L12 – Power - IEA · L12 – Power EIEN20 Design of Electrical Machines, IEA, 2016 2 Avo R Design of Electrical Machines 5 Industrial Electrical Engineering and Automation 0.5 1

L12 – Power

EIEN20 Design of Electrical Machines, IEA, 2016 1

Industrial Electrical Engineering and AutomationLund University, Sweden

L12: Power

Machine CharacteristicsConstant power speed range and field weakening

Machine Topology suitable for FW

Avo R Design of Electrical Machines 2

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Today’s goal

• Design challenges– Constant power at wide speed range

• Machine equations– Machine characteristics– Machine parameters

• Synchronous machines with field control


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-B

+A

-C+B-A+C

-B

+A

-C

+B

-A

+C-B +A -C

+B

-A

+C

-B

+A

-C

+B-A

+C

-B

+A

-C

+B

-A

+C

-B+A

-C

+B

-A

+C


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Machine characteristics

• Constant torque region– Limited current– Related to size and

“nominal” cooling

• Constant power region– Limited voltage and current

at minimum angle to give rated terminal voltage

– Related to speed and field weakening

speed

TorquePower

L12 – Power



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0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

Power, W

10001200 1200 1200

1400 1400 1400

16001600 1600

1800 1800 1800

2000 20002000

2000

2200

2200 2200

2200

Electromechanics via magnetism

• Power balance: Pem• Pm=ωmechTmech=3/2Np/2ωmechΨmNIm=3/2EmIm=Pe

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

Torque, Nm

3 3 5

44 4 4

4.5 4.5 4.5

55 5 5

5.5 5.5 5.5

66 6

66.5

6.5 6.56.5

6.5

6.5

7

7

7

7

7

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

MMF, A

600 600650 650 650

650

700 700 700

700700

700

750 750 750

750750

750

750

800800

800 800 800

800800

850850

850

850850

850

850

900 900900

900

900

950

950

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

flux linkage, Vs

0.00

2

0.00250.00250.0025

0.0030.003

0.0030.00350.0035

0.0035

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

induced voltage per turn, V/turn

11.2

1.4

1.41.4 1.4

1.6

1.6 1.6

1.8

1.8 1.8

2 2

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

number of turns

180180180

200200

200

220220220

240240

240

240

260

260

280300

3200.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

q

Np

current, A

22.5 2.5 2.5

33 3 3

3.53.5 3.5

4

4 4

4

4.5

4.5

4.5 4.5

0.5 1 1.5 22

2.5

3

3.5

4

4.5

5

5.5

6

qN

p

Power, W

10001200 1200 1200

1400 1400 1400

1600 1600 1600

1800 1800 1800

2000 20002000

2000

2200

2200 2200

2200


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Torque capability over wide speed range

• Field Weakening required for over base speed operation: P=UI=const T=P/ω and Ψ=U/ω, U=cns

• SPMSM – short pitch windings with high self inductance

• IPMSM – built in rotor saliency


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Torque production → machine topology

ddLii

ddLi

ddLiT 12

2122

212

1 21

21

• Excitation torque – forces between “active magnets”• Reluctance torque – forces between “caused magnets”


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Torque waveforms

0 30 60 90 120 150 180 210 240 270 300 330 360-1.5

-1

-0.5

0

0.5

1

1.5

angle, [deg]

torq

ue, T

* [-]

excitation torquereluctance torque Lsx<Lsyresultanr torque Lsx<Lsy

0 30 60 90 120 150 180 210 240 270 300 330 360-1.5

-1

-0.5

0

0.5

1

1.5

angle, [deg]

torq

ue, T

* [-]

excitation torquereluctance torque Lsx>Lsyresultant torque Lsx>Lsy

0 30 60 90 120 150 180 210 240 270 300 330 360-1.5

-1

-0.5

0

0.5

1

1.5

angle, [deg]

torq

ue, T

* [-]

