent-waveform factor (the ratio between the peak valueand the root-mean-square (rms) value); KL is the aspectratio coefficient with respect to a specific machine structureand keeping in view the consequence of loss, temperaturerise and design efficiency requirements. m1 is the number ofphases of each stator; Bg is the flux density in air-gap; f is


the converter frequency; p is the machine pole pairs; λ isthe AFPM machine’s diameter ratio Di/Do; Do is themachine’s outer surface diameter; Di is the machine’s innersurface diameter. A and Ke are the total electrical loadingand EMF factor, respectively

A = 2m1NtIrms

pDg(3)

Ke =Epk

fa · p ·C(4)

Nt is the number of winding turns per phase; Irms is the rmsvalue of phase current; Dg is the average diameter ofmachine air-gap surface; Ψ is the flux linkage coupled byper pole; fα = np/60 is the angle frequency; n is thesynchronous speed of the machine.The machine power density for total volume is defined as

Pden =Pout

(p/4)D2totLtot

(5)

where Dtot and Ltot are the machine’s total outer diameter andtotal length respectively, including the stack’s outer diameterand end-winding protrusion from radial and axial iron stacks.

2.3 Real-coded genetic algorithm (RCGA)

The GA includes operations such as reproduction, crossoverand mutations. Reproduction is a process in which a newgeneration of population is formed by selecting the fitnessindividuals in the current population. Crossover is the mostdominant operator in GA. It is responsible for producingnew offspring by selecting two strings and exchangingportions of their structures. The new offspring may replacethe weaker individuals in the population. Mutation is a localoperator, which is applied with a very low probability. Itsfunction is to alter the value of random position in a string.The RCGA is illustrated in Fig. 1; chromosomerepresentation, crossover and mutation operators aredescribed as in the following sections.

2.3.1 Chromosome representation: Fig. 1a illustrateseach chromosome’s 1 × 6-array for the proposed GA, whileBg, λ, g, A, Kw and Nph are air-gap flux density, inner toouter diameter ratio, air-gap length, electrical loading,winding coefficient and winding turns in each phase,respectively. Every generation has a chromosomepopulation of 1400 and gets randomly selected from thefirst generation.It is to be noted that, the presented chromosome contains

the genes ‘g’,’ Kw’ and ‘Nph’, although they are not directlyappeared in (3). The fitness function depends on all thementioned genes implicitly as the ratios ‘Ke’, ‘Ki’, ‘Kp’, andparameters ‘Dtot’, ‘Ltot’ are functions of the genes. Theauthors only present the main results as the details areprovided in [18].Chromosome variables or genes have real values, and

hence real coding is applied for normalising each gene asshown in Fig. 1b. Linear normalisation results from

Gnormal =0.8− 0.2

Gmax − GminGi − Gmin

( )+ 0.2 (6)

where Gi is the chromosome gene value varying between

IET Electr. Power Appl., 2013, Vol. 7, Iss. 5, pp. 338–349doi: 10.1049/iet-epa.2012.0377

Fig. 1 Real-coding GA process

a Chromosome representation (1 × 6 array)b Real-gene coding (linear normalisation)c Two-point crossover

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Gmin and Gmax. The normalised values are limited betweenupper and lower limits 0.8 and 0.2, respectively.

2.3.2 Crossover: For the present research, the elitistmethod is used as a selection operator for two-pointcrossover (Fig. 1c). Two random numbers between ‘1’ and‘chromosome length − 1’ are first generated (1≤ randomnumber≤ chromosome length – 1). Each chromosome iscut from the specified points in Fig. 1c, and the equivalentsections are then exchanged.

2.3.3 Mutation: In this research, mutation is executedwith a probability Pm (0.005 ≤ Pm ≤ 0.05) and theoutcome needs to be a valid chromosome. In real coding,for instance, genes are randomly chosen such that a randomvalue is selected from the interval mentioned, after which itis added to, or removed from, the gene pool. Table 1 listsall genes’ permitted optimisation variations.A key issue in GA programming is the selection of a

fitness function for obtaining the best solution to a problem[26]. An inappropriate fitness function may lead to thewrong answer. Another potential problem may arise whenthe produced genes are relatively better than other genes[27], and the answer may lead towards a local solution.The AFPM machine power density ((3)) is chosen as thefitness function and is calculated for each step andchromosome.

