Optimal Design of Inductive Components Based on Accurate Loss and Thermal Models

Transcription

1 Optimal Design of Inductive Components Based on Accurate Loss and Thermal Models Dr. Jonas Mühlethaler

2 Introduction System Layer (GeckoCIRCUITS) Component Layer (GeckoMAGNETICS) 2

3 Introduction GeckoMAGNETICS How are magnetic components modeled in GeckoMAGNETICS? (Gecko-Simulations; 3

4 Introduction System Layer Component Layer Material Layer 4

5 Introduction Application of Inductive Components (1) : Buck Converter (DC Current + HF Ripple) Schematic Current / Flux Waveform Modeling Difficulties Solutions - Non-sinusoidal current / flux waveform - Current / flux is DC biased - FFT of current waveform for the calculation of winding losses - Determine core loss energy for each segment and for each corner point in the piecewise-linear flux waveform - Loss Map enables to consider a DC bias 5

6 Introduction Application of Inductive Components (2) : Inductor of DAB Converter (Non-Sinusoidal AC Current) Schematic Current / Flux Waveform Modeling Difficulties - Non-sinusoidal current / flux waveform - Core losses occur in the interval of constant flux Solutions - FFT of current waveform for the calculation of winding losses - Improved core loss equation that considers relaxation effects 6

7 Introduction Application of Inductive Components (3) : Three-Phase PFC (Sinusoidal Current + HF Ripple) Schematic Current / Flux Waveform Modeling Difficulties Solutions - Non-sinusoidal current / flux waveform - Major loop and many (DC biased) minor loops - FFT of current waveform for the calculation of winding losses - Determine core loss energy for each segment and for each corner point in the piecewise-linear flux waveform (-> minor loop losses) - Add major loop losses 7

8 Introduction Overview of Different Flux Waveforms Sinusoidal DC Current + HF Ripple Non-Sinusoidal AC Current Minor Loop Sinusoidal Current + HF Ripple Major Loop 8

9 Introduction System Layer Component Layer Material Layer 9

10 Introduction Overview of Other Modeling Issues Heat Dissipation Core Type Flux Density Distribution Air Gap Stray Field Winding Type / Arrangement Current Distribution 10

11 Introduction Wide Range of Realization Options Inductors / Transformers Core Shapes Conductor Shapes

12 Introduction Modeling Inductive Components (1) Procedure 1) A reluctance model is introduced to describe the electric / magnetic interface, i.e. L = f(i). 2) Core losses are calculated. Reluctance Model 3) Winding losses are calculated. 4) Inductor temperature is calculated. 12

13 Introduction Modeling Inductive Components (2) The following effects are taken into consideration: Magnetic Circuit Model (e.g. for Inductance Calculation): Air gap stray field Non-linearity of core material Core Losses: DC Bias Different flux waveforms (link to circuit simulator) Wide range of flux densities and frequencies Different core shapes Winding Losses: Skin and proximity effect Stray field proximity effect Effect of core on magnetic field distribution Litz, solid, and foil conductors 13

14 Introduction System Layer Component Layer Material Layer 14

15 Introduction Motivation for an Accurate Loss Modeling : Multi-Objective Optimization (1) PFC Rectifier with Input LCL filter Filter Losses vs. Filter Volume Converter Losses vs. Converter Volume Converter = Cooling System + Switches Sometime there are parameters that bring advantages for one subsystem while deteriorating another subsystem (e.g. frequency in above example). 15

16 Introduction Motivation for an Accurate Loss Modeling : Multi-Objective Optimization (2) Losses of a Loss-Optimized Design Optimal Frequency 6 khz In order to get an optimal system design, an overall system optimization has to be performed. It is (often) not enough to optimize subsystems independent of each other. 16

17 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 17

18 Magnetic Circuit Modeling Reluctance Model Electric Network Magnetic Network Conductivity / Permeability Resistance / Reluctance Voltage / MMF Current / Flux R l / ( A) P 2 V Eds I P 1 A J da Rm l / ( A) V m P 2 H ds P 1 B d A A 18

19 Magnetic Circuit Modeling Why a Reluctance Model is Needed A reluctance model is needed in order to calculate the inductance ( L = N 2 /R tot ) calculation the saturation current calculate the air gap stray field calculate the core flux density Accurate loss modeling! 19

20 Magnetic Circuit Modeling Core Reluctance Core Reluctance Dimensions Reluctance Calculation R m li A 0 r i Mean magnetic length Mean magnetic cross-sectional area 20

21 Magnetic Circuit Modeling Air Gap Reluctance : Different Approaches (1) Assumption of Homogeneous Field Distribution R m l g A 0 g l g l g A g Air gap length Air gap cross-sectional area a Increase of the Air Gap Cross-Sectional Area e.g. [1] (for a cross section with dimension a x t): a R m l g ( a l )( t l ) 0 g g a [1] N. Mohan, T. M. Undeland, and W. P. Robbins - Power Electronics Converter, Applications, and Design, John Wiley & Sons, Inc.,

22 Magnetic Circuit Modeling Air Gap Reluctance : Different Approaches (2) Schwarz-Christoffel Transformation Transformation Equation z(t) l z( t) 2ln 1 1t ln t 2 1t (z and t are complex numbers) Transformation Equation v(t) V v( t) ln t [2] K. J. Binns, P. J. Lawrenson, and C. W. Trowbridge, «The Analytical and Numerical Solution of Electric and Magnetic Fields», John Wiley & Sons, Inc.,

23 Magnetic Circuit Modeling Air Gap Reluctance : Different Approaches (3) Solution to 2-D problems found in literature, e.g. in [3] Can t be directly applied to 3-D problems. Some 3-D solution to problem found in literature; however, they are complex [4] and/or limited to one air gape shape [5] More simple and universal model desired. [3] A. Balakrishnan, W. T. Joines, and T. G. Wilson - Air-gap reluctance and inductance calculations for magnetic circuits using a Schwarz-Christoffel transformation, IEEE Transaction on Power Electronics, vol. 12, pp , July [4] P. Wallmeier, Automatisierte Optimierung von induktiven Bauelementen für Stromrichteranwendungen, PhD Thesis, Universität Gesamthochschule Paderborn, [5] E. C. Snelling, Soft Ferrites - Properties and Applications, 2 nd edition, Butterworths,

24 Magnetic Circuit Modeling Aim of New Model Air gap reluctance calculation that - considers the three dimensionality, - is reasonable easy-to-handle, - is capable of modeling different shapes of air gaps, - while still achieving a high accuracy. Illustration of Different Air Gap Shapes: 24

