INVESTIGATION OF THE COST-EFFECTIVENESS OF NEW DESIGNS OF ELECTRIC MACHINES

(USING COMMUTATOR AND BRUSHLESS ELECTRIC MACHINE AMPLIFIERS—EMU—AS AN EXAMPLE)

A. S. Baturin, A. I. Skorospeshkin

(Recommended by the seminar of the Departments of Electrical Machines and General Electrical Engineering)

The development of new designs of electric machines requires the solution not only of technical problems, but also of economic ones. As a rule, new designs have technical parameters and economic indicators that differ from those of previously developed machines, both in manufacture and in operation. In addition, they may have different qualitative characteristics, which must be taken into account when evaluating an electric machine. In connection with this, it becomes necessary to investigate the cost-effectiveness of new designs under various operating conditions, and also to determine those areas in which they can be used most economically.

The initial data for investigating cost-effectiveness are the designs of new electric machines and experimental data obtained after all necessary laboratory tests have been carried out. All these data are systematized in the form of tables. Along with this, all qualitative features of the new design that may affect manufacture and operation are clarified.

On the basis of these data, the cost and the estimated price of the new product are determined. The value of the cost is established by aggregated methods, since at this stage of development there is no manufacturing technology. In doing so, however, it is necessary to strive for the most accurate possible determination of cost and to take into account data from plants manufacturing similar products. The choice of an aggregated method for determining the cost (or price) of a new product depends on the conditions and on the data that are available or can additionally be obtained. The following methods have found the widest application in practice: by the specific weight of the cost of basic materials, semi-finished products, and purchased components in the cost of analogous products; the method of calculating cost (or price) from the average cost per unit weight of the product; the method based on the average cost (or price) of individual assemblies; the method of paired or multiple correlation; and the correction method.

Using one of the listed methods, or a combination of them, the cost of the new product is determined; this cost is then used as the basis for establishing the estimated price. By adding to the price, if necessary, additional expenses for transportation to the consumer, installation costs, and packaging, the value of the basic capital investments \((K)\) is determined, which is one of the principal economic indicators.

In order to compare new designs with previously developed ones that perform the same functions, it is necessary to bring their technical and economic indicators to a comparable form. For these purposes it may be necessary to establish the dependence of the cost (or price) on the parameters of the electrical machine. Finding these relationships is carried out by the method of paired or multiple correlation [1]. On the basis of the obtained dependencies, the cost (and price) of the new design is adjusted so that its technical parameters correspond to those with which the comparison will be made. The designs being compared must perform the same functions with equal technical parameters. All further work must be carried out using comparable technical and economic indicators.

One of the important indicators of the economy of a new design is the annual operating costs \((C)\).

The magnitude of the individual elements of operating costs (depreciation, repair costs, cost of the electrical energy consumed, etc.) depends substantially on the conditions and factors of operation. Therefore, consideration of possible operating conditions and factors precedes the determination of operating costs in an investigation of economy.

For electrical machines, the factors and conditions of operation include:

1) the number of hours switched on per year \((T_g)\);
2) the ratio between the operating time under load \((t_1)\) and without load \((t_2)\);
3) the power load factor \((K_z)\);
4) the magnitude of the two-part tariff for electrical energy \((S_e)\);
5) the conditions under which operation is carried out (normal, difficult, etc.);
6) reliability of operation under the specified conditions;
7) overloads in operation, etc.

For all possible operating conditions and factors, the annual operating costs \((C)\) and the cost of one hour of operation \((c)\) are calculated. These indicators, together with the magnitude of the basic capital costs \((K)\), characterize the economy of the design under various operating conditions.

Final conclusions on economy can be drawn only when making an assessment from the standpoint of the national economy. Such an assessment can most correctly be made by the formula for annual reduced costs [2]:

\[ Z_g^{(i)} = C_i + E_n K_i, \tag{1} \]

where

\(Z_g\) — annual reduced costs for the \(i\)-th variant (rubles/year);
\(C_i\) — annual operating costs for the \(i\)-th variant;
\(E_n\) — normative coefficient of comparative economic efficiency;
\(K_i\) — total capital investments for the \(i\)-th variant.

The total capital investments include not only the basic investments, but also associated investments connected with the need for capital investments in other branches of the national economy (in power engineering with a larger amount of energy consumed; in nonferrous metallurgy with a larger quantity of copper for manufacture, etc.). It is necessary to take economy into account both in manufacture and in operation [2], without allowing double counting of one and the same saving. The smallest value of the annual reduced costs \((Z_g)\) cha-

characterizes the national-economic efficiency of a design variant under specific operating conditions.

