slot winding

7/29/2019 slot winding

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Slot winding for an electrical machine


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The winding has to be distributed on the poles and phases.

The air-gap periphery is divide into 2p poles. The pole pitchis

ip

2

D

p

p ipb

2

D

m pm

wherep is the number of polepairs andDi is the air-gapdiameter.

The pole pitch is furtherdivided into m phase belts

R

S

T

-R

-S

-T

R

-T

S -R

T

-S

Phase belts of a three-phase,four-pole winding

2p


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The average number of slots per phase belt is

whereQ is the number of slots.

q is called the number of slots per pole and phase. If it is aninteger, all the phase belts have an equal, integer numberof slots and the winding is called an integral slot winding. Ina more general case, q is a fractional number

where z and n are integers. In this case, the winding iscalled a fractional slot winding and the number of slotsdiffers from one phase belt to another.

2

Qq

pm

2

Q zq

pm n


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The fundamental flux-density wave in the air gap

should induce a balancedm-phase voltage in the winding.The phase shift between the voltages of phase windings

should be

and the amplitudes of the phase-winding voltages should

be equal.

ph2

m

, cosp pb t b p t


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Electromotive force on a coil side

1 1, cosb t b t

Using electrical radians, the fundamental flux-density wave

becomes

Time variation of flux linkage induces a total electromotiveforce in a coil. Considering the flux in the yoke, the emf can

be written per coil side

1b peak value of the flux-densitydistribution, circumferential coordinate, angular frequencyandt time.

nn coil p i 1d 1 cosd

e N l b tt


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Slot star

Presenting the electromotive forces of coil sides as phasorsand plotting the phasors of one pole pair, a slot star isobtained.

The slot star on the left is for anintegral slot three-phase windingwith q = 4. The phase shift

between the voltage phasors is = 2/24. The natural choice ofphases to which the 24 slotsbelong to is indicated by thecolours.


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If we can consider the electrical machine as a linear, time-invariant system and the supply voltage is sinusoidal, themagnetic field, currents and voltages of the machine can beexpressed using phasor quantities. In the 2D case, the vectorpotential and current density are

The phasors are solved from the combined field and circuitequations

eff

+j 0 A A

Phasor presentation of fields and voltages

1d j d

b b

a a

u

l J A l

j jR I

j jR I

Re ( , )e Re , j ,

Re ( , )e Re , j ,

t tz z

t tz z

A x y A x y A x y e

J x y J x y J x y e

A

J

e e

e e


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Phasor presentation of fields and voltages II

If an idealised conductor of a winding can be considered to beinfinitely thin but have a finite resistance, the circuit equationfor the winding can be transformed to the form

The first term is a resistive voltage drop in the conductor, thesecond term is the electromotive force induced in theconductor.

1j d j d

b b

a a

U RI

A l A l

Using this formulation in 2D to calculatethe electromotive force induced in thecoil group shown in the figure, we get the

result

4 5 6

1 2 3

jA A A

e lA A A

1

6


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Slot star for an integral slot winding

n 2 pQ

Integral slot winding => all the phase belts are similar

Slots belonging tothe first pole pair

Second polepair, etc.


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Slot star for a fractional slot windingFractional slot winding => The number of slots andconfiguration of slot phasors changes from one phase belt

to phase belt.


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Design of a single layer winding

Number of slots = Q, Number of coils = Q/2, as one coilside fills a slot completely.

One of the phase belts is chosen forthe positive coil sides of phase A. It ismarked + A.

Moving 120 electrical degrees from

+ A to the positive direction of rotationof the rotor (clockwise in the figure),phase belt + B is reached.

An additional 120 electrical degreesbrings phase belt + C.

The negative phase belts are found bymoving 180 electrical degrees fromthe corresponding positive phasebelts.


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Design of a single layer winding

All the coil sides of one phase have currents of equalmagnitude. The magnetomotive force of the phase is shown

in figure a). It is independent from the exact connection ofthe positive coil side to the negative ones.

Figures b) and c) show twopossible configurations of

coils, which give exactly thesame magnetomotive forcedistribution in the air gap.


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Design of a double layer winding

In a double layer winding,there are even more

possibilities to put the coilsinto the slots but all thesewindings produce equalmmf waves in the air gap.


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Chording

Changing the coil pitch may strongly affect the emf induced

by a higher harmonic. In this way, the effects of someharmful harmonic component can be eliminated. A windinghaving non-diagonal coils is called a chorded winding.


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Problem: High-speed two-

pole PM generator with 18stator slots. The winding is asingle layer winding. Calculatethe winding factor of the statorwinding starting from the slotstar.

The phase shift between the emfvectors induced in the conductorsof adjacent slots is . There are18 vectors (slots). To gain themaximum voltage, the phases arechosen as indicated by the coloursin the slot star on the left.

Example of winding factor


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Winding factor

The total emf induced in a phase is obtained by adding the

slot-star vectors. The sum of the positive coil sides forphase A is

The negative coil sides give an equal amplitude butopposite sign. The total emf, obtained as the difference ofthe two vectors, is twice the vector shown above.

In this case, the winding factor is

1 s

j /92 s

j2 /93 s

e

e

e e

e e

e e

1e2e

3e

3

1

ii

e

3/9 j2/9

s 1

1 11 e e 0,960

3 3i

i

ee


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Winding factor

More generally, the winding factor can be calculated from

equation

Where is the order of the harmonic, n is the slot pitchangle, q is the number of slots per pole and phase and mis the number of phases. This equation is not valid for achorded winding.

n

n

sin sin2 2

sin sin2 2sin sin

2 2

qm

q qmq

slot winding

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