25 Magnetic Circuit Modeling New Model (1) Basic Structure for the Air Gap Calculation (2-D) [3] Next Core Corner R ' basic 1 w 2 h 0 1 ln 2l 4l 25

26 Magnetic Circuit Modeling New Model (2) 2-D (1) Basic Structure for the Air Gap Calculation 26

27 Magnetic Circuit Modeling New Model (3) Basic Structure for the Air Gap Calculation 2-D (2) Air Gap Type 1 R ' basic 1 w 2 h 0 1 ln 2l 4l Air Gap Type 2 Air Gap Type 3 27

28 Magnetic Circuit Modeling New Model (4) 2D 3D : Fringing Factor (1) Illustrative Example zy-plane Air gap per unit length ' R zy y R l ' zy g a 0 zx-plane Idealized air gap (no fringing flux) ' R zx x R l ' zx g t 0 28

29 Magnetic Circuit Modeling New Model (5) 2D 3D : Fringing Factor (2) Illustrative Example 3-D Fringing Factor: R g lg at 0 x y Idealized air gap (no fringing flux) Alternative Interpretation: Increase of air gap cross sectional area 1 x A A A 1 y [6] J. Mühlethaler, J.W. Kolar, and A. Ecklebe, A Novel Approach for 3D Air Gap Reluctance Calculations, in Proc. of the ICPE - ECCE Asia, Jeju, Korea,

30 Magnetic Circuit Modeling FEM Results 3-D FEM Simulation Modeled Example Results a = 40 mm; h = 40 mm 30

31 Magnetic Circuit Modeling Experimental Results Inductance Calculation EPCOS E55/28/21, N = 80 Saturation Calculation EPCOS E55/28/21, N = 80, l g = 1 mm, B sat = 0.45 T Measurement I sat = 3.7 A 31

32 Inductance [ml] Magentic Flux Density [T] APEC 2015 Magnetic Circuit Modeling Non-Linearity of the Core Material Flux and Reluctance Calculation Inductance Calculation This equation must be solved iteratively by using a numerical solving method, e.g. the Newton s method. Reluctance Model Inductance Current [A] B-H Relation Magnetic Field [A/m] 32

33 Example Introduction Schematic Aim Design PFC rectifier system. Show trade-off between losses and volume. Illustrative example. Modeling of boost inductors (three individual inductors L 2a = L 2b = L 2c ) will be step-by-step illustrated in the course of this presentation. 33

34 Example Reluctance Model (1) Photo & Dimensions Reluctance Model Calculation of Core Reluctances R c1 (2 a) do 2a 2 8 (2 ) 0 rat a 0 rt 2 (220mm) 60mm 220mm 8 A (2 20mm) 0 20'000 20mm 28mm Vs 0 20'00028mm 2 R c2 (2 a) do 2a 2b 2 8 (2 ) 0 rat a 0 rt 2 (220mm) 60mm 220mm + 2h 8 A (2 20mm) 0 20'000 20mm 28mm Vs 0 20'00028mm 2 Material Grain-oriented steel (M165-35S) 34

35 ' zy,2 0 g g 1 2 ( ) 1 ln R a b a l l Mittwoch, 4. März Example Reluctance Model (2) Photo & Dimensions Material Grain-oriented steel (M165-35S) Calculation Air Gap Reluctances zy-plane zx-plane ' zy,1 0 g g ln R a a l l ' zy g y R l a ' zy,3 0 g g ln 2 4 R a b l l Basic Reluctance ' zx,1 0 g g ln R t a l l ' zx g x R l t g g 0 MA 1.66 Wb x y l R at Inductance 2 c1 c2 g1 g2 2.66mH N L R R R R meas mh basic 0 1 ' 2 1 ln 2 4 R w h l l ' ' zx,1 zx,2 ' zx 2 R R R Gecko-Simulations AG Jonas Mühlethaler ' zx,2 0 g g 1 2 ( ) 1 ln R t b a l l ' ' ' zy,1 zy,2 zy,3 ' zy ' ' ' zy,1 zy,2 zy,3 R R R R R R R

36 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 36

37 Core Loss Modeling Overview of Different Core Materials (1) Magnetic Materials Soft Magnetic Materials Hard Magnetic Materials Iron Based Alloys - ferromagnetics - Alloys with some amount of Si, Ni, Cr or Co. Low electric resistivity. High saturation flux density. Ferrites - ferrimagnetics - Ceramic materials, oxide mixtures of iron and Mn, Zn, Ni or Co. High electric resistivity. Small saturation flux density compared to ferromagnetics. Laminated Cores Powder Iron Cores Amorphous Alloys Nanocrystalline Materials Laminations are electrically isolated to reduce eddy currents. Consist of small iron particles, which are electrically isolated to each other. Made of alloys without crystallyine order (cf. glasses, liquids). Ultra fine grain FeSi, which are embedded in an amorphous minority phase. 37

38 Core Loss Modeling Overview of Different Core Materials (2) Selection Criteria Ferrite Powder Iron Core Saturation Flux Density Power Loss Density (Frequency Range) Price etc. Low Sat. Flux Density (0.45 T) Low Losses Low Price Many Different Shapes Very Brittle High Sat. Flux Density (1.5 T) Moderate Losses Low Price Many Different Shapes Distributed Air Gap (low rel. permeability) Laminated Steel Cores Amorphous Alloys Nanocrystalline Materials Very High Sat. Flux Density (2.2T) High Losses Low Price Many Different Shapes High Sat. Flux Density (1.5T) Low Losses High Price Limited Available Shapes High Sat. Flux Density (1.1T) Very Low Losses Very High Price Limited Available Shapes LF: B SAT = B max. HF: B max is limited by core losses. 38

39 Core Loss Modeling Overview of Different Core Materials (3) [7] [7] M. S. Rylko, K. J. Hartnett, J. G. Hayes, M.G. Egan, Magnetic Material Selection for High Power High Frequency Inductors in DC-DC Converters, in Proc. of the APEC

40 Core Loss Modeling Physical Origin of Core Losses (1) Weiss Domains / Domain Walls B-H-Loop - Spontaneous magnetization. - Material is divided to saturated domains (Weiss domains). - In case an external field is applied, the domain walls are shifted or the magnetic moments within the domains change their direction. The net magnetization becomes greater than zero. - The flux change is partly irreversible, i.e. energy is dissipated as heat. - The reason for this are the so called Barkhausen jumps, that lead to local eddy current losses. - In case the loop is traversed very slowly, these Barkhausen jumps lead to the static hysteresis losses. 40

