DYNAMICS OF FREQUENCY REVERSAL OF AN ASYNCHRONOUS MOTOR

V. I. PANTELEEV, B. P. SOUSTIN

(Presented by the Scientific and Technical Seminar of the Scientific Research Institute of AEM)

At the present time the dynamics of frequency starting of an asynchronous motor (a.m.) has been investigated fairly completely, although most often the drive must be reversible. In this connection there arises the need to investigate the dynamics of frequency reversal, taking into account electromagnetic transient processes; however, in the literature there are no works devoted to this question. Evaluation of the reversal dynamics from static mechanical characteristics, or from the characteristics of reversal by switching the phase sequence, leads to incorrect conclusions because a number of features that occur during frequency reversal of an a.m. are not taken into account.

The aim of the present work is to clarify the features of the dynamics of frequency reversal and to investigate the influence on it of the rate of change of frequency.

Frequency reversal of an a.m. is a process that necessarily begins with a nondecayed field. Nevertheless, the character of the variation of rapidity, smoothness as a function of the rate of frequency change, as well as the general physical picture of the processes, can be considered more simply and clearly for reversal with a decayed field. Therefore, reversal with a decayed field is investigated using an analog computer.

Features of frequency reversal of an a.m.

It is known that reversal of an a.m. by switching the phase sequence (for brevity we shall hereafter call it reversal by switching) begins at a value of the relative slip \(s = 2\), or close to it. In this connection it is recommended [1], when investigating reversal on an analog model, to use a.m. parameters corresponding to \(s = 2\). In frequency reversal, at the initial moment of time, Fig. 1, the value of the slip is determined only by the load and lies in the range from 0 to \(s_x\). Thus a regime occurs that is similar to reclosing. In addition, it is seen from Fig. 1 that the slip during the entire transient process only slightly exceeds its maximum values during starting; consequently, when modeling frequency reversal the same a.m. parameters should be used as when modeling starting.

The second feature of frequency reversal is as follows. In reversal by switching, the control signal (the direction of rotation of the resultant voltage vector) changes abruptly, and the transient electromagnetic processes begin at high values of speed and, consequently, at large values of the coefficients

of attenuation of these processes. As a result, the electromagnetic transient processes decay rapidly, and in the acceleration interval of the induction motor their influence is practically absent. Under frequency reversal, however, the time over which the control signal changes has a finite value, comparable with the time of the entire process. That is, transient electromagnetic processes are artificially maintained at a certain level; moreover, at high values of speed they are only beginning, while the main time of their course falls at low values of speed, at which the values of the damping coefficients are considerably lower [1]. In addition, because the pulsation frequency of the transient torque is proportional to the half-sum of the supply frequencies and the absolute slip [2], the time of the first torque pulsation increases appreciably, Fig. 1, and its amplitude has a considerably greater effect on the duration of the process than during starting.

It is known that reversal consists of two stages: braking and starting. When reversal is considered from static mechanical characteristics, it is assumed that braking takes place, most often regenerative braking, followed by a standstill zone and ordinary frequency starting. From an analysis of the reversal dynamics with allowance for electromagnetic transients it is seen, Fig. 1, that the occurrence of a standstill zone is not obligatory even under a load of the type \(M_c = \mathrm{const}\). It is possible only when, during the passage of speed through zero, a dip occurs in the transient-torque curve, or when the time of frequency change considerably exceeds the time of reversal by switching. In addition, starting of the induction motor in the reverse direction begins with nonzero initial conditions and almost always at a frequency and voltage greater than in ordinary frequency starting, which causes increased oscillation of the electromagnetic transient torque after the speed passes through zero, Fig. 1. This is the third feature of frequency reversal.

Fig. 1.

All that has been said above indicates that electromagnetic transient processes have a significant effect both on speed of response and on other indices of the dynamics of reversal of an induction motor, and that they must be taken into account.

Dynamic characteristics of an induction motor under frequency reversal.

The study of the dynamics of frequency reversal of an induction motor was carried out by solving the differential equations of the induction motor on an analog computer of the MN-14 type. Reversal from the “backward” rotation position to “forward” was modeled using a system of equations written in terms of the flux linkages of the stator and rotor [1]. The parameters of a DAT 250-8 induction motor were used.

