SELECTION OF A METHOD FOR CONFIGURING THERMISTORS FOR BUILT-IN ELECTRIC MOTOR PROTECTION

V. L. Bryzgalov, O. P. Muravlev, E. K. Strelbitskii

(Presented by the scientific seminar of the Department of Electrical Machines and the Electrical Machines Division of the Scientific Research Institute of AEМ)

One of the main issues in developing temperature protection is determining the permissible scatter of tripping temperatures [1]. Simple reasoning leads to the conclusion that there exists an optimal scatter of tripping temperatures, deviations from which in either direction lead to increased costs on the scale of the national economy. Increasing the permissible scatter reduces the costs associated with setting the protection, but leads to increased insulation wear under overloads if the winding temperature in the rated mode is not changed. If, in designing the protection, the maximum permissible winding temperature under overload is specified, then the temperature rise in the rated mode must be reduced, which is associated with an increase in the manufacturing cost of the electric motor.

Reducing the permissible scatter leads to an increase in the cost of the protection system. The most correct approach is to determine the magnitude of the scatter on the basis of the requirement that the sum of the costs of manufacturing the motor, increased wear under emergency conditions, and the cost of the protection be minimized. However, solving the problem in this formulation is beyond the scope of the present work, since it is connected with a statistical study of the overload flow in various areas of electric drive. These difficulties are aggravated by the fact that, by its very concept, protection is installed on motors whose load characteristics are insufficiently known and are characterized by a large scatter.

Under these circumstances, the following approach to determining the permissible scatter of tripping temperatures is expedient. In designing, designers provide for a certain thermal margin equal to \(6 \div 10^\circ\text{C}\). This margin is necessary because of the presence of a certain scatter of temperatures in the rated mode, caused by scatter in motor losses, scatter in thermal conductivities, deterioration of cooling conditions, etc. Since the thermal receiver responds directly to the actual temperature of the given motor, we may allow a scatter of tripping temperatures within the limits of the existing thermal margin without reducing the thermal utilization of the motor; that is, we may take the permissible scatter as \(\delta = 6 \div 10^\circ\text{C}\).

\[ \delta \leq \sqrt{\delta_1^2 + \delta_2^2 + \delta_3^2 + \delta_4^2}, \tag{1} \]

where \(\delta_1\) is the permissible scatter of the characteristics of batches of thermistors; \(\delta_2\) is the error in setting thermistors; \(\delta_3\) is the error from non-

stability of actuation of thermal receivers; $\delta_4$ is the error due to deviations of the temperature at the installation point from the temperature of the hottest point of the winding.

In turn, the error $\delta_4$ has the following components: $\delta_5$—the error due to deviation of the temperature from disturbance of the thermal field of the winding when thermal receivers are embedded; $\delta_6$—the error due to temperature skew in the winding; $\delta_7$—the error due to deviation of the temperature at the installation point (inaccuracy of mounting in depth and around the circumference) from the temperature of the hottest point of the winding.

\[ \delta_4=\sqrt{\delta_5^2+\delta_6^2+\delta_7^2}. \tag{2} \]

The error in setting the thermal receivers is $\delta_2=2^\circ\mathrm{C}$, which depends on the accuracy class of the instruments used. The error due to instability of thermistor actuation does not exceed $\delta_3=2^\circ\mathrm{C}$. The studies carried out showed that the error $\delta_4$ does not exceed $4^\circ\mathrm{C}$.

Taking the above into account and adopting $\delta=8^\circ\mathrm{C}$, we obtain the permissible spread of actuation temperatures of a batch of thermal receivers $\delta_1$ for electric motors with built-in protection

\[ \delta_1=\sqrt{\delta^2-\left(\delta_2^2+\delta_3^2+\delta_4^2\right)}\simeq 6^\circ\mathrm{C}. \tag{3} \]

Industry produces thermistors for temperature protection, according to nameplate data, with a spread of actuation temperatures

Fig. 1

of $20\%$, which is $(18\text{–}25)^\circ\mathrm{C}$. Therefore, their use in temperature-protection circuits is possible after measures that reduce this spread.

To determine the distribution law of the operating temperature of TR-33 thermistors, produced by the Sevkavelektropribor plant, Nalchik, a batch of thermistors of size \(n = 100\) pieces was tested. The tests were carried out according to the circuit in Fig. 1.

Statistical processing of the test results shows that the distribution of operating temperatures obeys the normal law.

Let us consider possible methods for setting the temperature protection [2] and the costs of providing them.

A. Selection of thermistors by groups with similar parameters

In this case, thermistors are selected whose operating temperature lies within the limits

\[ \Theta_{\mathrm{cp}} \pm \delta_1, \]

where \(\Theta_{\mathrm{cp}}\) is the setting temperature of the thermal protection.

