CADFEM-Symposium
Energieeffizienz – Elektrische Antriebe und Wandler
Evaluation of Iron Losses and Efficiency
Improvements in Electric Machines
EAA
Gurakuq Dajaku
Dieter Gerling
FEAAM GmbH
D-85577 Neubiberg, Germany
Universität der Bundeswehr München
D-85577 Neubiberg, Germany
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Overview
Various Estimation Methods for Iron Losses
–
Fundamental Steimnetz Model
–
Extended Analytical Method
–
Iron Loss Model Considering Harmonics
–
Direct Flux-Density Method Consider the Major and Minor Hysteresis Loops
–
Iron Loss Model with Variable Iron Loss Coefficients
Efficiency Improvement using Novel Windings
–
Concentrated Windings
–
New 12-teeth/10-poles Winding
–
New 24-teeth/10-poles Winding
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Power Losses
Generally, the losses of electrical machines are decomposed into:
Copper losses;
>> DC-Ohmic losses, skin and approximyty effect losses
Mechanical losses;
>> bearing friction, windage on the rotor, ventilation fan and cooling pump
Iron losses;
>> hysteresis and eddy current losses
Eddy current losses;
>> in rotor permanent magnets (PM)
With the increasing demand on high efficiency and high power density in high-speed applications
such as electric vehicles (EVs), it is important to estimate the iron loss of electrical machines
accurately
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Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Iron Losses
Iron losses in a magnetic material occur when the material is subjected to a time varying magnetic
flux density
Hysteresis loss - is due to the energy expended in the redirection of the magnetic domains of the
material during every flux direction reversal
Eddy current - is the circulating current induced in the material by changing magnetic flux as a
consequence of the electromagnetic induction
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Analytical calculation of iron losses
Steinmetz model for determination of iron losses:
piron = phys + pedd = khys ⋅ f ⋅ Bˆ β + kedd ⋅ f 2 ⋅ Bˆ 2
The above iron-loss expression is only valid for sinusoidal flux density
In most electric machines, the variation in flux density in the stator core is far from sinusoidal
Minor hysteresis loops are due to the flux fluctuations (air-gap harmonics)
a) Minor hysteresis loops;
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b) Definition of flux variations.
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Analytical calculation of iron losses
Improved analytical model for iron loss calculation:
piron = phys + pedd = kch ⋅ khys ⋅ f ⋅ Bˆ β + kce ⋅ kedd ⋅ f 2 ⋅ Bˆ 2
c N
Correction factors: kch = 1 + ∑ ∆Bi
Bˆ i =1
2
N


and kce =  B1  ⋅ ∑  i ⋅ Bi 
 Bˆ  i =1  B1 
2
Extended model:
piron = phys + pedd + pexc
T
1 k
= kch ⋅ khys ⋅ Bˆ β ⋅ ω + ∫ edd2
T 0 2π
EAA
2
T
1 kexc
 dB (t ) 
⋅
⋅
dt
+

T ∫0 2π 43
 dt 
( )
3
 dB(t )  2
⋅
 ⋅ dt
dt


Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Harmonic iron losses using Fourier transformation
This method is based on the Fourier transformation of the waveforms of the flux density at
each finite element
The total iron losses is assumed to be the sum of the losses that are caused by the radial and
peripheral components of the flux density
M
Pedd = ∑∑ kedd ⋅ mi ⋅ ( nf ) ⋅ { Br2,n + Bθ2,n }
i =1
2
n
M
Phys = ∑∑ khys ⋅ mi ⋅ ( nf ) ⋅ { Brβ,n + Bθβ,n }
i =1
n
This method is very useful to understand the each harmonic loss component
However, the hysteresis loss cannot be decomposed into harmonic components because of its
nonlinear characteristics. Also, the hysteresis losses are over-estimated using this method
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Iron loss calculation using the waveform of the flux density
Eddy current losses:
2
T
k
1  dB (t ) 
= edd2 ⋅ ∫ 
 dt
2π T 0  dt 
pedd
⇒ Pedd
N Step
M 
 N Step
2
2 
kedd


2
= 2 ⋅ N Step ⋅ f ⋅ ∑ mi ⋅  ∑ ( Br ,k +1 − Br ,k ) + ∑ ( Bθ ,k +1 − Bθ ,k )  
2π
i =1 
k =1

 k =1
 
Hysteresis losses
 N pr β N pθ β 
= khys ⋅ f ⋅ ∑ mi ⋅  ∑ Bˆr ,ij + ∑ Bˆθ ,ij 
i =1
j =1
 j =1

