Contents
The paper describes how a general-purpose electronic analogue computer and the phase space method may be used to solve the transient stability problem of a synchronous machine connected to an infinite bus. In the machine analysis emphasis is placed on the effects of the flux-decay, damping power and saliency during transient disturbances. The swing equation of the machine is a third-order nonlinear differential equation. In the paper the phase plane method is extended to this third-order nonlinear swing equation and the system trajectories, the boundary surface of asymptotic stability and the critical clearing time of the system have been obtained by the use of an analogue computer. A numerical example is given.
Übersicht
Diese Arbeit beschreibt die Lösung des Problems der transienten Stabilität für Synchronmaschinen in starren Netzen mittels Simulation auf Analogrechnern und die Methode der Phasenvariablen. Besonders wird der Flußabfalleffekt, die Dämpfungsleistung und die Polausprägung bei transienten Störungen berücksichtigt. Eine nichtlineare Differentialgleichung dritter Ordnung beschreibt das dynamische Verhalten. Die Phasenvariablenmethode wird erweitert auf diese nichtlineare Differentialgleichung dritter Ordnung und es werden auf dem Analogrechner die Systemtrajektoren, die Grenzfläche der asymptotischen Stabilität und die kritische Löschzeit bestimmt. Ein numerisches Beispiel wird angegeben.
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Abbreviations
- δ:
-
rotor angle with respect to a synchronously rotating reference
- δ0, δ s :
-
value of δ at the prefault and postfault stable-equilibrium point respectively
- δ u :
-
value of δ at the saddle point
- M :
-
inertia constant of the machine
- P i :
-
mechanical input power
- \(P_d \frac{{d\delta }}{{dt}}\) :
-
damping power
- x d ,x q :
-
direct-axis and quadrature-axis synchronous reactances
- x′ d :
-
direct-axis transient reactance
- x 12 :
-
total reactance between generator terminals and infinite bus
- x l :
-
reactance of each transmission line
- T′ d0 :
-
open-circuit transient-time constant of the generator
- E′ q :
-
instantaneous voltage proportional to field flux linkage
- E ex :
-
exciter voltage referred to armature circuit
- E ∞ :
-
voltage of infinite bus
- t c1 :
-
clearing time
- t cr :
-
critical clearing time
- λ:
-
measure of the distance of the fault from the machine terminals
References
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Miles, G. J.: Analysis of overall stability of multimachine power systems. Proc. IEE, paper No. 3715 S (1961) 203
Levite: Methods for solving engineering problems using analog computers. New York: Mc-Graw Hill 1964
Machias, A. V.; Papadias, B. C.: Transient stability of an a.c. generator with governor action by use of the phase space method and an analog computer. Arch. Elektrotech. 67 (1984) 9–16
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Yokogawa electric works, textbook of analog computer ACS 11216
Jennes; Smith; Wolford: Analog and digital computer methods in engineering analysis. Seranton, Int. Textbook Comp. 1964
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Machias, A.V., Papadias, B.C. Analogue computer simulation and phase space study of a synchronous machine with flux-decay effect transient stability. Archiv f. Elektrotechnik 69, 61–68 (1986). https://doi.org/10.1007/BF01573981
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DOI: https://doi.org/10.1007/BF01573981