2.3.4 Flowchart: GA starts with a population whichis the initial set of random solutions. The populationconsists of chromosomes that are string-structuredconcatenated lists of digits which code the problem’scontrol parameters. In this paper, a 1400-string population


is randomly created and the chromosomes are normalised.Chromosomes evolve from generation to generation viasuccessive iterations; a new generation is made byselection according to fitness value, parents and someoffspring, whereas others are rejected to limit thepopulation size. Half the genes from previous steps areomitted, and a new generation is created by performingcrossover and mutation on selected genes. From every twoselected genes, two children are created, replacing omittedgenes, thus creating a new generation with an equalpopulation as before (1400). The stopping criterion is thenverified; upon validation, the algorithm stops and the finalgenes are selected, otherwise, new chromosomes oroffspring are produced. The new generation undergoes allprevious steps, and after several generations, the algorithmends when the stopping criterion is fulfilled. Finally,appropriately selected genes optimise the motor dimensionsor offer close to optimal dimensions with the highestpower density.

2.4 GA-based computed results

For a three-phase, two-pole-pair AFPM motor, the potentialnumber of stator slots is assumed to be 9, 12, 15, 18, 21and 24; the GA program is then executed based on thesestator-slot numbers. The present algorithm stops when thefitness function value ((3)) for the best current-populationpoint is less than, or equals, the fitness limit (Gn + 1−Gn ≤ ɛ). An AFPM machine may have any even number ofpermanent-magnet poles (2p) and any number of stator slots(Ns). From this infinite set, only a few permanent-magnetpole and stator-slot count combinations can maximizestator-slot utilisation and result in efficient production oftorque. The number of stator slots in each pole, per polepair, for 9, 15, 18 and 21 stator-slot counts, is fractional.The fractional slot-pitch winding configuration is morecomplicated than full slot-pitch, but all values areconsidered important because they reduce current andvoltage harmonics, and also cogging torque.Table 2 lists various motor design parameters, with various

stator-slot numbers optimised through GA optimisation. Theoptimised winding configurations for different stator-slotmachines are also found using FEA-based simulation [28].As a sample, the winding configurations for 15-stator-slotmachine are shown in Table 3. As a sample, Fig. 2 showsthe MATLAB-programming fitness function variations for120 generation (which are not fully optimised) used foroptimising the various stator-slot counts.

3 Finite element analysis

GA facilitates getting the maximum power density, sodimensions obtained via GA are considered raw data, thusfurther analysis is needed for sufficiently mature finaldesign. Three-dimensional (3D)-FEA is employed foranalysing the double-sided TORUS AFPM motor’smagnetic circuit and power density evaluation, providingan overall picture of different parts of the proposed motorssaturation levels and extracting their characteristics.The AFPM motors have a unique construction; its lackof symmetry makes 3D-FEA a design requisite. Anadvantage of 3D-FEA is that various components of fluxdensity can be calculated highly accurately. The designwas simulated using commercial Vector Field Opera 14.03D software [29].


Table 2 Dimensions of the motor, with highest power density obtained via GA for different number of stator-slot counts

No.of slots

Pden,W/cm3

Do, mm Nph, turns A, A/m g, mm Lpm, mm Lcs, mm Lcr, mm Bg, T λ Ds, mm

9 0.35 157 71 16 089 1.20 4.60 13.44 12.9 0.49 0.52 16.9012 0.35 166 64 14 370 1.07 2.73 12.00 11.7 0.40 0.46 16.6415 0.36 161 70 15 198 1.10 3.60 13.00 13.0 0.48 0.48 15.6018 0.36 158 76 16 757 1.26 3.00 13.00 12.5 0.46 0.55 17.2521 0.36 152 69 16 503 1.29 3.76 13.30 12.8 0.51 0.50 17.9024 0.36 162 67 15 070 1.21 2.63 12.99 12.4 0.46 0.50 16.00

Table 3 Stator winding optimised configuration for 15-stator-slot machine

Slot No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

up + A −B + C + C −A +B −C +A +A −B + C −A +B + B −Cdown −B −B + C −A +B − C −C +A −B + C −A −A +B −C +A

Phase A Phase B Phase Cin out in out in out1 4 6 9 11 148 5 13 10 3 158 11 13 1 3 69 12 14 2 4 715 12 5 2 10 7