excitation torque

0 30 60 90 120 150 180 210 240 270 300 330 360-1.5

-1

-0.5

0

0.5

1

1.5

angle, [deg]

torq

ue, T

* [-]

reluctance torque Lsx>Lsyreluctance torque Lsx<Lsy

L12 – Power



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nNon-salient machines

• Stator excitation– I1=cns, Ψ1=cns, L1=cns, Ψ2=var,

• Rotor excitation– I2=cns, Ψ2=cns, L2=cns, Ψ1=var,

• Double excitation– I1=I2=cns, Ψ1= Ψ2=var, L12=var


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Rotor-salient machines

• Stator excitation– I1=cns, Ψ1=var, L1=var, Ψ2=var,

• Rotor excitation– I2=cns, Ψ2=cns, L2=cns, Ψ1=var,

• Double excitation– I1=I2=cns, Ψ1≈ Ψ2=var, L12=var


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Stator-salient machines

• Stator excitation– I1=cns, Ψ1=cns, L1=cns, Ψ2=var,

• Rotor excitation– I2=cns, Ψ2=var, L2=var, Ψ1=var,

• Double excitation– I1=I2=cns, Ψ1 ≈ Ψ2=var, L12=var


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Double-salient machines

• Stator excitation– I1=cns, Ψ1=var, L1=var, Ψ2=var,

• Rotor excitation– I2=cns, Ψ2=var, L2=var, Ψ1=var,

• Double excitation– I1=I2=cns, Ψ1 ≈ Ψ2=var, L12=var

L12 – Power



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Magnetically coupled rotating and stationary coil

• s=d/dt• M=f(θ)

2

1

2221

1211

2

1

ii

sLRsMsMsLR

uu


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Reference frame

• Stator reference frame• us=Ris+dψs/dt• ur=Rir+dψr/dt-jωψr

• Rotor reference frame• us=Ris+dψs/dt+jωψs

• ur=Rir+dψr/dt

quadrature axis

direct axis

iA

uA

ψA

iα

uα

ψα

iB

uBψB

iβ

uβψβ

quadrature axis

direct axis

iD

uD

ψD

id

ud

ψd

iQ uQ

ψQ

iq uq

ψq

θ


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Machine equations

• Space phasors– Stator and rotor– Currents, flux-linkages, …

• Electric equations– U=Rsi + dΨ/dt

• Magnetic equations– Ψ=Lsdi/dt + Ψr/dt

• Mechanic equations– T= P/2 Ψ x i


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PMSM: Rated OP-point

• Step 1 – Heat transfer: find(Jm) @ (limit,ωbase,Bm,hcool)• Step 2 – Electromagnetism: Tem=f(Jm)• Step 3 – ‘Rough Optimisation’: Tem=f(x1,x2,..)

L12 – Power



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nψ & T mapping

• [T,ψ]=f(isx,isy,r) → [Tav,ψav]=f(isx,isy)


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Accelerating vs magnetisingIsx>0,isy=0 Isx=0,isy>0

Isx<0,isy=0 Isx=0,isy<0


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Computer Aided Design

• Rapid CAD/CAE designtool for electrical machines

• The design environment is established in Matlab that calls 2D or 3D FEM

• Leave tedious work to computer

Initializationgeom, md, bnd

Rough Optimization

[T,ψ, B]=f(isx,isy,r)

[Tav,ψav, Bm]=f(isx,isy)

Tmax=f(Imin,ψlimit,ω) max=f(Imin,ψlimit,ω)

Pout=f(T,ω) η=f(T,ω)

OK?

