Considerations on Selecting Fractional-Slot Nonoverlapped Coil Windings

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Considerations on Selecting Fractional–SlotNon–Overlapped Coil Windings

Emanuele Fornasiero, Luigi Alberti, Member, IEEE,Nicola Bianchi, Senior, IEEE, Silverio Bolognani Member, IEEE

Abstract—This paper focuses on the selection of a fractional–slot winding for PM machines. The choice of the proper com-bination of the number of slots and number of poles, togetherwith the corresponding winding layout, has a strong impact onthe PM machine performance, in terms of torque density, torqueripple, MMF harmonic content, induced rotor losses, as wellas capability to limit the short–circuit current and other fault–tolerance features. Considering these characteristics, the paperaim is to help the PM machine designer to select the properwinding configuration, giving useful indications. The windingchoice criteria are given using analytical equations, so that theirimplementation is easy. In this way, the collection of such criteriabecomes a helpful tool in the design process.

I. INTRODUCTION

A key issue of the fractional–slot PM machine design isthe selection of the proper number of slots and poles, and thecorresponding winding layout. The slot and pole combinationdetermines the coil throw (sometimes also referred to as coilspan or coil pitch), and the corresponding length of endwinding coil, the winding factor and the stator MMF harmoniccontent. An improper winding choice could heavily affect themachine performance. For example, torque ripple could beexcessive and unallowable, [1], [2] or the MMF harmoniccontent could be so high to induce high rotor losses, alsocausing a degrading of the machine power [3], [4], [5], [6].

These aspects have to be taken into account in both lowpower applications, in which the main interests are in reduc-ing cost, losses and torque ripple [7], [8], and high powerapplications, such as wind power generation [9], traction orship propulsion [10], where the main issues are the increaseof torque–to–weight ratio and the reduction of machine di-mension.

Although several papers dealt with the fractional–slot wind-ing of PM machines, there is not a general approach con-sidering the whole aspects giving complete indications onthe winding selection. Frequently, some papers focus on asingle aspect and give partial indications on the others [11],[12], [13], without providing a wide range of slot and polecombinations. This paper aims to fill this gap, trying to sum-marise the effects of the slot and pole combination on the PMmachine performance. Some aspects that are barely addressed,or postponed in the machine analysis as secondary effects,

This paper has been presented at ECCE 2010. Proposed for publication onTransaction on Industry Applications. Updated after comments of reviewersand Associate Editor. Original title: “Considerations on Selecting Fractional–Slot Windings”. Authors are with the Department of Industrial Engineering,University of Padova, via Gradenigo 6/A, I-35131 Padova (ITALY)

are here included, as the impact of the winding on coggingtorque, MMF harmonics, machine modularity, feasibility ofsingle–layer solutions, rotor losses, winding inductance, faulttolerance, flux–weakening capability, mechanical vibrations,and so on.

This paper highlights that the choice of a particular combi-nation of slots and poles (of a fractional–slot winding) yieldsa direct impact on the machine performance with advantages(e.g., reduction of coil length and reduction of cogging torque)and drawbacks (e.g., increase of MMF harmonic content androtor losses). Since the results found in literature are oftenachieved from numerical simulations only, or presented in anon–uniform way, an effort has been done to include thoseresults in the theory that is summarised in Section II. The mul-tilayer windings (Section II-D), even if already presented inliterature, are also introduced according to the same theoreticalbasis. In addition, some fractional–slot winding configurationsare presented for the first time. This is the case of the mixed–layer winding (Section VII). Modularity (section V) is clearlydescribed as a consequence of the fractional–slot windingchoice. Change of connections (section V-B) is original andnot published before.

II. GENERAL ANALYSIS OF FRACTIONAL–SLOT WINDINGS

The fractional–slot winding exists when the number of slotsper pole and per phase is not an integral number. Its advantagesand disadvantages are summarized hereafter.

A. Winding feasibility

For a given phase number m, not all combinations of slotsQ and poles 2p are feasible. A symmetrical winding is feasibleif

Q

mtis an integral number (1)

where t = GCD(Q, p) is the periodicity of the machine, givenby the greater common divisor (GCD) between Q and p.

For the sake of generality, a double–layer winding isconsidered, that is, a winding with two coils sides per slot.Later on, single–layer and multi–layer windings will be dealtwith. Then, as a further general statement, the coil throw isexpressed in number of slots and defined as the integer closestto the ratio between the number of slots and the number ofpoles, i.e., yq = round(Q/2p).



