EM Simulations using the PEEC Method - Case Studies in .../05 - em simulations using the... ·...
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Power ElectronicSystemsLaboratory
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EM Simulations using the PEEC Method -Case Studies in Power Electronics
Andreas Müsing
Swiss Federal Institute of Technology (ETH) ZürichPower Electronic Systems Laboratory
www.pes.ee.ethz.ch
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook
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■ Circuit simulation is daily business for PE engineer■ Increasing switching frequencies and fast transients require the
inclusion of parasitics and EM effects■ Device and system integration requires knowledge of EM behaviour■ Development of prototypes is expensive trend to virtual prototyping
The need for EM Simulators in Power Electronics
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Input filter
Heatsink
Fans
Output connectors
Control boards
2.9 kW/dm3=~
Input RMS voltage 230 VOutput power 6.8 kVARectifier switching frequency 12.5 kHzInverter switching frequency 25 kHzEfficiency 95.5 %Power density 2.9 kW/dm3
RB-IGBT Indirect Matrix Converter
Conducted Emission Noise Prediction
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RB-IGBT Indirect Matrix Converter Model
103 104 105 106 107
Frequency [Hz]
10-2
103
104
105
10-1
Impe
danc
e[Ω
]
102
102 108
Capacitance between two conductors
100
101
Measurement
Inductance of a single conductor
Model Measurement
Model
103 104 105 106 107
Frequency [Hz]
100
103
104
105
101
Impe
danc
e[Ω
]
102
102 108
Impedance across all inductors (measurement)
Impedance from one input terminal to PE (model)
Impedance from one input terminal to PE (measurement)
Impedance across all inductors (model)
cr
+−
i c
G(t)
ssv
ceu
C(u)
behavioral switch model layout parasitics
“backward” modeling from impedance measurements
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PCB Layout Parasitics Calculation
■ Java based program for the generation of PEEC models from PCB CAD data
■ PEEC solver calculates PCB track impedances, i.e. parasitic capacitances, inductances and mutual inductances
subsequent refinement of IMC circuit model
Parasitics Extraction (inductive and capacitive) using PEEC Simulation:
6 Layer IMC PCB layout
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Simulation results (CM and DM)
Conducted Emission spectrumcommon mode and differential mode
■ TD simulation of 1 mains period■ Timestep: 10 ns■ Simulation time:
approx. 4 hours on a 3 GHz PC with 1 GB of RAM
Simulation properties:■ Excellent agreement of CE level (CM and DM)
up to 5 MHz■ Deviation for f > 5 MHz probably
influenced by higher order parasitics( EMI filter couplings, heat sink, …)
Results:
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook
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PEEC-Based Numerical Optimization of Position Sensors
Context: Active Magnetic Bearing System for Mega-Speed Drives (> 500000 rpm)
576 Hz
4682 Hz
Power and control electronics of the motor
Power and control electronicsof the magnetic bearings
Challenges:• Materials → mechanical stress due to high rotational speeds• Position control and damping of rotor eigenmodes
FE simulation of rotor eigenmodes:
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Radial Position Sensors
Eddy Current Sensors:
• Radial sensors integrated into PCB• Excitation coil generates concentric
magnetic field around the rotor• Magnetic field rejected by eddy
currents within rotor material→ Field concentration between rotor
and excitation coil.
• Difference in the field strength is detectedby four sensing coils.
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Eddy Current Position Sensor Modeling
Screenshot of Sensor Model in the PEEC Design Environment
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Layout Optimization
■ Maximization of sensor output signal • Frequency dependence• Variation of winding ratios• Testing of different layouts• Influence of feed lines
■ Optimization hardly possible withoutthe help of simulation
alternative eddy current sensor layouts
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook
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Switching Transient Shaping
Boost converter• 2.5 MHz Switching Frequency• 30 kV / μs voltage slope• 2 kA / μs current slope• strong ringing during transistor
turn-on
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Switching Transient Shaping
How to damp the ringing?• RC snubber circuit?
