Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

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Modeling and control modes of PM synchronous motor drives Ld + Lq Lq −Ld j2( θr θK) j( θr θK) Ψ sK = ( ) IsK − ( ) I ∗ sK e − +Ψ PM e − (2.20) 2 2 Stator fixed system ( α, β ) Taking the angular speed of the reference frame to be Ω K = 0 and θ K = 0 , the set of synchronous machine vector equations (2.19) and (2.20) my be written as: U d Ψ sαβ sαβ = Rs Isαβ + (2.21) dt Ld + Lq Lq −Ld ∗ j2θr jθ r Ψ sαβ = ( ) I sαβ − ( ) Isαβ e +Ψ PM e (2.22) 2 2 Substituting to above equations the following expressions for complex vectors U U jU = s sα + , αβ sβ s sα sβ I αβ = I + jI , Ψ αβ =Ψ sα + jΨ sβ and splitting into real and s imaginary parts one can obtain the scalar form of the machine equations in stationary α, β reference frame: U U dΨ dt sα sα = RsIsα + (2.23a) dΨ sβ sβ = RsIsβ + (2.23b) dt Ld + Lq Lq −Ld Lq −Ld ( cos2 θ ) Is ( )sin2θ Is cosθ 2 2 2 Ψ = − − +Ψ (2.24a) sα r α r β PM r Lq − Ld Ld + Lq Lq −Ld Ψ sβ =− ( )sin 2 θrIsα + [( ) + ( )cos2 θr] Isβ +Ψ PM sinθ (2.24b) r 2 2 2 Note, that in the flux-current equations (2.24a and b) still we can observe that value of inductances depends on rotor position θ r . Stator flux fixed system ( x, y ) In order to take advantage of the set of equations (2.19) and (2.20) in rotating coordinate system, one assumes that the coordinate system rotates with the stator flux linkage angular speed Ω K =Ω Ψ and θK = θ Ψ . As a sx s Ψ =Ψ , δ = −( θ − θ ) Ψ r Ψ d Ψ U R I j dt sxy sxy = s sxy + + ΩΨsΨ (2.25) sxy Ld + Lq Lq −Ld ∗ − j2δΨ − jδΨ Ψ sxy = ( ) Isxy − ( ) Isxy e +Ψ PM e (2.26) 2 2 14
Modeling and control modes of PM synchronous motor drives Substituting to above equations the following expressions for complex vectors U U jU sxy = sx + sy, Isxy Isx jIsy = + , Ψ =Ψ s and splitting into real and imaginary parts sxy one can obtain the scalar form of the machine equations in stationary x, y reference frame: U dΨ dt s sx = Rs Isx + (2.27a) U = R I +ΩΨ Ψ (2.27b) sy s sy s s 1 1 Ψ s = [( Ld + Lq) −( Lq − Ld)cos 2 δΨ ] Isx + ( Lq − Ld)sin 2δΨIsy +Ψ PM cosδΨ 2 2 (2.28a) 1 1 0 = ( Lq − Ld)sin2 δΨIsx + [( Ld + Lq) + ( Lq −Ld)cos2 δΨ] Isy −Ψ PM sinδΨ 2 2 (2.28b) The current-flux equations can be expressed also in simplest form as: 2 2 s ( Ld cos δΨ Lqsin δΨ) Isx ( Lq Ld)sinδΨcosnδΨIsy PM cosδΨ Ψ = + + − +Ψ (2.29a) 2 2 q d δΨ δΨ sx d δΨ q δΨ sy PM δΨ 0 ( L L )sin cos I ( L sin L cos ) I sin = − + + −Ψ (2.29b) Rotor flux fixed system ( dq) , In order to take advantage of the set of equations (2.19) and (2.20) in rotating coordinate system, one assumes that the coordinate system rotates with the rotor flux angular speed Ω K = pbΩ m and θK = pbγm = θr d Ψ U sdq R I jp dt sdq s sdq b m = + + Ω Ψ (2.30) sdq Ld + Lq Lq −Ld ∗ Ψ sdq = ( ) Isdq − ( ) Isdq +Ψ PM (2.31) 2 2 Substituting the following expressions for complex vectors U = Usd + jUsq, I I jI sdq = sd + sq, sdq sd j sq Ψ =Ψ + Ψ to (2.30) and (2.31), and splitting for real and imaginary parts the scalar form of the machine equations in rotational fixed reference frame can be obtained: dΨ sd Usd = Rs Isd + − pbΩmΨ sq (2.32a) dt sdq 15
Page 1 and 2: POLITECHNIKA WARSZAWSKA WARSAW UNIV
Page 3 and 4: Contents Table of Contents Chapter
Page 5 and 6: Introduction Chapter 1 INTRODUCTION
Page 7 and 8: Introduction to surface-mounted mac
Page 9 and 10: Introduction vector control, which
Page 11 and 12: Introduction presented and studied.
Page 13 and 14: Modeling and control modes of PM sy
Page 17: Modeling and control modes of PM sy
Page 39 and 40: Voltage source PWM inverter for PMS
Page 57 and 58: Control methods of PM Synchronous m
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Direct Torque Control with Space Ve
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Sensorless Speed Direct Torque Cont
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DSP implementation of DTC-SVM contr
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Summary and closing conclusion Chap
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Appendices APPENDICES A1 Rotor and
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Appendices ⎡ ⎤ ⎢ 1 0 ⎥ ⎡K
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Appendices i(t1->t0)+=it1 it1: it1=
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Appendices A7 PWM technique - six s
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List of symbol List of symbols Symb
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References Books and PhD-Thesis 1.
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References 39. J.-I. Itoh, N. Nomur
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References 74. N. Ertugrul, P. Acar
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References 108. D. Świerczyński,
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