To assess the quality of controlled reversal, the following criteria were applied [2]:

\[ \tau_p = t_{\mathrm{ch}}/t_{\mathrm{sw}} \]

— relative reversal time, the ratio of the time of frequency reversal to the reversal time by switching;

\[ \mu_{\max}=\frac{M_{\max}}{M_k} \]
— the maximum torque, the ratio of the maximum transient torque to the critical torque;

\[ \Delta\mu=\frac{M_{\max}-M_{\min}}{M_k} \]
— an index of the oscillatory character of the transient torque, the ratio of the difference between the maximum and minimum values of the transient torque to the critical torque;

\[ \Pi=\frac{dM_{\mathrm{rp}}/dt}{dM_{\mathrm{ch}}/dt} \]
— a smoothness index, the ratio of the derivative of the torque during reversal by switching, at the time instant \(t=0\), to the same derivative during frequency reversal.

The task of the investigation consisted in determining the dependences of the indicated criteria on the rate of frequency change during reversal with the frequency varying in time according to the law of an exponential and according to the law of the sum of two oppositely directed exponentials [2]. The dependences of these criteria were analyzed for the following loads: ideal no-load operation (Fig. 2, curves 1), \(M_c=k\omega^2\) (curves 2), \(M_c=\mathrm{const}\) (curves 3),

Fig. 2.

Fig. 3.

\(|\Sigma = 3|_p\) (curves 4). It was assumed that the voltage is regulated according to the law of M. P. Kostenko. The coefficients \(K_2\), \(K_3\), and \(K_4\) in Figs. 2, 3 are the damping coefficients of the exponentials: \(K_2\) for the exponential law, \(K_3\) for the decreasing exponential, and \(K_4\) for the increasing exponential in the law of the sum of two opposite exponentials. Their dimension is the same as the dimension of the damping coefficients of electromagnetic processes, and the value was determined by the smaller of the latter [3].

For all loads except the fan load, reversal of an asynchronous motor by changing the frequency exponentially over a time \(t_i < 1\) proves possible; the minimum value of \(\tau_p\) for an asynchronous motor of type DAT 250-8 may be equal to 0.5. It is known that, with frequency starting in an open-loop electric drive, one can obtain \(\tau_p \ge 0.75\) [3]; however, if during starting, simultaneously with a decrease in \(\tau_p\), there is a reduction in the values of \(\mu_{\max}\) and \(\Delta \mu\) and an increase in \(P\), then with frequency reversal even an increase in these indicators is possible, Fig. 2; this is explained by the features noted above. As a rule, the minimum values of \(\tau_p\) do not coincide with the maxima \(\mu_{\max}\), \(\Delta \mu\), which occur at certain values of the rate of change of frequency.

The dependences of the quality criteria of the controlled process for the law of the sum of two oppositely directed exponentials on the rate of change of frequency (Fig. 3 for \(M_c=\mathrm{const}\)) have the same character as for the exponential law, but in this case the maximum values \(\mu_{\max}\) and \(\Delta\mu\) are somewhat smaller.

Analysis of the dependence of the smoothness index on \(K_{2,3,4}\) shows that, during reversal, \(P\) increases somewhat with increasing \(K\); i.e., the rate of formation of the torque is, to some extent, inversely proportional to the rate of change of frequency. A similar dependence may also be observed for \(\mu_{\max}\) and \(\Delta\mu\). However, as already noted above, the values of \(K\) that ensure minimum values of \(\tau_p\) do not coincide with the values of \(K\) corresponding to maximum values of \(\mu_{\max}\), \(\Delta\mu\). Therefore it may be concluded that, for a drive with a load of the type \(M_c=\mathrm{const}\), the most advantageous frequency variation will be that in which, over the braking interval, the frequency changes 3–5 times faster than over the entire starting interval. For operation with \(I_\Sigma=3I_p\), the best values of the indices are obtained with a linear change of frequency over time.

REFERENCES

1. M. M. Sokolov, L. P. Petrov, L. B. Masandilov, V. A. Ladenzon. Electromagnetic Transient Processes in an Asynchronous Electric Drive. Moscow, “Energiya,” 1968.

2. V. I. Panteleev, B. P. Soustin. Influence of the law of frequency variation on the dynamics of a frequency-controlled asynchronous motor. Collected Scientific Papers of the Electrotechnical Faculty of the Krasnoyarsk Polytechnic Institute. Krasnoyarsk, Publishing House of the Krasnoyarsk Polytechnic Institute, 1972.

3. V. I. Panteleev, B. P. Soustin. On the choice of the rate of frequency variation in frequency control of an asynchronous motor. Sverdlovsk, “Znanie,” 1972.