Fuel Consumption in a Power System with Hydroelectric Power Plant Current Supply*

I. N. Butakov

In the construction and operation of complex power systems that include hydroelectric power plants, thermal power plants, and independent boiler houses, it is very important to have a method for determining the fuel consumption of the power system and to find the conditions for obtaining the most advantageous values of this consumption.

The widely expanding construction of hydroelectric power plants in the USSR makes these questions very timely.

The heat balance of the above-mentioned power system may be represented in the following form:

\[ Q = Q_{m} + Q_{k} + Q_{kot}, \tag{1} \]

where \(Q\) is the total heat consumption, in kcal, for the time interval under consideration, for example, for a year;

\(Q_{m}\) is the same for the back-pressure parts of the thermal power plants included in the power system, with full utilization of heat;

\(Q_{k}\) is the same for the condensing parts of the system;

\(Q_{kot}\) is that from independent boiler houses, if such are included in the power system.

The heat balance (1) may be presented in another form:

\[ \frac{860\left(E - E_{hidr}\right) + Q_{vyr} + Q_{kot}}{\eta} = \frac{860E_{m} + Q_{vyr}}{\eta_{m}} + \frac{860\left(E - E_{m} - E_{hidr}\right)}{\eta_{k}} + \frac{Q_{kot}}{\eta'_{ky}\eta'_{pot}} . \tag{2} \]

Here

\(E\) is the total generation, in kWh, by the entire power system over the time interval under consideration, for example, over a year;

\(E_{m}\) is the generation, in kWh, at thermal power plants for heat consumption;

\(E_{hidr}\) is the same for hydroelectric power plants;

\(Q_{vyr}\) is the number of kcal generated for heat consumers over the same interval of time by extracting steam from intermediate stages of turbines or after back-pressure turbines and reduced-vacuum turbines;

\(\eta_{k}\) is the efficiency of the condensing parts of the units;

\(\eta_{m}\) is the efficiency for the back-pressure parts of units with full utilization of the extracted heat;

\(\eta'_{ky}\) and \(\eta'_{pot}\) are the full net efficiencies of independent boiler houses and of the heat flow within the latter.

All efficiencies should be understood as weighted-average values for the thermal power plants and boiler houses of the power system.

\(\eta\) is the overall economic efficiency of the entire power system.

* Editor’s note: Published as a discussion contribution.

It is known that the fuel consumption of thermal-power installations is proportional to the reciprocal of their economic efficiency, i.e., in the present case it will be proportional to \(1/\eta\). Therefore, from expression (2) we determine:

\[ \frac{1}{\eta} = \frac{1}{ 1+(Q_{vyr}+Q_{kot})\cdot \frac{1}{860(\mathcal{E}-\mathcal{E}_{gidr})} } \cdot \frac{1}{\eta_t} \cdot \left\{ \frac{\eta_t}{\eta_k} - \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{gidr}} \times \right. \]

\[ \left. \times \left(\frac{\eta_t}{\eta_k}-1\right) + \left( \frac{\eta_t}{\eta_{ku}\cdot \eta_{pot}}Q_{kot}+Q_{vyr} \right) \cdot \frac{1}{860(\mathcal{E}-\mathcal{E}_{gidr})} \right\}. \tag{3} \]

From formula (3) it follows:

1. Any increase in \(Q_{kot}\), with the total heat supply to heat subscribers unchanged, \(Q_{vyr}+Q_{kot}=\mathrm{const}\), increases \(1/\eta\), and hence also the fuel consumption in the power system, since in this case the output \(\mathcal{E}_t\) for heat consumption will decrease. Nevertheless, it is advisable to include independent boiler plants for cutting the peaks of the heat load in the power system, in order to increase the coefficient of utilization of steam extractions, the more expensive equipment of the thermal power plant, bearing in mind the cheaper equipment of independent heating boiler plants, which therefore permits lower values of utilization coefficients.

2. With an increase in the initial steam parameters, for a given value of \(Q_{vyr}\), \(\mathcal{E}_t\) will increase and, consequently, the fuel consumption in the power system will decrease; at the same time, this will be aided by the increase in the initial parameters and the rise in \(\eta_k\).

A decrease in the pressure of steam extractions increases \(\mathcal{E}_t\), thereby reducing fuel consumption, while the development of regeneration raises \(\eta_k\), which likewise reduces fuel consumption.

1. Expression (2) may be represented, taking approximately

\[ \frac{\eta_t}{\eta_{ku}\cdot \eta_{kot}} \simeq 1, \]

and thus

\[ \frac{1}{\eta} = \frac{1}{ 1+(Q_{vyr}+Q_{kot})\cdot \frac{1}{860(\mathcal{E}-\mathcal{E}_{gidr})} } \cdot \frac{1}{\eta_t} \cdot \left\{ \frac{\eta_t}{\eta_k} -1 - \right. \]

\[ \left. - \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{gidr}} \left(\frac{\eta_t}{\eta_k}-1\right) \right\} + \frac{1}{\eta_t}. \tag{4} \]

It is seen from this that an increase in the total heat supply to subscribers \((Q_{vyr}+Q_{kot})\) reduces the fuel consumption of the power system for the specified other quantities.

