Section 8: Magnetic Components

Transcription

1 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 are used in power frequency applications and are operated at around 50Hz, cannot be used in many power electronic converters because of the high eddy current losses in such materials. Inductors Filters Transformers Magnetic steel: Fe+Si+r; B Sat 1.8T. onductivity σ is rather high, leading to considerable eddy current losses even at 50Hz. Laminations are used; useful up to nearly khz, in power transformer and machines. Powdered iron: Fe+o+Ni: particle dimension less than, the skin-depth, for the highest frequency of switching. Magnetic omponents 1 F. ahman/sep/010

2 B Sat 0.75T at room temperature. Example: Metglas fabricated as ribbon of microns to form laminations. Good for operation up to a few 10s of khz. Ferrites: iron oxide + other magnetic materials. B Sat 0.3T, no eddy current loss, ie, very low σ. Good for switching frequency more than 100kHz. For further reading: see Section 3.3 from Mohan s & Sections 1.1 to 1.1 from Erikson s book. Losses in Magnetic ircuits 1. opper loss: represented in the D equivalent circuit of converters by L. Ploss IMS L + loss due to skin & proximity effects.. ore loss: Hysteresis and eddy current losses in the core material. 3. Proximity loss: aused by induced (eddy) current in conductors. Magnetic omponents F. ahman/sep/010

3 1. opper loss g L l Ohm Figure 7.1 L N g g l l g g ni g B Magnetic omponents 3 F. ahman/sep/010

4 B 1 1 g ni / m B Figure 7. The air gap reduces the temperature dependence of L and the remanent B, at the cost of reducing the flux/ampere of current. l is determined by the necessary number of turns. is determined by the required wire-gauge. rea of the core window is determined by the required space for the winding l is determined by the required space for winding. Magnetic omponents 4 F. ahman/sep/010

5 Skin effect in windings Because of self eddy currents Figure 7.3 Frequency (khz) δ (mm) Magnetic omponents 5 F. ahman/sep/010

6 Because of lack of penetration of current into copper, the ac resistance of the conductor increases with frequency. By making the conductor thickness (area of cross-section) consistent with δ, relevant to, the current density can be forced to become evenly distributed. Nevertheless, there will be some increase of resistance, compared to the D resistance given by l. If d, this increase of ac resistance is negligible. With Litz wires, which are essentially thin foils satisfying the above expression, additional loss due to skin effect are minimized. Magnetic omponents 6 F. ahman/sep/010

7 Proximity effect In addition to skin effect, the magnetic field of one conductor induces eddy currents in neighbouring conductors. Figure 7.4 Spacing factor: 4 n 1 d L Magnetic omponents 7 F. ahman/sep/010

8 Effective ratio of d / : d F ac dc where d = conductor diameter, assumed round n 1 = number of layers L ω = depth of each layer δ = skin depth F in a function of and number of layers P P ac dc Figure 7.5 Magnetic omponents 8 F. ahman/sep/010

9 Interleaving of windings in transformers reduces loss due to proximity effects. ore loss P Ph Pe in the material of the magnetic core. The hysteresis loss P h is due to the cyclic traversal of the B- H loop. Ph l fs HdB n P K f B m h h s max / 3 B B max i L i L min i L max i L H Figure 7.6 Filter inductor. e.g., for the Buck converter inductor; low P h. Magnetic omponents 9 F. ahman/sep/010

10 i L B max Figure 7.7 i L in a boost converter with DM for Boost inductor. i m B max Figure 7.8 Magnetizing current and core flux in a squarewave inverter. Magnetic omponents 10 F. ahman/sep/010

11 Eddy urrent loss P e KB f e for laminated steel i Figure 7.9 Eddy-current flow in laminations. 3 W/cm 1 1MHz 500kHz 00kHz 100kHz 50kHz 0kHz ˆB Figure ore loss, P, for ferrite cores. Magnetic omponents 11 F. ahman/sep/010

12 Steps in filter inductor design f s, il max and L are known. l 1 i L n l l g ll 1 Figure 7.11 L n n I g L H ni L. l g B H; B c c c c c K u n u u is area of cross-section of conductor. K 0.3 for round wire. u K for Litz wire u Magnetic omponents 1 F. ahman/sep/010

13 Selection of allow l to be determined. From the B-H characteristic of the suitable material, B and can be selected. opper loss in windings For a filter inductor, of the wire l P cu = I MS, is the u loss. L, Lg, L, and B are iterated until the P u is acceptable. Transformer design, pri N pri K u, pri u, pri,sec N sec K u,sec u,sec, pri,sec V N pri pri db max sin dt t Magnetic omponents 13 F. ahman/sep/010

14 N. f B ^ pri s ^ B found from this ^ B and ^ Vpri allow to be selected. L m N pri g ^ ^ ( ) g im N pri g should be selected for a desired i ^m. Leakage inductance, L 1 0Nprilb 3h l = length a single turn. Magnetic omponents 14 F. ahman/sep/010

15 b pri sec h Figure 7.1 Magnetic omponents 15 F. ahman/sep/010