Mechanical design of IM. Torque Control of. Induction Machines... Slip ring rotor. Mathematical model. r r. Stator same as PMSM Rotor:

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Sheryl Short
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1 Toqe ontol of Incton Machne... a copae to PMSM Intal Electcal Engneeng an Atoaton Mechancal egn of IM Stato ae a PMSM oto: at aln Won coppe /Slp ng Intal Electcal Engneeng an Atoaton n Unvety, Sween Nan Nan Föeagttel Slp ng oto Matheatcal oel Intal Electcal Engneeng an Atoaton The oto can be: Shot ccte Gven an extenal oto etance Fe by powe electonc Intal Electcal Engneeng an Atoaton Stato oto λ δ λ Nan Nan Föeagttel Nan Nan Föeagttel

2 Intal Electcal Engneeng an Atoaton How oe t wo? Iagne the followng eqence : A agnetzng tato cent tatonay v. the oto. The cent ntantly ove an nceae. The oto coneve the (oto-)flx an th the tato flx Intal Electcal Engneeng an Atoaton T Stato flx oentaton Toqe oto flx oentaton δ Nan Nan Föeagttel Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton Vecto contol of Incton oto Flx etaton (oto- o tato- the ot ffclt pat) Intal Electcal Engneeng an Atoaton oto flx etaton o eqaton -> 4 eqaton. ewtng a lot gve: - τ τ θ l q q τ - - y β ω σ q σ q - q - ω σ σ q θ l θ θ x α Nan Nan Föeagttel Nan Nan Föeagttel

3 Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton oto flx etaton τ Sn o Poweap. τ Toqe an flx- contol α β q ωl ω ω θ ontolgnal AM T e - j θ a b c Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton Fll Flx Obeve j j ω ω Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton Fll Flx Obeve ( ) ( ) ( ) ( ) j whee ω (,:) - - B B A - ob - - Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton Voltage eaeent Etaton by oftwae Eo pone at low pee Analoge flteng an aplng low Dect ntegaton Nee galvanc olaton

4 Intal Electcal Engneeng an Atoaton A A A Splt eqaton olvng A Solve patly ote the copoceo A ob, ob, ob, ob, ob, A A A A A ob, ob, ob, ob, ob, Solve entely n the copoceo Intal Electcal Engneeng an Atoaton Dect ntegaton pleente Nan Nan Föeagttel Nan Nan Föeagttel Stato Flx Oente Vecto ontol of Toqe an Flx Eqaton, agan... Intal Electcal Engneeng an Atoaton avantage: In a ynchonoly otatng efeence fae, thee ae no tatonay eo nce all efeence vale ae contant n tatonaty The tato flx o can n ot cae be obeve wth hgh accacy an low paaete entvty Dect flx contol can be apple Intal Electcal Engneeng an Atoaton o eqaton,.e. 4 cala eqaton, ewtten gve : θ l σ ω l σ q τ τ q σ τ q q q τ σ τ ω Nan Nan Föeagttel Nan Nan Föeagttel

5 Dect Flx Vecto ontol ontol of the Toqe pocng cent coponent : Intal Electcal Engneeng an Atoaton ( t) ( t) ( t) ( ( ( (, ) T { n tatona ty} ( ( ( T Intal Electcal Engneeng an Atoaton The eanng two ewtten cala eqaton: q q ω q σ τ q τ - σ τ q q ( ) q σ ω q ( ) q ( λ λ ) ω Nan Nan Föeagttel Nan Nan Föeagttel ontol of the Toqe pocng cent coponent : Pef Vecto ontol Syte ef yef act y e PIE o GonStato flx contol Intal Electcal Engneeng an Atoaton Ue genec -phae loa... λ λ T ( n ( T ( ( ) ( ( n) ( n) ) q q q ω ( λ λ T q n q Intal Electcal Engneeng an Atoaton P 4 Tef ect Scope Mx Ot ec_to_pol - Mx /q > alfa/beta Ot Dex ef act y Ü> & q e yqef PIE alfa/beta Ü> /q Toqe contol /p Ü> q_ef Sataton Scope Ot Dex ogh oto pee eplaceent Ü>P &P q_ol ol alfa/beta Ü> /q /T e- elta w Tanfe Fcn ol p Nan Nan Föeagttel Nan Nan Föeagttel

6 DT DT yte Intal Electcal Engneeng an Atoaton opae to D. eplace wth eplace wth T q Intal Electcal Engneeng an Atoaton 4 P T 4 q Ot P - alfa/beta Ü> /q Dex -> & q o ect ef ec_to_pol nceae/ eceae In Ot low pee? -D T[] f() ecto nceae/ eceae q f() XY Gaph Scope f() o 7 8 et Scope Scope [ - -] [ -] [- -] [- ] [- - ] [ - ] [ ] [- - -] Meoy f() 5 e a b c Nan Nan Föeagttel Nan Nan Föeagttel Intal Electcal Engneeng an Atoaton Splfe Stato Flx Moel y no loa nnng β q θ θ l θ - - τ x α Intal Electcal Engneeng an Atoaton Vc Vb Va Splfe Stato flx oel p - p α Vc Vb p - p β Nan Nan Föeagttel Nan Nan Föeagttel

7 Intal Electcal Engneeng an Atoaton θ l Splfe Stato Flx Moel σ ω l σ q τ τ q σ τ q τ σ τ q q ω Intal Electcal Engneeng an Atoaton.5.5 Splfe etaton eo Mäoent Halvt äoent Togång 4 5 tato feven.5.5 Nan Nan Föeagttel 4 5 Nan Nan Föeagttel tato feven Intal Electcal Engneeng an Atoaton elaton q/ n tato flx fae q [A] Nonal loa No loa o Nan Nan Föeagttel [A] Intal Electcal Engneeng an Atoaton Fll Flx Obeve ( ) F ob ( ) G ob (, ) K ob (, ) F ob e A obt e ( T e T / e ( T e T / e jω T / F ob,ω e jω T / F ob I A ob T I A ob T I A ob T Nan Nan Föeagttel

PMSM. Mechanical Design

PMSM. Mechanical Design PMSM Indutial Electical Engineeing and Autoation Lund Univeity, Sweden Mechanical Deign Indutial Electical Engineeing and Autoation 1 Indutial Electical Engineeing and Autoation y i b i β Matheatical Model