1. Let us further put \(Q_{vyr}=\mathcal{E}_t q\), where

\[ q= \frac{860}{\eta_{oe}\cdot H} \left(i_1-\eta_{oi}H-t_{kond}\right) \]

\[ \frac{\mathrm{kcal}}{\mathrm{kWh}}, \]

where

\(i_1\) is the initial heat content of the steam in the turbines;

\(\eta_{oe}\) and \(\eta_{oi}\) are the electrical and internal efficiencies of these turbogenerators;

\(H\) — the adiabatic drops in them up to the steam extraction point, kcal/kg;
\(t_{\mathrm{kond}}\) — the temperature of the condensate of the heating steam in the boilers.

Then the expression inside the braces in formula (3) may be represented as follows:

\[ \begin{aligned} &\left\{ \frac{\eta_t}{\eta_k} - \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{\mathrm{gidr}}} \left(\frac{\eta_t}{\eta_k}-1\right) + \left( \frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\cdot \frac{\eta_t}{\eta'_{ku}\cdot\eta'_{\mathrm{pot}}} +1 \right) \frac{q\cdot\mathcal{E}_t}{860(\mathcal{E}-\mathcal{E}_{\mathrm{gidr}})} \right\} = \\[0.6em] &= \left\{ \frac{\eta_t}{\eta_k} - \left[ \left(\frac{\eta_t}{\eta_k}-1\right) - \left( \frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\cdot \frac{\eta_t}{\eta'_{ku}\cdot\eta'_{\mathrm{pot}}} \right)\cdot \frac{q}{860} \right] \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{\mathrm{gidr}}} \right\} = \\[0.6em] &= \left\{ \frac{\eta_t}{\eta_k} - \varphi\, \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{\mathrm{gidr}}} \right\}, \end{aligned} \tag{5} \]

where

\[ \varphi= \left[ \left(\frac{\eta_t}{\eta_k}-1\right) - \left( \frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\cdot \frac{\eta_t}{\eta'_{ku}\cdot\eta'_{\mathrm{pot}}} +1 \right) \frac{q}{860} \right]. \]

If we now carry out the actual division of the fraction

\[ \frac{\mathcal{E}_t}{\mathcal{E}-\mathcal{E}_{\mathrm{gidr}}} \]

in formula (5) by the denominator of the common factor preceding the braces of formula (3):

\[ 1+\left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)\cdot \frac{q\cdot\mathcal{E}_t}{860(\mathcal{E}-\mathcal{E}_{\mathrm{gidr}})}, \]

then we obtain:

\[ \frac{1}{ \left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)\frac{q}{860} } - \frac{ 1 }{ \displaystyle \frac{(1+Q_{\mathrm{kot}}/Q_{\mathrm{vyr}})\,q}{860} } \cdot \frac{ 1 }{ \displaystyle 1+ \left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)\cdot \frac{q\cdot\mathcal{E}_t}{860(\mathcal{E}-\mathcal{E}_{\mathrm{gidr}})} }, \]

so that

\[ \begin{aligned} \frac{1}{\eta} &= \frac{ 1 }{ \displaystyle 1+ \left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)\cdot \frac{Q_{\mathrm{vyr}}}{860(\mathcal{E}-\mathcal{E}_{\mathrm{gidr}})} } \, \frac{1}{\eta_t} \left\{ \frac{\eta_t}{\eta_k} + \frac{860\,\varphi}{ \left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)q } \right\} \\[0.6em] &\quad - \frac{860\,\varphi}{ q\left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right) } \cdot \frac{1}{\eta_t}. \end{aligned} \tag{6} \]

From this it is clearly established that the change in \(1/\eta\), and hence also in the fuel consumption in the power system, as a function of the energy coefficient

\[ Z= \frac{Q_{\mathrm{vyr}}+Q_{\mathrm{kot}}}{860(\mathcal{E}-\mathcal{E}_{\mathrm{gidr}})} \]

will follow the law of the hyperbola (6), whose asymptotes are, on the one hand, a straight line parallel to the \(Z\) axis and lying above it at the distance

\[ 1/\eta= \frac{1}{\eta_t}\cdot \frac{860\,\varphi}{ \left(1+\frac{Q_{\mathrm{kot}}}{Q_{\mathrm{vyr}}}\right)q }, \]

and, on the other hand, a straight line parallel to the \(1/\eta\) axis, drawn from it at the distance \(Z=-1\).

In Fig. 1 two hyperbolas have been constructed for the cases when \(\dfrac{Q_{kot}}{Q_{vyr}}=0\) and when \(\dfrac{Q_{kot}}{Q_{vyr}}=1\), with \(\eta_m \simeq \eta'_{ku}\cdot \eta'_{pot} \simeq 0.8\), \(\eta_k \simeq 0.2\), and \(q \simeq 5000\ \text{kcal/kWh}\) adopted as weighted-average values for some power system. From Fig. 1 it is seen that an increase in \(\dfrac{Q_{kot}}{Q_{vyr}}\) causes, for all values \(Z>0\), an increase in \(1/\eta\), and hence in fuel consumption.

