Proceedings of the Tomsk Polytechnic Institute Named after S. M. Kirov, Holder of the Order of the October Revolution and the Order of the Red Banner of Labor

Volume 284　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1974

STARTING OF AN SRRM WITH A SHORT-CIRCUITED WINDING ON THE ROTOR

A. A. Buimov, B. P. Targaneev, G. M. Goloshevsky, E. V. Kononenko

To meet the needs of industry for electric drives with a low rotational speed, electric motors with electromagnetic speed reduction are used. Differing in design and in operating principle, they have one common drawback—poor starting properties. These motors are started by means of various disconnecting and non-disconnecting, electrical and mechanical starting devices. The choice of starting device depends on many factors, such as the number of motor windings, the direction of rotor rotation, the type of voltage, etc. The main requirements imposed on starting devices are reliability and simplicity of construction, and the absence of sliding contacts.

Synchronous reluctance reduction motors (SRRMs) make it possible to use a short-circuited winding on the rotor as the starting device. The use of this winding is possible in motors with a ratio of stator and rotor teeth satisfying the equality \(z_2 = z_1 + 2p\), since only in this case do the direction of rotation of the rotor and that of the stator magnetic field coincide.

The additional torque of the starting device must have its maximum value with the rotor at standstill and decrease to zero at synchronous rotational speed. However, starting devices—except for mechanical devices and built-in starting electric motors—operate on the fundamental wave of the magnetic field, and at the nominal synchronous speed their torque is not equal to zero. In this case the magnitude of the total electromagnetic torque in synchronous operation increases, while the synchronization conditions may worsen, since under the action of the torque from the starting device the rotor accelerates and in most cases begins to rotate at a speed possible for the starting device. Disconnection of the starting device in this case is necessary, although it complicates the design of the machine and reduces the reliability of its operation.

A starting short-circuited rotor winding can be used to improve the starting of a synchronous reluctance reduction motor without disconnecting it in synchronous operation. By changing the value of the active resistance of the rotor winding, various starting characteristics can be obtained. However, in addition to the parameters of the short-circuited winding, other parameters also influence the starting of a synchronous reluctance reduction motor. Therefore, the investigation of starting

…it is advisable to carry out studies of the operating modes of the SRM using the complete system of differential equations.

The derivation of the system of equations describing the behavior of an SRM with allowance for the parameters of the short-circuited rotor winding is given in the literature [1, 2]. With variable rotor speed, this system of equations is nonlinear, and the study of transient electromechanical processes encounters certain difficulties. The simplest way to study them is by modeling on analog computers (ACs). The use of an AC requires a minimum time to obtain a solution and provides the necessary accuracy and visual clarity of the processes, since the dependences of interest can be obtained directly in the form of oscillograms.

The system of equations of an SRM in relative units and in a form convenient for modeling can be written as follows:

\[ p\psi_d=-U\sin\theta+\psi_q k_p\omega_p-ri_d; \]

\[ p\psi_q=U\cos\theta-\psi_d k_p\omega_p-ri_q; \]

\[ p\psi_{rd}=(k_p-1)\omega_p\psi_{rq}-r_r i_{rd}; \]

\[ p\psi_{rq}=(k_p-1)\omega_p\psi_{rd}-r_r i_{rq}; \]

\[ i_d=\frac{x_{rd}}{x_d x_{rd}-x_{ad}^2}\psi_d -\frac{x_{ad}}{x_d x_{rd}-x_{ad}^2}\psi_{rd}; \]

\[ i_q=\frac{x_{rq}}{x_q x_{rq}-x_{aq}^2}\psi_q -\frac{x_{aq}}{x_q x_{rq}-x_{aq}^2}\psi_{rq}; \]

\[ i_{rd}=\frac{x_d}{x_d x_{rd}-x_{ad}^2}\psi_{rd} -\frac{x_{ad}}{x_d x_{rd}-x_{ad}^2}\psi_d; \tag{1} \]

\[ i_{rq}=\frac{x_q}{x_q x_{rq}-x_{aq}^2}\psi_{rq} -\frac{x_{aq}}{x_q x_{rq}-x_{aq}^2}\psi_q; \]

\[ p\omega_p=\frac{1}{H}(\psi_d i_q-\psi_q i_d) +\frac{1}{H}\cdot\frac{k_p-1}{k_p}(\psi_{rd}i_{rq}-\psi_{rq}i_{rd})- \]

\[ -\frac{1}{H}k_M\omega_p-\frac{1}{H}M_c; \]

\[ p\theta=\omega_1-k_p\omega_p. \]

For specified parameters and voltage \(U\), this system of equations (1) consists of ten equations and contains ten variables \(\psi_d,\psi_q,\psi_{rd},\psi_{rq},i_d,i_q,i_{rd},i_{rq},\omega_p,\theta\). Time \(t\) is the independent variable.

