Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research...
Transcript of Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research...
![Page 1: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/1.jpg)
Dartmouth Magnetics and PowerE l ec tr on i c s Res ea r c h Gr oup
1
Overview of Modelling Methods
Prof. Charles R. [email protected]
http://power.engineering.dartmouth.edu
![Page 2: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/2.jpg)
Winding models vs. Core models
Linear, well known material properties.
Behavior is a solution to Maxwell’s equations.
Numerical, analytical, or mixed solutions.
Can be accurately approximated by linear circuit networks, given enough RLC elements (usually just RL).
Nonlinear material properties, known only through measurements.
Models are behavioral, based on measurements.
Physics-based micromagneticmodels exist, but can’t address ferrite loss yet.
Circuit models based on RLC elements only can’t capture nonlinear behavior.
power.thayer.dartmouth.edu 2
![Page 3: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/3.jpg)
Winding models
power.thayer.dartmouth.edu 3
Physical DesignGeometry & Materials
Loss
ElectricalMeasurements
Circuit model for simulation
![Page 4: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/4.jpg)
Winding models
power.thayer.dartmouth.edu 4
Physical DesignGeometry & Materials
Loss
ElectricalMeasurements
Circuit model for simulation
Currentwaveforms
![Page 5: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/5.jpg)
Winding models
Winding ac resistances?
power.thayer.dartmouth.edu 5
Physical DesignGeometry & Materials
Loss
Currentwaveforms
?
![Page 6: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/6.jpg)
Loss calculated from currents
Conventional, incorrect, model for transformer winding loss (assume sine waves for now).
Pwinding= I12R1 + I2
2R2
Problem: Loss varies drastically depending on relative phase/polarity.
Factor of 4 error in this case.
Correct model options:
R1 and R2 that are only for specific phase relationship.
Resistance matrix.
power.thayer.dartmouth.edu 6
Primary Secondary
0°
180°
![Page 7: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/7.jpg)
Winding models
Winding ac resistances?
Frequency-dependent resistance matrix R(f).
Captures interactions between windings.
power.thayer.dartmouth.edu 7
Physical DesignGeometry & Materials
Loss
Currentwaveforms
R(f)
![Page 8: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/8.jpg)
Winding models
See poster D09 on Thursday for how-to on this by Benedict Foo.
power.thayer.dartmouth.edu 8
Physical DesignGeometry & Materials
Loss
Currentwaveforms
R(f)
Electrical
Measurements
Removecoreeffect
![Page 9: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/9.jpg)
Predictions from physical structure1-D fields 2-D or 3-D fields
Rectangular conductors(e.g. foil and PCB)
Analytical Numerical (Finite Element, PEEC, etc.)
Round-wireconductors (including litz)
Simulation-tuned physical model
Simulation-tuned physical model + dc field simulation
9
![Page 10: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/10.jpg)
Winding models: 1D, rectangular conductors
power.thayer.dartmouth.edu 10
Physical DesignGeometry & Materials
Loss
Circuit model for simulation
M2SPICE(MIT)
Dowell,Spreen
![Page 11: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/11.jpg)
power.thayer.dartmouth.edu 11
Round conductor: Textbook problem
Cylinder subjected to uniform field
Dowell’s model is a crude approximation.
![Page 12: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/12.jpg)
power.thayer.dartmouth.edu 12
Textbook solution
Exact solution, described by Bessel functions.
Use for winding loss analysis pioneered by Ferreira.
![Page 13: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/13.jpg)
power.thayer.dartmouth.edu 13
Actual problem
Array of cylinders subjected to uniform field
![Page 14: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/14.jpg)
power.thayer.dartmouth.edu 14
Using the Bessel solution for the real problem
Not a valid solution! Real Solution (FEA)
![Page 15: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/15.jpg)
power.thayer.dartmouth.edu 15
Simulation Results
1 10
1
100
d/d
Pro
xim
ity lo
ss fa
cto
r
Dowell
Bessel
10
0.1
0.01
Real behavior is between Dowell and Bessel.
Sometimes closer to Dowell.
Identical in low-frequency range with simple correction.
![Page 16: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/16.jpg)
power.thayer.dartmouth.edu 16
Xi Nan’s model
0 2 4 6 8 10 120
20
40
60
80
100
Rac/R
dc
d/d
Bessel function methodDowell methodExperimental DataOur model
▪ Weighted average of Dowell-like and Bessel-like behavior: “Simulation tuned physical model”
▪ Fits experimental results better than Dowell or Bessel.
▪ Can be applied to 2D or 3D field configurations …
![Page 17: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/17.jpg)
Full winding loss model: 2-D, full frequency range, multi-winding interactions
Hybridized Nan’s method
(Zimmanck, 2010)
power.thayer.dartmouth.edu 17
Homogenization with complex permeability (Nan 2009, Meeker, 2012)
Available in FEMM
![Page 18: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/18.jpg)
Winding models
power.thayer.dartmouth.edu 18
Physical DesignGeometry & Materials
Loss
ElectricalMeasurements
Circuit model for simulation
Currentwaveforms
R(f)
Round wire/2D: “Hybridized Nan’s method”
M2SPICE(MIT)
?
![Page 19: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/19.jpg)
Linear RL networks for winding models Three standard networks topologies that provide:
R increases with frequency.
L decreases with frequency.
Can obtain identical behavior with any of the three.
