On Some Features of the Behavior of Power Transformers under Conditions of Intensive Cooling

V. M. VYSOTSKAYA, A. A. GURCHENOK

(Presented by the seminar of the departments of the electromechanical faculty)

As is known, at the present time various branches of industry are developing rapidly in many regions of the Far North; in connection with this, the need has arisen for the operation of oil-filled transformers under conditions of intensive cooling.

Earlier studies \[1—4\] explain the behavior of power transformers installed in the middle zone of the USSR under conditions of low temperatures. The influence of wind in this case, as a rule, is not taken into account. However, in the operation of electrical installations in most regions of the Arctic, besides the low temperature of the surrounding air, one must also take into account one further feature—a high wind velocity (up to 30 m/sec). Thus, for example, it turns out that at temperatures on the order of \(-40^\circ\)C and below, and in the presence of wind, in tubular radiators with thin flattened tubes, where the oil layer is less than 30 mm, oil circulation ceases, which causes overheating of the transformer \[5\].

In connection with the above, it is of interest to investigate the dependence of transformer cooling on the outside temperature and wind velocity. To solve the problem posed, calculations were carried out for the cooling of a transformer of type TM 100/6 by the standard method and with the use of criterion equations of heat transfer. The latter was dictated by the fact that the indicated method makes it possible to determine the magnitude of the heat loss with allowance for wind velocity, which is not taken into account in the standard calculation.

Standard calculation of thermal loads and temperatures

The results of the standard calculation of the TM 100/6 transformer are given in a calculation note. The note shows the thermal loads and temperature rises at normal load (100%). According to the data of the note, the temperature in the core and windings of the transformer is determined from the relation

\[ t = \varepsilon + \Theta + t_{\mathrm{a}}. \tag{1} \]

The temperature of the oil and of the cooling surface are assumed to be identical and equal to

\[ t_{\mathrm{st}} = \Theta + t_{\mathrm{a}}. \tag{2} \]

CALCULATION SHEET

Three-phase transformer with natural oil cooling

voltages 6600—6300—6000; 230 V

number of turns 832—794—757; 29 turns

No-load current 6.5 A

According to the calculation note, we obtain \(t = 105^\circ\mathrm{C}\), \(t_{\mathrm{st}} = 80^\circ\mathrm{C}\), which is permissible under the operating standards for transformers.

Calculation of Transformer Cooling by Heat-Transfer Equations

The process of heat transfer from the cooling surface of a transformer to the surrounding air may occur under conditions of free convection at various temperatures, and under conditions of air blowing at a certain velocity. Let us consider these conditions.

a) Heat transfer under conditions of free convection

Under conditions of free convection, the cooling process will consist of heat transfer by convection and by radiation,

\[ q = q_k + q_l . \tag{3} \]

Heat transfer by convection is determined from the equation

\[ q_k = \alpha (t_{\mathrm{st}} - t_v)\ \mathrm{W}/\mathrm{m}^2 . \tag{4} \]

The heat-transfer coefficient \(\alpha\) is found from the criterion equation

\[ \mathrm{Nu} = C \cdot (\mathrm{Gr}\cdot \mathrm{Pr})^m , \tag{5} \]

where \(\mathrm{Nu}\), \(\mathrm{Gr}\), \(\mathrm{Pr}\) are, respectively, the Nusselt, Grashof, and Prandtl criteria;
\(C, m\) are coefficients whose magnitude depends on the value of the product \(\mathrm{Gr}\cdot \mathrm{Pr}\) [6].

Heat transfer by radiation is determined from the equation

\[ q_l = 5.4\cdot \varepsilon \cdot \left[ \left(\frac{t_{\mathrm{st}} + 273}{100}\right)^4 + \left(\frac{t_v + 273}{100}\right)^4 \right]\ \mathrm{W}/\mathrm{m}^2 , \tag{6} \]

where \(\varepsilon\) is the degree of blackness of the cooling surface.

In Fig. 1 (curves 1, 2, 3) the results are given of calculating the dependence of heat transfer on air temperature for different values of tank-wall heating. The calculation results from the heat-transfer equations agree with the data obtained by the standard calculation method (curve 1, \(t_{\mathrm{st}} = 80^\circ\mathrm{C}\)). In addition, the graphs show that at low air temperatures the heat transfer increases: at \(t_v = -14^\circ\mathrm{C}\) it doubles, and at \(t_v = -55^\circ\mathrm{C}\) it triples in comparison with the heat transfer at the calculated air temperature of \(+35^\circ\mathrm{C}\).

If the temperature of the tank wall is reduced, the heat transfer decreases. At \(t_{\mathrm{st}} = 40^\circ\mathrm{C}\), the heat released will be removed at \(t_v = -20^\circ\mathrm{C}\); at \(t_{\mathrm{st}} = 0^\circ\mathrm{C}\), at \(t_v = -60^\circ\mathrm{C}\).

