STUDY OF SELF-OSCILLATION OF A SYNCHRONOUS RELUCTANCE MOTOR ON AN ANALOG COMPUTER

E. V. Kononenko, A. F. Fink

(Presented by the scientific seminar of the departments of electrical machines and general electrical engineering)

When designing a synchronous reluctance motor (SRM), special attention must be paid to investigating the stability of its operation. It is known from practice that in some cases of SRM operation, self-excited oscillations of the rotor arise. Such a disturbance of stability is known in the literature under the name self-oscillation.

The onset of self-oscillation is possible when the active resistance of the stator winding is relatively large, since in this case negative damping arises. During self-oscillation the amplitude of the rotor oscillations increases sharply, and under certain conditions the motor falls out of synchronism. The process of self-oscillation has been considered previously in the literature [1]. However, in doing so the authors limited themselves to an investigation of stability “in the small,” using a linearized system of equations. Thus the influence of the parameters was determined only on the boundary of stable SRM operation, while how the motor behaves in the region of large oscillations, and how the frequency and amplitude of the oscillations change, remained unclear.

In the present work, assuming that the SRM operates at constant line voltage, the influence of active resistance and the inertia constant on the amplitude and frequency of oscillations during no-load operation of the motor is considered, and the boundary of stable operation is also determined. The analysis of self-oscillation was carried out on the basis of the Park–Gorev equations [2].

The investigations are based on a method for calculating transient electromechanical processes of an SRM on an EMU-10 analog computer [3]. According to this method, operation of the motor is considered stable if the amplitude of oscillations of the angle $\Theta$ does not exceed $0.05^\circ$. The influence of the parameters on self-oscillation was investigated in the plane of two parameters. The remaining parameters were taken as constant. Figure 1 gives an oscillogram characterizing the process of growth of the oscillation amplitude when active resistance is introduced into the stator-winding circuit. The solution is represented in the phase coordinate system $S=f(\Theta)$. The resulting limiting cycle of oscillations is determined by the parameters $S_{\max}=\pm 0.05$; $\Delta\Theta_{\max}=\pm 25^\circ$. The calculation was performed for an SRM of power 4 kW, $n=1500$ rpm, having the following parameters:

\[ x_d=2.33;\quad x_q=0.45;\quad x_{ad}=2.23;\quad x_{aq}=0.35;\quad x_{rd}=2.31;\quad x_{rq}=0.428; \]

\[ r_{rd}=0.0557;\quad r_{rq}=0.0428;\quad T_j=0.5\ \text{s};\quad r=0.3. \]

Fig. 1. Phase trajectory during self-oscillation of an SRM.

As the calculations showed, when the motor operates at no load, the magnitude of the active resistance of the stator winding and the inertia constant have a great influence on the amplitude and frequency of the oscillations.

As follows from the curves (Fig. 2), with an increase in the active resistance of the stator winding and a decrease in the inertia constant, the amplitude of the rotor oscillations increases sharply, and the motor falls out of synchronism.

The frequency of the rotor oscillations, as can be seen from Fig. 3, when self-oscillation arises, increases to a maximum value, and then, as \(r\) increases, decreases almost linearly.

Fig. 2. Influence of the active resistance of the stator winding and the inertia constant on the oscillation amplitude.

Fig. 3. Effect of the active resistance of the stator winding and of the inertia constant on the oscillation frequency.

The studies also made it possible to establish that more heavily loaded motors are less prone to self-oscillation. Figure 4 presents the boundaries of stable operation of the SRM, plotted in the plane of two parameters \(M=f(r)\), for various inertia constants. Analysis of the results obtained makes it possible to establish that an increase in the resisting torque on the shaft and in the inertia constant expands the region of stable operation.

Fig. 4. Effect of the motor load and inertia constant on the location of the boundary of the stable-operation region.

To check the accuracy of the calculation of the influence of the parameters on the self-oscillation process, experimental studies were carried out.

for a synchronous reluctance motor with a power of 4 kW and 1500 rpm, operating from a constant-voltage network through series-connected active resistances. The motor had the following parameters:

\[ x_d=2.06;\quad x_q=0.48;\quad x''_d=0.15;\quad x''_q=0.24;\quad T_d=54.2\ \text{elec. sec.}; \]
\[ T_q=11.9\ \text{elec. sec.};\quad T_j=0.62\ \text{sec.} \]

In this case, the boundary of stable operation of the motor was determined as a function \(M=f(r)\). The method for determining this dependence was as follows. An additional active resistance of such magnitude was introduced into the stator-winding circuit of the synchronous reluctance motor that stable undamped oscillations arose. By smoothly increasing the load on the motor shaft, the disappearance of the oscillations was achieved. An electromagnetic brake served as the motor load. The onset of oscillations of the rotational speed was assessed visually, by the stroboscopic method. An ST-type strobotachometer was synchronized from the network through a frequency divider so that no double image would arise. This method makes it possible, more accurately than by the change of current in the stator circuit, to record the onset of oscillations of the synchronous reluctance motor and to note deviations of the rotor motion from synchronous speed of less than one degree.

The investigations carried out make it possible to draw the following conclusions:

1. In the operation of a synchronous reluctance motor, self-excitation is inadmissible, since the amplitude of rotor oscillations increases sharply, which may lead to falling out of synchronism.

2. The proposed method makes it possible, with sufficient simplicity and accuracy, to select the parameters of a synchronous reluctance motor that exclude self-excitation.

REFERENCES

1. E. V. Kononenko, A. L. Kislitsyn, A. F. Fink. Study of self-oscillations of a synchronous reluctance motor during operation from a regulated generator. Izvestiya TPI, vol. 132, 1964.

2. E. V. Kononenko, A. F. Fink. Influence of parameters on the process of pulling into synchronism. Published in the present collection.

3. E. V. Kononenko, A. F. Fink. Application of the EMU-10 computing machine for investigating transient electromechanical processes in synchronous reluctance motors. Izvestiya TPI, vol. 160, 1966.