Vol. 243

1972

STUDY OF PRICE DEPENDENCES ON THE MAIN PARAMETERS OF SEMICONDUCTOR ELEMENTS OF STATIC CONVERTERS

A. S. BATURIN, S. I. KOROLEV

(Presented by the scientific and technical seminar of the Research Institute of AEM)

In developing static converters it is necessary to solve, in an interrelated way, both technical and economic problems. The most important goal in this should be to obtain optimal solutions.

One of the economic questions that must be considered in this connection is the establishment of multiple correlation dependences of the prices of semiconductor elements of static converters \((Ц)\) on their principal technical parameters. The dependences obtained can be used for orientation when choosing semiconductors for static converters. But, most importantly, with their help it will subsequently be possible to establish the relationship between price and technical parameters in various circuit solutions, which will make it possible to approach the implementation of economic optimization.

To establish dependences of price on the principal parameters of semiconductors for static converters, we used a power function, which is widely applied in practice for similar purposes [1, 2, 4]. In choosing the function, a number of considerations relating to the specific conditions of the study were taken into account: the absence of zero values of the parameters (arguments), the possibility of mathematical processing, and the ease of statistical evaluation.

The initial data for the studies were taken from the current wholesale price list [3], with additions taken into account. A preliminary analysis of the initial data showed that it is inadmissible to combine into one group the indicators for elements having the same designation but different types (grades), since in our case the prices of such semiconductors, for the same technical parameters, differ substantially in magnitude. In this connection, the dependences were established separately for a definite designation and type (grade) of element.

The choice of the principal technical parameters was determined by technical and economic considerations, and was also confirmed by analysis of the initial data.

The results of the work carried out are presented in Table 1.

The correlation dependences obtained were assessed for adequacy to the initial price values by the indicator of the mean approximation error. As a result, satisfactory agreement was established between the calculated prices \((Ц)\) and their actual values according to the price list [3].

Analysis of the dependences presented (Table 1) makes it possible to draw a number of conclusions, which may also be used for practical recommendations.

Table 1

Dependence of Price on the Main Technical Parameters of Semiconductor Elements of Static Converters

Designations: $C$ — adjusted value of the price, determined by the correlation relationship;
$V$ — rated current voltage in volts;
$I$ — rated current strength in amperes.

It is known that, for a power-law dependence, the measure of the influence of a change in a parameter (argument) on the price (function) is characterized by the exponent, which is called the coefficient of elasticity [1, 4]. In the dependences obtained (Table 1), all exponents of the parameters are positive, which indicates that an increase in the parameters—one or two simultaneously—causes an increase in the price of the semiconductor element. But this increase is not the same for different parameters and elements, since the exponents in the relationships given are not equal. The data in Table 1 are arranged in such a way as to make it clearer to trace the effect of parameter changes in individual groups of semiconductor elements on price.

For the first group of elements, including four types (makes) of semiconductors (VK and VK2, VKDL, T, and PTL), a characteristic feature of the correlation relationships is the greater value of the exponent for rated voltage than for current. In this group of semiconductors the price increases to a greater extent from an increase in voltage. Hence it follows that, for one and the same power, semiconductors of this group having a higher current make it possible to obtain a gain in price; and, conversely, at the same power, semiconductors with a high value of rated voltage have a higher price.

The second group of elements (avalanche thyristors TL2, silicon thyristors VKDU and VKU, and symmetrical thyristors VKDUS) consists of semiconductors in which the opposite regularity is manifested in comparison with the first. In this group, the change in current has the greater effect on the change in price as a whole. However, the difference between the exponents of the parameters is comparatively small, and therefore in practice it may be considered that neither parameter has priority in its effect on the change in price; that is, at one and the same power, semiconductors with high rated voltage and low current, or with high current and low voltage, have approximately the same price.

Also of interest is the total value of the elasticity coefficients of the parameters, which indicates by what factor the chan-

the price changes when the parameters are changed simultaneously by one and the same number of times [1]. In our case this indicator ranges from 0.6083 to 1.6395; that is, the greatest influence on price from changes in both parameters occurs for avalanche thyristors PTL, and the smallest for silicon thyristors VKDU and VKU. Proceeding from this, when selecting the parameters of semiconductors that have a large total coefficient of elasticity of the relation (PTL), their correspondence to the calculated data must be as exact as possible, since otherwise this will lead to a noticeable increase in the cost of the circuit. For semiconductors with a smaller value of the total coefficient of elasticity, when selecting parameters it is possible to allow certain discrepancies (in the permissible direction) between the actual and calculated values of the parameters, without causing a substantial change in price. For completeness of the analysis it may be noted that for valves VK and VK2 the sum of the elasticity coefficients (1.0458) is close to unity. In this case the correlation may be represented by a linear function [1].

Conclusions

1. For semiconductor elements of static converters, an increase in the parameters (current or voltage, or a simultaneous increase in current and voltage) causes an increase in price.

2. The degree to which a change in the rated voltage and current affects price is not the same for different semiconductors.

3. In the group of semiconductors (VK and VK2, VKDL, T and PTL), a change in the rated voltage has the greater effect on the change in price. To obtain a price advantage, at the same power, elements with low voltage and a high current value should be selected.

4. In the group of semiconductors (TL2, VKDU, VKDUS), on the whole, the rated current has a somewhat greater effect on the change in price. But since the difference in the exponents of the parameters is comparatively small, in practice it may be considered that neither parameter has priority in affecting the change in price.

5. The greatest change in price when the parameters are changed simultaneously by one and the same number of times occurs for avalanche thyristors PTL, and the smallest for silicon thyristors (VKDU and VKU).

References

1. A. A. Koshuta. Prices for Machine-Building Products. Ekonomika Publishing House, Moscow, 1969.

2. A. A. Matlin. Prices and the Economic Efficiency of Machines. Mashinostroenie Publishing House, Moscow, 1968.

3. Price List No. 15—05, Part 2. Preiskurantniz, Moscow, 1967.

4. A. A. Frenkel. Mathematical Analysis of Labor Productivity. Ekonomika Publishing House, Moscow, 1968.