The formula for annual reduced costs (1) most accurately characterizes the economy of the design of an electric machine, since in it \(E_{\mathrm{n}}\) is assumed to be a differential standard value. In this respect formula (1) differs from the formula:

\[ E=\frac{C_2-C_1}{K_1-K_2}>E_{\mathrm{n}}, \tag{2} \]

where

\[ \begin{aligned} E &\text{ is the actual coefficient of comparative economic efficiency;}\\ C_1 \text{ and } C_2 &\text{ are the annual operating expenses for variants 1 and 2,}\\ &\text{and } K_1 \text{ and } K_2 \text{ are the capital investments for the same variants.} \end{aligned} \]

In formula (2) the quantity

\[ E=\frac{C_2-C_1}{K-K_2} \]

is calculated in finite differences and compared with the normative \(E_{\mathrm{n}}\). Moreover, a greater value of \(E\) relative to the normative \(E_{\mathrm{n}}\) is admitted. Such a representation contradicts the theoretical foundations of economic efficiency [7], where it is proved that the quantity \(E_{\mathrm{n}}\) is differential and must have one and the same value for all variants of the optimal plan. This explains the fact that, in analysis by formula (2), cases occur in which practically equally economical variants are regarded as ineffective. For example, \(E_{\mathrm{n}}=0.20\); \(C_1=1000\); \(C_2=1001\); \(K_1=510\); \(K_2=500\), then

\[ E=\frac{1001-1000}{510-500}=1.10<E_{\mathrm{n}}=0.2, \]

variant 1 is rejected as ineffective, although it differs little from the first in economic indicators \((C,K)\). At the same time, however, it may have qualitative advantages. Using formula (1), we obtain the solution:

\[ Z_{\mathrm{r}}=C_1+E_{\mathrm{n}}\cdot K_1=1000+0.2\cdot510=1102\ \text{rubles/year}; \tag{1} \]

\[ Z_{\mathrm{r}}=C_2+E_{\mathrm{n}}\cdot K_2=1001+0.2\cdot500=1101\ \text{rubles/year}, \tag{2} \]

the difference in annual reduced costs is only 0.09 percent, and the variants are practically equivalent.

Thus, according to the formula for annual reduced costs, the decision proved to be different, and it is confirmed by the analysis of \(K\) and \(C\), since the saving in operating expenses is only \(C_2-C_1=1001-1000=1\) ruble (0.1 percent), while the difference in capital costs is \(K_1-K_2=510-500=10\) rubles (2 percent). As we see, the capital investments \((K)\) and annual operating expenses \((C)\) differ little. This confirms the equal economy of the variants.

On the basis of the method set forth, an investigation was carried out of the economy of commutator and brushless electric-machine amplifiers [3, 4, 5, 6]. As a result, formulas were obtained for calculating annual operating costs \((C)\), calculations of \(Z_{\mathrm{r}}\) were made, and graphs were constructed. Figure 1 presents a graph of the dependence of annual operating costs \((C)\), the cost of one hour of operation \((c)\), and annual reduced costs \((Z_{\mathrm{r}})\) on the number of hours of switching-on per year \((T_{\mathrm{g}})\).

From the graph in Fig. 1 it is seen that \(C\) and \(Z_{\mathrm{r}}\), with increasing \(T_{\mathrm{g}}\), increase

Fig. 1. Graph of the dependence of annual operating expenses \((C)\), reduced costs \((Z_g)\), and the cost of one hour of operation \((c)\) for EMU-12P (normal operating conditions \(t_1 : t_2 = 1 : 1\), \(S_e = 0.013\) rub. (kW·h))

slowly along the curve. The cost of one hour of operation \((c)\), however, decreases as \(T_g\) increases. From this one may conclude that, in operating an EMU, it is advantageous to increase the number of hours of operation per year. It should be borne in mind that the parameters of the curves \(C\), \(Z_g\), and \(c\) change under different operating conditions and factors.

The dependence between the output power of the EMU \((P_{\text{out}})\), the reduction in annual operating expenses \((C)\), and losses of electrical energy, for different power load factors \((K_z = 1,\ K_z = 0.7,\ K_z = 0.4)\), on the number of hours of operation \((T_g)\) was also investigated.

The graph of this dependence is presented in Fig. 2.