• better: magnetically coupled damping layer inside PCB
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook
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Partial Element Calculations
Problem: calculation of partial elements (L and P) for nonorthogonal geometries
• orthogonal case: analytic formulas• general: multidimensional integration is required• high computational effort due tofull matrices
• accuracy critical TD stability
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33
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... ... ...
... ... ...
... ... ...
L L L LL
LL
L
⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎝ ⎠
$ $'
' ' '
' ( ( , , ), ( ', ', ')) ' ' ''
1( ( , , ), ( ', ', '))4 '
aaa b c a b c
r rLp a a G r a b c r a b c da db dc da db dca a
G r a b c r a b cr r
μ
π
∂ ∂=
∂ ∂
=−
∫ ∫ ∫ ∫ ∫ ∫r r
r r r r
r rr r
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Partial Element Calculations
Solution approach: analytic formulas for arbitrary alignedFilaments order reduction of integration possible
1 2 1 4
3 4 2 3
((( ) arctanh ( ) arctanh
arctanh arctanh ) cos( ),sin( )
m lLpFilFil l mR R R R
m l dR R R R
μ ν
μ ν εε
= + ⋅ + + ⋅+ +
Ω− ⋅ − ⋅ −
+ +
2 2 2 2
1 12 2 2 2
1 1
cos( ) ( )( )sin cos( ) ( ) sinarctan arctansin( ) sin( )
cos( ) sin cos( ) ( )sin arctan arctansin( ) sin( )
d l m d ldR dR
d d mdR dR
ε μ ν ε ε μ ν εε ε
ε μν ε ε μ ν εε ε
+ + + + +Ω = −
+ + ⋅ ++ −
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Partial Element Calculations
$ $' 0 0 0 0
' ' '
0 0 0 0
( , ' ', , ' ') ' ( , ') ''
( , ', , ')
aaa b c a b c
r rLp b b b b c c c c a a G r r dV dVa a
LpFilFil b b c c
μ δ ∂ ∂= − − − −
∂ ∂
=
∫ ∫ ∫ ∫ ∫ ∫r r
r r r r
0 0( ) ( ) ( )x x f x dx f xδ − =∫
' 0 0 0 0' ' '
( , ' ', , ' ') ( , ', , ') 'aaa b c a b c
Lp b b b b c c c c LpFilFil b b c c dV dVδ= − − − −∫ ∫ ∫ ∫ ∫ ∫
Mutual inductance between two filaments:
' 0 0 0 0'
( , ' ', , ' ') ( , ', , ') ' 'aab b c c
Lp b b b b c c c c LpFilFil b b c c db db dc dcδ= − − − −∫ ∫ ∫ ∫
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Partial Element Calculations
''
( , ', , ') ' 'aab b c c
Lp LpFilFil b b c c db db dc dc= ∫ ∫ ∫ ∫Full three-dimensional inductance:
Numerical integration using an adaptive Simpson-Rule
Advantages of Filament approach:
• more accuracy with less computational effort
• usable for mutual and self partial inductances
• same principle is valid for coefficients of potential calculation:
' '
1 ( ( , , ), ( ', ', ')) ' 'a b a b
P G r a b c r a b c da db da dbε
= ∫ ∫ ∫ ∫r r
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Partial Element Calculations: Benchmark
Partial element computation time:
analytic < 10 sec
Gauss-Legendre integration 6 min
filament integration 1 min
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Outlook: Where do we want to go tomorrow?
PEEC Simulation Environment
Circuit Simulator
3D FEM Thermal Solver
Macro-Modeling
PEEC simulation environments builds submodels:• EMI filter components: HF resonances, parasitic couplings ( inductive and capacitive )
• Full 3D EM design modeling environment ( PCB‘s, heat sink, busbars,discrete components, power modules, cables )
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Outline
■ Motivation: The need for EM simulators in Power Electronics
■ Application Case Studies• Conducted Emission Noise Prediction• PEEC-Based Numerical Optimization of Position Sensors• Switching Transient Current Shaping
■ Generating a Quadrilateral Mesh: “Paving”
■ Partial Element Calculations
■ Outlook