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

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4. Direct Power and Torque Control with Space Vector Modulation – DPTC-SVM VSR I dc I load VSI U L VM U dc I c U S 3 ~ IM Fig.4. 1. Configuration of the AC/DC/AC converter-fed induction motor drive with PF loop The mathematical models of the VSR and VSI are given in Chapter 2 and description of the DPC-SVM, and DTC-SVM have been presented in Chapter 3. Here the whole system with PF will be discussed and studied. Note again that, the coordinates system for control of the VSR is oriented with VF vector. Therefore, I Lxc is set to zero to meet the unity power factor – UPF condition. With this assumption the VSR input power can be calculated as: P VSR 3 ( I LxU px + I LyU py ) = I LyU py 3 = (4. 1) 2 2 Under steady states operation I Ly = const. and, with assumption that resistance of the input choke is R = 0 , the following equation can be written: 3 PVSR = I LyU Ly (4. 2) 2 On the other hand the power consumed/produced by the VSI-fed IM is defined by: VSI ( I U I U ) 3 P = + 2 Sx Sx Sy Sy (4. 3) Another form of the above equations can be derived based on power Eq. (3.51) in Subsection 3.3.2 where is clearly seen that the active power of the VSR is proportional to the virtual torque - VT. Therefore, based on Subsection 3.3.2, the Eq. (4.1) can be written that: 3 ( Ψ LxI Ly −Ψ LyI Lx ) = ωLΨ LxI Ly 3 PVSR = ωL (4. 4) 2 2 On the VSI-fed IM side electromagnetic power of the motor is defined by: P = Ω (4. 5) e M e m Taking into account Eq. (2.39) yields: 70
4. Direct Power and Torque Control with Space Vector Modulation – DPTC-SVM mS Pe = pb ΩmΨ SxISy (4. 6) 2 Moreover, it can be assumed (neglecting power losses) that electromagnetic power of the IM is equal to an active power delivered to the motor P p m 2 Ω Ψ I P = P e VSI , hence: S VSI = b m Sx Sy (4. 7) But this is not sufficient assumption because of power losses P losses in the real system, so it should be written: m 2 S P VSI = pb ΩmΨ SxI Sy + P losses Further, please consider a situation at stand still ( = 0) m (4. 8) Ω when nominal torque is applied. In such a case the electromagnetic power will be zero but the IM power P VSI will have a significant value. Estimation of this power is quite difficult, because the parameters of the IM and power switches are needed. Hence, for simplicity of the control structure a power estimator based on command stator voltage current I S will be taken into consideration: U Sc and actual VSI ( I U I U ) 3 P = + 2 Sx Sxc Sy Syc (4. 9) 4.2.1. Analysis of the Power Response Time Constant Based on Eq. (3.68) the time constant delay of the VSR response T IT is determined. With assumption that power losses of the converters can be neglected, power tracking performance can be expressed by: VSR () PVSRc + sTIT P 1 s = (4. 10) 1 Similarly for the VSI can be written: VSI () PVSIc + sTIF P 1 s = (4. 11) 1 Where, T IF is the equivalent time constant of the VSI step response. 4.2.2. Energy of the DC-link Capacitor The DC-link voltage can be described as (for more detail see Section 2.5.2): 71
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POLITECHNIKA WARSZAWSKA WARSAW UNIV
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Acknowledgements The work presented
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Contents 4.2.2. Energy of the DC-li
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Chapter 1 1. Introduction 1.1. AC/D
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1. Introduction Tab. 1. 1. Current
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1. Introduction DC-link voltage to
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1. Introduction then nominal speed
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1. Introduction [69]. From that tim
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Chapter 2 2. Voltage Source Convert
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2. Voltage Source Converters - VSC
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Page 25 and 26: 2. Voltage Source Converters - VSC
Page 39 and 40: Chapter 3 3. Vector Control Methods
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Page 99 and 100: Chapter 5 5. Passive Components Des
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Page 111 and 112: Chapter 6 6. Simulation an Experime
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6. Simulation and Experimental Resu
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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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