ON THE USE OF ALUMINUM WINDINGS IN 110 kV THREE-PHASE POWER TRANSFORMERS

I. D. KUTYAVIN, G. B. DEL

The question of the use of aluminum in transformer construction has been discussed many times in the domestic and foreign press. Nevertheless, there is still no unified opinion on this matter, despite the experience accumulated in the manufacture and operation of transformers with aluminum windings. This applies especially to transformers with a high-side voltage of 110 kV.

This article presents some results of a study of the geometry of “aluminum” three-phase two-winding power transformers with ratings of 2.5–40 MVA. The study was carried out with a variable fill factor of the winding area by conductor material, analogously to [1]. The basic calculation formulas were also taken from [1]. As we have shown earlier, the number of independent variables for low-power power transformers is equal to three. The independent variables adopted were: the radial width of the HV winding coil, \(x_1\); its axial height (without insulation), \(y_1\); and the number of turns in the LV winding coil, \(\omega_{k2}\).

In the case of using a helical-type winding on the low-voltage side (medium-power transformers) with a definite number of starts, one may take \(\omega_{k2} = \mathrm{const}\). Then the number of independent variables is reduced to two \((x_1, y_1)\).

All calculations were carried out on a high-speed electronic digital computer using the blind-search method.

Comparison of the calculated data for aluminum and copper transformers showed a similarity in the nature of the behavior of the calculated costs and certain other parameters with respect to the adopted independent variables. Only a quantitative difference is observed in the values of the minimum costs and optimal quantities. For example, according to [1], the optimal value of the specific heat loading \(\sigma\) for transformers of 5.6–15 MVA ranges from \(0.1\) to \(0.15\ \mathrm{W/cm^2}\) (taking \(\sigma_1 = \sigma_2\)). With the same constants (except for the different physical constants of copper and aluminum), for aluminum transformers the value \(\sigma_{\mathrm{opt}}\) lies within \(0.07\)–\(0.1\ \mathrm{W/cm^2}\), i.e., lower than for copper ones.

The optimal value of the induction in the core of an “aluminum” transformer remains the same as for a “copper” one.

The situation is somewhat different with respect to the optimum value of the reactive component of the short-circuit voltage. Calculations give a smaller value of \(u_{r\,\mathrm{opt}}\) for transformers with copper windings (allowing for the cost of compensating the reactive short-circuit losses). Thus, with a compensation cost of 1 kvar at 1.5 rubles, for a “copper” transformer we have \(u_{r\,\mathrm{opt}} = 0.065\), and for an “aluminum” one, respectively, \(0.08\) (for transformer rating \(S = 10\) MVA).

Let us dwell in more detail on the dependence of the calculated costs on the number of turns of the secondary-winding coil, since this dependence was not investigated in [1]. Table 1 gives the percentage change in the calculated costs as a function of \(w_{k2}\) for transformers of different ratings.

Table 1

| \(S\), kVA | \multicolumn{5}{c}{\(w_{k2}\)} |
|---:|---:|---:|---:|---:|---:|
| | \multicolumn{5}{c}{\(W_{k2}/W_{k2\min}\)} |
| 2500 | 7 | 10 | 13 | 16 | 19 |
| 2500 | 103 | 100.4 | 100 | 100.2 | 100.5 |
| 6300 | 3 | 5 | 7 | 9 | 11 |
| 6300 | 112.5 | 100.6 | 100 | 100.4 | 101.4 |
| 10000 | 2 | 3 | 5 | 7 | 9 |
| 10000 | 110 | 101.6 | 100 | 100.8 | 102.1 |
| 16000 | 1 | 2 | 3 | 5 | 7 |
| 16000 | 132 | 102.2 | 100 | 100.8 | 102.7 |

A characteristic feature is the gently sloping dependence \(Z(w_{k2})\) in the region of the minimum calculated costs and toward values \(w_{k2} > w_{k2\,\mathrm{opt}}\). When, however, the number of turns of the LV winding coil approaches unity (which means a transition from a continuous-type winding to a helical one), there is a sharp increase in the calculated costs. This is evidence of the economic disadvantage of using an ordinary helical winding for transformers rated up to 25 MVA, even when aluminum is used.

The weak variation of the calculated costs with \(w_{k2}\) is explained by Fig. 1, which shows an almost direct proportionality between \(w_{k2}\) and the axial dimension of the LV coil, \(y_2\). And according to [1], the change in the calculated costs with \(y_2\) (as also with \(y_1\)) is very weak. If we take into account the expression for the magnetomotive force of the secondary-winding coil [1]

\[ I_2 w_{k2} = \frac{x_2 y_2 \Delta_2}{1 + k_2 y_2 \Delta_2}, \tag{1} \]

and assume (see Fig. 1)

\[ y_2 = w_{k2}, \tag{2} \]

then we obtain the constancy of the expression

\[ \frac{x_2 \Delta_2}{I_2(1+\lambda_2 y_2 \Delta_2)}=\mathrm{const}. \tag{3} \]

for any values of \(w_{k2}\).