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B. Non–overlapped coils windings (yq = 1)

Among the fractional–slot windings, the more used config-uration is that with non–overlapped coils, that is, with unitycoil throw, yq = 1. The main reason is the short length of theend–windings.

In the most of cases, for a given number of poles, thisshortening yields a reduction of the copper losses with respectto the traditional integral–slot machines. However, such anadvantage depends on the motor length and has to be analysedfrom case to case [7]. Other reasons include the requirementof very low speed machine, characterized by a high numberof poles, and a simplification of the automatic winding of thestator coils.

Some non–overlapped coil windings are shown in Fig. 1.Non–overlapped coil windings are used in direct–drive appli-cations [14], as for wind power generation, lifting or automo-tive applications [15] and also in linear motor and actuators[16]. Such solutions require that the number of slots is closeto the number of poles, i.e. Q ≈ 2p. Some studies, e.g. [17],focused on solutions with

|Q− 2p| = 1 and |Q− 2p| = 2 (2)

(a) Inner stator (b) Outer stator

(c) Single–layer winding (d) Axial flux single–layer machine

Fig. 1. Some solutions that feature non–overlapped coils

Such solutions tend to group the coils of the same phase inone part of the stator (|Q−2p| = 1), as in Fig. 2(a), or in twoparts of the stator (|Q− 2p| = 2) as in Fig. 2(b).

This property can be used in order to rearrange the statorstructure, also reducing the number of the coils of the winding[11].

In addition, the non–overlapped coil solution allows aseparation of the stator teeth, Fig. 2(c), increasing the slot fillfactor [18], with a consequent increasing of the torque density.Finally the non–overlapped coil windings are well–suited forfault–tolerant applications, allowing a magnetic de–couplingbetween phases, that is a mutual inductance almost equal tozero, M = 0 [19].

(a) A 15/14 double–layerwinding

(b) A 12/10 double–layerwinding

(c) Separation of stator teeth (d) Double–layer winding with a sep-arator between two coil sides

Fig. 2. Other winding examples

C. Double– and single–layer windings

There are two main winding topologies: the double– and thesingle–layer winding, according to the number of coil sideswithin each slot. If the feasibility condition (1) is verified,the double–layer winding is always possible. Two examplesof such a winding are shown in Fig. 1(a) or 1(b).

Conversely, the single–layer winding is only possible ac-cording to the following two constraints [20]:{

the number of slots Q must be even, andthe coil throw yq, as defined above, must be odd.

(3)

These two conditions determine when the single–layer wind-ing is feasible.

When a non–overlapped coil winding is adopted, with yq =1, the second condition is always verified.

Fig. 3 shows a sketch of the double and the single–layer winding for a 18/12 machine. Examples of single–layerwindings are shown in Fig. 1(c) and 1(d).

The single–layer windingexhibits a distribution factor higher than the corresponding

double–layer winding when the ratio Q/(2t) is even.However, it is always characterized by a higher amplitude

of the MMF harmonics, as highlighted in Fig. 4.

(a) Double–layer winding

(b) Single–layer winding

Fig. 3. 18–slot 12–pole double– to single–layer transformation



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0 20 40 60 80 1000

50

100

150

Harmonic order

MM

F (

%)


0 20 40 60 80 1000

50

100

150

Harmonic order

MM

F (

%)


Fig. 4. MMF harmonic content of a 12–slot 10–pole machine

D. Four–layers winding

The choice of the number of layers is not limited totwo. Three–layer or four–layer windings [16], [21], [22] arealso feasible. A recent patent [23] presents a solution basedon doubling the two–layer winding in the 12–slot 10–poleconfiguration and shifting the two halves of winding by oneslot. In this way the main winding factor is reduced by3.4% but some space harmonics result to be reduced or evencanceled [24].

To achieve a four–layer winding, starting from a dual–layer winding, the number of coils is doubled, arranging twolevels for the coils within the slots. Then, the coils of onelevel are shifted with respect the coils of the other level.The transformation from two–layer to four–layer winding isillustrated in Fig. 5. The corresponding star of slots are shownin Fig. 6.

Fig. 5. Four–layer winding concept.

Adopting a four–layer winding, a reduction of the amplitudeof the MMF harmonics (mainly the sub–harmonic) is achieved,see Fig. 7 in comparison with Fig. 4.