41 Core Loss Modeling Physical Origin of Core Losses (2) B-H-Loop - If the process would be fully reversible, going from B 1 to B 2 would store potential energy in the magnetic material that is later released (i.e. the area of the closed loop would be zero). - Since the process is partly irreversible, the area of the closed loop represents the energy loss per cycle 41

42 Core Loss Modeling Classification of Losses (1) (Static) hysteresis loss Rate-independent BH Loop. Loss energy per cycle is constant. Irreversible changes each within a small region of the lattice (Barkhausen jumps). These rapid, irreversible changes are produced by relatively strong local fields within the material. Eddy current losses Residual Losses Relaxation losses 42

43 Core Loss Modeling Classification of Losses (2) (Static) hysteresis loss Eddy current losses Depend on material conductivity and core shape. Affect BH loop. Residual Losses Relaxation losses Measurements VITROPERM 500F i [A] t [s] 43

44 Core Loss Modeling Classification of Losses (3) (Static) hysteresis loss Eddy current losses Residual losses Relaxation losses Rate-dependent BH Loop. Reestablishment of a thermal equilibrium is governed by relaxation processes. Restricted domain wall motion. 44

45 Core Loss Modeling Typical Flux Waveforms Sinusoidal e.g. 50/60 Hz isolation transformer Triangular e.g. Buck / Boost converter Trapezoidal e.g. boost inductor of Dual Active Bridge Combination e.g. Boost inductor in PFC 45

46 wwww.epcos.com APEC 2015 Core Loss Modeling Outline of Different Modeling Approaches Steinmetz Approach Loss Map Approach P α β k f B (Loss Database) - Simple - Steinmetz parameter are valid only in a limited flux density and frequency range - DC Bias not considered - (Only for sinusoidal flux waveforms) - Measuring core losses is indispensable to overcome limits of Steinmetz approach Loss Separation P Physt Peddy Presidual - Needed parameters often unknown - Model is widely applicable - Increases physical understanding of loss mechanisms Hysteresis Model (e.g. Preisach Model, Jiles-Atherton Model) - Difficult to parameterize - Increases physical understanding of loss mechanisms 46

47 Core Loss Modeling Overview of Hybrid Modeling Approach The best of both worlds (Steinmetz & Loss Map approach) Loss Map (Loss Material Database) (2)/(3) Outline of Discussion - Derivation of the i 2 GSE. (1) - How to measure core losses in order to build loss map. (2) - Use of loss map. (3) - How to calculate core losses for cores of different shapes? (4) k, k,,,,, q, i r r r P v T T 1 db ki dt 0 B dt n l1 Q rl P rl (1) P V (4) 47

48 Core Loss Modeling Derivation of the i 2 GSE Motivation (1) Steinmetz Equation SE P v α β k f B - Only sinusoidal waveforms ( igse). ˆ P v : time-average power loss per unit volume igse T 1 db Pv ki B dt T dt 0 ki 2 1 (2 ) cos 2 d 0 k - DC bias not considered - Relaxation effect not considered ( i 2 GSE) - Steinmetz parameter are valid only for a limited flux density and frequency range 48

49 Core Loss Modeling Derivation of the i 2 GSE Motivation (2) igse [8] T 1 db Pv ki B dt T dt 0 ki 2 1 (2 ) cos 2 d 0 k Idea - Generalized formula that is applicable for different flux waveforms - Losses depend on db/dt For Sinusoidal Waveforms 1 db B Pv ki B dt kf T dt 2 How to apply the formula? T 0 k i B B Pv DT B (1 D) T B... T DT (1 D) T [8] K. Venkatachalam, C. R. Sullivan, T. Abdallah, and H. Tacca, Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters, in Proc. of IEEE Workshop on Computers in Power Electronics, pp ,

50 Core Loss Modeling Derivation of the i 2 GSE Motivation (3) Waveform Results igse T 1 db Pv ki B dt T dt 0 Conclusion Losses in the phase of constant flux! 50

51 Core Loss Modeling Derivation of the i 2 GSE B-H-Loop Relaxation Losses Rate-dependent BH Loop. Reestablishment of a thermal equilibrium is governed by relaxation processes. Restricted domain wall motion. Current Waveform 51

52 Core Loss Modeling Derivation of the i 2 GSE Model Derivation 1 (1) Waveform Derivation (1) Relaxation loss energy can be described with Loss Energy per Cycle E E 1 e t1 is independent of operating point. How to determine E? 52

53 Core Loss Modeling Derivation of the i 2 GSE Model Derivation 1 (2) E Measurements Waveform Conclusion E follows a power function! E k r d dt B( t) r B r 53

54 Mittwoch, 4. März Model Part 1 n l l T i P t B t B k T P 1 r 0 v d d d 1 1 r r e 1 ) ( d d 1 r r t l B t B t k T P Core Loss Modeling Derivation of the i 2 GSE Model Derivation 1 (3) Gecko-Simulations AG Jonas Mühlethaler

55 Core Loss Modeling Derivation of the i 2 GSE Model Derivation 2 (1) Waveform Power Loss Explanation 1) For values of D close to 0 or close to 1 a loss underestimation is expected when calculating losses with igse (no relaxation losses included). 2) For values of D close to 0.5 the igse is expected to be accurate. 3) Adding the relaxation term leads to the upper loss limit, while the igse represents the lower loss limit. 4) Losses are expected to be in between the two limits, as has been confirmed with measurements. 55

56 Core Loss Modeling Derivation of the i 2 GSE Model Derivation 2 (2) Waveform Model Adaption P v T T 1 db ki dt 0 B dt n l1 Q rl P rl Q rl should be 1 for D = 0 Power Loss Q rl should be 0 for D = 0.5 Q rl should be such that calculation fits a triangular waveform measurement. db( t )/dt qr db( t )/dt qr Q l 1 r e e D D 56

57 Core Loss Modeling Derivation of the i 2 GSE Model Derivation 2 (3) Waveform Power Loss 57

58 Core Loss Modeling Derivation of the i 2 GSE Summary The improved-improved Generalized Steinmetz Equation (i 2 GSE) [9] P v T 1 db ki dt 0 T B dt n l1 Q rl P rl with P rl 1 T k r d dt B( t) r t1 r B 1 e and Qr l e q r db( t )/dt db( t )/ dt [9] J. Mühlethaler, J. Biela, J.W. Kolar, and A. Ecklebe, Improved Core Loss Calculation for Magnetic Components Employed in Power Electronic Systems, in Proc. of the APEC, Ft. Worth, TX, USA,