Fig. 1.

Central boiler houses, which usually are under the jurisdiction of various industrial ministries, often operate under conditions of lower efficiency, and also with lower values of economic efficiency. Being in the district of a given power system, but not being formally included in it, they can significantly reduce the overall efficiency of the power system.

For example, Fig. 1 shows that if \(\dfrac{Q_{kot}}{Q_{vyr}}=1\), and

\[ \frac{\eta_m}{\eta'_{ku}\cdot \eta'_{pot}\cdot \eta'_{khoz}}=1.5, \]

then the dashed hyperbola corresponding to this case will lie considerably above the same hyperbola, but with

\[ \frac{\eta_m}{\eta'_{ku}\cdot \eta'_{pot}\cdot \eta'_{khoz}}=1. \]

Thus the fuel consumption in the power system will increase still more because of the presence of such boiler houses with insufficiently well organized operation, with their lower efficiencies; for example, at \(Z=2\) by 25% in comparison with the case when \(\dfrac{Q_{kot}}{Q_{vyr}}=0\), increasing still more with a further increase in \(Z\).

An increase in the energy coefficient

\[ Z=\frac{Q_{vyr}+Q_{kot}}{860\left(E-E_{gidr}\right)} \]

under all conditions reduces fuel consumption. To increase \(Z\), however, it is necessary, str...

per month, to an increase in the generation of \( \mathrm{kWh}\ E_{\text{hyd}} \) by the hydroelectric stations of the power system, while at the same time expanding heat consumption \((Q_{\text{heat}}+Q_{\text{boil}})\) by heat consumers in every possible way, being guided chiefly by an increase in \(Q_{\text{heat}}\).

Let us now dwell on the values of the partial efficiencies appearing in the formulas given above,

\[ \begin{aligned} \eta_{\ell} &=\eta_{\text{cu}}\cdot\eta_{\text{flow}}\cdot\eta_{\text{eco}}\cdot \frac{(i_{1}-i_{n})\eta_{0i}\cdot\eta_{\text{mech}}\cdot\eta_{\text{gen}}+i_{1}-(i_{1}-i_{n})\eta_{0i}-t_{\text{cond}}}{i_{1}-t_{\text{cond}}} \\ &=\eta_{\text{cu}}\cdot\eta_{\text{flow}}\cdot\eta_{\text{eco}}\cdot \left[ 1-\left(1-\eta_{\text{mech}}\cdot\eta_{\text{gen}}\right) \frac{(i_{1}-i_{n})\eta_{0i}}{i_{1}-t_{\text{cond}}} \right] \\ &=\eta_{\text{cu}}\cdot\eta_{\text{flow}}\cdot\eta_{\text{eco}}\cdot \eta'_{\text{mech}}\cdot\eta'_{\text{gen}} . \end{aligned} \tag{7} \]

In formula (7), \(i_{1}\) and \(i_{n}\) are the heat content of the steam at the beginning and at the end of adiabatic expansion, and \(t_{\text{cond}}\) is the temperature of the condensate heating the steam in the boilers.

Here, by \(\eta_{\text{cu}}\) one must understand the net total \(\eta_{\text{cu}}\), i.e.

\[ \eta_{\text{cu}}= \frac{ D^{r}_{k}(i^{r}_{k}-i) +D^{n}_{k}(i^{n}_{k}-i_{\text{fw}}) +Q^{\text{aux}}_{\text{pr}} -D_{\text{pr}}i_{\text{pr}} -\sum Q^{\text{own}}_{\text{cu}} -\dfrac{860(E_{\text{own,flow}}+E_{\text{own,cu}})}{\eta} }{ B_{\text{us}}\,7000 }, \]

where, in contrast to the MES formula, the following subtracted heat consumption is also introduced into \(\eta_{\text{cu}}\):

\[ \frac{860(E_{\text{own,flow}}+E_{\text{own,cu}})}{\eta} \]

for satisfying the station service requirements of boiler houses and fuel depots with fuel supply.

The plant efficiency \(\eta_{\text{eco}}\) characterizes the increase in fuel consumption due to its unloading and losses during storage, and also due to the need for firing up boilers and the impaired operation of boiler houses, nonfulfillment of the initial and final steam parameters, due to steam losses from leaks and purging of superheaters and steam lines, due to the need for testing steam mechanisms, etc. \(\eta_{\text{eco}}=0.95\div0.8\), depending on the operating standards and the arrangement of the thermal power station.

The efficiency of the heat flow during its transport within the thermal power station, \(\eta_{\text{flow}}\), characterizes the losses of all heat schemes of the stations included in the power system, including steam lines, feed lines with heaters, boilers and steam generators, as well as turbine casings.