Such a decrease is slight for the main harmonic and theslot–harmonics. The order of slot–harmonics in fractional–slot

Fig. 6. Star of slots corresponding to the configurations of Fig. 5.

machine is computed as ν = kQ± p, where Q and p are thenumber of slots and poles, respectively, while k is a positiveinteger. A proof is given in [25].

0 20 40 60 80 1000

50

100

Harmonic order

MM

F (

%)

Fig. 7. MMF harmonic content of a 12–slot 10–pole four–layer machine.

The four–layer windings yields a reduction of the rotorlosses, with respect to the double–layer winding [26]. SeeSection IV.

E. Cogging torqueIn a PM machine, the cogging torque is caused by the

interaction between the PMs and the stator slotting. Thenumber of slots and poles has a direct impact on the coggingtorque. The number of periods of the cogging torque waveformduring a rotation of a slot pitch is:

Np =2p

GCD(Q, 2p)(4)

In order to minimize the cogging torque, the number Np hasto be maximized so that the periodicity between Q and 2pis reduced [27]. In [1], [2], [3] some solutions are proposedso as to achieve high winding factor, high output torque andlow torque ripple. Among the others, the configuration withQ/2p = 12/10 is suggested.

F. Winding inductanceMachines with fractional–slot windings are characterized

by inductances higher than the corresponding integral–slotwinding

(i.e., windings with the same number of poles and one slotper pole per phase).

The synchronous inductance is strictly related to the mag-netic energy in the slots and in the air gap. The formerincreases due to the higher number of conductors per slot.The latter is mainly influenced by the choice of the winding.Let Bk be the air gap flux density in front of the kth tooth,the average magnetic energy density can be expressed as

wm =t

Q

12µ0

Q/t∑k=1

B2k (5)



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which is easily determined once the winding coils are dis-placed in the stator slots.

In a fractional–slot double–layer winding such energy den-sity can be two or three times that of the integral–slot windingmachines. In addition, in a single–layer winding machine themagnetic energy is twice as big than that in a double–layerwinding machine [20].

Some examples of MMF distribution are shown in Fig. 8,together with the harmonic component of order ν = p = 5(the main harmonic) and ν = 1 (the sub–harmonic).



Fig. 8. MMF distribution of a 12–slot 10–pole machine; solid line: actualMMF waveform; dashed line: main harmonic (ν = p = 5); thin line: sub–harmonic of order ν = 1.

The higher inductance yields two direct consequences:1) The flux–weakening capability increases. The machine

can exhibit a wide (theoretically infinite) constant powerspeed range [28].

2) The fault tolerance capability increases, and the currentflowing in the event of short–circuit is limited. The PMmachine gets the capability to resist a short–circuit faultwithout demagnetizing the PMs or exceeding the ratedtemperature.

G. Vibration modes

A further aspect that has to be considered during the designof the machine is the unbalanced magnetic pull. This is dueto a radial force acting on the rotor and it causes considerablevibration and noise during the machine operation. This aspectsis more and more important as the machine under design isadopted in applications where a silent and smooth operationis required, i.e. household application, more electric vehiclesand so on. The radial force and vibration effects have to becarefully considered in order to avoid mechanical resonancewith the motor structure.

This topic has recently raised the interest of many re-searchers [29], [30]. The main results of such a phenomenonare reported hereafter.

At first, the radial force at no load is considered. When thestator has an odd number of slots, there is a radial force alsoat no load. This is due to the lack of symmetry of the statorwith respect to the rotor. This is the case of machines havingnumber of poles and number of slots differing by one.

Then, when the machine operates under load, the interactionbetween the harmonics of PM flux and the harmonics ofarmature reaction yields a further contribution to the radialforce. Since the MMF harmonic content depends on the slot–pole combination, different radial force is expected changingthe number of slots and poles.

As a general rule, the worst case is when the order ofvibrations is low. In fact, the motor structure is, in general,stiffer to short–wave distortion which correspond to high orderof the vibration mode. In fractional–slot machines, the orderof the dominant vibration mode can be as low as 1 or 2, evenif 2p > 2. The following remarks can be done [31]:

• In machines with 2p = Q± 2 and double–layer windingthe lowest order of radial force is 2.

• In machines with 2p = Q ± 2 and single–layer windingthe lowest order of radial force is 2 when Q/t is evenand is 1 when Q/t is odd.

• In machines with 2p = Q± 1 the lowest order of radialforce is 1. The amplitude of the first radial force harmonicis higher in machines with 2p = Q+ 1.