59 Core Loss Modeling Derivation of the i 2 GSE Example i 2 GSE Evaluated for each piecewise-linear flux segment Evaluated for each voltage step, i.e. for each corner point in a piecewise-linear flux waveform. Example P v T T 1 db ki dt 0 B dt n l1 db dt Q rl P rl B for t 0 and t T 2 t T 2 t 0 for t T 2 t and t T 2 B for t T 2 and t T t T 2 t 0 for t T t and t T T 2t 2 B v i rl rl T T 2 t l1 P k B Q P with Q r1 = Q r2 = 0 r t 1 B r Pr1 Pr2 kr B 1 e T T 2 t 59

60 Core Loss Modeling Derivation of the i 2 GSE Conclusion i 2 GSE Evaluated for each piecewise-linear flux segment P v T T 1 db ki dt 0 B dt n l1 Q rl P rl Remaining Problems Evaluated for each voltage step, i.e. for each corner point in a piecewise-linear flux waveform. Steinmetz parameter are valid only in a limited flux density and frequency range. Core Losses vary under DC bias condition. Modeling relaxation and DC bias effects need parameters that are not given by core material manufacturers. Measuring core losses is indispensable! 60

61 Core Loss Modeling Overview of Hybrid Modeling Approach The best of both worlds (Steinmetz & Loss Map approach) Loss Map (Loss Material Database) (2)/(3) Outline of Discussion - Derivation of the i 2 GSE. (1) - How to measure core losses in order to build loss map. (2) - Use of loss map. (3) - How to calculate core losses for cores of different shapes? (4) k, k,,,,, q, i r r r P v T T 1 db ki dt 0 B dt n l1 Q rl P rl (1) P V (4) 61

62 Core Loss Modeling Core Loss Measurement Measurement Principle Waveforms Excitation System Schematic Sinusoidal Triangular Trapezoidal Voltage V Current 0 25 A Frequency khz Loss Extraction 1 B( t) u( ) d N A Ht () N t 2 e 0 i() t l 1 3 e PW [ ] Vm [ ] 62

63 Core Loss Modeling Core Loss Measurement - Overview System Overview P/V T T 1 H t le e N () N d Bt ( ) f i ( t) v ( t) dt f N A dt P N N N dt V A l A l e e e e BT ( ) f H ( B)dB B(0) 63

64 Core Loss Modeling Overview of Hybrid Modeling Approach The best of both worlds (Steinmetz & Loss Map approach) Loss Map (Loss Material Database) (2)/(3) Outline of Discussion - Derivation of the i 2 GSE. (1) - How to measure core losses in order to build loss map. (2) - Use of loss map. (3) - How to calculate core losses for cores of different shapes? (4) k, k,,,,, q, i r r r P v T T 1 db ki dt 0 B dt n l1 Q rl P rl (1) P V (4) 64

65 Core Loss Modeling Needed Loss Map Structure Typical flux waveform Content of Loss Map 65

66 Core Loss Modeling Minor and Major Loops Idea Minor Loop Major Loop Losses due to Minor and Major Loops are calculated independent of each other and summed up. Implementation P V P V Major Piecewise Linear Segment (+ Turning Point) Actually, it is not considered how the minor loop closes: each piecewise linear segment is modeled as having half the losses of its corresponding closed loop (cf. next slides). P P P V V V Major Piecewise Linear Segment (+ Turning Point) 66

67 Core Loss Modeling Hybrid Loss Modeling Approach (1) H DC / B DC (I) (II) 67

68 Core Loss Modeling Hybrid Loss Modeling Approach (2) Loss Map Evaluated for the according corner point in a piecewise-linear flux waveform. Evaluated for the according piecewiselinear flux segment P v T T 1 db ki dt 0 B dt n l1 Q rl P rl (I) (II) Three loss map operating points are required in order to extract the parameters,, and k (or k i ). 2 P k f B v1 i P k f B v2 i P k f B v3 i 3 3 P V These equations arise when one evaluates the i 2 GSE for symmetric triangular waveforms. 68

69 Core Loss Modeling Hybrid Loss Modeling Approach (3) Interpolation and Extrapolation (H DC *, T*, B*, f*) H DC and T B and f 69

70 Core Loss Modeling Hybrid Loss Modeling Approach (4) Advantages of Hybrid Approach (Loss Map and i 2 GSE): Relaxation effects are considered (i 2 GSE). A good interpolation and extrapolation between premeasured operating points is achieved. Loss map provides accurate i 2 GSE parameters for a wide frequency and flux density range. A DC bias is considered as the loss map stores premeasured operating points at different DC bias levels. 70

71 Mittwoch, 4. März Core Losses Summary of Loss Density Calculation Sinusoidal Triangular Trapezoidal α β P k f B n l l l T i P Q t B t B k T P 1 r r 0 v d d d 1 with Q 0, n = 1 n l l l T i P Q t B t B k T P 1 r r 0 v d d d 1 with Q = 1, n = 2 n l l l T i P Q t B t B k T P 1 r r 0 v d d d 1 with different Q s and n >> 0. Combination Gecko-Simulations AG Jonas Mühlethaler

72 Core Loss Modeling Overview of Hybrid Modeling Approach The best of both worlds (Steinmetz & Loss Map approach) Loss Map (Loss Material Database) (2)/(3) Outline of Discussion - Derivation of the i 2 GSE. (1) - How to measure core losses in order to build loss map. (2) - Use of loss map. (3) - How to calculate core losses for cores of different shapes? (4) k, k,,,,, q, i r r r P v T T 1 db ki dt 0 B dt n l1 Q rl P rl (1) P V (4) 72

73 Core Loss Modeling Effect of Core Shape Procedure Reluctance Model 1) The flux density in every core section of (approximately) homogenous flux density is calculated. 2) The losses of each section are calculated. 3) The core losses of each section are then summed-up to obtain the total core losses. 73

74 Core Loss Modeling Effective Core Dimensions of Toroid Motivation for Effective Core Dimensions Core loss densities are needed to model core losses. It is difficult to determine these loss densities from a toroid, since the flux density is not distributed homogeneously in a toroid. Illustration Definition: Ideal Toroid A toroid is ideal when he has a homogenous flux density distribution over the radius (r 1 r 2 ). Idea for Real Toroid Find effective core magnetic length and cross section, so one can calculate as if it were an ideal toroid, i.e. as if the flux density distribution were homogenous. Effective magnetic length Effective magnetic cross-section l A e e 2 ln r / r 1/ r 1/ r h r r 1/ r 1/ r 2 ln 2 /