For \(\eta_{\text{flow}}\), there is as yet an insufficient number of observations. One of the possible ways of determining \(\eta_{\text{flow}}\) is seen from formula (8), namely:

\[ \eta_{\text{flow}}= \frac{ \sum Q^{\text{cu}}_{i} +860E +\left(1-\eta_{\text{mech}}\cdot\eta_{\text{gen}}\right)860E +Q_{\text{cond}} +Q_{\text{boil}} +Q_{\text{heat}} +Q_{\text{aux}} }{ Q_{\text{fuel}} }, \tag{8} \]

where \(\sum Q^{\text{cu}}_{i}\) are the heat losses of boiler installations, \(Q_{\text{cond}}\) is the loss of heat to the condensers of turbogenerators, \(Q_{\text{aux}}\) is the heat consumption for the economic and technical needs of the thermal power stations of the power system, and \(Q_{\text{fuel}}\) is the quantity of heat in the fuel consumed over the time interval under consideration.

For the time being, one may take \(\eta_{\text{flow}}\cong 0.96\text{--}0.97\).

Finally,

\[ \eta_{k}=\eta_{\text{cu}}\cdot\eta_{\text{flow}}\cdot\eta_{\text{eco}}\cdot\eta_{t0}\cdot\eta_{0i}\cdot\eta_{\text{mech}}\cdot\eta_{\text{gen}}, \]

where \(\eta_{t0}\) is the efficiency of the theoretical machine.

The product of the efficiencies \(\eta'_{mech}\cdot\eta'_{gen}\) reflects the losses of the back-pressure parts of turbogenerators using the heat of steam extractions, as reducers, since such losses here are mechanical and electrical losses, apportioned in this case to the electric and heat consumers, in contrast to a condensing power plant, where electrical and mechanical losses are attributed entirely to electric power as the sole product of the condensing plant.

It remains to dwell on the objections that have been raised against the foregoing. Candidate of Technical Sciences, engineer A. S. Gorshkov, in the article “On a Method for Calculating the Efficiency of Power Installations with Combined Use of Heat” (Elektricheskie stantsii, 1948, No. 6, p. 37), wrote: “In the article by I. N. Butakov (see the same issue) ... no answer is given to what would seem to be the basic question: how does fuel consumption change in a power system with hydroelectric stations. By merely introducing new letter symbols into a formula one cannot express the complex dependence that exists between technical-economic indicators and fuel consumption in a power system with hydroelectric stations. Analyzing his formula, Prof. Butakov established that any increase in \(E_{hydr}\) increases the efficiency of the system, which occurs at the expense of kWh generated in the condensing mode. But are such complicated formulas needed in order to understand the advantage of hydroelectric power, obtained without expenditure of fuel?” ...

I. N. Butakov asserts that, by increasing generation at hydroelectric stations, “we shall be able to paralyze the decrease in efficiency resulting from the inclusion of independent boiler houses, and thereby justify the expediency of their use.”

The same is also asserted by I. N. Butakov’s formula, according to which “it is indeed advantageous to develop the supply of heat without generating electric power at heat consumption.”

From all that has been said above, it was evident that I. N. Butakov, using generally accepted letter symbols, did indeed express the complex dependence between technical-economic indicators and fuel consumption in a power system receiving current from hydroelectric stations, contrary to A. S. Gorshkov’s denial of such a possibility. Analyzing his formula, I. N. Butakov established not only that any increase in \(E_{hydr}\) decreases the reciprocal of the system efficiency, proportional to fuel consumption, but also by what law such a decrease occurs (namely, hyperbolically), being at the same time connected with heat consumption as part of the energy coefficient

\[ Z=\frac{Q_{prod}+Q_{boil}}{860\left(E-E_{hydr}\right)}, \]

as an argument. The dependence of \(1/\eta\) on a number of partial efficiencies and on \(Q_{boil}/Q_{prod}\) also became clear.

In Section 4 of the present study I. N. Butakov clearly showed that any increase in \(Q_{boil}/Q_{prod}\) worsens the efficiency of the system, increasing \(1/\eta\) at a given \(Q_{prod}+Q_{boil}=\text{const}\); therefore, from the standpoint of the specific expenditure of heat of fuel per one kilocalorie generated, it is inexpedient to use independent boiler houses, whose negative effect can be paralyzed by the current of hydroelectric stations, making it possible to displace a certain quantity of less advantageous condensing kWh. Despite the indicated disadvantage of supplying heat from independent boiler houses, such boiler houses, for cutting the peaks of the heat load, should nevertheless be included in power systems in order to increase the utilization factor of extractions, the expensive equipment of thermal power plants, and the generation of kWh at heat consumption by reducing the condensing kWh of the power system. This was stated in my article (Elektricheskie stantsii, 1948, No. 6, p. 35). A. S. Gorshkov here applied the well-known sophism: my thought, correct with respect to peak—

boiler houses, he extended it to boiler houses in general, presenting I. N. Butakov as a defender of the expediency of “developing the supply of heat without generating electric power for heat consumption.”