III. WINDINGS FOR FAULT–TOLERANT MACHINE

The fractional–slot windings allow the fault–tolerance capa-bility of the PM machine to be increased. Among the others,some aspects are commented hereafter:

• the synchronous inductance increases, limiting the currentin the event of short–circuit.

• With non–overlapped coils (yq = 1), there is a physicalseparation between coils. With double–layer winding, aseparator is necessary between the two coil sides asshown in Fig. 2(d). With single–layer winding, there is astator tooth that separates each coil, Figs. 1(c) and 1(d).

• The modularity of the machine (see section V) allows aneasy replacement of the faulty part of the machine.

• Some combinations of slots and poles yield a minimummutual coupling between phases. It is required that:

yq = 1 is unity,Q/t is even with double–layer winding,Q/2t is even with single–layer winding.

(6)

Two examples are shown in Fig. 9.In both cases, the flux is linked only by coils of the samephase. In double–layer winding, there is a low mutualinductance M , due to the leakage flux in the slots wherethere are coil sides of different phases.In single–layer winding, there is not coupling neither dueto the leakage flux in the slots, since each slot containsonly one coil side. In this case, a theoretically M = 0 isachieved.



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Fig. 9. Flux lines (dashed lines) due to one phase in configurations withminimum mutual inductance

IV. ROTOR LOSSES

Rotor losses in fractional–slot machine can be so high tocompromise the machine operations [32], [21], [33]. Theyaffect greatly the efficiency of the machine [34] and, some-times, they can be so high to lead to the choice of distributedwindings [4]. A rough estimation of such losses is manda-tory during the design process of fractional–slot machines.Hereafter, a simplified approach to compare the rotor lossesis presented.

Rotor losses are caused by the stator slotting and by thepresence of MMF harmonics in the air gap.

Open slots are sometimes used in combination withfractional–slot winding, expecially with single–layer solution[10]. However, in such solutions, expecially when Q ≈ 2p,that is, when the PM pitch approximates the slot pitch, theflux pulsation is very high, causing high rotor losses.

The second cause of rotor losses is the high content of statorMMF harmonic. Only the main harmonic is synchronous withthe rotor, while other harmonics have a relative speed withrespect to the rotor, inducing currents in all rotor conductiveparts.

In particular, the MMF sub–harmonics produce high andrapid flux pulsations, so that they are the main cause ofrotor losses [35]. MMF sub–harmonics arise in almost all thefractional–slot windings, but those with q = 0.5 slots per poleper phase.

In order to compare different rotor losses impact of variousfractional–slot machines, the following index of rotor lossesis brought into use:

Irl =∑ν

ξ4

4√

(ξ4 + π4)3

(kwνkw

)2ν

pkgap (7)

where ν is the harmonic order, ξ is the specific wavelength fora given harmonic order, and kgap is a sort of low–pass filterdepending on the ratio between air gap and diameter of themachine [36]. Since it is independent on the particular geom-etry of the machine, the index (7) allows a rapid comparisonamong various slot and pole combinations.

V. MODULARITY

A machine can be defined to be modular when it can besplit in parts. Such a feature allows the groups of coils to beseparately removed. As an example, separate teeth are shownin Fig. 2(c).

A. Modular solutions with identical groups of coils

In very large machine, there is a particular interest inmodular solutions, that is, solutions in which the machine canbe split up in several identical parts. The whole machine isachieved by composing these single components.

If a fault involves only a part of the machine, this partcan be removed without disassembling the whole machine,making maintenance easy. Another advantage, always in largemachines, is their assembly [37]. A modular machine can beeasily assembled with the further possibility to operate only apart of the machine.

Fig. 10 shows some examples of such modular solution.On the left, adopting the double–layer winding, each part isachieved cutting the slot in the middle. On the right, adoptingthe single–layer winding, each part is achieved cutting theteeth in the middle. The coils result to be more protected inthe solutions with single–layer winding: a better insulation ispossible, and the assembly/disassembly is easier.

double-layer single-layer

Fig. 10. Separated parts of the stator, adopting double–layer winding on theleft hand side and single–layer winding on the right hand side.

A further constrain of the modularity system is that thesingle parts have coils of the same phase. This simplifies theconnections of the machine, making easier the disassemblyand replacement of the faulty parts. From [38], the coils ofthe same phase result to be arranged in Ngrp groups, whereNgrp = |Q − 2p|. In Fig. 2(a), Q/2p=15/14, it is Ngrp = 1.In Fig. 2(b), Q/2p=12/10, it is Ngrp = 2. In general, thesegroups containing a different number of coils. However, someparticular cases exist in which the groups are formed by thesame number of coils [38]. It occurs when the number of coilsper group Ncpg is integer, being

Ncpg =Q

m|Q− 2p|(8)

From (8), it is possible to determine those combinations ofslots Q and poles 2p that satisfy the condition to have groupsof identical number of coils. Some combinations of slots andpoles are reported in Table I.