75 Core Loss Modeling Impact of Core Shape on Eddy Current Losses Eddy current loss density can be determined as [5] P eddy ( Bfd ˆ ) k ec 2 For a laminated core it is P eddy ( Bfd ˆ ) 6 2 The eddy current losses per unit volume depend not on the shape of the bulk material, but on the size and geometry of the insulated regions. In case of laminated iron cores, it is still appropriate to calculate with core loss densities that have been measured on a sample core with a geometrically different bulk material, but with the same lamination or tape thickness. [5] E. C. Snelling, Soft Ferrites - Properties and Applications, 2 nd edition, Butterworths,

76 Core Loss Modeling Effect in Tape Wound Cores Thin ribbons (approx. 20m) Wound as toroid or as double C core. Amorphous or nanocrystalline materials. Losses in gapped tape wound cores higher than expected! 76

77 Core Loss Modeling Effect in Tape Wound Cores - Cause 1 : Interlamination Short Circuits Machining process Surface short circuits introduced by machining (particular a problem in in-house production). After treatment may reduce this effect. At ETH, a core was put in an 40% ferric chloride FeCl 3 solution after cutting, which substantially (more than 50%) decreased the core losses. 77

78 Core Loss Modeling Effect in Tape Wound Cores - Cause 2 : Orthogonal Flux Lines (1) Fringing flux Eddy current Main flux Eddy current A flux orthogonal to the ribbons leads to very high eddy current losses! 78

79 Core Loss Modeling Effect in Tape Wound Cores - Cause 2 : Orthogonal Flux Lines (2) An experiment that illustrates well the loss increase due to an orthogonal flux is given here. Displacements Horizontal Displacement Vertical Displacement Core Loss Results 79

80 Core Losses (W) APEC 2015 Core Loss Modeling Effect in Tape Wound Cores - Cause 2 : Orthogonal Flux Lines (3) Core loss increase due to leakage flux in transformers. Measurement Set Up Results Secondary Winding Primary Winding Secondary Current (A) A higher load current leads to higher orthogonal flux! FEM 80

81 Core Loss Modeling Effect in Tape Wound Cores - Cause 2 : Orthogonal Flux Lines (4) In [10] a core loss increase with increasing air gap length has been observed. Figures from [10] [10] H. Fukunaga, T. Eguchi, K. Koga, Y. Ohta, and H. Kakehashi, High Performance Cut Cores Prepared From Crystallized Fe-Based Amorphous Ribbon, in IEEE Transactions on Magnetics, vol. 26, no. 5,

82 Example Core Loss Modeling (1) Photo & Dimensions Flux Density Distribution Reluctance Model An approximately homogeneous flux density distribution inside the core. Flux Density Waveform GeckoMAGNETICS Presentation Material Grain-oriented steel (M165-35S) 82

83 Example Core Loss Modeling (2) SiFe vs. Ferrite 2 khz vs. 20 khz Modeling with GeckoMAGNETICS

84 Example Core Loss Modeling (3) 2 khz / Tmax = 65 C / L = 2.5 mh / Solid Round Wires SiFe (M165-35S) Ferrite (N87) Sat. Limit

85 Example Core Loss Modeling (4) 20 khz / Tmax = 65 C / L = 1 mh / Litz Wires SiFe (M165-35S) Ferrite (N87) Therm. Limit

86 Example Core Loss Modeling (5) Gecko-Simulations AG Jonas Mühlethaler 86

87 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 87

88 Winding Loss Modeling Skin Effect (1) H-field in conductor Ampere s Law Induced Eddy Currents Faraday s Law 88

89 Winding Loss Modeling Skin Effect (2) FEM Simulation 50 Hz 5 khz 20 khz 100 khz Current Distribution Outer radius of conductor 89

90 Winding Loss Modeling Skin Effect (3) Skin Depth (, where the current density has 1/e of surface value) 1 f 0 [19] Power Loss Increase with Frequency P F ( f ) R I F ( f) R S R DC ˆ2 d 2 90

91 Winding Loss Modeling Skin Effect (4) Current Distributions Parallel-connected (not twisted) conductors! Figure from [19] 91

92 Winding Loss Modeling Proximity Effect (1) H-field of neighboring conductor induces eddy currents Ampere s Law Faraday s Law 92

93 Winding Loss Modeling Proximity Effect (2) Eddy Currents in Conductor 50 Hz 5 khz 15 khz 100 khz Induced Eddy Currents (H e,rms = 35 A/m parallel to conductor) Current Concentration I I I I Figures from [19] 93

94 Winding Loss Modeling Skin vs. Proximity Effect Situation Results (f = 100 khz, I peak = 1 A, H e,peak = 1000 A/m) Conductor length l = 1 m P Total P Prox P Skin Definition Skin Effect Losses P Skin Losses due to current I, including loss increase due to self-induced eddy currents. Proximity Effect Losses P Prox Losses due to eddy currents induced by external magnetic field H e. 94

95 APEC 2015 Winding Loss Modeling Litz Wire (1) - What are Litz wires? Idea Advantages of Litz wires HF losses can be reduced substantially Disadvantages of Litz wires High price Heat dissipation difficult Higher R DC Implementation 95

96 Winding Loss Modeling Litz Wire (2) - Why Litz Wires Have to be Twisted? (1) Bundle-Level Skin Effect Current Distributions (Ampere s Law) Internal Proximity Effect (will be explained later) (Faraday s Law) 96

97 Winding Loss Modeling Litz Wire (3) - Why Litz Wires Have to be Twisted? (2) Bundle-Level Proximity Effect (Ampere s Law) (Faraday s Law) Figures from [19] 97

98 Winding Loss Modeling Litz Wire (4) Strand-Level Effects Internal and External Fields lead to Internal and External Proximity Effects Losses in Litz Wires Losses in Solid Wires Internal prox. effect Skin effect l = 1 m Ext. prox. effect l = 1 m Skin effect Prox. effect (25 x d i = 0.5 mm, I peak = 5 A, H e,peak = 300 A/m) (d = 2.5 mm, I peak = 5 A, H e,peak = 300 A/m) 98

99 Winding Loss Modeling Litz Wire (5) Types of Eddy-Current Effects in Litz Wire Figure from [11] Ch. R. Sullivan, Optimal Choice for Number of Strands in a Litz-Wire Transformer Winding, in IEEE Transactions on Power Electronics, vol. 14, no. 2,