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Usually, permanent-magnet skewing is beneficial forreducing the cogging torque in electric machinery. It alsoeliminates some undesired harmonics reducing theback-EMF THD. It should be noted that the back-EMFamplitude is also reduced slightly with skewing. Skewingangle should be less or equal slot pitch. Through GAanalysis, motor dimensions are obtained for eachstator-slot count. The FEA then provides the THD ofback-EMF at various skew angles for the designcandidates presented in Table 2. Fig. 3 shows THDvariation against permanent-magnet skew angles.Minimum THD is clear to see for the motor with 15-statorslots and 9° permanent-magnet skew. So, the optimumselected chromosome is the one that represents a motorwith 15-stator slots per pole pair in Table 2. It is to bementioned that the adopted fractional winding q = 5/4(slots per pole per phase) considered for back-EMFwaveform analysis includes the phase coils of one entirestator side, suitably series connected.

Fig. 2 Fitness function variation during GA optimisation


4 Final design and motor construction

The best motor design dimensions are selected based on theproposed candidates from GA and FEA simulation.However, the final optimised design is made possible byminute changes effectuated by the powerful FEA with thestrenuous task of changing permanent-magnet thickness,air-gap length and length of stator yoke and rotor yokeseveral times. Table 4 lists the machine design’s finaldimensions and specifications. It is to be noted that theouter bearing option is chosen as it provides better balanceoperation as compared with conventional inner bearingoption.Fig. 4 shows the snapshot of rotor and stator of the

prototype AFPM synchronous motor. The design challengein manufacturing the AFPM motor is maintaining theair-gap between stator and rotor. Electromagnetic interactionbetween the rotor permanent magnet and the stator slots isquite large. (1000 N simulated value for this motor). The


Fig. 3 Back-EMF THD variation against permanent-magnet skew angles for machines with different number of slots

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air-gap needs to be as small as 1 mm. Fig. 4a shows the singledisc of rotor with 9° skewed permanent magnets. Themachine rotors were constructed by using mild-steel. Ineach rotor disc, four axially magnetided Nd–Fe–Bpermanent magnets are mounted on the disc surface facingthe stator. The permanent magnets used in the machineprototype have 1.3 T remanence and 900 kA/mdemagnetising field.

Table 4 Motor’s final design dimensions and specifications

nominal voltage (rms line-to-line) Vnom 90 Vnominal power Pnom 1 kWnumber of poles 2 × p 4number of phases m 3drive frequency f 50 Hzefficiency η 90.5%outer diameter Do 170 mminner diameter Di 80 mminner to outer diameter’s ratio λ 0.47magnet’s axial length Lpm 2.5 mmpole pitch γp 118°permanent-magnet skew angle tp 9°stator-yoke thickness 2 × Lcs 30 mmrotor-yoke thickness Lcr 11 mmslot width Ws 10 mmslot depth 2 × Ds 16 mmnumber of stator slots 2 × Ns 30number of winding turns per phase Nph 2 × (15 × 18)/3air-gap flux density Bg 0.47 Tair-gap length g 1 mm

Fig. 4 Snapshot of stator and rotor of the prototype AFPMsynchronous motor

a Rotor disc with 9° skewed permanent magnets mountedb Winding configuration for the 15-stator-slot counts


Windings are hand-made professionally as shown inFig. 4b. They are placed on slotted-stator surface withstar connection. The fractional slot-pitch windingconfiguration for the 15-stator-slot counts (as shown inTable 3) is implemented. To prevent the windings frommissing their position and from vibration during motoroperation and to increase the insulation capability of thewinding, a type of resin is applied giving the windingscharacteristics such as stiffness in working temperature,original dimensions and good thermal conductivity forheat release.An axial-flux motor’s stator is theoretically either

laminated spirally or axially. The spiral lamination is wellknown; however, the axial lamination of the stator,creating the slots, and to maintain the stator mechanicallyintegral is too difficult. In this paper, spiral laminationsilicon steel paper with thickness of 0.5 mm is utilised,which is quite fair as the supply frequency is 50 Hz. It isworth mention that the thinner paper (e.g. 0.1 mm sheet)may lead to poor stacking factor. Fig. 5 is a snapshot ofthe prototype 1 kW, three-phase, 50 Hz, four-pole AFPMsynchronous machine.