Performance sheet


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PMSM

• Rated operation point = base point

– Tb – base torque, – Ωb – base speed, – Vb – base voltage– Ib = 2/3*Tb*Ωb/Vb – base

current– Φb = Vb/(Np/2*Ωb) – base

flux– Lb = Φb/Ib– base

inductance

• Any other steady state operation point

• Normalised values• No resistance,

saturation, losses or cross-couplings

222

22222

yx

yyxxmyx

yxyxymxyyx

iii

ililv

iilliiiT

L12 – Power



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Shaping Circle Diagram = Selecting machine magnetisation

• Circle diagram– Operation modes: 1 - 3

• Machine construction– PM, RM, RM+PM=IPM

•Current limited region•Voltage and current limited region•Voltage limited region


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Constant Power Speed Range

• Rotor saliency vs PM magnetisation

• CPSR=nnominal / nmax


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Machine characteristics• Tracking operation points

– Circle diagram: Ψ=f(I), T=f(I), where I2=Ix2+Iy2 is a circle

– Torque speed diagram: I=f(ω)→T=f(ω)

– Power speed diagram: T=f(ω)→P=f(ω)

• Constant torque– I=const, Ψ=const– Max Torque Per Ampere - MTPA

• Constant power– I=const, U=const– Const. Power Speed Range - CPSR

• Constant voltage– U=const– Minimum Flux Per Torque - MFPT


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Assignment A5

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

1

1

1

1

1

11

11.

2

1.2

1.2

1.2-0.8 -0.8

-0.6 -0.6

-0.4 -0.4

-0.2 -0.2

0 0

0.2 0.2

0.4 0.4

0.6 0.6

0.8 0.8

0.85

0 .9

0 .9

0 .9

0 .9 5

0 .95

0.9 5

1

11

1 .0 5

1.05

1.05

1 .1

1.1

1.1

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

Lsx*=0.14 Lsy*=0.14 Psim*=0.99

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

1

1

1

1

1

11

1

1.2

1.2

1.2

1.2

-1

-0.5

-0.5

0 0

0.5

0.5

1

0.6

0.6

0.8

0.8

0.8

1

1

1

1

1.2

1.2

1.2

1.4

1.4

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

Lsx*=0.44 Lsy*=0.87 Psim*=0.90

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

1

1

1

1

1

11

11.

2

1.2

1.2

1.2

-0.6 -0.6

-0.4 -0.4

-0.2 -0.2

0 0

0.2 0.2

0.4 0.4

0.6 0.6

0.2

0.4

0.4

0.6

0 .6

0.6

0.8

0 .8

0.8

1

1

1

1.2

1.2

1.2

1.4

1. 4

1.4

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

Lsx*=0.71 Lsy*=0.71 Psim*=0.70

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

1

1

1

1

1

11

11.

2

1.2

1.2

1.2-0.8

-0.6

-0.4

-0.4

-0.2

-0.2

0 0

0.2

0.2

0.4

0.4

0.6

0.8

0.2

0.2

0.2

0.4

0.4

0.4

0.4

0.60.6

0.6

0. 8

0.8

0 .8

1

11

1.21.2

1.2

1.41.4

1.4

1.4

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6Lsx*=0.80 Lsy*=0.40 Psim*=0.60

L12 – Power



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nMagnet loading PM vs PM+RM


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Sensitivity study

• Dimensions:– Rso=110 mm,– Hact=240 mm,

• Design parameters:– Rg=60…90 mm, – Np=20…40 poles,

• Design target: – Pcon=18kW @

6000 rpm, – Pint=25kW– FWratio=2…3

+A-B

+B-C

+C-A

75.50 110.0050.00

air Am1 Br=1.26TAi1 Ac1 1117 SteelBc1 SM2CBi1 Bw1 Jm=5.00A/mm2

Bw2 Jm=5.00A/mm2

Bw3 Jm=5.00A/mm2

ext 0.06

0.07

0.08

0.09

roto

r out

er ra

dius

, ror

[m]

average torque, T [Nm]

5

10

152025

3035

power, P [W]

50001000

0

1500

0

200 0

0

induced voltage, E/N [V/turns]

