V. Subrahmanyam

On the steady state analysis of a current fed induction motor

ContentsThe performance equations of an induction motor operating on a current source inverter are derived using a stationary reference frame of two of the three phases. The equations are well suited for simulation of a current controlled inverter fed induction motor on a digital computer using well known numerical methods of integration. A method is presented for the steady state analysis via state transition signal flow graph. This method is found to offer several advantages over the methods available in the literature using state space techniques. The steady state solution of the equations can be used to show that the rotor flux varies sinusoidally and it induces a sinusoidal voltage in the stator phases accompanied with voltage spikes during commutation.ÜbersichtFür einen Asynchronmotor, der über einen Umrichter mit eingeprägtem Strom arbeitet, werden die Gleichungen in einem auf zwei Strangachsen bezogenen Koordinatensystem aufgestellt. Diese sind für die Simulation des Motors unter Benutzung bekannter Integrationsmethoden auf einen Digitalrechner gut geeignet. Es wird eine Methode zur Untersuchung des stationären Zustands mit Hilfe von Signalflußdiagrammen vorgelegt. Diese Methode weist gegenüber der Darstellung im Zustandsraum einige Vorteile auf. Anhand der Lösungen wird gezeigt, daß der Fluß sich sinusförmig ändert und in den Ständersträngen sinusförmige Spannungen mit überlagerten Spitzen induziert.

On the analysis of induction motor with square wave currents in the rotor via state transition signal flow graph technique

The performance equations of an induction motor are given in the rotor reference frame of two of the three phases. These equations are used to analyse the steady state performance of an induction motor with square wave currents in the rotor and sinusoidal voltages on the stator. A closed form solution for stator flux linkages in the time domain is obtained using state transition signal flow graph technique. It is found that the stator current is essentially sinusoidal superimposed by slip dependent harmonics. The torque developed by the motor has pulsations both at six times and twelve times slip frequency.ÜbersichtFür einen Asynchronmotor werden die Spannungsgleichungen in einem auf zwei Strangachsen bezogenen läuferfesten Koordinatensystem aufgestellt. Diese Gleichungen werden zur Analyse des stationären Verhaltens bei rechteckförmigen Strömen im Läufer und sinusförmigen Spannungen am Ständer angewendet, und führen über Signalflußdiagrammdarstellung zu einer geschlossenen Lösung. Der Ständerstrom hat schlupfabhängigen Schwingungen. Das Drehmoment enthält Schwankungen, die Komponente sechster und zwölfter harmonischen Ordnung des Schlupfes entsprechen.

ON THE UTILITY OF SIGNAL FLOW GRAPHS IN THE ANALYSIS OF CURRENT CONTROLLED INDUCTION MOTOR

A novel method is presented for the analysis of a current controlled induction motor via the state transition signal flow graph. The state transition matrix is computed in a simple, elegant and straightforward fashion by this method, with the result the solution can be obtained in a closed form. The solution automatically takes into account of the effect of different inputs thereby eliminating the necessity of evaluating the convolution integrals. Computationally too, this method is found to be superior to the other methods, as it requires lesser C.P.U. time. The solution obtained can be used to show that the locus of the rotor flux vector under steady state conditions is a circle and the rotor flux induces a sinusoidal voltage in the stator phases accompained with voltage spikes during commutation intervals, although the stator current is nonsinusoidal. It can also be shown that the motor torque pulsates with sixth harmonic oscillations, whose relative magnitude increases with the increase in rotor speed. The current-fed induction motor can also be shown to exhibit a Shunt type speed-torque characteristic by suitably adjusting the stator frequency.

On the Utility of Signal Flow Graphs in the Analysis of Current Controlled Induction Motor

Summary A novel method is presented for the analysis of a current controlled induction motor via the state transition signal flow graph. The state transition matrix is computed in a simple, elegant and straightforward fashion by this method, with the result the solution can be obtained in a closed form. The solution automatically takes into account of the effect of different inputs thereby eliminating the necessity of evaluating the convolution integrals. Computationally too, this method is found to be superior to the other methods, as it requires lesser C.P.U. time. The solution obtained can be used to show that the locus of the rotor flux vector under steady state conditions is a circle and the rotor flux induces a sinusoidal voltage in the stator phases accompained with voltage spikes during commutation intervals, although the stator current is nonsinusoidal. It can also be shown that the motor torque pulsates with sixth harmonic OSCillations, whose relative magnitude increases with the increase in rotor speed. The current-fed induction motor can also be shown to exhibit a shunt type speed-torque characteristic by suitably adjusting the stator frequency.

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

ContentsD-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 Parks 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.ÜbersichtZur 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.

On the performance characteristics of a synchronous motor fed from a voltage source inverter

ContentsUsing two axis model the steady state characteristics of a voltage controlled synchronous motor drive are investigated for different modes of operation based on signal flow graph technique. The input voltages are assumed to be quasi square wave. The analysis shows that depending upon the mode employed the machine can be made to possess shunt, series or mixed characteristic. The torque developed is of pulsating nature. All the modes of operation have sixth harmonic pulsations which are roughly 20 percent of the mean value. A voltage fed motor is found to have reduced torque pulsations when compared to a current fed one with the same flux levels.ÜbersichtAufgrund des Signalfußdiagramms wird das stationäre Verhalten des Spannungsgespeisten Synchronmotorantriebs bei rechteckförmiger Spannung für verschiedene Betricbsarten der Maschine untersucht. Dafür werden die Gleichungen der Maschine auf der Basis des Zweiachsenmodells aufgestellt. Die Untersuchungen zeigen, daß das Drehmoment Schwankungen hat, deren Amplitude um etwa 20 Prozent des Mittelwerts liegen. Weiter wird gezeigt, daß diese Schwankungen kleiner als die des stromgespeisten Synchronmotors sind. Je nach der Betriebsart besitzt die Maschine eine Drehmoment-Drehzahl Kennlinie, die der des Nebenschluß- oder Reihenschlußmotors ähnlich ist.