Overview Electrical Machines and Drives

Overview Electrical Machine and Drive 7-9 1: Introduction, Maxwell equation, magnetic circuit 11-9 1.-3: Magnetic circuit, Princile 14-9 3-4.: Princile, DC machine 18-9 4.3-4.7: DC machine and drive 1-9 5.-5.6: IM introduction, IM rincile 5-9 Guet lecture Emile Brink 8-9 5.8-5.10: IM equivalent circuit and characteritic -10 5.13-6.3: IM drive, SM 5-10 6.4-6.13: SM, PMACM 1-10 6.14-8.3: PMACM, other machine 19-10: ret, quetion 9-11: exam 1

Induction machine Introduction (5.1) Rotating magnetic field (5., alo for SM) Why doe an induction machine rotate? Induced voltage (5.3, alo for SM) Definition (5.4, 5.5) Equivalent circuit and voltage equation (5.7) Parameter identification (5.8) Performance characteritic (5.9) Power flow in three mode of oeration (5.10) Seed control (5.13) Linear induction motor (5.16)

Recaitulation Why i the induction machine the workhore of indutry? How doe the tator of an induction machine create a rotating magnetic field? Why doe the induction machine develo torque? 3

Why doe an IM work? B ( θ, t) = Bˆ co( θ ωt) 1 Sketch the flux linkage of dd. Sketch induced voltage in dd'. The rotor turn dd and qq' are hort-circuited via a large reitance R r. 3 Sketch the current through dd'. 4 Sketch the flux denity at the location of d B(π/,t). 5 Sketch the flux denity at the location of d' B(3π/,t). 6 Sketch the torque on dd'. 7 Sketch the torque on qq' in the ame way. 4

Reult 5

Concluion contant torque with two turn at ynchronou eed: no torque torque roortional to rotor frequency (li frequency) if the effect of the rotor current on the field i negligible 6

Induced voltage (alo for SM) Air ga flux denity: Maximum air ga flux er ole (t =0): π / ( θ, t) = Bˆ co( θ ωt) π / Φ d ˆ co( ) d ˆ = B n A = B θ ωt lr θ = lrb Flux linkage of hae a if hae i a concentrated full-itch winding with N turn: B λ = NΦ a co( ωt) Induced voltage: e a = d λa dt = ωnφ in( ωt) In equation (5.3), a minu i inerted 8

Induced voltage and winding factor e e e E E a b c = ωnφ = ωnφ = ωnφ in( ωt) in( ωt in( ωt 3 4 3 π ) π ) ωnφ = = πfnφ = 4. 44 = k w πfnφ fnφ A hae winding i generally not a concentrated full-itch winding, but a ditributed winding. Therefore, the voltage induced in the different turn are not in hae and the reulting induced voltage i lower. Thi i taken into account by including the winding factor. 9

Standtill oeration: tranformer A wound rotor induction machine with blocked rotor work a a tranformer E = k fn Φ 1 w1π 1 E = k w πfn Φ 11

-ole machine i the number of ole (in ome other book: number of ole-air) N N a ( θ ) = in( θ ) ˆ B ( θ, t) B co( θ ωt) θ θ = ed = md 1

Three-hae tator winding 13

Running oeration n i the ynchronou eed of the rotor for f 1 =50Hz n i the actual eed of the rotor i the li n = f 60 1 4 6 8 10 0 n (rm) 3000 1500 1000 750 600 300 n n n f i the rotor frequency E π = n = ( 1 ) n π f = f 1 = fkwnφ = f1kwnφ = E n = n + What i the eed of the rotor field with reect to the tator field? n 14

Three mode of oeration demo 15

Equivalent circuit in Sen When an induction machine i in tandtill, it work a a tranformer. When the rotor rotate, alo a voltage will be induced in the rotor winding. Therefore an equivalent circuit i aumed which i comarable to a tranformer. 17

18 Develoment j E I R L ω = + j E I R L ω = + 1 j E I R L ω = + 1 R R R + =

Equivalent circuit develoment L 1 and L are the tator and rotor leakage inductance. Where are the leakage field? 19

Voltage equation d λ1 u1 = R1i 1 + dt d λ 0 = R i + dt U 1 = R1 I1 + jωλ1 0 = R I + jωλ or uing haor where u U ωt j 1 = Re( 1 e ) λ1 = L1 I1 + Lm 1I1 + MI λ = L I + L I + MI m 1 L 1 and L are the tator and rotor leakage inductance L m1 and L m and are the tator and rotor main inductance that give the ratio between the hae flux linkage and the hae current auming three-hae current M i the mutual inductance between tator and rotor that give the ratio between the hae flux linkage and the hae current auming three-hae current 0

Tranformation of the voltage equation The rotor voltage equation i divided by the li: U 1 = R1 I1 + jωl1 I1 + jωlm 1I1 + jωmi = R1 I1 + jωl1 I1 + E1 R R 0 = I + jωl I + jωl I + jωmi = I + jωl I + E m 1 1

Tranformation of voltage equation Referring the rotor quantitie to the tator in a ower invariant way L m 1 M Lm 1 E I = E = I R = R M M uing Lm1 M = L m 1L m give L M m1 L = L U 1 = R1 I1 + jωl1 I1 + j ωlm 1( I1 + I ) = R1 I1 + jωl1 I1 + E1 R R 0 = I + jωl I + j ωl ( I + I ) = I + jωl I + E m1 1 1

Γ-equivalent circuit U 1 = R1 I1 + jωl1 I1 + j ωlm 1( I1 + I ) R I L I L I I 0 = + jω + j ω m1( 1 + ) U1 = R1 I1 + j ωl ( I1 + I R ) R R 0 = I + jω L σ I R + j ω L ( I 1 + I R ) where L ( Lm 1 + L ) Lσ = 1 L Lm 1 L R R = R L m1 ubtituting I L = I R Lm 1 L = L + L m1 1 3

Other equivalent circuit aroximation IEEE-recommended 4

Parameter identification (5.8) reitance meaurement (dc current) - which reitance? no-load tet - which arameter? blocked-rotor tet - which arameter? 6