Such a sophism is one of the varieties of the sophism of the “primary falsehood” (Proton pseudos).

The use of sophistical devices in scientific polemics is characteristic of A. S. Gorshkov. Thus, for example, on p. 38 (ibid.) he states that, “not seeing the differences between electrical and thermal energy, Prof. Butakov quite naturally came to the conclusion that, for the characterization of the production process of a thermal power plant, only one efficiency is sufficient for both kinds of energy.” Meanwhile, from the right-hand side of equation (1) of the heat balance (Electric Stations, 1948, No. 6, p. 35) and from equation (2) of the present article it is evident that here the terms are distinguished according to the type of product; moreover, the generation of electric power for heat consumption is separated from condensing generation of kWh in exactly the same way as heat from turbine extractions is separated from heat directly from the boilers, whereas in the practice of the Moscow Power System, defended by A. S. Gorshkov, there is an absence of distinction here. The overall economic efficiency $\eta$ of the left-hand side turns out to be a consequence of the right-hand side of the balance, which follows from the proposition of Marxist dialectics that states: “the separate does not exist otherwise than in that connection which leads to the general” (V. I. Lenin, Philosophical Notebooks, p. 329, 1947).

Thus, A. S. Gorshkov in this case too employs a sophism bearing in logic the name “primary falsehood” (error fundamentalis).

A. S. Gorshkov considers it (p. 39) illogical “to connect the process of transmission of mechanical energy with the supply of heat”; he points to “an attempt at incorrectly establishing a direct connection between the process of generating electric power and the supply of heat.”

From the heat balance presented by A. S. Gorshkov (Fig. 2 on p. 41) it is evident that, in his scheme, the extraction of heat $Q^{T}$ for external consumers and the heat losses $q_{\mathrm{con}}$ to the condenser come first, and only afterward the generation of electric power $860N^{T}$ and $860N_{k}$, which, of course, fundamentally contradicts the actual process at a thermal power plant, where the obtaining of electric power precedes $Q^{T}$ and $q_{\mathrm{con}}$, which are the final stages of the process. Naturally, therefore, that $q_{\mathrm{mech}}$ and $q_{\mathrm{el}}$ are also derived from the heat balance before the formation of $Q^{T}$ and $q_{\mathrm{con}}$, as is indicated for the back-pressure engine in the balance diagram of Fig. 1 (p. 38), reproduced again here in Fig. 2.

Fig. 2.

The heat flow “Into the boiler house,” incidentally, is not at all a part of the heat branched off to the boiler house for its own needs, as A. S. Gorsh—

boilers, and the return to the boiler house of the heat of the condensates of the boilers. Since mechanical and electrical losses (Fig. 2) are deducted from the balance before electric energy and the utilized exhaust heat are formed, it is clear that mechanical and electrical losses affect both kinds of energy obtained. The back-pressure part is here a kind of reducer, which is why the losses of the latter (mechanical and electrical losses), as well as \(\eta_{oi}\), cannot fail to affect the heat consumers as well. Therefore the viewpoint of A. S. Gorshkov, that “heat energy is produced in the boiler house and is characterized by the indicators of the boiler house,” for which reason he takes the efficiency of the turbogenerator with respect to heat release equal to unity, is one-sided and therefore harmful, since it in effect removes from the personnel of the thermal power station responsibility for the condition of its back-pressure part.

Consequently, all of A. S. Gorshkov’s reasoning in this paragraph proceeds from an arbitrary premise, being a typical example of the sophism petitio principii.

At the end of his article No. 6 in Elektricheskie stantsii (p. 4), A. S. Gorshkov stated: “Prof. Butakov has given a complicated mathematical formula, which only makes it difficult to understand simple physical phenomena and production processes.” In the theoretical study of questions in which reality is broadly encompassed—as, in the case under consideration, an entire power system—the appearance of complicated mathematical relationships is inevitable if the possibility is to be provided of covering a large number of influencing factors. For practical use, however, the matter is usually simplified, and here, as applied to the present case, a method tested at the MPS can be used for determining partial efficiencies, with the necessary corrections, namely:

\[ B'_t=\frac{Q_{\mathrm{vyr}}}{\eta_m \cdot Q_r^{\,n} \cdot \eta_{\mathrm{khoz}} \cdot \eta_{\mathrm{snt}} \cdot 10^3} \quad \text{t — fuel consumption for heat} \]

consumers when steam is taken from turbines;

\[ B''_t=\frac{Q_{\mathrm{kot}}}{\eta_{\mathrm{ku}} \cdot \eta_{\mathrm{pot}} \cdot Q_r^{\,n} \cdot \eta_{\mathrm{khoz}} \cdot \eta_{\mathrm{snt}} \cdot 10^3} \quad \text{t—the same when heat is taken from} \]

boilers, where

\[ \eta_{\mathrm{snt}}=\frac{E-E_{\mathrm{snt}}}{E} \]

is the coefficient characterizing the consumption of electric energy for the station’s own heat-supply needs (pumping of the heat carrier, consumption of electric energy for lighting and boiler-house repairs). If now \(B\) is the total fuel consumption at the thermal power station over the same period of time, in tonnes, then the fuel consumption attributable to electric consumers is

\[ B_e=B-B'_t-B''_t, \]

whence the overall electrical efficiency of the MPS is

\[ \eta_e=\frac{860\,(E-E_{\mathrm{gidr}})}{B_e \cdot Q_r^{\,n} \cdot 10^3}. \]

