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NTNU NTNU NTNU Slide 319 Slide 321 Slide 323 Dynamisk modell for PM synkron maskin ■ Fluksene som tilstandsvariable: 1 dψ d u d = rs ⋅ i d + − n ⋅ ψ q ωn dt 1 dψ q u q = rs ⋅ i q + + n ⋅ ψ d ωn dt ψ d = x d ⋅ i d + ψ m ψ q = x q ⋅ i q m e = ψ d ⋅ i q − ψ q ⋅ i d = ψ m ⋅ i q − ( x q − x d ) ⋅ i d ⋅ i q ■ Strømmene som tilstandsvariable: x d did u d = rs ⋅ i d + − n ⋅ x q ⋅ i q ωn dt ψ d = x d ⋅ i d + ψ m ψ q = x q ⋅ i q me = ψ m ⋅ i q − ( x q − x d ) ⋅ i d ⋅ i q x q diq u q = rs ⋅ i q + + n ⋅ x d ⋅ i d + n ⋅ ψ m ωn dt Blokkskjema for en PM-maskin med strømmene som tilstandsvariable Trondheim 2000 Trondheim 2000 De optimale d- og q-komponenter for en gitt i s ■ Den optimale q-komponent (maks moment pr. ampere): 2 2 m e = ψ m ⋅ i q - (x q - x d ) ⋅ i d ⋅ i q = ψ m ⋅ i q + (x q - x d ) ⋅ i s − i q ⋅ i q 2 2 hvor i d = − is − i q 2 2 ∂m i e s − 2 ⋅ i q = ψ m + (x q - x d ) ⋅ = 0 ∂i 2 2 q i s − i q ⇒ 2 ψ m ⋅ i d i q = ± i d − x q − x d 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 Trondheim 2000 NTNU NTNU NTNU Slide 320 Slide 322 Slide 324 Dynamisk modell for PM synkron maskin ■ Kobling mellom aksene: di d ωn r ωn x s q ωn = − ⋅ i d + n ⋅ ⋅ i q + ⋅ u d dt x d x d x d di q ωn rs ωn x d ωn ωn = − ⋅ i q − n ⋅ ⋅ i d − n ⋅ ⋅ ψ m + ⋅ u q dt x q x q x q x q ψ d = x d ⋅ i d + ψ m ψ q = x q ⋅ i q m e = ψ m ⋅ i q − ( x q − x d ) ⋅ i d ⋅ i q ■ Ingen kobling ved null turtall x d Td = ωn rs x q Tq = ωn rs ■ Skal oppheve koblingen med foroverkobling i reguleringen IPMSM_dq_i_regtot ■ Fluksregulator: i Regulatorstruktur for PM maskiner ➨ Merker at u st er nære 1 ➨ Prøver å påtrykke mere negativ d-strøm for å redusere fluksen ➨ Dette går på bekostning av tillatt qaksestrøm qref , max = = 2 dref1 i 2 sref i = f − ( i qmax dref1, qref1, dref + i ( i 2 qref1 dref1 − ( i + δi i dref1 2 dref ) Feltsvekking δi + δi ) 2 dref ) s is β d s us β - + q β θ a s s isα + s α us α - Trondheim 2000 Trondheim 2000 c s Trondheim 2000
NTNU NTNU NTNU Slide 325 Slide 327 Slide 329 Strømregulatorer for PM synkronmaskinen ■ Statororientert regulator: ➨ Arbeider med acstørrelser stasjonært ➨ Får sine referanseverider transformert fra dq-systemet ■ dq-orientert regulator: ➨ Må transformere utgangen fra regulatorer over til statoroirentert system ➨ Den fysiske omformer er i stator ■ Med PI-reg: s is β d s us β - + Strømregulatorer i dq-systemet Åpne sløyfes transferfunksjon q β θ a s s isα + s α us α - ■ Deler på U dc i regulator for å slippe å oppdatere regulatorparametre ved varierende dc-spenning ■ Benytter tallverdi optimering c s Trondheim 2000 Trondheim 2000 1 + Ti, d ⋅ s ω 1 T s n ⋅ Td ⋅ u + i, d ⋅ dc −sT ωn ⋅ Td ⋅ u v dc h oid = K pd ⋅ e ≈ K pd Ti, d ⋅ s x d ⋅ ( 1 + Td ⋅ s) ⋅ ( 1 + Tfd ⋅ s) Ti, d ⋅ s x d ⋅ ( 1 + Td ⋅ s) ⋅ ( 1 + Tsum ⋅ s) 1 + Ti, q ⋅ s ωn ⋅ Tq ⋅ u dc 1 + Ti, q ⋅ s ωn ⋅ Tq ⋅ u −sT dc v h oiq = K pq ⋅ e ≈ K pq Ti, q ⋅ s x q ⋅ ( 1 + Tq ⋅ s) ⋅ ( 1 + Tfq ⋅ s) Ti, q ⋅ s x q ⋅ ( 1 + Tq ⋅ s) ⋅ ( 1 + Tsum ⋅ s) x x d q K pd = T = T K = T = T 2 ⋅ ωn v fd n v fq i, d d pq i, q q ⋅ ( T + T ) 2 ⋅ ω ⋅ ( T + T ) Trondheim 2000 NTNU NTNU NTNU Slide 326 Slide 328 Slide 330 IPMSM_dq_i_reg_ac Statororientert regulator Dekoblingsnettverk for PM synkron maskin ■ Kobling mellom aksene: di x d ω r ω n s n q ωn = − ⋅ i d + n ⋅ ⋅ i q + ⋅ u d dt x d x d x d di q ωn rs ωn x d ωn ωn = − ⋅ i q − n ⋅ ⋅ i d − n ⋅ ⋅ ψ m + ⋅ u q dt x q x q x q x q ■ Dekoblingsnettverk: u = u + u u = u + u d dI dII u dII = −n ⋅ x q ⋅ iq u qII = n ⋅ x d ⋅ i d + n ⋅ ψ m di d ωn rs ωn = − ⋅ i d + ⋅ u d dt x d x d di q ωn rs ωn = − ⋅ i q + ⋅ u q dt x q x q q qI qII x d Td = ωn rs x q Tq = ωn rs Ta hensyn til tillatt rippel ut fra strømregulatorene ■ Med PI-reg: ~ wˆ id u std = 2 ⎛ 1 Tfd ⎞ ⎛ Tfd ⎞ 2 ⋅ ⎜ + 1 2 2 T ⎟ ⋅ + ⎜ π sw T ⎟ ⎝ ⎠ ⎝ sw ⎠ 10 0 10 -1 10 -2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -3 x d Td = ωn rs x q Tq = ωn rs Trondheim 2000 Trondheim 2000 wˆ ~ iq u stq = 2 ⎛ 1 Tfq ⎞ ⎛ Tfq ⎞ 2 ⋅ ⎜ ⎟ 1 ⎜2 ⎟ ⎜ + ⋅ + 2 T ⎟ ⎜ π sw T ⎟ ⎝ ⎠ ⎝ sw ⎠ Trondheim 2000
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