Since in the graph (Fig. 2) the values of \(P_{\text{out}}\), \(C\), and \(P_e\) are presented in percent, for \(K_z = 1\) one obtains a single straight line parallel to the \(T_g\) axis. On this straight line the values of \(P_{\text{out}}\), \(C\), and \(P_e\) coincide. It is clear that for \(K_z = 1\), \(P_{\text{out}} = 100\) percent; in this case we also take \(C = 100\) percent and \(P_e = 100\) percent. The rest requires no explanation.

Analysis of the graph (Fig. 2) makes it possible to establish that incomplete utilization of the EMU power causes an insignificant reduction in operating expenses \((C)\), and therefore the power of the amplifier must be used as fully as possible. Electrical energy losses at \(K_z = 0.7\) decrease almost in proportion to the load factor. However, at smaller load factors there is a sharp drop in the efficiency of the unit, and the reduction in losses due to this is diminished. Thus, at \(K_z = 0.4\) the value of the losses differs little from the same quantities at \(K_z = 0.7\).

The most important result of the investigations is the establishment of the regions of economical application of various designs of commutator and brushless EMUs.

The new model of electric-machine amplifier with a smooth armature (EMUG-12P), in comparison with the standard EMU-12P, insignificantly pro—

Fig. 2. Graph of the ratio of the values of the output power \((P_{\text{out}})\) of the amplifier, annual operating expenses \((C)\), and losses of electrical energy \((P_{\text{e}})\) at various load factors by power \((K_z)\), in %, (for EMU-12P; \(S_{\text{e}}=0.013\) rub/kWh, \(t_1:t_2=1:1\))

loses in cost-effectiveness in terms of annual reduced costs at the minimum electricity tariff (3–9.7 percent). At the same time, the cost-effectiveness of the EMUG-12P decreases with increasing \(T_g\) and increases under difficult operating conditions. The use of the EMUG-12P at the maximum cost of electrical energy increases the gap in cost-effectiveness to 12 percent. This is explained mainly by the lower efficiency of the EMUG-12P in comparison with the EMU-12P. However, the better response speed and higher operating reliability of the EMUG with sparkless commutation provide it with lower annual reduced costs in automatic control systems (ACS), where increased reliability is required.

The nonreversible design of the brushless electric-machine amplifier (BEMU-12A) according to the scheme of two synchronous generators and two DC machines, under almost all conditions and operating factors,

have lower annual operating costs compared with the commutator EMU-12A and are more economical when there is no requirement for reversibility. At the same time, the brushless EMU-12A using a two-DC-machine circuit is more economical owing to its higher efficiency. Since the brushless EMU-12A have no sliding contact, they are characterized by higher reliability and therefore possess still greater economy in automatic control systems with stringent reliability requirements.

Reversible versions of the brushless EMU-12A compete economically with the EMU-12A only under difficult operating conditions, at the highest electricity tariff, and with the maximum number of operating hours per year.

The main reason reducing their economy is the high cost of manufacturing the control circuit, since it uses expensive controlled diodes—thyristors—the production of which began comparatively recently. Calculations have shown that if the price of thyristors is reduced by a factor of 10, reversible brushless EMU-12A will be more economical under all operating conditions and factors.

For automatic control systems with high reliability, the economy of reversible brushless EMU-12A in comparison with EMU-12A increases, and the area in which they become competitive expands. However, for the time being this area extends mainly only to operation at the highest electricity tariff.

REFERENCES

1. A. A. Koshuta. Determination of costs in electrical-machine building by the method of mathematical statistics. In: Problems of the Economics and Organization of Production at Enterprises of the Electrical-Engineering Industry. TsINTI EI, Moscow, 1963.

2. Standard methodology for determining the economic efficiency of capital investments. Moscow, 1966.

3. A. I. Skorospeshkin, G. G. Konstantinov. Some results of investigating the characteristics and commutation of a transverse-field EMU with a smooth armature. In: Proceedings of TPI, vol. 160, 1966.

4. A. I. Skorospeshkin, E. N. Podborskii. Investigation of the characteristics of a brushless DC electric-machine amplifier (BEMU). In: Proceedings of TPI, vol. 160, 1966.

5. A. S. Baturin, A. I. Skorospeshkin, G. G. Konstantinov. Techno-economic assessment of an electric-machine amplifier with a smooth armature (EMUG-12P). In: Proceedings of TPI, vol. 172, Tomsk, 1967.

6. A. S. Baturin, A. I. Skorospeshkin, E. N. Podborskii. Techno-economic justifications for the development of brushless electric-machine amplifiers (BEMU). In: Proceedings of TPI, vol. 172, 1967.

7. V. N. Bogachev. Time Factor. The Theory of Comparing Planned Variants. Ekonomika Publishing House, Moscow, 1966.