Direct Power and Torque Control of AC/DC/AC Converter-Fed ...

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2. Voltage Source Converters – VSC 2.4.1. IM Mathematical Model in Rotating Coordinate System with Arbitrary Angular Speed The model of the IM in natural ABC coordinates is very complicated. Therefore, in order to reduce the set of equations (Appendix A.1.3) from 12 to 4, the complex space vectors are used. Moreover, based on transformation into a common rotating coordinate system with arbitrary angular speed Ω K and referring rotor quantities to the stator circuit, a following set of equations can be written [63]: Voltage equations: U U dΨ dt SK , SK = RSI SK + + jΩ K Ψ SK (2.5) dΨ dt ( Ω − p Ω ) Ψ , rK rK = RrI rK + + j K b m rK (2.6) Flux-currents equations: Ψ = L I + L I (2.7) SK rK S r SK rK M M rK , Ψ = L I + L I (2.8) SK , And motion equation: dΩ dt 1 ⎡ ⎢ p J ⎣ m 2 ⎤ ( I ) − M ⎥ ⎦ Im Ψ * m S = b SK SK L (2.9) 2.4.2. IM Model in Stationary αβ Coordinates Adopting a system of coordinates rotating with the angular speed Ω = 0 , the set of induction motor vector equations (2.5) and (2.6) may be rewritten as: dΨS U S = RSI S + , (2.10) dt U r dΨ r = RrI r + − jpbΩ mΨ r , (2.11) dt While, flux-current equations (2.7) and (2.8), and motion equation (2.9) remain unchanged. Knowing that, total leakage factor is expressed as: Where: L L L − L w 1 L L L L L L gL L 2 2 σ = 1− M = S r M = = (2.12) S r S r S r S r K 16
2. Voltage Source Converters – VSC 1 1 g = = (2.13) w L L − L S r 2 M Equations (2.7) and (2.8) can be rewritten: I S Lr LM = ΨS − Ψr, (2.14) w w Lr LM Ir = Ψr − ΨS , w w (2.15) In the case of a squirrel cage motor U = 0 . Therefore, the block diagram in stationary αβ coordinates can be constructed as in Fig. 2. 7. [16]. r R S U Sα + − 1 s Ψ S α L R + − g I S α L M − U Sβ + − 1 s R S Ψ Sβ L R STATOR + L M − g I Sβ m s p b 2 M e − M L − − R r 1 s Ψ r L S + L M − g I rα 1 sJ Ω m p b L M + − 1 s R r Ψ r αβ L S ROTOR + − g I rβ 1 1 g = = w L L − s r 2 L M Fig. 2. 7. Model of an induction motor - in stationary αβ coordinates 17
Page 1 and 2: POLITECHNIKA WARSZAWSKA WARSAW UNIV
Page 3 and 4: Acknowledgements The work presented
Page 5 and 6: Contents 4.2.2. Energy of the DC-li
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Page 13 and 14: 1. Introduction then nominal speed
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3. Vector Control Methods of AC/DC/
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Chapter 4 4. Direct Power and Torqu
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4. Direct Power and Torque Control
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Chapter 5 5. Passive Components Des
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5. Passive Components Design 5.2.2.
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Chapter 6 6. Simulation an Experime
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Chapter 7 7. Summary and Conclusion
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7. Summary and Conclusion • easy
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References [18] G. Buja, M. P. Kazm
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References [58] J. G. Kassakian, M.
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References [96] H. Mao, D. Boroyevi
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References [133] A. Tripathi, A. M.
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References [167] M. Jasiński, D.
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Symbols Employed I L - I LA I r - r
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Symbols Employed U pA ,U pB , U pC
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A. Appendices A.1. Space vector in
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Appendices In the special condition
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Appendices A.2. Coordinate Transfor
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Appendices S 3 UI 2 m s * * = = - a
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Appendices Tab. A. 4. 3. Date of th
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Appendices LINE L1 L C F Fig. A. 4.
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Appendices Tab. A. 4. 6. Data of th
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