Fig. 5 Snapshot of the prototype 1 kW AFPM synchronousmachine


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5 Results and discussion
5.1 Simulation results

The optimised AFPM synchronous machine is extensivelysimulated using FEA software. Sample simulation resultsare presented below.One of the objectives of this work is to design the AFPM

motor with sinusoidal back-EMF waveform; in other words,the back-EMFs should be as sinusoidal as possible. Fig. 6ashows the three-phase back-EMFs at rated speed (1500 rpm)for 15-stator-slot AFPM synchronous machine for bothwith and without permanent-magnet skewing; alsoFEA-calculated maximum and rms value of back-EMF aredisplayed. The adoption of the fractional winding (q = 5/4) implies a beneficial filtering effect on the back-EMFwaveform and avoid high distortion. This fact is confirmedin Fig. 6b (Fourier transform analysis of the back-EMFwaveforms) by the amplitudes of fifth and seventhharmonics which are rather low, the most importantharmonics well known as the teeth harmonics of a q = 1winding. It is also found that the THD drastically

Fig. 6 Voltage and its harmonic spectrum obtained from FEA for the p

a Three-phase back-EMFs at 1500 rpm, with and without, PM skewingb Back-EMF harmonic components, with and without, PM skewing


decreases from 8.1 to 2.5% with 9° optimisedpermanent-magnet skewing for 15-stator-slot AFPMsynchronous machine.Fig. 7 shows the FEA simulation based torque

characteristics of the proposed 15-stator-slot machinewith and without PM skewing. It is also found that thecogging torque is significantly reduced with 9°permanent-magnet skewing, which is shown in Fig. 7a.Thus, the torque ripple of the designed machine isreduced, which satisfies the design criteria. The 9° skewmay not be the optimal skew angle for cogging torqueand it may be further reduced using a differentpermanent-magnet skew angle or other techniques butthe THD of the back-EMF will not be maintainedminimum.Fig. 7b shows the comparison of the speed–torque

characteristic for the motor designs with and withoutpermanent-magnet skewing. It shows that skewing designalso decreases the output torque. It is found that in variousspeeds the amount of torque for skew design is lower thanthat of without skewing; however, the torque difference isinsignificant near rated conditions.

roposed 15-stator-slot machine, with and without, PM skewing


Fig. 7 Torque characteristics obtained from FEA for the proposed 15-stator-slot machine, with and without, PM skewing

a Cogging torque, with and without, PM skewingb Speed–torque characteristic, with and without, PM skewing

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5.2 Experimental results

In order to test the performance of the prototype motor, anexperimental setup is built. The hardware schematic for theexperimental setup is shown in Fig. 8. Since the speed isnot very high, in-line torque transducer with suspendedinstallation and single-element coupling to create shorterdrive train are used. Hysteresis brake on the motor shaftprovides the desired load torque. The DC machine is usedas the prime mover for the prototype motor duringopen-circuit test and permanent-magnet braking torque

Fig. 8 Hardware schematic for experimental tests of prototype 15-stato


measurement. It should be noted that during cruising-speedtest, secondary measurement such as temperature rise in themotor’s critical sections are also monitored. Temperature ofthe motor during operation is found within acceptable range.The back-EMF and cogging torque are considered as the

main performance parameters to obtain. Fig. 9 shows thevoltage and its harmonic spectrum obtained experimentallyin open-circuit test. It is seen from the figure that the THDof the back-EMF is only 2.6% which is verifying thesimulation results. Further, three-phase back-EMFs ensurethe balanced operation of the machine.

r-slot synchronous AFPM machine


Fig. 9 Voltage and its harmonic spectrum obtained experimentally from open-circuit test

a Three-phase back-EMFs of the prototype machineb Back-EMF harmonic spectrum (THD is 2.6%)

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The comparisons between FEA-based computed andexperimental results are tabulated in Table 5 for twodifferent speed conditions (1500 and 750 rpm). It is seenthat the experimental results almost agree with those of theFEA-based computed results at different speed conditions.Fig. 10a shows the experimental cogging torque measured

from open-circuit test conducted at rated speed (1500 rpm),which is in close agreement with the ones predicted viaFEA simulation results. Fig. 10b shows the experimentalspeed–torque characteristic for prototype AFPM motor.