The efficiency of the condensing part, not determined by the MPS, is

\[ \eta_k=\frac{860\,(E-E_t-E_{\mathrm{gidr}})}{B_k \cdot Q_r^{\,n} \cdot 10^3} = \frac{860\left(E-\frac{Q_{\mathrm{vyr}}}{q}-E_{\mathrm{gidr}}\right)}{B_k \cdot Q_r^{\,n} \cdot 10^3}, \]

where

\[ B_k=B-B'_t-B''_t-\frac{860 \cdot Q_{\mathrm{vyr}}}{q \cdot \eta_m \cdot Q_r^{\,n} \cdot 10^3}. \]

The overall economic efficiency of a CHP plant or of the system, the impossibility of establishing which is defended by A. S. Gorshkov,

\[ \eta=\frac{860\left(\mathcal{E}-\mathcal{E}_{\text{gibr}}\right)+Q_{\text{vyr}}+Q_{\text{kot}}} {B\cdot Q_{p}^{\,n}\cdot 10^{3}} . \]

The quantities \(\eta_{tn}\) and \(q\), being known in advance for each individual CHP plant, are determined as weighted averages for the system.

A. S. Gorshkov, having unfortunately pointed to the complexity of the formula, which hampers the understanding of phenomena and processes, has here applied a sophism known in logic as “substitution of proof” (ignoratio elenchi), replacing the refutation of the incorrectness of the formula by an indication of its apparent complexity.

Fetishizing his “physical method,” A. S. Gorshkov indicates that it has been tested in practice, which has proved the effectiveness of its application and whose interests have not forced its abandonment (p. 41). Until 1943 the practice of the MES was based on Prof. Grinevetskii’s method, which was applied everywhere in our country and was regarded as tried and tested. Rumyantsev’s method for determining the cost of CHP products was also widely applied. Nevertheless, practice itself revealed the shortcomings of these methods and rejected them.

In practice there is always the advanced and the backward, and therefore one must treat it with sense. Now certain fundamental shortcomings of the “physical method,” with its dualistic system of indicators, have been discovered, and it is time to introduce the necessary corrections in order to bring it closer to reality.

A conservative attitude toward practice is usually characteristic of obstructionists, who do not wish to see new phenomena, thereby paralyzing the development of practice itself; and A. S. Gorshkov, without himself noticing it, has turned from a progressive worker in the field under consideration into a brake on the cause, defending untenable positions.

Sophists like to resort to the paralogism known in logic as argumentum ad populum (appeal to the people), when the proposition to be proved is replaced by another, capable of arousing agreement among readers or listeners, but having no relation to the proposition being proved. A. S. Gorshkov used this sophism too, numbering among the followers of I. N. Butakov the Ural branch of TEP, which determined the efficiency of CHP plants gross according to Prof. V. I. Grinevetskii’s formula—a formula which I. N. Butakov himself considers unsuitable for use—as well as a number of workers of Omsk CHP Plant No. 1, despite the fact that among the managerial personnel of Omskenergo there were at that time no pupils of I. N. Butakov.

To heighten the effect of the sophism, A. S. Gorshkov did not hesitate to add: “It is no accident that one most often has to encounter analogous facts in the East, where there are many pupils of I. N. Butakov.”

Of course, this is only a deft maneuver, since I. N. Butakov, pointing out in his lectures the errors of A. S. Gorshkov, always impresses upon his students that they are obliged to follow the MES provision exactly until we secure the introduction into it of the necessary corrections.

A. S. Gorshkov was then deputy head of the technical department of the MES, and therefore he bore responsibility for the poor instruction of the people entrusted to him in the East, where, owing to remoteness from Moscow, remnants of the 1943 reporting form, based on Prof. Grinevetskii’s method, for which I. N. Butakov, of course, cannot be responsible, could most easily have survived. The quoted phrase of A. S. Gorshkov may thus be understood as an unsuccessful attempt to absolve himself of responsibility.