1020304050607080

90

0.06

0.07

0.08

0.09

roto

r out

er ra

dius

, ror

[m]

torque ripple, P [Nm]

5

10

15

losses, Q [W]

200

250

300350400

efficiency, [%]

70

8090

20 25 30 35 400.06

0.07

0.08

0.09

number of poles, Np [-]

hotspot, m [C]

120

140

160180200

20 25 30 35 40number of poles, N

p [-]

surface temperature, i [C]

48

50

52

54565860

20 25 30 35 40number of poles, N

p [-]

surface temperature, o [C]100110120

130140150160170

0 1 2 34

0

20

40Pmax=16.3 kW @ n=12.0 krpm

T=f(n), [Nm]P=f(n), [kW]

0 1 2 34

0

10

20

0 1 2 3

x 104

0

20

40Pmax=24.1 kW @ n=6.6 krpm


0 1 2 3

x 104

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 34

0

20



0 1 2 34

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 34

0

20



0 1 2 34

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 34

0

20



0 1 2 34

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 34

0

20



0 1 2 34

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20

0 1 2 3

x 104

0

20



0 1 2 3

x 104

0

10

20


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22

yLyisfLfixLxipmsu

yixixLyLyisfLfipmpT

23

Excitation arrangementSeparate excitation: temporal, permanent or both i.e. hybrid

Torque capability

Voltage limitation

sffpm

pm

Li

-B

+A

-C

+B

-A

+C

ω

T


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Hybrid PM+EM+RM excitationEM excitation can use field regulation to achieve wider speed range and higher PEAK torquePM excitation has the advantage of high energy dense materialsHMSM can merge these benefitsUsing less PMs can potentially decrease the total cost of the machine

Torque boosting

Speed range

Energy conversion efficiency

L12 – Power



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nConcept visualization

Φpm

Rgap

Rgap Fem

Rem

Fa

Ra

Rpm

Φpm Rgap

Rgap Fem

Rem

Fa

Ra Rpm

Location and supplyof EM– Rotary EM slip-rings– Stationary EM extra

gap

Magnetic arrangement– PM & EM in series– PM & EM in parallel

• The balance between EM+PMmagnetization gives the choice between wide speed range and torque boost at given Udc/ω

– Field weakening– Field strengthening


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Alternating Pole ConfigurationMagnetic arrangement– Salient pole EM– Surface mounted PM

Hybridization factor α– Easy to define α for equally

strong EM and PM

Topology configuration– Magnetic and mechanic

balance– Cogging reduction


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Combined RM PM machines that give EM

• Wide speed range with PM + EM excitation

• 3kW, 2000rpm, 8 pole RFM

• 10kW, 2000rpm, 16 pole AFM

• Tapia, Aydin, Lipo, 2001-2002


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Design scope• 2D FEA of EMSM vs PMSM

– Same machine size– Inner and Outer rotor– Traction and Wind

• 3x5 analysis map– 3 different volumes (colors)

• Ro-Ri=[7 14 21] cm• Reference machine:

Ro=10 cm, V=6.4 dm3

– 5 radius/length ratios (rings)– Pole pairs varied by p ± 1 .. 2 (boxes)

L12 – Power



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nMagnetic analysis

• Broad analysis map– Initial data for applications– EMSM vs PMSM crossover related

to machine size– Comparing EM vs PM poles for the

benefit of HM-array

• Torque capability– Electric loading defined by

J=4A/mm2 and Kfill=50% in the insulated slot

– Magnets N35 hpm=6 mm

• Machine characteristics– Estimated from machine

parameters Ψ, L and R


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Thermal analysis

• Goals for the steady state heat transfer analysis

– Estimation of the temperature rise– Derive cooling specifications

• Power losses and heat dissipation– Windings k=0.3 W/mK, p=0.16

kW/dm3

– Radial cooling surfaces h=50W/m2K• Detect the EMSM designs that

suffer under excessive rotor losses– Large machines with larger slots


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Looking for torque capability