Expression (3) indicates an approximately hyperbolic dependence of the width of the LV winding coil on the current density in it, since \([(1+\lambda_2 y_2 \Delta_2)\approx \mathrm{const}]\). But this conclusion applies only to windings of the continuous type.

It should also be noted that the current density of the HV winding is almost completely independent of \(w_{k2}\).

Fig. 1.

Finally, on the techno-economic evaluation of transformers with aluminum windings. Table 2 gives the specific indices of “copper” and “aluminum” transformers per \(1\ \mathrm{kVA}\) of power, as calculated by us: \(Q'_c\), \(Q'_m\), \(Q'_n\), the weight of steel, windings, and reduced weight, referred to \(1\ \mathrm{kVA}\) of transformer power; \(P'_c\), \(P'_m\), and \(\sum P'\)—losses in the steel, in the winding, and total losses, referred to \(1\ \mathrm{kVA}\); \(Z'_c\), \(Z'_m\), and \(Z'\)—costs for steel, for the winding, and total costs, referred to \(1\ \mathrm{kVA}\).

The following conclusions follow from this table. The weight, losses, and costs for steel are greater in “aluminum” transformers (by approximately 10%). The weight of the windings and the reduced weight, on the contrary, are greater in “copper” transformers. The costs for the windings are always lower in “aluminum” transformers. The total calculated costs for transformers with aluminum windings are lower than for those with copper windings in cases of low ratings. As the rating increases, the reverse is observed: “copper” transforma-

Table 2

Comparative data of transformers with aluminum and copper

tors.” True, this difference in calculated costs (for both cases) fluctuates within the range of \(\pm 5\%\).

Figure 2 shows the variation of the calculated costs as a function of the width of the coil of the primary winding \(x_1\) for different values of the ratio \(\beta\) (the cost of \(1\ \text{kg}\) of the finished winding to the cost of \(1\ \text{kg}\) of the magnetic core) for a transformer with \(S = 10\ \text{MVA}\). On the basis of this figure one can draw the important conclusion that the optimum transformer dimensions are almost completely independent of the value of \(\beta\) (for \(\beta = 2\text{--}5\), the discrepancy in the values of \(x_{1\ \mathrm{opt}}\) is \(\sim 2.5\%\)). On the other hand, the magnitude of the calculated costs itself depends comparatively weakly

Fig. 2.

from \(\beta\) (when \(\beta\) is reduced from 3.8 to 3, the calculated costs fall by only 3.8%).

Transformers with aluminum windings, in comparison with copper ones, have a geometry that is more elongated in height and somewhat widened. The increased radial width of the coils of “aluminum” transformers indicates their greater resistance to axial forces under short-circuit conditions.

The mechanical stresses in the windings due to radial forces during a short circuit beyond a transformer of \(S = 40\) MVA are \(\sigma_{p1} = 247\ \text{kg/cm}^2\), and \(\sigma_{p2} = 275\ \text{kg/cm}^2\), i.e., less than the permissible value (taking \([\sigma_p] = 300\ \text{kg/cm}^2\)).

In conclusion, Table 3 gives the specific indices of aluminum transformers calculated by the method set forth in [1], and of factory-produced transformers.

Table 3

It is evident from the table that, in terms of weight indices, factory-produced transformers are inferior to the calculated ones. The steel losses in the calculated transformers are also lower. The winding losses and total losses for the calculated 2.5 MVA transformer are greater than those of the factory-produced transformer, while for 25 MVA they are approximately at the same level (taking into account that we did not calculate the magnitude of the additional losses).

Despite the higher losses in the calculated 2.5 MVA transformer, the total costs for it are 19% lower than for the corresponding factory-produced transformer.

CONCLUSIONS

1. The method of techno-economic investigations set forth in [1] and [2] is suitable for the investigation of transformers not only with copper windings, but also with aluminum windings. Used as a design method for calculating “aluminum” transformers, it also gives satisfactory results.

1. As a winding material for 110 kV transformers, aluminum is equivalent to copper, even without taking into account the shortage of the latter.

2. The specific thermal loading of “aluminum” transformers is lower than that of copper ones. The value of the optimum induction is the same.

3. The position of the minimum of the calculated costs is almost independent of the ratio of the cost of 1 kg of winding and steel—\(\beta\).

4. The character of the behavior of the dependences of the various parameters on the same independent variables is identical for “aluminum” and “copper” transformers.

REFERENCES

1. Del, G. V., Krasnov V. P. Techno-economic studies of the optimum dimensions of power transformers, Izvestiya TPI, vol. 132, 1965.

2. Kutyavin I. D., Del, G. V., Krasnov V. P. On the techno-economic determination of the optimum dimensions of substation three-phase two-winding transformers of high power, Izvestiya TPI, vol. 130, 1964.

3. Sagalov M. I. Transformers of the 110 kV class of low power and their application for the electrification of agriculture, Vestnik elektropromyshlennosti, No. 12, 1961.

4. Manufacture of the first transformer of the 110 kV series of a new design.
   Rădulescu Costin, Toma Gheorghe, Năzdrăvan Ilie, Realizarea primului transformator din Serile la 110 kv după principii constructive noi, Comun tehn, electrouput, 1963 (Rom.).