Post on 11-Jun-2020
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
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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
EIEN20 Design of Electrical Machines, IEA, 2016 2
Avo R Design of Electrical Machines 5
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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
Avo R Design of Electrical Machines 7
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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”
Avo R Design of Electrical Machines 8
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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
EIEN20 Design of Electrical Machines, IEA, 2016 3
Avo R Design of Electrical Machines 9
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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
EIEN20 Design of Electrical Machines, IEA, 2016 4
Avo R Design of Electrical Machines 13
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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
Avo R Design of Electrical Machines 15
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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
Avo R Design of Electrical Machines 16
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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
EIEN20 Design of Electrical Machines, IEA, 2016 5
Avo R Design of Electrical Machines 17
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nψ & T mapping
• [T,ψ]=f(isx,isy,r) → [Tav,ψav]=f(isx,isy)
Avo R Design of Electrical Machines 18
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Accelerating vs magnetisingIsx>0,isy=0 Isx=0,isy>0
Isx<0,isy=0 Isx=0,isy<0
Avo R Design of Electrical Machines 19
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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
Avo R Design of Electrical Machines 20
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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
EIEN20 Design of Electrical Machines, IEA, 2016 6
Avo R Design of Electrical Machines 21
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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
Avo R Design of Electrical Machines 23
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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
EIEN20 Design of Electrical Machines, IEA, 2016 7
Avo R Design of Electrical Machines 25
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nMagnet loading PM vs PM+RM
Avo R Design of Electrical Machines 26
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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
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 3
x 104
0
20
40Pmax=22.8 kW @ n=6.0 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 34
0
20
40Pmax=8.5 kW @ n=13.5 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=15.9 kW @ n=6.9 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 3
x 104
0
20
40Pmax=17.9 kW @ n=6.0 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 34
0
20
40Pmax=3.5 kW @ n=7.5 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=10.1 kW @ n=7.8 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 3
x 104
0
20
40Pmax=13.1 kW @ n=6.0 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 34
0
20
40Pmax=1.2 kW @ n=6.3 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=6.3 kW @ n=10.8 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 3
x 104
0
20
40Pmax=9.2 kW @ n=6.3 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 34
0
20
40Pmax=0.3 kW @ n=6.0 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=3.5 kW @ n=15.9 krpm
T=f(n), [Nm]P=f(n), [kW]
0 1 2 3
x 104
0
10
20
0 1 2 3
x 104
0
20
40Pmax=6.2 kW @ n=6.3 krpm
T=f(n), [Nm]P=f(n), [kW]
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
Avo R Design of Electrical Machines 28
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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
EIEN20 Design of Electrical Machines, IEA, 2016 8
Avo R Design of Electrical Machines 29
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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
Avo R Design of Electrical Machines 31
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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
Avo R Design of Electrical Machines 32
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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)