EM Simulations using the PEEC Method - Case Studies in Power Electronics

Transcription

1 EM Simulations using the PEEC Method - Case Studies in Power Electronics Andreas Müsing Swiss Federal Institute of Technology (ETH) Zürich Power Electronic Systems 1

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 2

3 The need for EM Simulators in Power Electronics 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 3

4 Conducted Emission Noise Prediction RB-IGBT Indirect Matrix Converter Input filter Control boards Output connectors Input RMS voltage 230 V Output power 6.8 kva Rectifier switching frequency 12.5 khz Inverter switching frequency 25 khz Efficiency 95.5 % Power density 2.9 kw/dm 3 Fans Heatsink = ~ 2.9 kw/dm 3 4

5 RB-IGBT Indirect Matrix Converter Model behavioral switch model layout parasitics i c u ce G(t) r c + v ss C(u) Impedance [Ω] Capacitance between two conductors Inductance of a single conductor Model Measurement Measurement Model Frequency [Hz] Impedance [Ω] Impedance from one input terminal to PE (measurement) Impedance across all inductors (measurement) Impedance from one input terminal to PE (model) Impedance across all inductors (model) Frequency [Hz] backward modeling from impedance measurements 5

6 PCB Layout Parasitics Calculation Parasitics Extraction (inductive and capacitive) using PEEC Simulation: 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 6 Layer IMC PCB layout 6

7 Simulation results (CM and DM) Conducted Emission spectrum common mode and differential mode Simulation properties: TD simulation of 1 mains period Timestep: 10 ns Simulation time: approx. 4 hours on a 3 GHz PC with 1 GB of RAM Results: 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, ) 7

8 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 8

9 PEEC-Based Numerical Optimization of Position Sensors Context: Active Magnetic Bearing System for Mega-Speed Drives (> rpm) Challenges: Materials mechanical stress due to high rotational speeds Position control and damping of rotor eigenmodes Power and control electronics of the motor Power and control electronics of the magnetic bearings FE simulation of rotor eigenmodes: 576 Hz 4682 Hz 9

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 detected by four sensing coils. 10

11 Eddy Current Position Sensor Modeling Screenshot of Sensor Model in the PEEC Design Environment 11

12 Simulation Results 12

13 Simulation Results 13

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 without the help of simulation alternative eddy current sensor layouts 14

15 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 15

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 16

17 Switching Transient Shaping How to damp the ringing? RC snubber circuit? better: magnetically coupled damping layer inside PCB 17

18 Switching Transient Shaping PEEC model 18

19 Switching Transient Shaping - Results 19

20 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 20

21 Generating a Quadrilateral Mesh: Paving 21

22 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 22

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 to full matrices accuracy critical TD stability r r r$ r$ r r r r Lpaa ' = μ a a ' G( r( a, b, c), r( a ', b ', c ')) da db dc da ' db ' dc ' a a' a b c a' b' c' r r 1 L11 L12 L13 L14 Grabc ( (,, ), ra ( ', b', c')) = r r... L π r r' L 22 = L L 44 23

24 Partial Element Calculations Solution approach: analytic formulas for arbitrary aligned Filaments order reduction of integration possible m l LpFilFil = ((( μ + l) arctanh + ( ν + m) arctanh R + R R + R m l Ωd μ arctanh ν arctanh ) cos( ε), R + R R + R sin( ε ) d cos( ε) + ( μ+ l)( ν + m)sin ε d cos( ε) + ( μ+ l) νsin ε Ω= arctan arctan dr1sin( ε) dr1sin( ε) d cos( ε) + μνsin ε d cos( ε) + μ ( ν + m)sin ε + arctan arctan dr sin( ε) dr sin( ε)

25 Partial Element Calculations δ ( x x0) f( x) dx = f( x0) Mutual inductance between two filaments: r r r$ r$ r r r r Lpaa ' = μ δ( b b0, b ' b0', c c0, c ' c0') a a ' G( r, r ') dv dv ' a a' a b c a' b' c' = LpFilFil( b, b ', c, c ') Lp = δ ( b b, b ' b ', c c, c ' c ') LpFilFil( b, b ', c, c ') dv dv ' aa ' a b c a' b' c' Lp = δ ( b b, b' b ', c c, c' c ') LpFilFil( b, b', c, c') dbdb' dcdc' aa ' b b c c' 25

26 Partial Element Calculations Full three-dimensional inductance: Lp LpFilFil( b, b ', c, c ') db db ' dc dc ' aa ' = b b c c' 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 r r P = Grabc ( (,, ), ra ( ', b', c')) dadbdadb ' ' ε a b a' b' 26

27 Partial Element Calculations Benchmark: Aircoil-Reactor 27

28 Partial Element Calculations: Benchmark Partial element computation time: analytic Gauss-Legendre integration filament integration < 10 sec 6 min 1 min 28

29 Outlook: Where do we want to go tomorrow? PEEC Simulation Environment Macro- Modeling Circuit Simulator 3D FEM Thermal Solver 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 ) 29

30 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 30

31 Thank you for your attention! 31