M
Phys
i
i
Using this method, the major and minor hysteresis
losses are considered
The hysteresis loss are calculated as the sum of
the area of all hysteresis loops
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(4)
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Iron loss calculation using the waveform of the flux density
The current ripple in the current curve leads to minor hysteresis loops. The total hysteresis
loss is the sum of the main and minor hysteresis loops.
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Comparison of results
B_total
B_1
B_3
B_5
1,4
1,0
Eddy current Loss
0,2
3
-0,2
-0,6
-1,0
2,5
1,5311
2
0,79616
1,5
1
1,5847
1,5847
0,5
-1,4
0
4
8
12
16
20
0
Cal. FFT
time [ms]
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Hys. Loss
3,5
Iron Loss [W]
B [T]
0,6
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Cal. Direct
Evaluation of Iron Losses
Variable Iron loss Coefficients
Conventional iron loss model with constant loss coefficients are not suitable for the machine
using field-weakening control where the frequency and the flux density of the flux waveform
are varied dramatically according to its driving condition
Model with variable coefficiens
piron = khys ( f , B) ⋅ f ⋅ Bˆ 2 + kedd ( f , B ) ⋅ f 2 ⋅ Bˆ 2
Iron loss coefficients depends on the flux density
and frequency
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Variable Iron loss Coefficients
Division of the iron loss model by f and B² leads to the following linear equation,
piron
= khys ( f , B) + kedd ( f , B) ⋅ f
f ⋅ Bˆ 2
Linear model with slope identifying kedd and the
intersection with y-axis corresponding to khys
Measured specific losses
piron
f ⋅ Bˆ 2
y = ahys + bedd ⋅ f
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Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Evaluation of Iron Losses
Variable Iron loss Coefficients
Iron loss coefficients are derived using curve fitting method
Eddy-current loss coefficient
Hysteresis loss coefficient
kedd ( B ) = kedd ,0 + kedd ,1 ⋅ B + kedd ,2 ⋅ B 2 + kedd ,3 ⋅ B 3
khys ( B) = khys ,0 + khys ,1 ⋅ B + khys ,2 ⋅ B 2 + khys ,3 ⋅ B 3
-5
11.5
x 10
0.04
11
Khys [W/kg/(f*T²)]
Khys
[W/kg/(Hz*T²)]
Kedd [W/kg/(Hz*T²)]
0.035
10.5
10
9.5
0.03
0.025
9
0.02
8.5
8
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0.015
0
Induction [T]
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0.2
0.4
0.6
0.8
1
1.2
Induction [T]
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
1.4
1.6
1.8
2
Efficiency Optimisation of Electric Machines
Winding Topologies
Winding MMF
Winding MMF
Distributed Winding:
Concentrated Winding:
- Sinusoidal MMF distribution
- High nr. of slots per pole
- Large end-winding length; High parasitic end-effects
- High copper losses
- High production costs
- Compact design
- Shorter and less complex end-windings
- Low copper losses
- Low production costs
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- More space harmonics
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Efficiency Optimisation of Electric Machines
PM machine with 12-teeth/10-poles winding topology
MMF Harmonics [p.u.]
MMF [p.u.]
12-Teeth/10-Poles Winding topology
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- 5th or 7th => working harmonic
- Cause undesirable effect such as
losses, noise and vibration
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Efficiency Optimisation of Electric Machines
New 12-teeth/10-poles winding with
different turns per coil side
Comparison of Rotor (magnet) Losses
35
New 12-teeth/10-poles winding
with reduced subharmonics
Eddy Current Loss [ W ]
30
no-load
conv. winding, under load
new winding, under load
25
20
15
10
5
0
500
1000
1500
2000
2500
speed [ rpm]
New 12-teeth/10-poles winding
Comparison
Conventional 12-teeth/10-poles winding
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Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
3000
3500
Efficiency Optimisation of Electric Machines
New 24-teeth/10-poles winding
New 24-teeth/10-poles winding with
reduced sub- and high harmonics
PM machine with conventional
distributed winding, q=2
PM machine with new 24-teeth/10-poles
winding
Comparison
Winding distribution of one-phase
(phase-A)
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- No skewing is required
for the new machine
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Efficiency Optimisation of Electric Machines
New PM machine
Driving Cycle Simulations
Conventional PM machine
Efficiency difference:
Eff.new – Eff.conv
New 24-teeth/10-poles winding
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Losses reduction up to 20% with the new machine
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Conclusion
Different methods for iron losses calculation are presented
–
Conventional analytical methods are valid only for sinusoidal flux density variations
–
Harmonic iron losses method is very useful to understand the each harmonic loss component. It
overestimate the hysteresis losses
–
Iron loss calculation using the waveform of the flux density consider the major and minor
hysteresis loops
–
Iron loss model with variable loss coefficients increase the calculation accuracy
Different efficiency optimisation techniques
–
Tooth concentrated winding are characterised with high MMF harmonic contents
–
A simple technique using coils with different turns per coil-side reduce the sub-harmonics
–
24-teeth/10-poles winding is another solution for simultaneously reducing the sub- and high
harmonics
–
Loss reduction up to 20% per driving cycle are possible with the new winding
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling
Thank You for Attention
Gurakuq Dajaku
FEAAM GmbH, Neubiberg, Germany
gurakuq.dajaku@unibw.de
EAA
Elektrische Antriebstechnik und Aktorik - Electrical Drives and Actuators
Univ.-Prof. Dr.-Ing. Dieter Gerling