100 Winding Loss Modeling Litz Wire (6) Real Litz Wire Ideal Litz Wire (ideally twisted strands) Worst Case Litz Wire (parallel connected strands, no twisting) Operating Point f = 20 khz / n = 130 / d i = 0.4 mm How do real Litz wires behave? [12] Skin Effect / Internal Proximity Effect R R (1 ) R skin,λ skin skin,ideal skin skin,parallel R R (1 ) R External Proximity Effect prox,λ prox prox,ideal prox prox,parallel Litz Wire Type 1: 7 bundles with 35 strands each: skin 0.5 / prox 0.99 Litz Wire Type 2: 4 bundles with 61/62 strands each: skin 0.9 / prox 0.99 [12] H. Rossmanith, M. Doebroenti, M. Albach, and D. Exner, Measurement and Characterization of High Frequency Losses in Nonideal Litz Wires, IEEE Transactions on Power Electronics, vol. 26, no. 11, November

101 Winding Loss Modeling Litz Wire (7) - Are Litz Wires Better than Solid Conductors? Skin and Internal Proximity Effect Solid Wire (d = 2.5 mm, I peak = 5 A) l = 1 m Litz Wire (25 x d i = 0.5 mm, I peak = 5 A) Litz Wire (50 x d i = 0.35 mm, I peak = 5 A) Litz Wire (100 x d i = 0.25 mm, I peak = 5 A) External Proximity Effect l = 1 m Litz Wire of 25 strands with d = 0.5mm Solid Wire with d = 2.5 mm 101

102 Winding Loss Modeling Foil Windings Enclosed by Magnetic Material Conductor length l = 1 m d = 1.95 mm I peak = 1 A Same cross section! Advantages of foil windings HF losses can be reduced Lower price compared to Litz wire High filling factor Disadvantages of foil windings Increased winding capacitance Risk of orthogonal flux Skin of foil conductor larger than of round conductor with same cross section; hence, skin effect losses lower in foil conductor. 10 mm x 0.3 mm I peak = 1 A 102

103 Winding Loss Modeling Foil Windings Not Enclosed by Magnetic Material (1) Single Conductor Three Conductors 10 mm x 0.3 mm I peak = 1 A d = 1.95 mm I peak = 1 A l = 1 m 10 mm x 0.3 mm I peak = 1 A l = 1 m d = 1.95 mm I peak = 1 A 8 khz Orthogonal flux leads to increased skin and proximity effect. Orthogonal Flux! 103

104 Winding Loss Modeling Foil Windings Not Enclosed by Magnetic Material (2) (Foil) Windings with Return Conductors l = 1 m d = 1.95 mm I peak = 1 A 10 mm x 0.3 mm I peak = 1 A 8 khz 104

105 Winding Loss Modeling Overview About Different Winding Types Type Price Skin & Proximity Filling Factor Heat Dissipation Round Solid Wire Litz Wire Foil Winding Rectangular Wire Rectangular Wire Foil windings are better only in this region! Round conductor P 0 round conductor Table and Figure from [13] M. Albach, Induktive Komponenten in der Leistungselektronik, VDE Fachtagung - ETG Fachbereich Q1 "Leistungselektronik und Systemintegration", Bad Nauheim,

106 Winding Loss Modeling Skin Effect of Foil Conductor Geometry Considered Current Distribution P F ( f ) R I S F DC ˆ2 (Loss per unit length) with F F evaluated v sinh v sin v FF 4 cosh v cos v 1 RDC bh h v 1 f 0 [19] 106

107 Winding Loss Modeling Proximity Effect of Foil Conductor Geometry Considered with P G ( f ) R Hˆ 2 P F DC S (Loss per unit length) 2 sinh v sin v GF b v cosh v cos v 1 RDC bh h v 1 f 0 Current Distribution G F evaluated [19] (b = 1 m) 107

108 Winding Loss Modeling Skin Effect of Solid Round Conductor Geometry Considered P F ( f ) R I S R DC ˆ2 (Loss per unit length) with F R evaluated R F 4 d d DC f 0 ber ( )bei ( ) ber ( )ber ( ) bei ( )ber ( ) bei ( )bei ( ) R ber 1( ) bei 1( ) ber 1( ) bei 1( ) 108

109 Winding Loss Modeling Proximity Effect of Solid Round Conductor Geometry Considered P G ( f ) R Hˆ 2 P R DC S (Loss per unit length) with G R evaluated R G 4 d d DC f 0 d ber ( )ber ( ) ber ( )bei ( ) bei ( )bei ( ) bei ( )ber ( ) R ber 0( ) bei 0( ) ber 0( ) bei 0( ) (d = 1 m) 109

110 Winding Loss Modeling Skin and Proximity Effect of Litz Wire Skin Effect Iˆ PS n RDC FR ( f ) n (Loss per unit length) 2 Proximity Effect P P P P P,e P,i 2 2 Iˆ n RDC GR ( f ) He da (Loss per unit length) Losses in Litz Wires l = 1 m Internal prox. effect Skin effect Ext. prox. effect Average internal field H i under the assumption of a homogeneous current distribution inside the Litz wire. (25 x d i = 0.5 mm, I peak = 5 A, H e,peak = 300 A/m) 110

111 Winding Loss Modeling Orthogonality of Winding Losses P ( P P ) i0 It is valid to calculate the losses for each frequency component independently and total them up. S,i P,i It is valid to calculate the skin and proximity losses independently and total them up. [14] J. A. Ferreira, Improved analytical modeling of conductive losses in magnetic components, in IEEE Transactions on Power Electronics, vol. 9, no. 1,

112 Winding Loss Modeling Calculation of External Field H e (1D - Approach) Un-Gapped Transformer Cores P R F I NM NG H l M ˆ2 ˆ 2 DC R/F R/F avg,m m m1 with 1 H H H 2 avg left right it is P R Iˆ F NM N MG 2 3 DC R/F R/ F 2 4M 1 l 2 12bF m where Hleft Havg Hright N the number of conductors per layer (i.e. N = 1 for foil windings) (Ampere s Law) M the number of layers. Figure from [19] 112

113 Winding Loss Modeling Short Foil Conductors Porosity Factor Nb b F L Redefinition of Parameters ' ' 1 f ' 0 ' h ' 113

114 Winding Loss Modeling FEM Simulations : Foil Windings N = 2 x 10 h = 0.3 mm b L = 33 mm b F = 37 mm I peak = 1 A Error < 6.5% N = 2 x 7 h = 0.4 mm b L = 37 mm b F = 37 mm I peak = 1 A 114