B. Change in connections

To the purpose of achieving a solution with identical groupsof coils, it is also possible to modify the connections of thecoils.

The coils are normally connected so as to achieve themaximum distribution factor of the main harmonic, i.e. oforder ν = p. By means of the star of slots [39], drawn forthe main harmonic, the coils of a phase are selected so as to



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TABLE ICONFIGURATIONS WITH GROUPS OF EQUAL NUMBERS OF COILS (ONLY

CONFIGURATIONS WITH Q > 2p ARE REPORTED).

Ncpg Q/(2p)t = 1 t = 2 t = 3 t = 4 ...

1 3/2 6/4 9/6 12/8 ...2 12/10 24/20 36/30 48/40 ...3 9/8 18/16 27/24 36/32 ...4 24/22 48/44 72/66 96/88 ...5 15/14 30/28 45/42 60/56 ...

get the minimum angular displacement among the directionsof their corresponding vectors.

However, instead of connecting the coils of the samephase in such a “natural” way, they could be connected soas to achieve the coil of the same phase to be placed inadjacent slots. For instance, let us consider the machine withconfiguration 12/10 and a single–layer winding (so that themodules are cut in the middle of the teeth), shown in Fig. 11.The corresponding star of slots is shown in Fig. 12, only theodd vectors exist considering a single–layer winding (the evenvectors are removed [38]).

For the phase A, the “natural” connection is to rearrangethe coil in slot 1 in series with the coil in slot 7. The vectorsrepresenting the two coils are inside a cone with angle equalto 60 degrees, and the angular displacement between the twovectors is equal to zero (the coil in slot 7 has to be connectedwith reversed polarity). The vector of each phase has to besummed together so as to achieve the resulting vector. Itis imperative that the resulting phase vectors have the sameamplitude and are shifted of 120 degrees each other.

In order to achieve the coils of the same phase to be closeeach other, it is possible to connect the coil in slot 1 in serieswith the coil in slot 3, that is the adjacent coil. In this way,phase A is formed by vector 1 and 3, phase B is formed byvector 9 and 11, and phase C is formed by vector 5 and 7.This corresponds to consider three half–cones of 120 degrees,and the vectors inside them to be connected together. The finalconfiguration is reported in Fig. 11.

Fig. 11. Concept of connection change so as to achieve modularity.

The advantage of this change of connection is that the coilsof the same phase result to be adjacent. They are placed in thesame module (see Fig. 10) connected and insulated together,

Fig. 12. Star of slots with change of connection (single–layer winding of12/10 configuration).

easily assembled and disassembled. As a drawback, the distri-bution factor decreases, with a corresponding decrease of EMFand electromechanical torque per given line current. In theexample above, the distribution factor for the main harmonicdecreases from kd = 1 down to kd =

√3/2 = 0.866, which

is a reduction higher than 13%. In addition, for each changeof connections, the MMF harmonic content and its impact onthe machine performance has to be evaluated.

VI. THE MIXED SINGLE/DOUBLE–LAYER WINDING

In the previous section V, it has been shown that themodularity is often required in large machines. Modularityallows a simplification in machine assembly and maintenance,making easier the replacement of a faulty section without dis-assembling the whole stator. For getting higher strength of thesingle parts, the single–layer is preferred to the double–layer,so as to protect the removable parts by half–tooth boundaries.However, the adoption of the single–layer winding, yieldsan MMF harmonic content higher than that resulting from adouble–layer winding. In particular, it was highlighted [38]that the amplitude of the sub–harmonics increases, with adirect impact on rotor losses, which can reach unsafe highvalue in large machines.

Therefore, a mixed single/double–layer fractional–slotwinding is proposed. Hereafter, it will be referred to as themixed–layer winding. It represents a sort of compromise be-tween the necessity to maintain the strength of the removablepart and to reduce the MMF harmonic content of the finalsolution. Such kinds of winding are achieved starting fromdouble–layer winding, satisfying the condition to have anintegral Ncpg (see Table I). The transformation is shown inFig. 13. In Fig. 13(a) the 24/20 double–layer winding is shown.The corresponding star of slots is shown in Fig. 14(a). Thisconfiguration has Ncpg = 4, according to Table I. To obtainthe mixed–layer winding, one coil per group is removed (thefirst coil of each group), as shown in Fig. 13(b). The resultingwinding allows the stator to be split in parts as highlightedin Fig. 13(c). The corresponding star of slots of the mixed–layer winding is reported in Fig. 14(b). The spokes of theremoved coils are not present and their numbers are reportedfor reference between parentheses.

