EM Simulations using the PEEC Method - Case Studies in .../05 - em simulations using the... · Power ElectronicSystems Laboratory 1 EM Simulations using the PEEC Method - Case Studies

Power ElectronicSystemsLaboratory

1

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


2

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


3

■ 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


4

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


5

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


6

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


7

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:


8

Outline





■ Outlook


9

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:


10

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.


11

Eddy Current Position Sensor Modeling

Screenshot of Sensor Model in the PEEC Design Environment


12

Simulation Results


13

Simulation Results


14

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


15

Outline





■ Outlook


16

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


17

Switching Transient Shaping

How to damp the ringing?• RC snubber circuit?

• better: magnetically coupled damping layer inside PCB


18

Switching Transient Shaping – PEEC model


19

Switching Transient Shaping - Results


20

Outline





■ Outlook


21

Generating a Quadrilateral Mesh: „Paving“


22

Outline





■ Outlook


23

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

11 12 13 14

22

33

44

... ... ...

... ... ...

... ... ...

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


24


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 = −

+ + ⋅ ++ −


25


$ $' 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= − − − −∫ ∫ ∫ ∫


26


''

( , ', , ') ' '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


27


Benchmark: Aircoil-Reactor


28

Partial Element Calculations: Benchmark

Partial element computation time:

analytic < 10 sec

Gauss-Legendre integration 6 min

filament integration 1 min


29

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 )


30

Outline





■ Outlook


31

Thank you for

your attention !

Documents

EM Simulations using the PEEC Method - Case Studies in .../05 - em simulations using the... · Power ElectronicSystems Laboratory 1 EM Simulations using the PEEC Method - Case Studies