Can use any one to match measured behavior.
power.thayer.dartmouth.edu 19
Foster
Cauer 1
Cauer 2
![Page 20: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/20.jpg)
Core models
power.thayer.dartmouth.edu 20
Physics
Loss
ElectricalMeasurements
Circuit simulation
Fluxwaveforms
Losscalculation
Dynamic model
Loss
model
![Page 21: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/21.jpg)
Loss Calculation Models Steinmetz equation:
Sinusoidal waveforms only
Various types of modified/generalized/etc. Steinmetz equations.
Extend to non-sinusoidal waveforms.
Most common: improved Generalized Steinmetz Equation (iGSE).
Loss Map/Composite Waveform Method.
power.thayer.dartmouth.edu 21
![Page 22: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/22.jpg)
Loss Calculation Models Steinmetz equation:
Sinusoidal waveforms only
Various types of modified/generalized/etc. Steinmetz equations.
Extend to non-sinusoidal waveforms.
Most common: improved Generalized Steinmetz Equation (iGSE).
Loss Map/Composite Waveform Method.
power.thayer.dartmouth.edu 22
Comments:
iGSE vs. Loss Map:
Same predictions if you use the same data.
iGSE: sinusoidal data.
Loss Map
Loss map database can include dc bias effects.
iGSE can do any wave shape, whereas Loss Map is for rectangular only.
Barg 2017 improves iGSE for extreme duty cycles.
Weakness of most of these: “Dead time” affects loss in practice but not in the model. “Relaxation effects.”
![Page 23: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/23.jpg)
Core simulation models
Need to include nonlinearity.
Example: Cauer 1 network to model saturation behavior and frequency-dependent permeability in nanocrytallinetape-wound cores.
Successfully matched pulse behavior in high-amplitude operation (Sullivan and Muetze, IAS 2007)
Did not examine loss behavior.
Open question: what model structures capture dynamic nonlinear behavior correctly?
power.thayer.dartmouth.edu 23
![Page 24: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/24.jpg)
power.thayer.dartmouth.edu 24
Conclusions
Winding loss: Complex but feasible to model accurately. For 2 or more windings, need resistance matrix. 1D rectangular conductors: analytical solutions. 2D rectangular conductors: numerical simulations. 1D or 2D round wire: Simulation-tuned physical
models are better than Dowell or Bessel.
Core loss Nonlinear and can only be found experimentally. Open questions on data needed and models.
![Page 25: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/25.jpg)
References
Sobhi Barg, K. Ammous, H. Mejbri, and A. Ammous, “An Improved Empirical Formulation for Magnetic Core Losses Estimation Under NonsinusoidalInduction,” IEEE Trans. Pow. Electr. 32(3), March 2017
Spreen
Zimmanck
Meeker
Nan
Sullivan and Muetze, IAS 2007
power.thayer.dartmouth.edu 25
![Page 26: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/26.jpg)
Dartmouth Magnetics and PowerE l ec tr on i c s Res ea r c h Gr oup
Appendix: Further slides for reference or questions
power.thayer.dartmouth.edu 26
![Page 27: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/27.jpg)
power.thayer.dartmouth.edu 27
Relaxation effect
Assumption: Energy loss per cycle doesn’t change if waveform pauses.
Loss only when dB/dt >0.
Voltage
Flux
Cumulative
Energy
LossAssumed without
physical basis
t0
(Core loss reference 7, 13 )
![Page 28: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/28.jpg)
Measurements prove assumption wrong (Core loss reference 7, 13 )
Increase in loss per cycle with increasing off-time (ferrite (below)).
Not observed in powdered iron (right).
power.thayer.dartmouth.edu 28
1 μs,
2.51 V
6.31 μs,
1 V
![Page 29: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/29.jpg)
iGSE (improved Generalized SE)
Based on , plus compatibility with Steinmetz equation for sine waves.
Result:
Formula to get ki from sinsoidal data:
Formula for PWL waveforms:
29
z
dtdBw
i BktP )(
dtdB
i BktP
)(
354.1
7061.12761.02 11
kki
![Page 30: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/30.jpg)
Rectangular conductors with 1-D fields
Dowell’s analysis is correct, but limited.
Parallel windings and layers?
Extract inductance matrix as well as resistance matrix?
M2Spice: automatic generation of a SPICE model for a 1D system of windings.
Minjie Chen (Princeton) and Dave Perreault (MIT)
Concept:
power.thayer.dartmouth.edu 30
Result:
![Page 31: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/31.jpg)
Litz wire
Basic model is the same as for round wire.
Full model now available to predict effect of construction.
Simple rules to avoid problems due to poor construction can avoid the need for the full model
power.thayer.dartmouth.edu 31
125 5x25 25x5 5x5x50
0.2
0.4
0.6
0.8
1
1.2
1.4
skin
-effe
ct re
sis
tan
ce
, m
FastLitz
New model
Maxwell 2-D
![Page 32: Prof. Charles R. Sullivan - psma.com Workshop...Dartmouth Magnetics and Power Electronics Research Group 1 Overview of Modelling Methods Prof. Charles R. Sullivan chrs@dartmouth.edu](https://reader038.fdocuments.in/reader038/viewer/2022102613/5af068a37f8b9ac57a8e8d47/html5/thumbnails/32.jpg)
1D, 2D and 3D modeling approaches
1D: can use analytical models.
For Xfrmers and good (quasi-) distributed gap Ls.
Dowell isn’t precise but we know how to do better.
2D: Fast, easy, low-cost simulations.
Naïve sections for E-cores can be misleading.
Mimic return path for to reduce error 5X.
3D: Use for verification, not design.
power.thayer.dartmouth.edu 32