7. Inverter operated induction machines

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1 7. Invete opeated induction machine Souce: Siemen AG, Gemany Dept. of Electical Enegy Conveion Pof. A. Binde 7/1

2 Invete-fed induction machine Fequency convete (invete) geneate thee-phae voltage ytem with vaiable fequency f and vaiable amplitude U (m). Hence ynchonou peed i continuouly vaiable. With that induction machine i continuouly vaiable in peed. Reveal of peed Changing of two phae of tato winding. Changing of enegy flow (moto / geneato) by deceaing / inceaing phae hift between voltage and cuent : moto ϕ < π / geneato ϕ > π / Voltage amplitude U mut be changed in popotion to f to keep the flux in the machine contant. Thu toque will tay contant, if the the ame cuent i ued. Fo R 0: U jl σ I + jlh ( I + I ) U jl I jl ( I I ) j( ˆ ˆ ) / j ˆ σ + h + Ψ σ + Ψ h Ψ / cont. Rule fo contolling the invete: U f / f / Slip: Ω m p p Cuve M e (n) M e (Ω m ) a Cuve M e ( ) fo vaying i hifted in paallel! ~ Dept. of Electical Enegy Conveion Pof. A. Binde 7/

3 Dept. of Electical Enegy Conveion Pof. A. Binde 7/3 M(n)-Chaacteitic fo invete-fed induction machine R 0: KLOSS fomula: b b b b b b e M M M + + Beak down toque M b : / cont L U p m X p m U M b σ σ σ σ Beak down lip: b b L R X R σ σ ) / ( / b L R σ with Slip fequency

4 Influence of tato winding eitance R Voltage dop at tato eitance in tato voltage equation MUST NOT be neglected at mall angula fequency U R I + j L I + j L I + I ) Example: Induction machine: Rated data: f N 50 Hz, U N 30 V: σ NOTE: At mall f eitance R mut not be neglected. f h( R 0.06Ω 50 Hz : 0.0 L 3.0Ω f R 6 5 Hz : 0. 5 L Voltage dop at tato eitance educe at contant tato phae voltage U the intenal voltage U h. Hence beak down toque deceae with quae of intenal voltage! By inceaing of U by R I intenal voltage U h mut be kept contant fo contant M b. Dept. of Electical Enegy Conveion Pof. A. Binde 7/4

5 Invete with voltage ix tep opeation Bidge ectifie with thyito on gid ide GR (fiing angle α) geneate vaiable DC voltage U d in DC link ZK; voltage moothed by capacito. Invete WR geneate by ix-tep witching fom U d a block haped line-toline output voltage between teminal L1, L, L3. DC link voltage U d i changed by α popotional with output fequency f mot. Gid ide: At α > 90 : U d and hence dc link powe i negative powe flow back to the gid (geneato baking). Dept. of Electical Enegy Conveion Pof. A. Binde 7/5

6 Gid-ide ectification Bidge ectifie on gid ide GR: Maximum ectified voltage U d0 at fiing angle α 0. Zeo ectified voltage U d at fiing angle α 90 3 U ˆ dw 3 UTafo coα U π dw,max coα Dept. of Electical Enegy Conveion Pof. A. Binde 7/6

7 Voltage hamonic at ix-tep opeation Invete output phae voltage: u ; S1 us ul 1 L u u u ; u u + u 0; we get: S S 3 L L3 u S1 S1 + S S 3 ul 1 L + ul L3 Block haped line-to-line voltage, expanded a FOURIER-eie: u L ( t) ˆ 3 U L, k co( k t) k 1, 5,7,.. k 1+ 6g, g 0, ± 1, ±,... k 1, -5, 7, -11, 13,... ˆ L, k 3 Electical machine i fed with a blend of hamonic voltage of diffeent amplitude, fequency and phae angle. Only fundamental (odinal numbe k 1) i deied. Voltage hamonic ( k > 1) caue hamonic cuent in electic machine with additional loe, toque pulation, vibation and acoutic noie. U π U k d Dept. of Electical Enegy Conveion Pof. A. Binde 7/7

