THE INFLUENCE OF VARIOUS CONDITIONS AND FACTORS ON THE ECONOMY OF ELECTRICAL MACHINES

A. S. Baturin, A. I. Skorospeshkin

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

Electrical machines can operate under various operating conditions and factors, on which their economic indicators depend. In this connection there arises the need to develop a methodology for taking account of various operating conditions and factors.

1. One of the factors is the number of hours for which an electrical machine is switched on per year \((T_{\text{г}})\). This factor affects the magnitude of the cost of the consumed electrical energy, the cost of energy losses, and also the amount of repair expenses and depreciation.

The cost of the consumed energy and losses changes in proportion to \(T_{\text{г}}\) and is calculated by the corresponding known formulas.

To take account of the influence of annual operating time on repair expenses, one may use the data of the system of planned preventive repair (PPR) [1]. According to this system, when calculating repair expenses, the shift operation of electrical equipment is taken into account. For single-shift operation \((T_{\text{г}}=2000\ \text{h/year})\), the periodicity of repairs is multiplied by a coefficient of 1.4; for two-shift operation \((T_{\text{г}}=3950\ \text{h/year})\), by 1.0; and for three-shift operation \((T_{\text{г}}=5870)\), by 0.6. In accordance with this, the magnitude of repair expenses also changes.

The total number of operating hours per year \((T_{\text{г}})\) also affects the amount of depreciation charges \((A_{\text{т}})\), since with an increase in \(T_{\text{г}}\) more rapid physical wear occurs, which requires additional expenditures for major and medium repairs (with a periodicity of more than a year), carried out at the expense of part of the depreciation charges. On this basis, the depreciation rate for major repair is adjusted. The total annual depreciation rate \((H_{\text{A}})\) for electric motors with a power of up to 100 kW is 10.2 percent [2]. Of this, 3.7 percent of the total rate is used for major repair, and 6.5 percent for renovation. However, this rate is valid for two-shift operation \((T_{\text{г}}=2000\ \text{h/year})\). Under single-shift operation, the rate for major repair is multiplied by the coefficient 0.8, and under three-shift operation by 1.2. Consequently, for single-shift operation:
\(H_{\text{A}}=3.7\cdot0.8+6.5=9.5\) percent; for two-shift operation, \(H_{\text{A}}=3.7\cdot1+6.5=10.2\) percent; and for three-shift operation, \(H_{\text{A}}=3.7\cdot1.2+6.5=11\) percent. Hence it is seen that with an increase in the number of operating hours \((T_{\text{г}})\), the depreciation rate \((H_{\text{A}})\), and therefore also the depreciation charges \((A_{\text{т}})\), increase at a lower rate than \(T_{\text{г}}\).

1. The second factor is the ratio between the time of ra-

operation under load \((t_1)\) and the time of operation without load \((t_2)\), that is, \(t_1:t_2\), with \(t_1+t_2=T_{\text{g}}\). The ratio \(t_1:t_2\) affects the magnitude of the cost of the energy consumed and the magnitude of the cost of energy losses. On the basis of the ratio \(t_1:t_2\), the cost of the energy consumed \((E_{\text{g}})\) and the cost of losses \((P_{\text{e}})\) are determined from formulas. It is clear that as the time \(t_1\) increases, the absolute amount of energy consumed and the cost of losses increase, and vice versa. For asynchronous motors it is also necessary here to take into account the influence of the ratio \(t_1:t_2\) on the value of the power factor \((\cos\varphi)\), since operation without load sharply reduces \(\cos\varphi\) and requires the installation of additional compensating devices (for example, static capacitors), which in turn are associated with the need for additional capital investments \((K)\). Operation of compensating installations entails depreciation costs and the cost of electric-energy losses in them.

1. The magnitude of operating expenses is also influenced by the load factor of the electric machine with respect to power—\(K_{\text{z}}\). Its value is determined as the ratio of the actual output power \((P_{\text{v}})\) to the rated power \((P_{\text{n}})\). The value of \(K_{\text{z}}\) affects the magnitude of the cost of the energy consumed \((E_{\text{g}})\) and the cost of energy losses \((P_{\text{e}})\). Allowance for \(K_{\text{z}}\) when calculating the cost of the energy consumed and the losses is made by substituting the actual output powers \((P_{\text{v}})\) and the corresponding values of electric-energy losses at this power. The values of the efficiency, etc., for various values of \(P_{\text{v}}\) may be taken from graphs of the characteristics of electric machines. The magnitude of no-load losses does not change with \(K_{\text{z}}\).

