CERN ACCELERATOR SCHOOL Power Converters. Passive components. Prof. Alfred Rufer

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1 CERN ACCELERATOR SCHOOL Power Converters Passive components Prof. Alfred Rufer

2 Overview Part 1: (to be designed) Part 2: Capacitors (to be selected) Part 3: A new component: The Supercapacitor, component and applications

3 Overview, typical applications -AC-applications -DC applications -Filtering -Smoothing (limiting di/dt) -Components of resonance circuit References: P. Robert, «Matériaux de l électrotechnique, Traité d électricité, Vol II, PPUR, ISBN M. Jufer, F. de Coulon, Introduction à l électrotechnique, Traité d électricité, Vol I, PPUR, ISBN T. Undeland, N. Mohan, P. Robbins, Power Electronics, Converters, Applications and Design, Wiley, ISBN

4 2 main types: - Air inductors - with magnetic core Solenoid (air) 2 L= N µ 0 A/ l Toroid (core) A: area of coil L: length of coil N: number of turns 2 L= N µ A/ π dm A: section of core d m : mean diameter of tore N: number of turns

5 Toroidal inductor

6 Main parameters of inductors Inductance Quality factor Capacity Rated current Equivalent scheme R a : Losses related to AC current component R c : Resistance of winding C: Capacity of winding

7 Relations For: 2 ω LC << 1 Z R' + jω L' with R R R Q 2 ' = c + a /(1 + a) Q = R / ωl a a if 2 Q >> 1 a L' L R R L R 2 2 ' c +ω / a

8 Factor of losses and quality factor for Q >> 1 2 a tan δ = R'/ ωl' R / ωl+ ωl/ R tanδ = tanδ + tanδ Q= 1/ tan δ = ωl'/ R' c Important factor for resonant circuits c a a

9 Magnetic materials and cores 2 main classes of materials 1) Iron based Alloys of iron with chrome and silicon (small amounts) Electrical conductivity Large value of saturation limit Powdered iron cores (small iron particles isolated from each other) Greater resistivity, smaller eddy current losses Suited for higher frequencies Amorphous alloys of iron with other transition metals (METGLAS)

10 Magnetic materials and cores 2) Ferrites Oxide mixtures of iron and other magnetic elements Large electrical resistivity Low saturation flux density (0.3T) Have only hysteresis losses No significant eddy current losses

11 Hysteresis losses a Pmsp, kf ( Bac) d = (specific loss) k, a, d, constants depending from the material Loss increase with f and with B ac Bac Bˆ = If no time average B = Bˆ B If time average ac avg

13 Example of ferrite material (3F3) P, = 1.5*10 f ( B ) msp ac Pmsp, in mw/cm 3 when f in khz and B ac in mt For METGLAS: Pmsp, = 3.2*10 f ( B ) ac For 100 khz and 100 mt: P m,sp = 127mW/cm 3

14 Empirical performance factor PF=f*B ac

15 P m,sp depends finally on how efficiently theheat dissipated is removed P m,sp is even smaller because of presence of eddy current loss

16 Skin effect limitations (in core) - If conducting material is used: circulation of currents when the magnetic field is time-varying (eddy currents) - The magnetic field in the core decays exponentially with distance into the core y / By ( ) = Be 0 Skin depth: δ δ δ = 2/ ωµσ ω = 2πf µ : permeability σ : conductivity

17 Typical value of skin depth (Material with large permeability) 1mm at 60 Hz! > Thin laminations with each isolated from the other > Stacking factor ( ) Materials with increased resistivity: increase of skin depth but reduces the magnetic properties Reasonable compromise for transformers (50/60 Hz): Iron alloy, 97%iron, 3% silicon) and a lamination thickness of 0.3 mm

18 Example of stacking steel laminations

19 Eddy current loss in laminated cores Specific eddy current loss (estimated optimistic minimum) P ec, sp = d ω B 24ρ core d: thickness of the lamination d < δ (skin depth) B() t = B sin( ωt)

20 Core shapes and optimum dimensions Cross-sectional area of the bobbin: Aw = hw bw Widely used core: Double-E core b a =a, d=1,5a, h a =2,5a, b w =0,7a, h w =2a

21 Geometric characteristics of a near optimum core for inductors / transformer

22 Copper windings Advantages of copper: high conductivity, easy to bend - single round wire - Litz-wire diameter of each strand: a few hundred of microns (skin effect in copper) Copper fill factor k cu = NA A Cu w from 0,3 (Litz) to 0,5..0,6 for round conductors

23 Power dissipated in the winding(specific) P 2 Cu, sp = ρcu ( Jrms ) = / or P, = k ρ ( J ) wsp Cu Cu rms 2 J I A rms rms Cu

24 Skin effect in copper windings Circulating winding current > magnetic field > eddy currents The eddy currents «shield» the interior of the conductor from the applied current The current density decays exponentially «skin depth»

25 Skin depth: δ Frequency 50Hz 5kHz 20kHz 500kHz δ 10.6 mm 1.06 mm 0.53 mm mm Skin depth in Copper at 100 o C for several different frequencies

26 Thermal considerations Temperature increase of core and winding: - degrades the performance of the materials -The resistivity of the copper winding increases and so the loss increases - The value of the saturation flux density decreases It is important to keep the core and winding temperature under a maximum value In practice o C

27 Design of the thermal parameters R θsa, R θrad, R θconv T = R ( P + P ) θ sa core w R k a 1 θ sa = k 1 : constant 2 P P V core = c, sp c Pw = Pw, spvw P P = P for an optimal design csp, wsp, sp V (volume) ~ a 3 so with P P k a core 2 + w = 2 : P sp = k 3 a

28 Maximum current density J and specific power dissipation Psp as functions of the double-e core scaling parameter a P sp = k 3 a J rms = k k 5 Cu a

Section 8: Magnetic Components

Section 8: Magnetic Components Section 8: Magnetic omponents Inductors and transformers used in power electronic converters operate at quite high frequency. The operating frequency is in khz to MHz. Magnetic transformer steel which