On the Reserves for Improving Transformers

(Regarding the article by Eng. I. S. Kalinichenko, “Elektrotekhnika,” No. 3, 1964).

I. D. KUTYAVIN, L. I. VORONOVA

Eng. I. S. Kalinichenko, in his article, touched upon the very important national-economic problem of utilizing the reserves for improving transformers and increasing their limiting power. He showed the influence of increasing the coefficients of filling the window area with copper and the core cross-sectional area with steel on raising the limiting power of transformers.

Along with this, great importance is acquired by increasing the utilization of the most active materials themselves (copper, steel) by reducing electric-energy losses in transformers and improving their cooling.

For high-power transformers, a significant share of the total losses consists of the so-called stray losses. These include stray losses in the copper of the windings, in the steel of the core, in the clamping rings and beams, and in the transformer tank.

The present article considers the question of reducing losses in the clamping parts and in the tank (in the walls, cover, bottom, and supporting structures), which for large transformers reach 30–40% of the short-circuit losses [2].

Losses in the clamping parts and in the tank are produced by the transformer leakage magnetic fields closing through these elements. In this connection, the following methods may be outlined for reducing the losses under consideration:

1. The use of shell-type cores with split yokes.
2. The use of nonmagnetic materials for the clamping parts and the tank.
3. The use of shields.

Shell-type cores with split yokes, used by Brown Boveri for powerful transformers [1], are manufactured with radial lamination, thereby reducing stray losses in the steel of the core. The sectors of the single-phase core and the yoke are fastened at the ends with tie rods; therefore there are no losses here in the clamping devices either. A considerable share of the leakage fluxes in such transformers closes along the split yokes and does not penetrate into the tank walls, which reduces losses in it.

Losses in the steel structures of a transformer due to stray fields consist of magnetization losses and eddy-current losses. Magnetization losses can be eliminated by using nonmagnetic materials for the structures under consideration. Eddy-current losses, as is known [3], are proportional to the specific electrical conductivity of the material (when the reaction field of the eddy currents is neglected):

\[ p = k B_{\mathrm{p}}^{2} \sigma, \tag{1} \]

where

\(B_{\mathrm{p}}\) is the induction of the stray field in the part in which the losses are produced,

\(\sigma\) is the specific electrical conductivity of the material.

Consequently, a reduction of eddy-current losses can be achieved by using, for the clamping devices and the tank, a material with low specific electrical conductivity. In addition, the material for these products must have the strength of steel and an acceptable cost. Aluminum alloys possess such properties.

The reduction of losses in the structures under consideration, when made of another material, can for the time being be determined only indirectly, since an analytical determination of these losses is difficult because of the complexity involved. For these purposes the results of a very simple experiment may be used. Identical plates made of different materials, with the simplest thermal insulation, are placed in turn in a magnetic field with a frequency of 50 cps and with an induction close to that of the stray field. For each of the plates, the dependence of the increase in heating temperature above the ambient medium, \(\tau\), on the duration of the experiment, \(t\), is recorded, and on the basis of the observations the curves \(\tau(t)\), shown in Fig. 1, are plotted. Here curve \(C\) is constructed for steel, and curve \(D\) for the aluminum alloy D-1AT. The tangents drawn at the beginning of each curve give the law of growth of the temperature increment \(\tau(t)\) for the case without heat transfer to the surrounding medium. Each point lying on these straight lines (tangents), on some scale, corresponds to the amount of heat imparted to the pla-

Fig. 1.

by the magnetic field over the time elapsed since the beginning of the experiment. This amount of heat is determined by the expression:

\[ Q = C \gamma v \tau , \tag{2} \]

where

\(C\) is the specific heat capacity of the material,
\(\gamma\) is the specific weight,
\(v\) is the volume of the plate (the same for all experimental plates).

The increase in the heating temperature of the plate \(\tau\) is equal to the segment \(ab\) (Fig. 1), depending on the material.

If the amount of heat released by the magnetic field in the steel plate is taken as \(100\%\), then the amount of heat, in percent, absorbed by plates of other materials can be determined from the expression:

\[ Q_1 = Q_2 \frac{C_1 \tau_1 \gamma_1}{C_2 \tau_2 \gamma_2} = 100 \frac{C_1 \tau_1 \gamma_1}{C_2 \gamma_2 \tau_2}, \tag{3} \]

where

\(C_1, \gamma_1, \tau_1\) are for the material under investigation,
\(C_2, \gamma_2, \tau_2\) are for steel.

