On the Law of Temperature Rise in A02 Series Induction Motors under Emergency Conditions
Abstract Generated abstract
This paper examines the temperature rise of stator windings in A02 series induction motors under emergency conditions, specifically locked rotor operation with three-phase and two-phase short circuits. Using continuous oscillographic measurement of winding resistance, the authors experimentally determine heating curves for several motor types from cold and hot initial states and fit the results by least squares. They show that the temperature rise rate is not constant but decreases with time, and that temperature rise can be represented by a quadratic time relation while short-circuit current is also described by a polynomial expression. The reported coefficients are intended to improve calculations of winding temperature, motor wear, and protective trip settings, and the authors note that a commonly used formula overestimates temperature rise for longer short-circuit durations.
Full Text
ON THE LAW OF TEMPERATURE RISE IN A02 SERIES ASYNCHRONOUS MOTORS UNDER EMERGENCY CONDITIONS
B. A. Itkin, E. K. Strelbitskii
(Recommended by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering)
The rate of temperature rise in the stator winding of an asynchronous motor with a locked rotor—$T_v(t)_3$—is one of the main characteristics of the machine. When assessing the effect of emergency conditions on motor wear, and for the proper selection of protection, it is also necessary to know the rate of temperature rise in the stator winding when the machine operates on two phases—$T_v(t)_2$.
The article presents the laws of variation of $T_v(t)_3$ and $T_v(t)_2$ for the most widespread motors of the new series A02-52-4, A02-42-4, A02-32-4, and AOL2-11-4.
Usually the calculated value of the rate of temperature rise with a locked rotor is determined by the well-known formula of VNIIZM
\[ T_{v3}=\frac{\Delta^2}{200}, \tag{1} \]
where $\Delta$ is the current density in the stator winding during a short circuit of the motor on 3 phases.
It should be noted that, in a number of cases, $T_{v3}$ determined from (1) does not provide the required accuracy when calculating the temperature rise in the stator winding $\Theta$ during a short circuit,
\[ \Theta = T_{v3}t, \tag{2} \]
where $t$ is the duration of the emergency condition.
Formula (1) gives a single-valued value of $T_{v3}$ and was obtained on the assumption of the absence of heat transfer and of the constancy of the current magnitude during the short circuit. Our experimental studies of the heating of A02 asynchronous motors under emergency conditions showed that, in the general case, the assumption of a constant rate of temperature rise throughout the entire short-circuit process cannot be accepted. For $t>5 \div 10$ seconds, $T_v$ decreases because of increased heat transfer and a decrease in the current magnitude due to the increase in the ohmic resistance of the stator and rotor windings as a result of heating.
For the experimental determination of $T_v(t)_3$ and $T_v(t)_2$, the circuit [1] was used, which makes it possible to measure the average temperature of the winding without disconnecting the electric motor from the supply network. The circuit [1] was supplemented by us with the installation of galvanometers of an N700 oscillograph, which made it possible to produce a continuous recording of the ohmic resistance. Mathematical processing of the oscillogram data showed that
the change in temperature rise during a short circuit can be represented by a second-degree polynomial in time
\[ \Theta = T_{vo}t - at^2 + \Theta_{\text{init}}, \tag{3} \]
where \(T_{vo}\) is the initial rate of temperature rise;
\(a\) is the coefficient of equation (3);
\(\Theta_{\text{init}}\) is the initial temperature rise of the stator winding.
The law of variation of the rate of temperature rise is found by differentiating (3)
\[ T_v(t) = T_{vo} - 2at. \tag{4} \]
Table 1 gives the values of \(T_{vo}\) and \(a\) for three- and two-phase short circuits, both from the cold and from the hot states of the motors investigated, obtained by processing the experimental data by the method of least squares.