At a discussion held in January 1950 in Moscow, organized by ENIN of the Academy of Sciences and MONITOÉ, A. S. Gorshkov delivered a report, “Technical-and-Economic Indicators Organize the Personnel of Power Stations for the Struggle against Energy Losses,” in which he devoted considerable attention to criticism of I. N. Butakov. Here again the outline of a heat balance appeared, and A. S. Gorshkov again asserted that “heat energy is an intermediate withdrawal... and that the production of electrical energy with the corresponding losses is a further stage.” The extent to which this contradicts reality was mentioned above. Further, A. S. Gorshkov stated still more vigorously that “to connect the process of generating electrical energy with the delivery of heat is meaningless.” It was shown above how meaningless A. S. Gorshkov’s point of view is with respect to the back-pressure parts of cogeneration plants with complete utilization of heat, a view that in essence attempts to destroy the concept of the integral process of the latter. “A central boiler house—this is the ideal of an energy installation, if its efficiency is evaluated by the unified efficiency factor of Prof. Butakov,” said A. S. Gorshkov in his report. How far I. N. Butakov was from this ideal is evident from the foregoing. Equally unfounded was the statement made that “Prof. Butakov proposes to calculate a coefficient of useful actions, and not of a separate action,” since it is precisely Prof. Butakov who recommends, in contrast to A. S. Gorshkov’s depersonalization, adopting separate efficiency factors for each kind of product depending on its origin, as was said above.

Thus, in the year and a half that had elapsed since the publication of his article in the journal Elektricheskie stantsii, A. S. Gorshkov, as a scientific worker, was unable to overcome his inclination to use sophisms, despite the fact that in 1948 I sent objections to this article to the editorial office of the journal Elektricheskie stantsii, with which A. S. Gorshkov was undoubtedly acquainted, and which were one of the reasons for organizing the above-mentioned 1950 conference on the indicators of cogeneration plants.

Certain objections in his report during the 1950 discussion were advanced by engineer M. N. Nedlin, basing himself on my article in No. 6 (Elektricheskie stantsii, 1948).

M. N. Nedlin asserted that “the derivation of the overall efficiency factor of the process of combined utilization of heat in the production of electrical energy, representing the summation of energy of different quality, although comparable in terms of fuel consumption, mutually noninterchangeable electrical and thermal energy, is in principle inadmissible; it expresses neither the perfection nor the economy of the process.” This follows from M. N. Nedlin’s viewpoint that an efficiency factor may be called only such an indicator in which the unity of two aspects of a process is reflected—its perfection and its economy. These two features of efficiency no longer fit into a single indicator; the place of such an indicator must be taken by two indicators characterizing: one—the perfection of the processes of the system, the other—its economy.

A. S. Gorshkov also professes a dualistic system of indicators, denying, at the same time, the possibility of the existence of a unified indicator. In the foregoing we see that special efficiency factors must be assigned for each separate process of a cogeneration plant, whether it be the generation of kWh for thermal consumption or condensing generation, whether it be the delivery of heat from extraction points or from independent boiler houses. Only then can we correctly reflect reality with respect to the expenditure of heat in fuel, knowing the magnitude of the product for each separate process expressed in heat units.

The summation of these partial expenditures naturally gives us the total expenditure of the heat of fuel for the cogeneration plant or in the power system, which, when divided by the total output of the cogeneration plant or of the system in the same heat units,

determines the reciprocal value of the efficiency, \(1/\eta\), i.e., the number of kilocalories in the fuel per one kilocalorie produced, regardless of its purpose (for electric power or district heating). The efficiency \(\eta\) is therefore the economic efficiency of the thermal power plant or of the system, since \(1/\eta Q_r^H\) gives us the specific fuel consumption in kg per 1 kcal of the total output of the thermal power plant or system; that is, it shows the degree of perfection in the use of socially necessary labor with respect to the principal component—fuel consumption. This economic efficiency is closely connected with the partial efficiencies of the right-hand side of the heat balance (2), which already characterize the degree of perfection of the equipment and its operation, obliging one to satisfy the requirements of obtaining an expedient techno-economic unity at the thermal power plant and in the power system.

As early as A. I. Herzen (Selected Philosophical Works, vol. 1, p. 98) wrote: “Life is a self-preserving unity of manifoldness, a unity of the whole and of the parts.” Herzen gives a beautiful illustration of this: “Each branch of a tree, even each bud, has relative independence; they may be taken as separate plants; but their totality belongs to one whole, to the living plant of these plants—the tree; remove the branches (Prof. Grinevetskii’s method)—a dead stump remains; remove the trunk—the branches fall apart” (the MPS method). That is why we are obliged to consider the overall economic efficiency in connection with the partial efficiencies in a single heat balance, combining Prof. Grinevetskii’s method with the corrected MPS method.