2. One of the factors substantially affecting operating expenses is the magnitude of the two-rate tariff for electric energy. In the USSR the magnitude of this tariff depends on the power system that supplies the electric energy [3]. The lowest tariff is 0.0063 rubles/kWh (Krasnoyarskenergo); the average tariff for the USSR is 0.013 rubles/kWh; the highest tariff is 0.090 rubles/kWh (Kamchatskenergo). As can be seen from the figures given, the maximum tariff exceeds the minimum by 14.3 times. This factor is taken into account when calculating the cost of the energy consumed and the cost of electric-energy losses by substituting the corresponding tariff value.

3. The magnitude of operating expenses is also substantially affected by the conditions under which the electric machine operates, that is, the environmental conditions in which the machine is operated. These conditions can be taken into account by selecting the corresponding structure of the repair cycle according to the PPR system [1]. For various operating conditions, this system gives data on the structure of the repair cycle and its duration; on the basis of the structure of the repair cycle, the number of different repairs in the cycle is determined. On this basis the magnitude of repair expenses is determined from the formula:

\[ P_{\text{g}}=\left(\frac{n_{\text{s}}\cdot S_{\text{s}}+n_{\text{m}}\cdot S_{\text{m}}}{T_{\text{c}}}\right)R, \tag{1} \]

where

\(P_{\text{g}}\) — annual repair expenses, rubles/year;

\(n_{\text{s}}\) — number of medium repairs in the cycle with a periodicity of less than one year;

\(n_{\text{m}}\) — number of minor repairs in the cycle;

\(S_{\text{s}}\) — costs of carrying out one medium repair per one conventional repair unit;

\(S_m\) — the same for one minor repair;

\(R\) — category of repair complexity of the electrical machine;

\(T_c\) — duration of the repair cycle in years.

Along with this, when electrical machines operate under severe conditions (aggressive environment, high temperature, increased humidity), accelerated physical wear occurs and the service life is shortened. Therefore the general rate of depreciation charges (\(H_a\)) is increased by a factor of 1.5 [2]. Thus, for severe operating conditions the annual depreciation rate will be: for single-shift operation — \(H_a = 9.5 \cdot 1.5 = 14.25\) percent, for two-shift operation — \(H_a = 10.2 \cdot 1.5 = 15.3\) percent, and for three-shift operation — \(H_a = 11 \cdot 1.5 = 16.5\) percent (electric motors up to 100 kW).

1. In a number of cases certain reliability requirements are imposed on the operation of an electrical machine. If the reliability of the machine is insufficient, it may become necessary to install two or more machines in parallel (cold standby). Automation makes it possible, when one machine fails, to switch on the standby machine. However, such a solution increases capital costs (\(K\)) and, correspondingly, the amount of depreciation charges, thereby worsening the cost-related economic indicators.

2. Another possible factor is the requirement for overload capacity, since in a number of cases overloads cannot be avoided under the operating conditions. Under these conditions it is necessary that the electrical machine satisfy this requirement. Insufficient overload capacity of the machine may force the choice of one of higher power, which is economically disadvantageous, since it increases capital costs (\(K\)), depreciation in operating expenses, and also the cost of the energy consumed and the cost of losses may increase slightly.

All the listed factors must be taken into account when determining annual operating expenses (\(C\)).

The criterion of economy of an electrical machine is the minimum of annual reduced costs (\(Z_r\)) in comparison with all possible variants for solving the given technical problem. The magnitude of these costs is determined by the formula:

\[ Z_{r(i)} = C_i + E_n \cdot K_i, \tag{2} \]

where

\(i\) — number of the variant of the electrical machine by means of which the given technical problem can be solved;

\(E_n\) — normative coefficient of comparative economic efficiency;

\(K_i\) — total capital costs, including the basic and the associated costs arising from the fact that the proposed variants may have different costs of the energy consumed, different amounts of copper, and different values of \(\cos \varphi\). From the structure of the reduced formula (2) it is clear that the economy of an electrical machine depends on all the conditions and factors of operation.