The block diagram of the model that implements the operations and is constructed in accordance with equations (1) is shown in Fig. 1.

The presented model circuit makes it possible to study various operating modes of the SRM and to evaluate the influence of parameters on transient processes in the machine. By setting the transfer coefficients, the values of the active resistances of the stator and rotor windings, the values of the synchronous inductive reactances along the \(d\) and \(q\) axes, the mechanical constant of the rotating masses, and other parameters can be varied.

The use of a short-circuited rotor winding for starting an SRM is possible in the case when the asynchronous-torque curve has a special form. This means that the magnitude of the maximum asynchronous-

of the torque must be shifted toward negative values of the rotor speed. In this case the asynchronous torque will be greatest only at the beginning of starting and will decrease as the rotor speed increases. The need to reduce the asynchronous torque is due to the fact that, when the rotor reaches synchronous speed, the magnitude of the alternating component of the torque must be greater than the constant component. Otherwise, under the action of the asynchronous torque, the rotor will rotate at the speed usual for an induction motor.

Fig. 1. Structural diagram of the SRM model

It is known from the theory of induction motors that a mechanical characteristic with a large value of the critical slip can be obtained by increasing the active resistance of the rotor winding. Therefore, for starting an SRM, the short-circuited rotor winding is made of materials with high specific resistance or has a small bar cross section.

Neglecting electromagnetic transients, the rotational torque of an SRM with a rotor winding can be represented in the form of two components

\[ M = M_m \sin 2(\theta - \theta_0) + M_n . \tag{2} \]

The first component of the torque is a variable quantity depending on the angle \(\Theta\), which in the steady synchronous mode determines the load magnitude, and in other modes—the position of the \(q\)-axis relative to the voltage vector. The amplitude of the alternating component \(M_m\) depends mainly on the magnitude of the synchronous torque of the motor without a rotor winding. The magnitude of the constant component \(M_n\) is determined by the parameters of the short-circuited rotor winding and represents the asynchronous torque. Therefore, although the rotor winding affects the alternating component of the torque and the active resistance of the stator winding affects the constant component, in order to simplify terminology we shall henceforth call the alternating component the synchronous torque, and the constant--

—reluctance–asynchronous. And when analyzing the influence of motor parameters on starting, the question considered will be how particular parameters affect the magnitude of the synchronous and asynchronous torques.

The alternating component of the torque of a synchronous reluctance motor with the rotor at standstill varies at twice the frequency of the supply voltage, as in ordinary synchronous reluctance motors. As the rotor speed increases, the frequency of the torque pulsations decreases and becomes equal to zero at the synchronous rotational speed of the rotor. An increase in the rotor speed above synchronous is accompanied by an increase in the frequency of the torque pulsations.

The constant component of the torque decreases as the speed increases and becomes equal to zero at a rotor speed equal to the rotational speed of the magnetic field (if the influence of the active resistance of the stator winding is not taken into account).

The study of the influence of parameters on the starting of a synchronous reluctance motor gives an idea of the quantitative and qualitative changes in the starting process. The quality of starting should be assessed by the time during which the rotor reaches synchronous speed, by the possibility of pulling the rotor into synchronism, and by the duration of the damping of oscillations of the rotor rotational speed after pull-in to synchronism. In studying the influence of parameters on the starting process, the active resistances of the stator and rotor windings were varied over a wide range.

Fig. 2. Calculated oscillograms of starting of a synchronous reluctance motor
for \(H=5\) el. sec, \(\dfrac{x_d}{x_q}=1.4\),
a — \(r_r=3.6\),
b — \(r_r=7\)

Analysis of the calculated and experimental oscillograms shows that changing the value of the active resistance of the stator winding within practical limits has virtually no effect on the acceleration time of the rotor to synchronous speed or on the pulling of the rotor into synchronism. The duration of damping of speed oscillations after the rotor has been pulled into synchronism increases as the active resistance of the stator winding increases.

The active resistance of the rotor winding has a significant influence on the starting process of a synchronous reluctance motor. At small values of the resistance of the rotor winding, the asynchronous torque of the motor increases, and the starting process proceeds as in an ordinary asynchronous motor. The action of the synchronous torque appears only in the fact that pulsations appear in the torque and speed curves.