Primitive peoples did not have a general word denoting a tree as a general concept, but there were many words denoting particular trees. Only with the progress of cognition did this general concept of the tree gain the rights of citizenship. Yet even today semanticists, representatives of one of the fashionable trends of modern subjective idealism in the USA and other capitalist countries, declare general concepts to be devoid of objective meaning and content. A. S. Gorshkov asserts (p. 8 of the collection) that abstract indicators are unsuitable for organizing energy production. As though the semi-general efficiencies for its generation of electric and thermal energy were not abstract indicators. After all, they cannot be detected even with the most powerful microscopes. At the same time, one must not deny partial efficiencies either, because “the general exists only in the individual, through the individual” (Lenin); moreover, we repeat, one must not in one partial indicator combine the generation of electric power by condensation and for heat consumption, and in another partial indicator—the delivery of heat from turbine extractions and directly from boilers. Proceeding in this way, we essentially pass from partial efficiencies to the acquisition of more generalized indicators, already losing the partial ones, while being unable, on the other hand, to rise to the highest stage of generalization—to obtaining a single efficiency of the thermal power plant. We therefore stop halfway; whether we want to or not, we adopt the standpoint of the semanticists, declaring the overall efficiency to be devoid of meaning and content. Meanwhile, only such an efficiency, connected with the partial efficiencies, can correctly reflect the tendency of development of thermal stations, assigning at each stage a definite value to this efficiency. The semi-general efficiency of the MPS for the generation of thermal energy, being isolated from its partial efficiencies for the delivery of heat from turbine extractions and directly from boilers, inaccurately reflects reality, since it depersonalizes these two kinds of heat with respect to efficiency. Since the fuel consumption for the generation of electric power is obtained as the difference between the total fuel consumption at the thermal power plant and its consumption for heat consumers, calculated, as indicated, inaccurately, the natural efficiency for the generation of electric power also inaccurately reflects the actual process at the thermal power plant; all the more so since, deprived of its own partial efficiencies, it depersonalizes

electric power obtained by the condensation method and for heat consumption. As a correction, a new indicator appears here for the combined heat and power plant, in the form of the specific production of electric power for heat consumption,

\[ W=\frac{N_m}{Q_{otb}}, \]

which is completely heterogeneous in its structure with the efficiency, violates the harmony of the entire system of indicators, complicates standardization, and is unsuitable for comparing different thermal power plants with one another.

The viewpoint of M. N. Nedlin and A. S. Gorshkov has no connection with dialectical materialism, since it defends a dualistic system of two isolated efficiencies. It contains no broad mediation of validity, no connection between the whole and its parts.

M. N. Nedlin’s remark that “Prof. I. N. Butakov, in his article, set himself the task of deriving generalized expressions for the efficiency of a power system including thermal power plants, condensing power plants, hydroelectric power plants, and independent boiler houses,” and his perplexity “as to how one can determine the efficiency of a system consisting of thermal power plants consuming fuel and hydroelectric power plants consuming the energy of falling water,” are misplaced, since Prof. Butakov did not include hydroelectric power plants in the system at all. His article was entitled “Fuel Consumption in a Power System with the Inclusion of the Current of Hydroelectric Stations.” As can be seen, this is not the same thing as what M. N. Nedlin writes; he then, without foundation, states that “the main question named by the very title of the article was left unanswered by the author himself, unless one counts such generally known propositions as: the greater the output of a hydroelectric power plant, the lower the fuel consumption.” Meanwhile, my article established the change in fuel consumption as a function of the energy coefficient

\[ Z=\frac{Q_{vyr}+Q_{kot}}{860\,(E-E_{gidr})}, \]

which depends not only on the output of electric power by the hydroelectric power plant, but also on the magnitude of heat consumption, according to the hyperbola law, whose position in the drawing is determined by the efficiencies of the thermal units included in the system (qualitative indicators). This important dependence was established in the literature for the first time, and not to notice it means to take a superficial approach to one’s duties as a critic.

Prof. D. P. Gokhshtein, in his report at the conference, pointed out that the exhaust heat of the engine, shown in Fig. 3 by the area \(3'—3—2—1'—3'\), is, according to I. N. Butakov, used for heat consumption for useful utilization, like the heat shown by the area \(1—2—3—4—1\). This contradicts the second law of thermodynamics: at the ambient temperature \(T_0\), only a part can be usefully utilized

Fig. 3.

heat, represented by the area \(3''—3—2—1''—3''\), which is actually equivalent to \(860 N\). The part represented by the area \(3'—3''—1''—1'—3'\) cannot be converted into any other forms of energy: this is a region that plays, to a certain extent, a role analogous to that of the fuel zone. This, then, is where the error of Prof. Butakov and his followers lies.

One can only be astonished that Prof. D. P. Gokhshtein, being a thermodynamicist, could have allowed such paralogism here, since even students studying thermodynamics for the first time are told that the area \(3—2—1'—3'—3''\) represents the latent heat of vaporization, or a value close to it when point 2 lies outside the boundary curve, used by heat consumers. This same area, on the other hand, in principle, represents the work that the working heat could perform in the temperature interval \(T_2\) and \(T_2 = 0\), i.e. it may be regarded as equivalent to \(860 N\).

The foregoing has shown examples of methods of scientific criticism on the part of the scientific worker, Candidate of Technical Sciences A. S. Gorshkov, the MES engineer M. N. Tsedilin, and Prof. D. P. Gokhshtein.

Comrade Stalin (Works, vol. 10, p. 331) pointed out: “And precisely because we want to move forward, we must set as one of our most important tasks honest and revolutionary self-criticism. Without it there is no movement forward. Without it there is no development.”

The widespread use of sophistic devices in scientific polemics cannot, of course, be classified as honest criticism, just as the severance of such criticism from Marxist-Leninist theory cannot be classified as revolutionary criticism.