8 Pule width modulation (PWM) At gid ide: Diode ectifie GR ( fiing angle α 0): geneate contant DC link voltage U d, which i moothed by capacito: U ~ U cont. d gid Moto inde invete WR geneate fom U d by pule width modulation a line-to-line voltage between L1, L, L3. Width of pule i defined by compaion of aw tooth ignal u SZ (witching fequency f ch ) with AC efeence ignal u ef, which pulate with deied tato fequency f. With compaato a PWM-ignal i geneated to contol powe witche. Refeence ignal i mot often ine wave. Amplitude A1 of u ef define amplitude of fundamental of PWM voltage at moto teminal. So it i vaied popotional to f mot. Gid ide: co ϕ 1. No powe flow back into gid poible. (Fo that an anti-paallel econd diode bidge o a line-ide invete i neceay!). Geneato baking powe ha to be diipated in bake"-eito, which ae connected in paallel with capacito in DC link. Dept. of Electical Enegy Conveion Pof. A. Binde 7/8

Stato cuent ipple geneation DC link voltage ouce invete with witching tanito and fee-wheeling diode R neglected: U d U p, LL L di / dt a) Equivalent witching cheme of DC link

9 Stato cuent ipple geneation DC link voltage ouce invete with witching tanito and fee-wheeling diode R neglected: U d U p, LL L di / dt a) Equivalent witching cheme of DC link voltage ouce invete, connected to the two phae with witching tanito and feewheeling diode, b) Cuent ipple and chopped invete voltage Dept. of Electical Enegy Conveion Pof. A. Binde 7/9

10 Geneation of PWM voltage a) Compaion of aw tooth and efeence ignal lead to PWM contol ignal fo powe witche: Potential ϕ L1 (t) at teminal L1 vaie with that PWM ignal b) Diffeence of two teminal potential delive line-to-line voltage u L1-L (t) Dept. of Electical Enegy Conveion Pof. A. Binde 7/10

11 Voltage hamonic: Six-tep and PWM Six-tep modulation: FOURIER pectum of line-to-line invete output voltage: k Uˆ ˆ / Lk U L 1 PWM: FOURIER pectum of teminal electic potential ϕ L1 (t) and of line-to-line voltage u L1-L (t) (at modulation degee A and witching fequency ation f ch /f 9) k ( U / ) ˆ ϕ k / d 0.5 < ˆ / Uˆ U L, k L, k 1 Spectum of teminal potential ϕ L how big amplitude of fundamental, of witching hamonic (k 9) and at about twice witching fequency f p f ch (k 17 and 19). f p k ± 1 k 18 ± 1 17,19 f Voltage hamonic with odinal numbe, diviible by 3, do not occu in line-to-line voltage! At high witching fequency f ch the amplitude of all low fequency hamonic ae mall. Dept. of Electical Enegy Conveion Pof. A. Binde 7/11

12 Voltage hamonic caue cuent hamonic The voltage hamonic pe phae U,k (fequency k-time fundamental fequency kf ) caue cuent hamonic pe phae I,k in tato winding. Thee 3-phae hamonic cuent ytem excite in ai gap high-peed magnetic field wave (with pole count p due to winding): k th ynchonou velocity ( high peed ): n k f p yn, k / Roto lip with k th high-peed field k : A hamonic lip k i nealy unity, independent of bae lip, hamonic cuent amplitude I,k i nealy independent fom load. Cuent hamonic ae aleady peent at noload to full extent at 0. k nyn, k n knyn n 1 n (1 ) 1 n kn k n k yn, k yn yn High peed field induce oto, cauing oto cuent hamonic with high fequency: f k k f,k f,k ; cauing big eddy cuent in oto ba and big additional oto loe! U, k U, k 1 I k, k ( R + R ) + ( k ) ( L + L ) k ( Lσ + L σ ) σ σ Dept. of Electical Enegy Conveion Pof. A. Binde 7/1

13 Example: Cuent hamonic at ix-tep modulation Amplitude of cuent hamonic at ix tep opeation: I, k U, k 1 ~ k ( L + L ) k k Uˆ ˆ / Lk U L 1 I I , k /, k 1 Amplitude of cuent hamonic deceae with invee of quae of odinal numbe k, becaue leakage inductance moothe the hape of cuent ( educe the cuent hamonic!) σ σ Toque ipple FOURIER um of 5 cuent hamonic Exact olution of dynamic machine equation Dept. of Electical Enegy Conveion Pof. A. Binde 7/13