Table 5 Back-EMF comparison between experimental and FEAresults

Back-EMF Vmax Vrms THD%

1500 rpm experimental 73.4 52.0 2.6FEA-based computed 74.2 52.5 2.5

750 rpm experimental 37.1 26.2 2.8FEA-based computed 37.5 26.5 2.7

5.3 Efficiency

To accurately assess the machine efficiency, it is vital tocalculate the losses. The machine efficiency is given by

h = Pout

Pout + Pcu + Pcor + Prot(7)

where Pout, Pcu, Pcor, Prot are output power, copper loss, coreloss and rotational loss components, respectively. Core loss


and copper loss are calculated from the equations below

Pcor = Ph + Pe, and Pcu = RsI2 (8)

where Ph and Pe are the hysteresis and eddy current losses,respectively. Copper loss is responsible for most of the totallosses. Stator resistance (Rs) depends on load and windingtemperature which is calculated from [30]

Rs =2Nph−s l + le

( )sTNph−pscu

(9)

σT is the wire’s electric conductivity at temperature T, Nph-s is


Fig. 10 Experimental torque characteristics for the prototype AFPM machine

a Cogging torque over one cycleb Speed–torque characteristic

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the number of winding turns in series per phase, Nph-p is thenumber of winding turns in parallel per phase and scu is thewire’s cross-section. Thin parallel wires minimised the skineffect, therefore it is not considered in (7). l and le are coillength and end-winding length, respectively.Hysteresis loss (Ph) and eddy current loss (Pe) comprise the

motor core loss (Pcor) and can be calculated in terms of theSteinmetz equation as

Ph =kh · Bj

max · frc

, and Pe =ke · B2

max · f 2rc

(10)

kh, ke, Bmax, and ρc are hysteresis constant, eddy currentconstant, maximum flux density and core material density,respectively. ζ is the hysteresis coefficient which depend onthe lamination material, thickness and conductivity. Thepower loss data of the 0.5 mm silicon steel paper used to fitthe Steinmetz equation describes the specific loss in W/kg as

Pcor = 0.014492B1.8maxf + 0.00004219B2

maxf2 (11)

As it is seen, open slots are used in the stator design becauseof simplicity and cheapness. They cause slot harmonicscausing eddy current in this rotational speed and air-gaplength. These losses are also taken into account to computethe efficiency. For a fine calculation of stator core losses,


finite element-alternate current (FE-AC) analysis is donerepeatedly for each space harmonic component (up to the49th order) in combination with the current waveform’ssimulated time harmonic components, to obtain thelaminated-stator eddy current losses.Rotational loss (including windage and friction losses) for

analytical calculations is estimated from [31]

Prot =1

2cfrr pn

3( )D5

o − D5i

( )(12)

where cf is the friction coefficient, ρr is the density of rotatingpart and n is the rotation speed (in rps). Fig. 11 shows themotor’s efficiency for both predicted values via FEAsimulation and experimental test which are in closeagreement; however, the slight differences of simulationand experimental results are because of little deviation incoils winding and stator lamination during fabrication asthese processes were hand-made by a professional. Fig. 11ashows the efficiency at various speeds for full-load andlow-load (25% of full load) conditions. It shows the rise inefficiency with the increase in speed. Fig. 11b shows theefficiency against various loading conditions (from no-loadto full-load) at rated speed. It is found that the motormaintains high efficiency even at low-load condition. Thefinal optimal designed motor efficiency at full loading andrated condition reaches 90.5% at 1500 rpm.


Fig. 11 Motor’s efficiency comparison between predicted values via FEA simulation and experimental test

a Efficiency against speed for full-load and low-load conditionsb Efficiency against various loading conditions at rated speed

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6 Conclusion

The design, simulation and real-time performance analysis ofa prototype AFPM synchronous machine have been presentedin this paper. The design optimisation using GA and FEAbased on the machine sizing equation has also beendiscussed. The design objectives were maximum powerdensity, minimum THD of the back-EMF and low coggingtorque for the machine. Based on the optimised design aprototype 1 kW, three-phase, 50 Hz, four-pole AFPMsynchronous machine has been successfully built. Theperformance of the prototype machine has been tested andcompared with the FEA based computed results in terms ofTHD of induced EMF, cogging torque, torque–speedcharacteristic curve and efficiency. It is found that theprototype machine meets the design criteria. Therefore theproposed design technique could be utilised for designingany arbitrary capacity double-sided industrial AFPMsynchronous machine.

7 Acknowledgment

The authors thank the University of Malaya for the HighImpact Research Grant No. D000022-16001 that funds theHybrid Solar Energy Research Suitable for RuralElectrification.


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ISSN 1751-8660 Design and prototyping of an optimised ... generator considering practical...

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