The advantage of this method is that no additional adjustment is required, while the disadvantage is the large number of rejected thermistors, which is unacceptable given their scarcity. In Fig. 2 the shaded area determines the fraction of acceptable thermistors \(P\):

Fig. 2

\[ P = \Phi(x) = \Phi\left(\frac{\Theta_{\mathrm{cp}} - \delta_1,\ \Theta_{\mathrm{cp}} + \delta_1}{\sigma}\right) = 0.45, \tag{4} \]

\(\Phi(x)\) is the Laplace function. The values of \(\Phi(x)\) are determined from tables [3].

We shall calculate the economic efficiency of each setting method for a batch of \(n = 1000\) thermistors.

The cost of selecting thermistors is

\[ c_{\mathrm{n}} = n' c_{\mathrm{otb}}, \tag{5} \]

where \(n' = \dfrac{n}{P}\) is the number of thermistors that are subjected to checking or adjustment;

\(c_{\mathrm{otb}}\) is the cost of the work involved in checking or adjusting one thermistor, according to the cost estimate of the Volta plant. The cost of rejected thermistors is

\[ c_{\mathrm{b}} = (n' - n)c_{\mathrm{t}}, \tag{6} \]

where $c_t$ is the cost of a thermistor. For the TR-33, $c_t = 0.6$ rubles.

The thermistors are powered from auxiliary coils, which are placed on the contactor core. The production cost of these coils for supplying three thermistors, which are built into each motor to provide thermal protection, is

\[ c_k = \frac{n}{3} c'_k, \]

where $c_k$ is the production cost of the auxiliary coils for one motor.

The total costs for setting up the built-in temperature protection are

\[ c_\Sigma = c_n + c_b + c_k. \tag{7} \]

Using formulas (4)--(7), the costs for the various methods of setting up temperature protection are estimated.

B. Setting thermistors by changing the voltage

By changing the thermistor supply voltage, it is possible to change the operating temperature both upward and downward (Table 1). If, with an allowable batch scatter $\delta_1 = 6^\circ\mathrm{C}$, three taps are made on the thermistor supply coils, which would provide a voltage change $\Delta u = \pm 6$ V, then the share of thermistors that will be used (Fig. 3) will be

Fig. 3.

\[ P = \Phi(x) = \Phi\left(\frac{\Theta_{\mathrm{op}} - 2\delta_1,\ \Theta_{\mathrm{avg}} - 2\delta_1}{\sigma}\right) = 0.93 \]

Table 1

The advantage of this method is the small percentage of rejects and the simplicity of the adjustment technology; its disadvantage is the need to have a coil with taps, which complicates its manufacture.

C. Adjustment of Thermistors by Shunting with a Resistance

Shunting a thermistor with a resistance causes the volt-ampere characteristic to shift toward higher currents; therefore the tripping temperature is increased. The percentage of acceptable thermistors (Fig. 4) is

\[ P=\Phi\left(\frac{-\infty,\ \Theta_{\mathrm{cp}}+\delta_1}{\delta}\right)=0.726. \]

Fig. 4

The advantage of the method is that the supply coil is made without taps; the disadvantage is the high labor intensity of the adjustment operation and the need for a large set of resistances.

D. Combined Adjustment

It consists in the following: by changing the voltage, the mean tripping temperature of the thermistors \(\Theta\) is shifted to the left by \(2\tau\), and then, by shunting with a resistance, the required tripping temperature is set. This makes it possible to use almost the entire batch of thermistors (Fig. 5). With this method, the cost of ad-

Fig. 5

justment is ...

the setting is the same as in case V, and the cost of the coils is as in case B.

The economic evaluation of all methods of protection is given in Table 2.

Table 2

An increase in the permissible spread of the operating temperatures of the thermistors in a batch, \(\delta_1\), leads to increased wear of the insulation under overloads, which is undesirable. Reducing \(\delta_1\) will increase the reliability of the unit; therefore let us consider the costs at different adjustment accuracies of 3 and 4.5°C. The results of the calculation are presented in Table 3.

Table 3

Thus, Tables 2 and 3 make it possible to estimate the costs of built-in thermal protection depending on the selected accuracy and method of adjustment. Cases B and G are the most economical, but adjustment with only one voltage is the most expedient, since it is more technological: it does not require additional resistances, their selection, or adjustment. In the event of an acute shortage of thermistors, combined adjustment may be recommended.

LITERATURE

1. V. L. Bryzgalov. Built-in thermal protection of asynchronous motors. Scientific and Technical Collection of the Electrical Engineering Industry, Moscow, “Informelektro,” 1969, No. 334.

2. G. K. Negaev. Semiconductor thermoresistors in automation, “Tekhnicheskaya literatura,” Ukrainian SSR, 1962.

3. N. V. Smirnov, I. V. Dudin-Barkovskii. Course in probability theory and mathematical statistics for technical applications, “Nauka,” Moscow, 1965.