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Stability analysis of a variable frequency induction motor usingD-decomposition method

Stabilitätsuntersuchung eines mit variabler Frequenz gespeisten Asynchronmotors unter Verwendung der Methode derD-Zerlegung

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Contents

D-decomposition technique is used to determine the stability/instability regions of a variable frequency induction motor. The technique is more simple, straightforward and elegant when compared to the conventional classical methods like root locus technique, Nyquist criterion and Routh-Hurwitz criterion. The machine equations are used in Park's vector notation which reduces the order of the system equation to three. The equation, however contains complex coefficients. The linearised model based on small displacements is used in the stability analysis to investigate the effects of variation of machine parameters such as stator and rotor resistances, leakage reactances etc. on the stability regions of the motor.

Übersicht

Zur Bestimmung der Stabilitätsgrenzen eines mit variabler Frequenz gespeisten Asynchronmotors wird die Methode derD-Zerlegung verwendet. Diese zeichnet sich gegenüber dem klassischen Verfahren wie dem Wurzelortsverfahren, dem Nyquist-Kriterium und dem Routh-Hurwitz-Kriterium durch Einfachheit und Direktheit aus. Infolge der Verwendung der Parkschen Transformierten stellen sich die Spannungsgleichungen der Maschine lediglich als System dritter Ordnung, jedoch mit komplexen Koeffizienten dar. Das Modell wird für kleine Abweichungen linearisiert; danach erfolgt die Untersuchung der Auswirkungen von Parameteränderungen, u. a. der Widerstände von Stator und Rotor sowie der Streureaktanz, auf den Stabilitätsbereich des Motors.

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Abbreviations

f :

operating frequency

fb :

rated frequency

fr :

ratio of operating frequency to rated frequency

H :

inertia constant

i ds i qs :

two axis components of stator currents

i s :

Park's vector of stator currents

i dr ,i qr :

two axis currents of rotor currents

i r :

Park's vector of rotor currents

J :

moment of inertia

K :

gain constantP/J

l :

a parameter

L s ,L r :

self inductances of stator and rotor respectively

L m :

mutaual inductance

P :

pairs of poles

p :

differential operator d/dt

R s ,R r :

stator and rotor resistances per phase respectively

T d ,T L :

electromagnetic torque developed and load torque respectively

u ds ,u qs :

two axis components of stator voltages

u s :

Park's vector of stator voltages

u dr ,u qr :

two axis components of rotor voltages

u r :

Park's vector of rotor voltages

ψds, ψqs :

two axis components of stator flux linkages

ψs :

Park's vector of stator flux linkages

ψdr, ψqr :

two axis components of rotor flux linkages

ψr :

Park's vector of rotor flux linkages

ωs :

synchronous angular velocity

ωr :

rotor angular velocity

ωr0 :

rotor angular velocity at an operating point

Ω:

angular frequency used in the frequency domain plotting

σ:

leakage coefficient 1−L 2 m /(L s L r )

References

  1. Rogers, G. J.: Linearised analysis of induction motor transients. Proc. IEE 12 (1965) 1917–1926

    Google Scholar 

  2. Nelson, R. H.; Lipo, T. A.; Krause, P. C.: Stability analysis of a symmetrical induction machine. IEEE Trans. Power App. Syst., PAS 88 (1969) 1710–1717

    Google Scholar 

  3. Bedford, R. E.; Padhye, S. S.: Computational techniques in determining stability limits of inverter-fed induction motor, J. Inst. Eng. (India) (1975)

  4. Jordan, H.; Müller, J.; Seinsch, O. H.: Über elektromagnetische und mechanische Ausgleichvorgänge bei Drehstromantrieben. Wiss. Ber. AEG Telefunken 52 (1979) 263–270

    Google Scholar 

  5. Jordan, H.; Kulig, T. S.: Kopplung elektromagnetischer und mechanischer Systeme in Elektroantrieben, Teil 2. Dynamisches Verhalten von Asynchronmaschinen, Siemens Forsch. Entwicklungsber. 11 (1982) 133–138

    Google Scholar 

  6. Lawrenson, P. J.; Bowes, S. R.: Generalisation ofD-decomposition techique. Proc. IEE 116 (1969) 1463–1470

    Google Scholar 

  7. Lawrenson, P. J.; Bowes, S. R.; Stephenson, J. M.: Efficient application ofD-decomposition technique to determine stability boundaries for multiparameter system, with particular reference to induction machines. Electron Lett. 4 (1968) 435–437

    Google Scholar 

  8. Lawrenson, P. J.; Bowes, S. R.: Stability of reluctance motors. Proc. IEE 118 (1971) 356–369

    Google Scholar 

  9. Novotny, D. W.: Steady state performance of inverterfed induction machines by means of time domain complex variables. IEEE Trans. Power App. Syst., PAS 95 (1976) 927–935

    Google Scholar 

  10. Subrahmanyam, V.; Subbarayudu, D.; Rao, M. V. C.: Analysis of inverter-fed induction motor via state transition signal flow graph technique. Proc. IEE 124 (1976) 259–260

    Google Scholar 

  11. Subrahmanyam, V.; Subbarayudu, D.: Steady state analysis of an induction motor fed from a current source inverter using complex state (Park's) vector. Proc IEE 126 (1979)

  12. Lipo, T. A.; Cornell, E. P.: State variable steady state analysis of a current controlled induction motor drive. Conf. Rec. IEEE IAS (1975)

  13. Charlton, W.: Matrix methods for the steady state analysis of induction motors. Proc. IEE 120 (1973) 363–364

    Google Scholar 

  14. Kovacs, K. P.; Racz, I.: Transiente Vorgänge in Wechselstrommaschinen. Ungar. Akad. Wiss., Budapest 1959

    Google Scholar 

  15. Neimark Yu, I.: Determination of values of parameters for which an automatic control system is stable. Autom. Telech. (1948) 190–203

  16. Aizermann M. A.: Theory of automatic control. London: Pergamon press 1961

    Google Scholar 

  17. Mellitt, B.: The ANSI Fortran Program DDC2 forD-decomposition. Int. Commun., Dept. Electr. Electron. Eng., Univ. Birmingham

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Dar-es-Salaam, P.O. Box 35131, Dar-es-Salaam, Tanzania

    M. J. Mwandosya

  2. Department of Electrical Engineering, Indian Institute of Technology, 600036, Madras, India

    V. Subrahmanyam

  3. Tanzania Railways Corporation, Dar-es-Salaam, Tanzania

    M. R. Mohamed

Authors
  1. M. J. Mwandosya
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  2. V. Subrahmanyam
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  3. M. R. Mohamed
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Mwandosya, M.J., Subrahmanyam, V. & Mohamed, M.R. Stability analysis of a variable frequency induction motor usingD-decomposition method. Archiv f. Elektrotechnik 68, 345–353 (1985). https://doi.org/10.1007/BF01573585

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