Table 1 gives the ratio of losses in percent, found from (3), for steel, copper, aluminum, and duralumin (D-1AT). For this purpose, curves \(\tau(t)\) were also obtained for copper and aluminum, analogous to the dependences in Fig. 1. The dimensions of the plates were \(0.5 \times 10 \times 20\) cm.

The table also shows the e.m.f.’s induced in the measuring frame placed at the surface of the plate on the side of the magnetic-field source \(E_1\) (column 6), and on the opposite side \(E_2\) (column 7). To determine the influence of the reaction of eddy currents on the leakage field, the last item of the table gives the e.m.f.’s \(E_1\) and \(E_2\) for a getinax plate.

As can be seen from the table, the losses in the steel plate, under identical conditions, are almost twice as large as in copper, aluminum, and duralumin.

Table 1

This is explained by the fact that the magnetic resistance of the path through the steel plate in our experiment was 3–4 times smaller, and the leakage flux correspondingly greater, than through plates of nonmagnetic material (see the ratio \(E_1\) in column 6 for the different materials). In addition, the losses in the steel plate are further increased on account of the remagnetization of the steel.

It is clear from the table that expression (1), in the form of the ratio

\[ \frac{P_{\partial}}{P_{\mathrm{M}}} = \frac{\tau_{\partial}}{\tau_{\mathrm{M}}}, \tag{4} \]

is not satisfied, since the reaction of the eddy currents on the leakage field cannot be neglected. Nevertheless, the losses remain to some extent

proportional to the electrical conductivity of the material. It follows from this that all pressing and fastening parts, as well as transformer tanks (this may also be extended to electrical machines and apparatus), should be made of a nonmagnetic material with the lowest specific electrical conductivity.

Let us determine the economic advantage of replacing steel with D-1AT duralumin. According to [2], stray losses in high-power transformers amount to: in the core steel (10–12%), in the copper of the windings (5–8%), in the tank (15–25%), and in the pressing rings and beams (40–50%) of the total stray losses, which, in turn, may amount to (40–50%) of the short-circuit losses. Let us take the losses in the tank of a TDTs-60000/100 transformer as equal to 10% of the short-circuit losses, amounting to 300 kW, and the weight of the tank as 29 tons [4]. Let the cost of steel be taken as 100 rubles per ton and that of duralumin as 700 rubles. The expenditure of duralumin by volume is equal to the volume of steel.

Then the extra expenditure for making the tank of duralumin is:

\[ 29\left(\frac{\gamma_a}{\gamma_c}700 - 100\right) = 29\left(\frac{2.8}{7.8}700 - 100\right) = 4350\ \text{rub.} \tag{5} \]

Here no allowance has been made for the higher cost of the technology, which may turn out not to favor duralumin. According to item 4 (Table 1), the stray losses in the tank are reduced to 45.5%. The calculated cost of power losses, according to Prof. P. G. Grudinsky [5], is of the order of 500 rub./kW. Then the saving on electric-power losses is:

\[ \frac{10}{100}\,300\,\frac{100 - 45.5}{100}\,500 = 8170\ \text{rub.} \tag{6} \]

For manufacturing the tank, more highly alloyed grades of duralumin may also be used, which will increase the saving on losses. The losses in the pressing devices are greater, while their weight is smaller; therefore the saving from using nonmagnetic materials for them will be greater than for the tank. For a TDTs-60000/110 transformer, the power losses in the pressing devices reach 20% of the short-circuit losses. Then the saving from reducing losses in the pressing parts, if they are made of D-1AT duralumin instead of steel, is

\[ \frac{20}{10}300\left(\frac{100 - 54.5}{100}\right)500 = 16340\ \text{rub.} \tag{7} \]

The additional expenditure for making the pressing parts of duralumin will be small, in view of their low weight.

The foregoing indicates the economic expediency of replacing steel with highly alloyed duralumin for the construction of the tank and pressing parts.

Within the scope of the present article, the question of shielding parts of the tank and the pressing parts is not considered.

REFERENCES

1. Power Engineering Abroad. Transformers, issue 1, Gosenergoizdat, 1958.

2. V. V. Bondar. Requirements of transformer construction for materials and component products. Transformer Construction. Collection of Articles. Moscow, 1961.

3. K. A. Krug. Fundamentals of Electrical Engineering, 1936.

4. Electrical Engineering Handbook, edited by professors of the Moscow Power Engineering Institute. 3rd edition. Gosenergoizdat, 1962.

5. P. I. Tikhomirov. Calculation of Transformers. Gosenergoizdat, 1963.