4 6 8 10 12 14 16 18 20 22 240

500

1000

1500

2000

2500

3000

elec

trom

agne

tic to

rque

, Tem

[Nm

]

active length of the machine, la [cm]

34

6

57

8

8

9

11

10

12

13

13

14

16

PMSMEMSM

4 6 8 10 12 14 16 18 20 22 240

500

1000

1500

2000

2500

3000

elec

trom

agne

tic to

rque

, Tem

[Nm

]

active length of the machine, la [cm]

3

4

6

5

7

8

8

9

11

10

12

13

13

14

16

PMSMEMSM

Inner rotor (traction)– Target: 80kW & 6000rpm– T>130 Nm

Larger radius with higher number of poles has better chance for EMSM cooling

Outer rotor (wind power)– Target: >2kW & 50rpm– T> 380 Nm

EMSM compared to inner rotor is overmagnetizedand overheated


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Combining the slicesArranging EM PM poles (sectors) for HMSMTraction application – PM excitation according to

max speed requirements– EM according to torque

boost requirements– RM is used to extend the

natural FW range

– Wind Power application– PM “supply” for serially

magnetised synshronousmachine (SMSM)

L12 – Power



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nHMSM for Traction Application

Evaluation of HMSMsuitability for existing IPMCombine EM and PM – RM contribution Lx > Ly– EM used only for torque

boosting

Parameter Unit ValueActive length mm 224Stator outer diameter mm 200Rotor inner diameter mm 60Nominal speed rpm 6000Current density A/mm2 10

+A-A

-A +A

-B-B

+A+A

-C-C

+B+B-A-A+C+C-B

-B+A

+A-C-C+B+B

-A-A

+C+C

-B -B +A +A -C -C+B

+B-A

-A+C+C59.50 100.030.00


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IPMSM

Power speed characteristics

HMSM-1

HMSM-2

Control: MTPA for FW – select the best

combination of stator and rotor currents


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Outcomes EM vs HT

HMSMs designed only for torque boostMore rotor coolingneeded at low speed/high torqueLikely more core losses in the stator


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TOPOLOGYSelect machine type

EMSM, PMSM, RSM or in combination

A number of predefined constructions

Electromagnet

Permanent magnet

Reluctance magnet

PARAMETERISATION

L

Ro

Ri

Design specification

Geometry Materials Loading

Use default or specify proportions K, numbers N, dimensions d, etc

LOADING ESTIMATIONB, , J - distribution

Magnetostatics Heat transfer Find J for given

minimum of 2 calculations

ROUGH OPTIMIZATION

Des

ign

para

met

er 2

Design parameter 1

Design selection

Sensitivity study of 2 design parameters

Magnetostatics Heat transfer Early performance

visualization

minimum of 3x3 calculations

OPERATION POINTSXY-mapping of T, ψ, B ...

0,0,

,,

,,00,0,0

44

33

22

11

msxmm

msymsxmmm

msymm

m

ILI

ILILII

ILI

ψi

ψi

ψiψi

Usually many more operation points are read per revolution

[T,ψ,B]=f(isx,isy,r)

ψ1

ψ2ψ3

ψ4i1

i2i3

i4

minimum of 1x2x7 calculations

OPERATION CYCLEVoltage-speed conditioning

sysxsysxsym

sxsxmsyssy

sysysxssx

LLiiipT

iLiRu

iLiRu

2

find maximum torque for minimum current

consider flux limitation consider current limitation

TORQUE-SPEED CHARACTERISTICPower-temperature balance

The torque speed diagram T=f(ω)

The power speed diagram P=f(T,ω)

The efficiency map η=f(T,ω)

Documents

L12 – Power - IEA · L12 – Power EIEN20 Design of Electrical Machines, IEA, 2016 2 Avo R Design of Electrical Machines 5 Industrial Electrical Engineering and Automation 0.5 1