Proceedings of the Tomsk Polytechnic Institute
awarded the Order of the October Revolution and the Order of the Red Banner of Labor
named after S. M. Kirov

Volume 269 1976

ECONOMIC OPTIMIZATION OF SWITCHING CIRCUITS OF STATIC CONVERTERS

A. S. Baturin, I. I. Vucan, S. I. Korolev

(Presented by the scientific seminar of the Department of Industrial Economics)

One of the important component parts of a static converter is the switching circuit. At present a number of basic circuit solutions are known, as well as their variants [1]. Each circuit solution performs the functions of controlling a static converter, but differs in qualitative characteristics. However, there is the possibility of interchangeability of switching circuits under certain operating conditions. In addition, switching circuits may be used in other products and operate in a switching mode.

In order to select the most advantageous circuit, both technical and economic indicators must be taken into account. The quantitative criterion of the economy of a circuit is the minimum of annual reduced costs [2], in which both operating expenses and capital investments for the variant under study are taken into account. Each circuit solution must be studied separately and considered as an autonomous system.

In the study, the parameters of the input and output data (current and voltage) are varied; the interchangeable elements of the circuit that perform the same functions (makes or types of elements); and the operating conditions (number of hours of circuit operation per year, tariff for electrical energy). Changes in the listed factors affect capital costs and operating expenses and determine the magnitude of the annual reduced costs that characterize the degree of economy of the switching circuit. To carry out the study, an enumeration of potentially possible variants may be performed. The order of the study may be as follows: the first factor is varied while the others have constant values; then the second factor is varied while all the others remain unchanged, and thus a complete enumeration is carried out. When the values of each factor are varied, the minimum values of the annual reduced costs are identified, and, along with this, the absolute and relative deviations of the minimum from the maximum are determined. This is necessary in order to reveal the degree of optimality of the solution. For each minimum, all the data necessary for its practical implementation are required. In this way, the most advantageous optimal implementations of switching circuits for various operating conditions can be found.

On the basis of the study, for each switching circuit, economical implementations under specified operating conditions are determined.

In addition, research data on all circuits and their variants make it possible to determine at what values of current and voltage it is advantageous to use a particular circuit solution, and which circuit is more advantageous when they are interchangeable.

The data of economic optimization of switching circuits are of especially great importance in those cases when, under certain, previously known operating conditions, a large number of circuits will be put into service. If the variant of the switching circuit is not optimal for these conditions, then the users of these circuits will incur considerable economic losses in operating costs. Therefore, in such situations one must not be guided by average operating conditions.

Since varying the values of different factors leads to a very large number of potentially possible solutions, investigations for choosing optimal variants should be carried out on an electronic computer (EC) with the corresponding memory capacity. The use of an EC makes it possible to carry out a comprehensive investigation—computer-aided design and economic optimization.

Computer-aided design is performed in the same order as is done manually. The parameters of the elements are determined from mathematical relationships, and on the basis of a specified logical rule the machine selects the required element from the available set of standard parameter values. Then, from the correlation between price and parameters, the price of the element is determined. This can also be solved if not only the parameters but also the prices of the elements are entered into the machine memory. However, in this case the memory capacity of the machine may be insufficient. The sequential determination of the entire set of elements of the switching circuit makes it possible to establish the material expenditures for its implementation. From the specific weight of material expenditures in analogous products, the cost can be determined, and then, with the aid of the corresponding coefficients, the price and capital investments for the variant.

Capital investments are one of the important indicators for carrying out economic studies. Next, the elements of operating costs (depreciation, repair costs, the cost of electrical energy) and the total amount of annual operating expenditures are determined. The value of annual reduced costs is determined using the optimizing norm of comparative economic efficiency 0.12 [2]. According to a logical rule, the machine selects the minimum of the annual reduced costs from the set obtained by enumerating all values of one factor. And so the calculations are repeated many times, until a complete enumeration of all factors has been made. Simultaneous computer-aided design and economic optimization accelerate and reduce the cost of the research process. The expanded formula for annual reduced costs can be represented as follows:

\[ З_{\mathrm{г}}=\sum_{1}^{n} Ц_i \cdot K_1(E_{\mathrm{н}}+K_A)+T\cdot\left(\sum_{1}^{n} Ц_i\cdot K_2\cdot \lambda_i+P\cdot T_{\mathrm{э}}\right), \tag{1} \]

where

\(З_{\mathrm{г}}\) — annual reduced costs;
\(n\) — number of different elements in the switching circuit;
\(Ц_i\) — price of the \(i\)-th element of a given make (type);
\(K_1\) — coefficient taking into account the transition from material expenditures to cost, price, and capital expenditures;
\(E_{\mathrm{н}}\) — normative coefficient of comparative economic efficiency [2];

$K_A$ — depreciation coefficient for renovation;

$T$ — operating time of the switching circuit per year;

$K_2$ — aggregate coefficient taking into account transportation and procurement costs, wages, and overhead costs when replacing elements;

$\lambda_i$ — failure rate of the $i$-th element of the circuit;

$P$ — power at the circuit input;

$T_\mathrm{e}$ — two-rate tariff for electric power.

Optimization of switching circuits does not completely solve the problem, since in a static converter the use of one or another basic switching circuit entails a change in the set of elements. From this point of view, a systems approach to solving the problem is necessary, since the switching circuit must ensure a minimum of the annual reduced costs of the static converter as a whole. However, optimization of switching circuits makes it possible to find their most advantageous solutions for those cases in which they have independent significance and do not affect the subsequent solution of the overall, more complex system. At the same time, these studies will provide guidance material for developing decisions on limiting switching-circuit solutions for their block production.

REFERENCES

1. G. N. Busalaev, G. K. Shvarts. Evaluation of capacitor devices for thyristor turn-off. Elektrichestvo, 1968, No. 6.

2. Standard methodology for determining the economic efficiency of capital investments. Academy of Sciences of the USSR, 1969.