INVESTIGATION OF SWITCHING OVERVOLTAGES IN THE WINDINGS OF INDUCTION MOTORS

Yu. P. Pokhodkov

(Submitted by the scientific seminar of the Department of Electrical Machines and General Electrical Engineering)

Failure of the insulation of induction-motor windings in service is caused by a number of factors, among which an important role is played by overvoltages arising in the windings during switching on, switching off, and reversing of motors [1].

According to data from a number of authors, the amplitude level of switching overvoltages may be rather high and may exceed the values of the breakdown voltages of the insulation [1, 2, 3]. Thus, for high-voltage machines the level of switching overvoltages may be equal to \(7.8\sqrt{2}U_{\phi}\), where \(U_{\phi}\) is the phase operating voltage of the winding [1, 3]. Switching overvoltages are especially dangerous for machines whose insulation is aged and has defects of the through-crack type. In such machines insulation breakdown will occur if the level of switching overvoltages is equal to or exceeds the level of the breakdown voltage of air in a thickness equal to the insulation thickness.

Statistical investigations of switching overvoltages in the windings of induction motors make it possible to predict the probability of failure-free operation of the motor winding insulation [4].

The probability of failure-free operation of the windings of induction motors over the time \(t=m\cdot \Delta\tau\) may be estimated as follows:

\[ R_z=\left[1-\sum_{m=1}^{m}\sum_{i=1}^{i}\Delta q(m,U_i)P(m,U_i)\right]^N, \]

where
\(m\) is the number of time intervals of duration \(\Delta\tau\);
\(\Delta q(m,U_i)\) is the probability of breakdown of an elementary section of insulation in the \(m\)-th time interval, at the level of switching overvoltages \(U_i\);
\(P(m,U_1)\) is the probability of the occurrence of switching overvoltages

\[ U>U_i \]

during the time

\[ \tau=m\frac{\nu}{f_{\mathrm{on}}}; \]

\(\nu\) is the number of machine switchings during the time \(\tau\);
\(f_{\mathrm{on}}\) is the frequency of machine switching.

Thus, in order to estimate the reliability of the insulation of induction-motor windings it is necessary to know the parameters of the distribution law of the amplitudes of switching overvoltages in the machine winding.

In the present work, switching overvoltages in the windings of induction motors AO2-32-2, AO2-32-4, AO2-32-6 were investigated during

switching on, switching off, and reversing of motors.

The investigation of switching overvoltages in the windings was carried out using a DESO-1 oscillograph with the use of an ohmic divider. The electrical circuit for investigating switching overvoltages is shown in Fig. 1.

Fig. 1

During the investigation, 200 oscillograms of switching overvoltages were taken for each operation. The most characteristic oscillograms of switching-overvoltage pulses during switching on, switching off, and reversing of motors are shown in Fig. 2.

Switching on      Reversing      Switching off

Fig. 2.

Statistical processing of the test results made it possible to determine the nature of the distributions of the switching-overvoltage coefficient in the motor windings during switching on, switching off, and reversing in no-load operation. The switching coefficient...

… it is customary here to call the switching-overvoltage coefficient \(K_{\mathrm{p}}\) the ratio of the amplitude of the overvoltage pulse to the amplitude value of the rated phase voltage.

AO2-32-2

AO2-32-4

AO2-32-6

Fig. 3

Figure 3 shows the distribution curves of the overvoltage coefficient, respectively, for motors AO2-32-2, AO2-32-4, and AO2-32-6.

Table 1 gives the parameters of the distributions of the switching-overvoltage coefficients and pulse durations.

A check of the discrepancy between the mean values \(\overline{K}_{\mathrm{p}}\), carried out by Student’s criterion [5], showed that the difference between the mean values of \(\overline{K}_{\mathrm{p}}\) obtained when disconnecting the investigated motors is insignificant. The difference between the mean values of \(K_{\mathrm{p}}\) in the windings of different machines during switching on and reversing is recognized as significant according to Student’s criterion.

Analysis of the parameters of the distributions \(\overline{K}_{\mathrm{p}}\) and \(\sigma_{\mathrm{kp}}\) shows that the most dangerous overvoltages are those arising at the moment of switching on the motors, \(\overline{K}_{\mathrm{p}} = 5.5 \div 6.5\); next in degree of danger are

Table 1

overvoltages arising when reversing the motors, \(\overline{K}_{\mathrm{p}} \approx 5\), and when disconnecting the motors, \(\overline{K}_{\mathrm{p}} \approx 1.7 \div 1.8\). In this connection an approximation was carried out for the distribution of \(K_{\mathrm{p}}\) obtained when switching on the investigated motors. It was established that the distribution of \(K_{\mathrm{p}}\) is approximated by the superposition of two normal laws. The general expression for estimating the probability of the occurrence of \(K_{\mathrm{p}} > K_{\mathrm{p}i}\) may be written as follows:

\[ P(K_{\mathrm{p}} > K_{\mathrm{p}i}) = 1 - \left[ V_1 F\left(\frac{K_{\mathrm{p}i}-\overline{K}_{\mathrm{p}1}}{\sigma_1}\right) + V_2 F\left(\frac{K_{\mathrm{p}i}-\overline{K}_{\mathrm{p}2}}{\sigma_2}\right) \right], \]

where \(V_1\) and \(V_2\) are, respectively, the shares of the volumes of the first and second normal distribution laws in the overall distribution of \(K_{\mathrm{p}}\).