Table 1
| Motor type | Type of s.c. | From cold state: \(T_{vo}\), °C/sec | From cold state: \(a\) | From cold state: \(\Theta_{\text{init}}\), °C | From hot state: \(T_{vo}\), °C/sec | From hot state: \(a\) | From hot state: \(\Theta_{\text{init}}\), °C |
|---|---|---|---|---|---|---|---|
| A02-52-4 | 3-ph. | 6,2 | 0,0192 | 0,83 | 6,189 | 0,0125 | 41,6 |
| A02-52-4 | 2-ph. | 3,667 | 0,0048 | 4,6 | 3,554 | 0,0021 | 42,7 |
| A02-42-4 | 3-ph. | 5,863 | 0,0117 | 0 | 5,343 | 0,0076 | 43,9 |
| A02-42-4 | 2-ph. | 3,25 | 0,073 | 0 | 3,056 | 0,0074 | 51,6 |
| A02-32-4 | 3-ph. | 4,512 | 0,016 | 1,36 | 4,407 | 0,0193 | 48,4 |
| A02-32-4 | 2-ph. | 3,31 | 0,0151 | 0 | 3,278 | 0,0148 | 39,8 |
| A02-11-4 | 3-ph. | 3,975 | 0,0215 | 2,1 | 3,658 | 0,0197 | 49 |
| A02-11-4 | 2-ph. | 3,02 | 0,0137 | 0,42 | 2,545 | 0,0128 | 44,7 |
In the absence of experimental data, the value of \(T_{vo}\) is determined approximately from (1).
Oscillograph recording of the short-circuit current and subsequent processing of the experimental data by the method of least squares showed that the change in current during the emergency condition is well described by the equation
\[ I(t) - I_{\text{init}} - k_2t + k_3t^2, \tag{5} \]
where \(I_{\text{init}}\) is the initial short-circuit current;
\(k_2, k_3\) are the coefficients of equation (5).
Table 2 gives the ratio of \(k_2\) and \(k_3\) to the initial current for the motors considered under three- and two-phase short circuits.
For the three-phase condition from the cold state, absolute current values are given; in the other cases their ratio to this current is given.
Table 2
| Motor type | Type of short circuit | From the cold state | From the cold state | From the cold state | From the hot state | From the hot state | From the hot state |
|---|---|---|---|---|---|---|---|
| $I_{\mathrm{init}}$ | $\dfrac{K_2 \cdot 10^{-2}}{I_{\mathrm{init}}}$ | $\dfrac{K_3 \cdot 10^{-4}}{I_{\mathrm{init}}}$ | $I_{\mathrm{init}}$ | $\dfrac{K_2 \cdot 10^{-2}}{I_{\mathrm{init}}}$ | $\dfrac{K_3 \cdot 10^{-4}}{I_{\mathrm{init}}}$ | ||
| AO2-52-4 | 3-ph. | 146,17 a | 0,629 | 0,54 | 0,956 | 0,452 | 0,107 |
| AO2-52-4 | 2-ph. | 0,85 | 0,402 | 0,16 | 0,816 | 0,384 | 1,31 |
| AO2-42-4 | 3-ph. | 85,8 a | 0,51 | 0,2575 | 0,957 | 1,03 | 1,84 |
| AO2-42-4 | 2-ph. | 0,743 | 0,171 | 0,0879 | 0,693 | 0,232 | 0,121 |
| AO2-32-4 | 3-ph. | 41,48 a | 0,559 | 0,335 | 0,895 | 0,447 | 0,243 |
| AO2-32-4 | 2-ph. | 0,834 | 0,327 | 0,159 | 0,77 | 0,329 | 0,131 |
| AOL2-11-4 | 3-ph. | 7,84 a | 0,667 | 0,408 | 0,918 | 0,708 | 0,472 |
| AOL2-11-4 | 2-ph. | 0,866 | 0,529 | 0,323 | 0,774 | 0,429 | 0,198 |
Comparison of experimental data and calculation of the temperature rise during a short circuit according to the commonly used formula [2]
\[ \Theta = (235 + \vartheta_{\mathrm{n}})\left(e^{k_1 \Delta^2 t} - 1\right), \tag{6} \]
where $\vartheta_{\mathrm{n}}$ is the initial temperature of the winding,
$K_1 = 1{,}98 \cdot 10^{-5}$ (for copper windings),
showed that the values of $\Theta$ according to (6) for $t > 20$ seconds are overestimated by 10–20%.
Conclusions
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The rate of temperature rise in the stator winding of an asynchronous motor with a locked rotor on three and two phases does not remain constant and varies according to (4).
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The obtained equations (3) and (5), with experimental values of the coefficients, make it possible to significantly improve the accuracy of calculating temperature rise, wear, and the selection of the protection trip setting under emergency operating conditions of motors of the new AO2 series.
LITERATURE
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A. M. Sharipov. Device for measuring the ohmic resistances of windings of electrical machines in the presence of alternating e.m.f., TsITEIN collection, No. E-61-72/21, 1961.
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G. Gotter. Heating and Cooling of Electrical Machines, GEI, 1961.