115 Winding Loss Modeling Calculation of External Field H e (2D - Approach) Gapped cores: 2D approach is necessary! 115

116 Winding Loss Modeling Effect of the Air Gap Fringing Field The air gap is replaced by a fictitious current, which has the value equal to the magneto-motive force (mmf) across the air gap. P 2 P 2 I P 1 P 1 V m,air P 2 Hl d R P 1 air V m,air P 2 Hl d P 1 I An accurate air gap reluctance model is needed! 116

117 Winding Loss Modeling Effect of the Core Material The method of images (mirroring) Pushing the walls away 117

118 Winding Loss Modeling Calculation of External Field H e (2D - Approach) Gapped cores: 2D approach Winding Arrangement External field vector across conductor q xi;yk 118

119 Winding Loss Modeling Different Winding Sections Section 1 Many mirroring steps necessary in order to push the walls away. Section 2 Only one mirroring step necessary (only one wall). Normally, higher proximity losses in Section

120 Winding Loss Modeling FEM Simulations : Round Windings (Including Litz Wire Windings) (1) Major Simplification - magnetic field of the induced eddy currents neglected. - This can be problematic at frequencies above (rule-of-thumb) [15] f 2.56 max 2 0 d Results of considered winding arrangements f-range f < f max f > f max Error < 5% > 5% (always < 25%) [15] A. Van den Bossche, V. C. Valchev, Inductors and Transformers for Power Electronics, CRC Press. Taylor & Francis Group,

121 Winding Loss Modeling FEM Simulations : Round Windings (Including Litz Wire Windings) (2) FEM Simulation Results f max f max f max 121

122 Winding Loss Modeling Methods to Decrease Winding Losses (1) Interleaving Optimal Solid Wire Thickness l = 1 m P Total Optimal Foil Thickness [19] l = 1 m P Prox P Skin (f = 100 khz, I peak = 1 A, H e,peak = 1000 A/m) PTotal P Prox Litz Wire P Skin (f = 20 khz, I peak = 1 A, b = 20 cm, H e,peak = 1000 A/m) Avoid Orthogonal Flux in Foil Windings l = 1 m Push this point to higher frequencies! Increase number of strands. (resp.: find optimal number of strands) 122

123 Winding Loss Modeling Methods to Decrease Winding Losses (2) Arrangement of Windings Proximity losses increase in more compact winding arrangements. 123

124 Winding Loss Modeling Methods to Decrease Winding Losses (3) Aluminum vs. Copper [13] Proximity losses are lower in aluminum conductors over a wide frequency range. Figure shows a comparison of single round solid conductors in external field. d = 0.25 mm d = 0.50 mm d = 0.75 mm d = 1.00 mm [13] M. Albach, Induktive Komponenten in der Leistungselektronik, VDE Fachtagung - ETG Fachbereich Q1 "Leistungselektronik und Systemintegration", Bad Nauheim,

125 Example Winding Loss Modeling Photo & Dimensions Current Waveform Demonstration in GeckoMAGNETICS Material Grain-oriented steel (M165-35S) 125

126 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 126

127 Thermal Modeling Motivation & Model (1) Ambient Temperature Motivation Thermal modeling is important to avoid overheating. improve loss calculation (since the losses depend on temperature). 127

128 Thermal Modeling Motivation & Model (2) Model Inductor Transformer Determination of thermal resistors is challenging! 128

129 Thermal Modeling Heat Transfer Mechanisms R th T P f (T) Conduction Independent of temperature T for most materials Difficult to determine interfaces between materials R th T P l A Convection Combined effect of conduction and fluid flow Changes with changing absolute temperature (nonlinear) Good empirical calculation approach available R th T P 1 A Radiation Small compared to other mechanisms Modeling the system is demanding (nonlinear eq. / to describe which components sees the other component). P eff A 1 (T b 4 T a 4 ) 129

130 Thermal Modeling Thermal Resistance Calculation : (Natural) Convection (1) R th T P 1 A is a coefficient that is influenced by the absolute temperature, the fluid property, the flow rate of the fluid, the dimensions of the considered surface, orientation of the considered surface, and the surface texture. 130

131 Thermal Modeling Thermal Resistance Calculation : (Natural) Convection (2) Empirical solutions known for vertical plane horizontal plane -top: gap - horizontal: - bottom : - vertical: and more 131

132 Thermal Modeling Thermal Resistance Calculation : (Natural) Convection (3) Structure of Empirical Solutions - Theory g gravity of earth: 9.81 m/s 2 l characteristic length volumetric thermal expansion coefficient : 1/T (air) v kinematic viscosity: m 2 /s (air) Name Measure of Nusselt number Nu Grashof number Gr improvement of heat transfer compared to the case with hypothetical static fluid. ration between buoyancy and frictional force of fluid. l 1 l Nu A A 3 gl Gr T 3 v f ( Gr, Pr) Prandtl number Pr ratio between viscosity and heat conductivity of fluid. Pr 0.7 (for air) Rayleigh number Ra flow condition (laminar or turbulent) of fluid. Ra Pr Gr Procedure Nu( Gr, Pr) Nu( Gr, Pr) l is the heat conductivity of the fluid air = mw/(m 20 C [16] R th 1 A [16] VDI Heat Atlas, Springer-Verlag, Berlin,

133 Thermal Modeling Thermal Resistance Calculation : (Natural) Convection (4) Structure of Empirical Solutions - Example Vertical Plane Nu Ra f Pr 1/6 2 f Pr 9/ /9 Reference: [16] VDI Heat Atlas, Springer-Verlag, Berlin, 2010 R th Nu( Gr, Pr) l T P 1 A (l = h) T p T a Example (h = 10 cm, T p = 60 C, T a = 20 C, A = h h) R th = 16.6 K/W Increase of Winding Surface 133

134 Thermal Modeling Thermal Resistance Calculation : Conduction Overview Normally, with natural convection it is R th,w << R th,wa Round Conductor Foil Conductor R th,w is difficult to determine. One difficulty is, e.g., to model the influence of pressure on the thermal resistance. Litz wire shows low thermal conductivity. 134

135 Example Thermal Modeling (1) (1) Horizontal Plane - Top g gravity of earth: 9.81 m/s 2 l characteristic length : l = a*b / ( 2 ( a+b ) ) volumetric thermal expansion coefficient : 1/T (air) v kinematic viscosity: m 2 /s (air) 3 gl Gr T 3 v Pr 0.7 (for air) Ra Pr Gr Nu( Gr, Pr) l with ( Ra f ( Pr)) for Ra f ( Pr) 710 Nu 0.15 ( Ra f ( Pr)) for Ra f ( Pr) 710 f Pr 1/ / /20 20/11 (laminar) (turbulent) R th T P 1 A Resistor R th is now calculated for one operating point! ( more iterations are necessary!) 135