Their interaction determines the level of economy of the electrical machine under particular operating conditions.

According to the method described, a calculation was made of the economic indicators of various designs of electromachine amplifiers (EMA). In Figs. 1 and 2 are given graphs of the dependence of the cost indicators of EMA-12A on the number of operating hours (\(T_g\)). In the present case only one factor was changed—the tariff for electric energy (\(S_e\)). In Fig. 1 the value is \(S_e = 0.0063\) rub/kW·h (minimum tariff); and in Fig. 2 the tariff is \(S_e = 0.090\) rub/kW·h (maximum tariff). Let us make

analysis of the graphs. First of all, let us note that the graph in Fig. 2 is drawn on a reduced (by a factor of 2) scale in comparison with the graph in Fig. 1. However, even with this in mind, comparison of the annual reduced costs \((Z_{\mathrm{r}})\) in the graphs shows that in Fig. 2 they are noticeably larger. One more feature may be noted: the value of the annual reduced costs \((Z_{\mathrm{r}})\) in Fig. 2 increases more rapidly as the number of hours \((T_{\mathrm{r}})\) increases (the \(Z_{\mathrm{r}}\) curve has a steeper rise). Careful comparison of the graphs also reveals the main reason for the changes that have occurred: the higher tariff for electric power, which caused an increase in the cost of the energy consumed \((E_{\mathrm{r}})\). The \(E_{\mathrm{r}}\) layer in Fig. 2 has the greatest thickness, increasing with the growth of the number of operating hours \((T_{\mathrm{r}})\). If the different scales are taken into account, then the magnitudes of the remaining layers of the graph—

Fig. 1. Graph of the dependence of the cost indicators of the EMU-12A on the number of operating hours \((T_{\mathrm{r}})\) at \(t_1 : t_2 = 1 : 1\), \(S_{\mathrm{e}} = 0.0063\) rub/kW·h, \(K_{\mathrm{z}} = 1\), normal operating conditions: \(A_{\mathrm{r}}\) — depreciation, \(R_{\mathrm{r}}\) — repair costs, \(E_{\mathrm{r}}\) — cost of consumed electric energy, \(P_{\mathrm{e}}\) — cost of energy losses, \(C\) — operating expenses, \(Z_{\mathrm{r}}\) — reduced costs.

Fig. 2. Graph of the dependence of the cost indicators of the EMU-12A on the number of operating hours \((T_{\mathrm{r}})\) at \(t_1 : t_2 = 1 : 1\), \(S_{\mathrm{e}} = 0.090\) rub./kWh, \(K_{\mathrm{z}} = 1\).
\(A_{\mathrm{r}}\) — depreciation, \(P_{\mathrm{r}}\) — repair costs, \(E_{\mathrm{t}}\) — cost of consumed energy, \(P_{\mathrm{e}}\) — cost of energy losses, \(C\) — operating expenses, \(Z_{\mathrm{r}}\) — annual reduced costs.

… of Figs. 1 and 2 have the same meaning. The cost of electrical-energy losses \((P_{\mathrm{e}})\), which is a component of \(E_{\mathrm{r}}\), varies similarly to the latter.

Comparison of the economy of many EMU variants under different operating conditions and factors makes it possible to establish the regions in which it is economically expedient to use one variant or another.

Conclusions

1. Operating conditions and factors have a substantial influence on the cost-related economic indicators.
2. This influence can be taken into account by the proposed methodology.
3. The interaction of conditions and factors predetermines the level of annual reduced costs, which characterize the degree of economy of the electrical machines being compared.

References

1. Unified system of planned preventive maintenance and rational operation of technological equipment of machine-building enterprises. Moscow, 1964.

2. P. R. Filippov. New depreciation norms. Moscow, 1963.

3. Average wholesale prices and tariffs and the amounts of changes in average wholesale prices and tariffs for individual types of products and freight transport, introduced as of July 1, 1967. Reference Book No. 1. Preiskurantiz, Moscow, 1967.