\(\overline{K}_{\mathrm{p}1}\), \(\overline{K}_{\mathrm{p}2}\), \(\sigma_1\), \(\sigma_2\) are, respectively, the parameters of the first and second normal distribution laws in the overall distribution of \(K_{\mathrm{p}}\).

Table 2 gives the values of the volume shares and the distribution parameters of \(K_{\mathrm{p}}\) for the investigated motors during switching on.

Table 2

The reduction in the mean level of \(K_{\mathrm{p}}\) with an increase in the number of pole pairs in the motors of the A02 series of the third size is apparently associated with a change in the parameters of the oscillatory circuits formed by the winding.

The presence of two maxima in the distribution of \(K_{\mathrm{p}}\) is due to the presence of two oscillatory circuits formed by the winding. One of them may be formed by the interturn capacitance and the inductance of the winding; the other, by the inductance of the winding and the capacitance of the winding relative to the grounded frame. Approximation of the distribution of \(K_{\mathrm{p}}\) by a superposition of two normal laws made it possible to calculate the probability of the occurrence of dangerous overvoltages in the windings of the motors under investigation as a function of the number of switchings. A dangerous overvoltage coefficient was taken to mean such a coefficient at which, on one coil of a phase, there appears a voltage exceeding the average breakdown voltage of an air layer whose thickness is equal to twice the thickness of the conductor insulation \(\overline{U}_{\mathrm{b}}\). Then the dangerous overvoltage coefficient is determined as:

\[ K_{\mathrm{p.op}}=\frac{\overline{U}_{\mathrm{b}}\cdot n_{\mathrm{k}}}{U_{\mathrm{nom.max}}}, \]

where

\(n_{\mathrm{k}}\) is the number of series-connected insulated coils in a phase.
\(U_{\mathrm{nom.max}}\) is the amplitude value of the nominal operating voltage of the machine.

The probability of occurrence of \(K_{\mathrm{p.op}}\) during \(\nu\) switchings of the machine can be determined using the probability multiplication theorem [5]

\[ P_{\nu}(K_{\mathrm{p}}>K_{\mathrm{p.op}})=1-\left[1-P(K_{\mathrm{p.op}}>K_{ni})\right]^{\nu}. \]

Table 3 gives the probabilities of occurrence of \(K_{\mathrm{p.op}}\) in the windings of the motors under investigation as a function of the number of switchings.

Table 3

Dangerous switching overvoltages are most probable in the winding of the AO2-32-2 motor, which is apparently due to the electrical parameters of its winding, as well as to the reduced number of series-connected insulated coils in a phase.

Investigation and analysis of the amplitude and waveform of switching overvoltages will make it possible in the future to evaluate their influence on the rate of insulation aging in low-voltage electrical machines.

Conclusions

1. It has been established that switching overvoltages whose magnitude is dangerous for the insulation can arise in the windings of low-voltage asynchronous motors of the AO2 series, of the third frame size.

2. The most dangerous are the switching overvoltages that arise when the motor is switched on, and the least dangerous when the motor is switched off.

3. The distribution of the value of the switching-overvoltage coefficient when the machines under investigation are switched on has been approximated by a superposition of two normal laws. The parameters of the laws have been determined.

1. It has been established that the most dangerous switching overvoltages arise in the windings of two-pole machines, as compared with four- and six-pole machines.

REFERENCES

1. Z. G. Kaganov. Internal overvoltages and other effects on the turn insulation of electric motors. In: Testing of Turn Insulation of Electrical Machines, GEI, 1959.

2. P. Furnarier. Essais relatifs aux surtension de declenche mant des moteurs a haute tension. Bull. Soc. Franc. Elact., No. 75, 1953.

3. O. D. Goldberg, I. M. Komlev, N. I. Suvorov et al. The influence of switching overvoltages on the reliability of low-voltage induction motors. Elektrotekhnika, 1968, No. 5.

4. E. K. Strelbitskii, L. I. Shtuden, V. M. Fedorov, O. P. Murovlev, Yu. P. Pokholkov. Method for calculating the reliability of random-wound windings of induction motors No. OAE 174193. 1968, Tomsk.

5. A. K. Mitropol’skii. Techniques of Statistical Computations. Fizmatgiz, 1964.