An increase in the active resistance of the rotor winding is accompanied by a decrease in the asynchronous torque, and pull-

… the rotor of the SRRM being pulled into synchronism. Figure 2 presents calculated oscillograms of the starting of an SRRM, and Fig. 3 experimental ones. From these oscillograms it may be concluded that, with an increase in the active resistance of the rotor winding, the time in which the rotor reaches subsynchronous speed increases, as does the duration of the damping of speed oscillations after the rotor has been pulled into synchronism.

The process of pulling the rotor into synchronism imposes the principal limitation on reducing the active resistance of the rotor winding and, consequently, on increasing the asynchronous torque. For reliable

Fig. 3. Experimental oscillograms of SRRM starting
at $H = 10$ el. sec, $\dfrac{x_d}{x_q} = 1.4$, a — $r_r = 5$, b — $r_r = 10$

starting of the motor at no load, the active resistance of the rotor winding must be increased by a factor of 5–10 in comparison with the permissible values in the established synchronous regime, all other parameters being equal [3].

Operation in transient regimes and the starting of an SRRM depend substantially on the magnitude of the moment of inertia $H$ (or the mechanical time constant of the rotating masses). Its magnitude is determined both by the design of the motor itself and by the driven mechanism. From the calculated and experimental oscillograms (Figs. 4, 5) it is seen that, as $H$ increases, the time of acceleration of the rotor to synchronous speed increases. This can be explained by the fact that more energy is required to accelerate the rotor with increased flywheel masses to synchronous speed. At constant power, the acceleration time increases.

With an increase in the mechanical constant of the rotating masses, pull-in of the rotor into synchronism may become impossible, and it accelerates to a steady asynchronous speed. This is due to the fact that, as the rotor speed approaches synchronous speed, in addition to the load and friction torques, positive alternating and constant components of the electromagnetic torque act on the rotor. In this case the rotor accelerates and an excess dynamic torque is created, proportional to \(H\) and to the rotor acceleration \(\dfrac{d\omega_p}{dt}\). At \(\Theta=0\) the alternating component of the torque is also equal to zero. However, the dynamic torque and

Fig. 4. Calculated oscillograms of starting of an SRM at
\(r_r=4,\ \dfrac{x_d}{x_q}=1.4\),
a — \(H=5\) el. sec, b — \(H=15\) el. sec, c — \(H=25\) el. sec

the constant component of the electromagnetic torque remain positive and continue to act on the rotor in an accelerating manner. The rotor speed then exceeds synchronous speed. The angle \(\Theta\) begins to change from zero toward negative values, and the alternating component of the torque also becomes negative. Under the action of the negative torque the rotor speed decreases. If, for negative values of the angle \(\Theta\), the speed does not fall below synchronous, then the rotor is not pulled into synchronism and rotates at asynchronous speed. When the speed decreases to synchronous or below, the rotor is pulled into synchronism and the starting process ends with oscillations of the speed relative to synchronous speed.

The duration of damping of the rotor-speed oscillations after pull-in into synchronism increases with the growth of the mechanical constant of the rotating masses. The oscillation frequency decreases in this case.

Numerous calculations and experiments show that a short-circuited rotor winding is not a universal starting means for an SRM. Increasing the starting asynchronous torque by reducing the active resistance of the rotor winding to \(r_r=10\text{—}15\) improves motor starting at a resisting torque on the shaft equal to

Fig. 5. Experimental oscillograms of the starting of an SRM for \(r_r=10\), \(\dfrac{x_d}{x_q}=1.5\):
\(a\) — \(H=5\) electrical sec;
\(b\) — \(H=7\) electrical sec;
\(c\) — \(H=10\) electrical sec.

40–50% of the nominal value. With a further decrease in the resistance of the rotor winding, starting improves at large values of the load torque, but at the same time starting at no load and at small loads becomes impossible.

REFERENCES

1. P. Yu. Kaasik, B. V. Sidelnikov. Method of mathematical analysis of transient regimes of subsynchronous reluctance motors. Transactions of Higher Educational Institutions of the Lithuanian SSR, “Electronics and Automation,” VI, 1970.

1. A. A. Buimov, E. V. Kononenko. Basic equations of synchronous reluctance reduction motors. Izvestiya TPI, vol. 229, 1972.

2. A. A. Buimov, G. M. Goloshevsky, E. V. Kononenko. Operation of an SRRM with a short-circuited winding on the rotor in the synchronous steady-state mode. Present collection.