PROCEEDINGS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR POLYTECHNIC
INSTITUTE named after S. M. KIROV

Volume 89　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1957

I. N. BUTAKOV’S ERROR

IN CONSTRUCTING THE ENERGY BALANCE AND CALCULATING

INDICATORS OF ENERGY PRODUCTION¹)

A. S. GORSHKOV

In the article “Fuel Consumption in an Energy System in the Presence of Current Supply from Hydroelectric Stations,” I. N. Butakov repeated what he had said in an article of the same name published in the journal Elektricheskie stantsii No. 6 for 1948 and in an article in the collection based on the results of the discussion held in January 1950 at the Energy Institute of the Academy of Sciences of the USSR.

I. N. Butakov did not say a word about the decision of the indicated discussion meeting, where it was stated directly:

“The coefficient of utilization of the heat of fuel at a CHP plant, calculated from the sum of the amounts of electricity and heat generated, cannot serve as an indicator that unambiguously determines the degree of perfection of a CHP plant, since it does not reflect the advantages of generating electricity on the basis of heat consumption, because it equates the conditions of utilization of heat obtained from the boiler plant in the generation of both electricity and heat.”

I. N. Butakov continues to assert that the coefficient of utilization of the heat of fuel at a CHP plant can serve as an indicator of the perfection of the CHP plant. For clarity, let us turn to a concrete numerical example for the simplest turbine-unit installation with back pressure. At this installation, with normal initial and final steam parameters and with its serviceable condition, an electric power of 5000 kW was provided with heat delivery of 25 Mkcal/hour, or 200 kWh/Mkcal. Subsequently, because of a decrease in the initial and an increase in the final steam parameters and deterioration in the condition of the flow part of the turbine, the specific generation of electricity decreased from 200 to 160 kWh/Mkcal. Judging by the specific generation of electricity on the basis of heat consumption, we establish the obvious fact of a decrease in the efficiency of the CHP plant. Such an indicator is present in the technical reporting of electric power stations, and it is by this indicator that CHP personnel primarily evaluate the efficiency of such turbine-unit installations. The decrease in the quantity of electricity produced is reflected also in the economic indicators of the installation under consideration itself and of the system in which it operates.

Let us first turn to the economy indicators of the installation itself: its specific consumption or economic efficiency. Planning and costing practice requires separate accounting of expenditures for each kind of energy produced. The total expenditures of the CHP plant are distributed according to the production of which energy they are caused by. In the case under consideration, we have a turbine unit whose purpose is to convert thermal energy into mechanical energy and then into electrical energy, and therefore it is natural that all losses of the unit are attributed to the electricity produced in it. What these losses are—we shall indicate below in a concrete expression.

¹) Published for discussion.

At full load of the 5000 kW electric generator, its efficiency is 96%, the input power is \(5000 : 0.96 = 5208\) kW and, consequently, the losses in the generator are 208 kW, or, converted to heat, \(208 \times 0.86 = 0.179\) million kcal/h. The mechanical losses of the turbine amounted to 106 kW, or 0.091 million kcal/h. In addition, there are heat losses by radiation from heated surfaces, with steam leakage, start-up losses, and others, for a total of about 0.5 million kcal/h. All these losses, \(0.179 + 0.091 + 0.5 = 0.77\) million kcal/h, we assign to the generation of electricity, together with the useful energy \(5 \times 0.86 = 4.3\) million kcal/h, and obtain the specific heat consumption

\[ b^{э} = \frac{4.3 + 0.77}{5} = 1.014 \text{ million kcal/MW-h, or } 1014 \text{ kcal/kWh}. \]

From the specific consumption the economic efficiency of electricity generation is determined:

\[ \eta^{э} = \frac{4.3}{4.3 + 0.77} = 0.845. \]

This indicator can otherwise be represented as follows:

\[ \eta^{э} = \frac{1}{1 + \frac{0.77}{4.3}} = 0.845. \]