When the transformer walls are cooled to \(0^\circ\mathrm{C}\), circulation of oil in the external pipes ceases because the moisture in it freezes. Only the surface of the tank itself participates in heat transfer, which sharply reduces the cooling surface of the transformer. The oil in the tank heats up. Calculation shows that in this case, at \(t_{\mathrm{st}} = 80^\circ\mathrm{C}\), all the heat can be removed at \(t_v = -45^\circ\mathrm{C}\). At \(t_v = -20^\circ\mathrm{C}\), 75% will be removed; at \(t_v = 0^\circ\mathrm{C}\), 50% of the heat released under normal transformer load will be removed (curve 5, Fig. 1). This explains the observed cases of transformer overheating under conditions of low temperatures and wind [5].

b) Heat transfer under wind blowing

Calculation of heat transfer under wind blowing is carried out analogously to section (a), using equations (3), (4), and (6).

The heat-transfer coefficient \(\alpha\) is determined from the following criterion equation:

\[ \mathrm{Nu} = 0.18 \Psi \mathrm{Re}^{0.52}, \tag{7} \]

where \(\Psi\) is a coefficient taking into account the decrease in heat transfer under nonperpendicular blowing;

\(\mathrm{Re}\) is the Reynolds criterion.

In Fig. 1 (curve 4) the results of calculating heat transfer at various wind-speed values are given. It is evident from the graph that, with

Fig. 1. Curves of the dependence of heat transfer on air temperature under conditions of free convection: 1—\(t_{\mathrm{st}} = 80^\circ\mathrm{C}\), 2—\(40^\circ\mathrm{C}\), 3—\(0^\circ\mathrm{C}\); at \(t_{\mathrm{st}} = 80^\circ\mathrm{C}\); 4—heat transfer with wind, 5—upon cessation of circulation in the cooling pipes.

a wind of \(10\ \mathrm{m/sec}\), heat transfer increases by more than a factor of two; at \(20\ \mathrm{m/sec}\), by a factor of three.

Cooling of a Transformer during Overload Operation

In the operation of transformers, operation with overload is permitted in emergency cases. The values of permissible overloads and their durations are presented in Table 1.

The longest are overloads by factors of 1.3 and 1.6. Moreover, an overload by a factor of 1.3 may also be permitted in nonemergency

Table 1

provided that the filling factor of the transformer daily load curve is less than unity.

The results of calculating the magnitude of the specific heat releases and the permissible oil temperature inside the transformer under overload operating conditions are presented in Fig. 2.

A comparison of the data on transformer cooling makes it possible to determine the conditions under which prolonged operation with overload is possible. Thus, from Fig. 1 and Fig. 2 it is easy to establish that, for a mode with a 30% overload, the temperature of the tank wall must be no higher than 66° C. Under the conditions of external cooling in this case, prolonged operation is possible under the following conditions:

a) at an air temperature below 0° C without wind;

b) at an air temperature of +35° C with a wind of 9 m/sec or more.

For an operating mode with a 60% overload, we similarly obtain: the temperature of the tank wall must not exceed 49° C. Prolonged operation is possible at:

a) an air temperature of minus 40° and below without wind;

b) at an air temperature of +35° C with a wind of 18 m/sec and above.

According to experimental investigation data, during prolonged operation of the transformer with a 40% overload under conditions of natural frost with a temperature \(t_{\mathrm{v}} = -30^\circ\) C, the oil temperature did not rise above 40° C, which is in good agreement with the calculated data given in Fig. 2 [3]. There, too, data are given on the steady-state temperature

Fig. 2. Curves of dependence: 1—of specific heat releases, 2—of the permissible oil temperature, on the magnitude of transformer overload.

of the oil inside the transformer under conditions of natural frost with a temperature \(t_{\mathrm{v}} = -30^\circ\) C during prolonged operation with a 55% overload. According to the experimental data, the value of the oil temperature in this mode rose and stabilized at the level of +53° C.

Consequently, it may be concluded that prolonged operation of transformers with overloads of 30 and 60% is possible provided that sufficient external cooling is ensured.

Conclusions

1. The theoretical calculations of cooling that were carried out, and the results of an experimental study of putting a transformer under load at low air temperature, have shown the feasibility and usefulness of calculating transformer cooling by means of criterion equations that make it possible to take the presence of wind into account.

2. In the presence of wind, the external cooling conditions of a transformer are substantially improved and make it possible to remove two to three times more heat than at the calculated maximum temperature without blowing.

3. When switching on a transformer that is in a frozen state, or when oil circulation in the external tubes has ceased, the following rule must be observed: at \(t_{\mathrm{v}} = 0^\circ\mathrm{C}\) the transformer is switched on at 50%; at \(t_{\mathrm{v}} = -20^\circ\mathrm{C}\), at 75%; at \(t_{\mathrm{v}} = -45^\circ\mathrm{C}\), at 100% power.

Literature

1. L. M. Shnider. Elektrichestvo, No. 4, 1939.
2. E. K. Zavadovskaya. Elektrichestvo, No. 8, 1939.
3. E. K. Zavadovskaya, A. K. Krasin. Proceedings of SFTI, Vol. VI, 1945.
4. N. N. Zyuzyukov. Electric Power Stations, No. 3, 1946.
5. A. A. Aleksandrov. Industrial Power Engineering, No. 2, 1960.
6. M. A. Mikheev. Theory of Heat Transfer. Gosenergoizdat, 1956.