14 Example: Cuent hamonic at PWM Refeence ignal: ectangula Refeence ignal: tapezoidal Switching atio: f ch /f 6 Switching atio: f ch /f 9 Dept. of Electical Enegy Conveion Pof. A. Binde 7/14

15 Hyteei band contol fo tato cuent No fixed pule patten of witched DC link voltage, but witching intant ae detemined by compaion of meaued cuent with hyteei band limit. No fixed witching fequency! Hyteei band Dept. of Electical Enegy Conveion Pof. A. Binde 7/15

16 Doubly fed induction machine Aim: Speed vaiable opeation with mall invete: invete ating le than moto ating S Um < S Mot Solution: Line-fed lip-ing induction machine, fed by mall invete in the oto via lip ing but: Speed ange nmin nyn n max mall. If we want n min 0, we get S Um S Mot. Invete feed with oto fequency an additional oto voltage U into oto winding. - Via vaiable amplitude of U the peed i changed, - Via phae hift of U the eactive component of tato cuent I i changed Explanation with implified T- equivalent cicuit pe phae: R 0, L 0 σ U jx h ( I I ) jx h I 0 U ( R + jx ) I + jx h I U U Roto cuent: I R + jx σ U U ( w jb) Roto additional voltage: Dept. of Electical Enegy Conveion Pof. A. Binde 7/16

17 Simplified toque-peed cuve of doubly fed machine Electomagnetic toque M e : Appoximation fo mall lip << 1: I P U R + U jx U U R U R + σ in P δ m Re ( w jb) * U { U I } m ( w) R <<1 ( w) By eal pat of additional oto voltage w the M e -n-cuve ae hifted in paallel! Toque i ZERO at no-load lip L w. - If no-load lip L i poitive (SUB-ynchonou no-load point) Active component of additional oto voltage IN PHASE with tato voltage - If L i negative (SUPER-ynchonou no-load point) Active component of additional oto voltage i in PHASE OPPOSITION with tato voltage U active M e 0 w 0, L w U S 3U I Invete ating: Inv At n min ( L,max ) both U and S Um ae at maximum, thu defining invete ating. M e P Ω δ yn mu Ω R yn Dept. of Electical Enegy Conveion Pof. A. Binde 7/17

18 Doubly-fed wind geneato Wind tubine with vaiable peed allow to extact maximum poible wind powe at each wind velocity v. P Wind ~ v 3 3 P Tubine ~ n Doubly fed induction machine ued a vaiable peed geneato, opeating at gid with contant gid fequency! Additional oto voltage with oto fequency geneated by 4-quadant PWM invete via lip ing fed into oto winding. Example: Wind velocity vaie between 0.65v max and v max : Geneato and gea to tubine ae deigned hence fo peed angen yn ± 0% ( ±0.): Wind velocity Geneato peed lip add. voltage powe v max n 1.n yn n max -0. w -0. P 100% v min 0.65v max n 0.8n yn 0.65n max +0. w +0. P 30% Rated powe of invete at teady tate opeation and ated toque: PInvete P δ PN 0. PN Hee invete ating i only 0% of geneato ating, thu it i a vey cheap olution, which i ued nowaday widely at big wind tubine MW. Dept. of Electical Enegy Conveion Pof. A. Binde 7/18

19 Invete opeated cage induction machine IGBT invete with gid ectifie and machine-ide convete, feeding tato winding: - powe electonic - contol unit - gid filte Ai-ai cooled cage induction machine with heat topmounted exchange Souce: Siemen AG, Gemany Dept. of Electical Enegy Conveion Pof. A. Binde 7/19

20 Roto ide voltage ouce PWM invete fo doubly-fed 3 MW induction geneato Souce: Winegy, Gemany Dept. of Electical Enegy Conveion Pof. A. Binde 7/0

LECTURE 24 INDUCTION MACHINES (1)

ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURE 24 INDUCTION MACHINES (1) Acknowledgment-Thee handout and lectue note given in cla ae baed on mateial fom Pof. Pete Saue ECE 330 lectue note. Some lide