Here we see that the magnitude of this economic efficiency is determined by the specific value of the unit losses, assigned to a unit of electricity generated in the unit. With a reduction of the specific generation to 160 kWh/million kcal and of the electric power to 4000 kW, while maintaining the same external heat supply of 50 million kcal/h, the losses in the electric generator will decrease by only 0.015 million kcal/h, and the total losses—to 0.755 million kcal/h. In this case we shall have

\[ b^{э} = \frac{0.86 \cdot 4 + 0.755}{4} = 1.049 \text{ million kcal/MW-h, or } 1049 \text{ kcal/kWh}, \]

\[ \eta^{э} = \frac{860}{1049} = 0.82. \]

As we see, simultaneously with the reduction in the specific generation of electricity, the specific heat consumption increased and the economic efficiency of electricity generation decreased, since the specific value of the losses per unit of electricity increased from

\[ \frac{0.77}{4.3} = 0.180 \]

to

\[ \frac{0.755}{4} = 0.188. \]

Now let us turn to the overall efficiency, which is insistently recommended by I. N. Butakov for evaluating the perfection of a CHP plant. In the first case

\[ \eta_{0} = \frac{4.3 + 50}{4.3 + 50 + 0.77} = 0.98601. \]

In the second case

\[ \eta_{0} = \frac{3.44 + 50}{3.44 + 50 + 0.755} = 0.98606. \]

As we see, the value of the overall efficiency for the generation of electricity and the supply of heat is considerably higher, and this is quite understandable when the formula is considered in this form:

\[ \eta_0=\frac{1}{1+\frac{0{,}77}{4{,}3+50}}. \]

The overall efficiency is determined by the reduced value of the specific losses, referred not only to electric energy but also to the considerably larger amount of heat energy; and, with the reduced value of the specific losses from

\[ \frac{0{,}77}{4{,}3} \]

to

\[ \frac{0{,}77}{4{,}3+50} \]

the corresponding efficiency increases.

It is important to note that, with a decrease in the specific generation, the overall efficiency has a tendency not to decrease but to increase, since the specific magnitude of the losses referred to electric and heat energy decreases in the example under consideration from

\[ \frac{0{,}77}{4{,}3+50}=0{,}01418 \quad \text{to} \quad \frac{0{,}755}{3{,}44+50}=0{,}01412. \]

Next let us suppose that, alongside the supply of heat from exhaust steam, there has appeared a supply of heat by live steam of another \(50\) Mkcal/hour. Then, according to I. N. Butakov,

\[ \eta_0=\frac{3{,}44+50+50}{3{,}44+50+50+0{,}755}=0{,}9918. \]

Conclusion: the overall efficiency of a CHP plant increases with a reduction in the generation of electric energy on the basis of heat consumption and with an increase in the supply of live steam instead of exhaust steam. Such a coefficient cannot be called the coefficient of efficiency of CHP plants, which must increase the generation of electric energy on the basis of external heat consumption. Such a coefficient is not useful either for practice or for theoretical investigations.

The indicators of CHP plants adopted in the technical reporting of power stations—the specific heat-supply generation of electric energy and the specific heat consumption—comprehensively characterize the effectiveness of CHP plants: in terms of capacity and generation of electric energy on the basis of heat consumption, and also in terms of the economy of the use of heat in the process of converting it into work.

I. N. Butakov himself acknowledges that practice has revealed the shortcomings of the overall efficiency (see p. 19), but nevertheless he places it at the basis of his analysis of the economy of individual power installations and systems, attempting to provide for it a physical, mathematical, and philosophical justification.

I. N. Butakov’s principal error lies in his physical understanding of the process of a CHP plant. In I. N. Butakov’s opinion, the obtaining of electric energy precedes the heat process. In his understanding, the obtaining of heat, and not electric, energy is the final stage of the CHP-plant process. This is stated by him directly on p. 17 and is graphically presented in the peculiar energy balance constructed in Fig. 2. With such a staging of the process as I. N. Butakov presents it, the method he proposes for calculating indicators—orienting CHP-plant personnel toward the final goal he indicates, the supply of heat—is quite understandable. Such an orientation is elementary erroneous and harmful.