136 Example Thermal Modeling (2) (2) Core to Winding R CF l K 1.05 A W R W R WA Heat flow via mechanical attachment has not been considered. Drawing represents the cross-section of one coil former side (there are total 2 x 4 coil former sides). Quantity Values R th,ca 17.4 K/W R th,wa 5.8 K/W 136

137 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 137

138 Multi-Objective Optimization Volume vs. Losses Introduction to the PFC Rectifier Simplified Schematic Converter Specifications Photo of Converter Goal: Design boost inductor such that the max. current ripple is 4A. 138

139 Multi-Objective Optimization Volume vs. Losses Boost Inductor Selected Inductor Shape Photo of Inductor Material Grain-oriented steel (M165-35S, lam. thickness 0.35 mm) 139

140 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor Simplified Schematic Boost Inductance Constraints concerning boost inductors max. current ripple I HF,pp,max = 4 A max. temperature T max = 120 ºC L 2,min can be calculated based on the constraint I HF,pp,max.. The maximum current ripple I HF,pp,max occurs when the fundamental current peaks. 140

141 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor - Simplifications Simplified current / voltage waveforms for optimization procedure Expectations Loss overestimation in L 2 expected. 141

142 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor - Design Space in GeckoMAGNETICS Start L Boost = 2.53 mh T max = 120 ºC Core UI 39 UI 90 cores of DIN41302 Material M165-35S gap mm (by 0.25 mm) stacked sheets (by 10) Winding Solid round wire with fill factor 0.3 Split windings 142

143 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor - Waveform/Cooling in GeckoMAGNETICS Waveform Cooling Forced convection (-> 3 m/s) I LF,peak = 21.8 A 143

144 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor - Performing Calculation Procedure 1) A reluctance model is introduced to describe the electric / magnetic interface, i.e. L = f(i). 2) Core losses are calculated. 3) Winding losses are calculated. 4) Inductor temperature is calculated. Considered effects Air gap stray field Non-linearity of core material DC Bias Different flux waveforms Wide range of flux densities and frequencies Skin and proximity effect Stray field proximity effect Effect of core to magnetic field distribution 144

145 Multi-Objective Optimization Volume vs. Losses Pareto-Optimized Design of Boost Inductor - Results Filter Losses vs. Filter Volume Pareto Front Prototype built Pareto-front 145

146 Multi-Objective Optimization Volume vs. Losses Detailed Modeling in GeckoMAGNETICS GeckoCIRCUITS GeckoMAGNETICS 146

147 Multi-Objective Optimization Volume vs. Losses Results Photo Conclusion Loss modeling very accurate. 147

148 Outline Magnetic Circuit Modeling Core Loss Modeling Winding Loss Modeling Thermal Modeling Multi-Objective Optimization Summary & Conclusion 148

149 Summary & Conclusion Magnetic Circuit Modeling Air Gap Reluctance Calculation zy-plane Air gap per unit length ' R zy y R l ' zy g a 0 zx-plane Results ' R zx x R l ' zx g t 0 R g l g x y 0 at 149

150 Summary & Conclusion Core Loss Modeling The best of both worlds (Steinmetz & Loss Map approach) Loss Map (Loss Material Database) k, k,,,,, q, i r r r P v T T 1 db ki dt 0 B dt n l1 Q rl P rl P V 150

151 Summary & Conclusion Winding Loss Modeling Optimal Solid Wire Thickness Foil vs. Round Conductors P Total l = 1 m 10 mm x 0.3 mm I peak = 1 A l = 1 m d = 1.95 mm I peak = 1 A P Prox P Skin (f = 100 khz, I peak = 1 A, H e,peak = 1000 A/m) Losses in Litz Wires Gapped cores: 2D approach l = 1 m Internal prox. effect Skin effect Ext. prox. effect 151

152 Summary & Conclusion Magnetic Design Environment Core Material Database GeckoDB Magnetics Design Software GeckoMAGNETICS Circuit Simulator GeckoCIRCUITS Automated Measurement System Prototype Verification (e.g. with Calorimeter) 152

153 Summary & Conclusion Multi-Objective Optimization PFC Rectifier Inductor Pareto Front 153

154 GeckoMAGNETICS Save Time Fast and accurate design of magnetic components Easy-to-use for non-expert Increase Flexibility Tool shows more than one realization possibility In-house design of magnetics crucial for optimal designs. Most Loss Effects are Considered Skin- and proximity losses in litz, round and foil windings, air gap stray field losses, DC bias core losses, thermal model,

155 Additional References [6] J. Mühlethaler, J.W. Kolar, and A. Ecklebe, A Novel Approach for 3D Air Gap Reluctance Calculations, in Proc. of the ICPE - ECCE Asia, Jeju, Korea, 2011 [9] J. Mühlethaler, J. Biela, J.W. Kolar, and A. Ecklebe, Improved Core Loss Calculation for Magnetic Components Employed in Power Electronic Systems, in Proc. of the APEC, Ft. Worth, TX, USA, [19] Jürgen Biela, Wirbelstromverluste in Wicklungen induktiver Bauelemente, Part of script to lecture Power Electronic Systems 1, ETH Zurich, 2007 [20] J. Mühlethaler, J.W. Kolar, and A. Ecklebe, Loss Modeling of Inductive Components Employed in Power Electronic Systems, in Proc. of the ICPE - ECCE Asia, Jeju, Korea, 2011 [21] J. Mühlethaler, J. Biela, J.W. Kolar, and A. Ecklebe, Core Losses under DC Bias Condition based on Steinmetz Parameters, in Proc. of the IPEC - ECCE Asia, Sapporo, Japan, [22] B. Cougo, A. Tüysüz, J. Mühlethaler, J.W. Kolar, Increase of Tape Wound Core Losses Due to Interlamination Short Circuits and Orthogonal Flux Components, in Proc. of the IECON, Melbourne, [23] J. Mühlethaler, M. Schweizer, R. Blattmann, J.W. Kolar, and A. Ecklebe, Optimal Design of LCL Harmonic Filters for Three-Phase PFC Rectifiers, in Proc. of the IECON, Melbourne, 2011 Contact Jonas Mühlethaler jonas.muehlethaler@gecko-simulations.com 155