After the transformation, the slot sizes have to be rear-ranged. The removed turns have to be added to the coilsremaining within the slots, so that their slots have to beincreased. Then, the slots containing only one coil side arereduced. In addition, the coil span can be increased, soas to link higher flux, increasing the winding factor [40].



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(a)

(b)

(c)

Fig. 13. Conceptual transformation from a double–layer to a mixed–layerwinding (Configuration 24/22).

(a) (b) (c)

Fig. 14. Star of slots of 24/22 double– and mixed–layer winding. Last figureshows the star of slots after rearranging the slot angles, improving the windingfactor.

Fig. 14(c) shows the rearranged star of slots after the slotsangles optimization. As can be noted, the spokes of each phaseare closer.

Some other examples are reported in Fig. 15 according toNcpg = 3, 4 and 5, respectively.

Finally, adopting mixed–layer windings, the rotor lossesresult to be lower than those of single–layer windings buthigher than those of double–layer windings.

VII. AN EXAMPLE OF WINDING SELECTION

The remarks summarized in of the previous sections, are thebasis for the choice of proper combination of slots and poles.As an example, let us refer to the design of a three–phasefractional–slot winding according to the following constraints:

• the single–layer solution has to be feasible,

Fig. 15. Examples of mixed–layer winding solutions (Configurations withNcpg = 3, 4, and 5, see Table I).

• the winding factor of the main harmonic has to be greaterthan 0.95,

• the index of rotor losses has to be properly low (for thematerial used in the simulation, the index should be lowerthan 55),

• the mutual inductance between phases has to be theoret-ically zero, and

• the machine has to exhibit the modularity capability.

Table II reports the combinations of slots and poles thatsatisfy the previous constraints, in the range 36 ≤ Q ≤ 60,while Table III reports the combinations of slots and poles inthe range 120 ≤ Q ≤ 132.

TABLE IICOMBINATIONS OF SLOTS AND POLES SATISFYING PREFIXED

CONSTRAINTS IN THE RANGE 36 ≤ Q ≤ 60 (f = 50Hz).

Q 2p t Q/(2t) yq kwdl kwsl Irl,dl Irl,sl

36 34 1 18 1 0.953 0.956 52.0 53.936 38 1 18 1 0.953 0.956 46.8 48.548 46 1 24 1 0.954 0.956 29.2 30.048 50 1 24 1 0.954 0.956 27.0 27.860 58 1 30 1 0.954 0.955 18.8 19.260 62 1 30 1 0.954 0.955 17.7 18.2

TABLE IIICOMBINATIONS OF SLOTS AND POLES SATISFYING PREFIXEDCONSTRAINTS IN THE RANGE 120 ≤ Q ≤ 132 (f = 50Hz).

Q 2p t Q/(2t) yq kwdl kwsl Irl,dl Irl,sl

120 116 2 30 1 0.954 0.955 4.9 5.1120 118 1 60 1 0.955 0.955 4.9 5.0120 122 1 60 1 0.955 0.955 4.8 4.9120 124 2 30 1 0.954 0.955 4.7 4.9132 130 1 66 1 0.955 0.955 4.3 4.3132 134 1 66 1 0.955 0.955 4.2 4.2

VIII. CONCLUSIONS

This paper investigates the impact of the fractional–slotwinding choice on the PM machine performance, capabilityand potentiality. To this aim, the different issues are expressedanalytically, sometimes adopting simplified equations. Thanksto the analytical formulation, several constraints can be takeninto account in selecting the more appropriate combination ofslots and poles for any given application.

APPENDIX

Fig. 16 shows the graphics interface that allows an easyselection of the constraints concerning the choice of thewinding. It is a part of the program KOIL, a tool for thedesign of both integral– and fractional–slot windings, whichis available at http://koil.sourceforge.net/.

ACKNOWLEDGEMENTS

This work was financed by the University of Padova,Padova, Italy (Project CPDA081750/08).



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Fig. 16. The KOIL graphics interface.

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Considerations on Selecting Fractional-Slot Nonoverlapped Coil Windings

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