ON THE RATIONAL ALLOCATION OF SPECIFIC FUEL CONSUMPTION TO CHP PLANT PRODUCTS

I. N. BUTAKOV

It is known that the current methodology of the former Ministry of Power Plants for allocating specific fuel consumption at CHP plants proceeds from the premise that the heat received by heat consumers has the same valuation in kcal regardless of whether the heat comes from turbine extractions or directly from boilers. This is explained by the fact that in both cases the heat is generated in boilers, while the turbines are supposedly irrelevant here. This fundamental error in the basic premise has the consequence that the entire benefit from combined production of energy falls to the electric consumers, while the cost of one kcal turns out to be overstated.

Meanwhile, fuel savings, in accordance with the actual process at a CHP plant, are due to the fact that the turbines have back-pressure sections with full utilization of the heat of exhaust steam, eliminating large heat losses to the condenser.

The latent heat of the exhaust steam is utilized by heat consumers. Therefore, naturally, it must be considered that the savings obtained here in heat and fuel consumption through the displacement of condensing kWh should be attributed to the heat consumers, by whose presence this saving is created. The electric consumers, on the other hand, have nothing to do with it, receiving only a smaller generation of electric power because of the reduction in the heat drop from the initial steam parameters, just as in the case of operation with exhaust to the atmosphere. From what has been said it is clear that the savings in fuel consumption at a CHP plant must be assigned to the heat consumers.

If the generation of electric power without loss to the condenser over the period of time under consideration, for example, over a year, is \(E_t\) kWh, with the efficiency of condensing generation \(\eta_k\), and in heat consumption \(\eta_t\), then the heat saving will be

\[ 860E_t \left(1/\eta_k - 1/\eta_t\right)\ \text{kcal}. \]

The value \(1/\eta_t\) changes little with changes in the operating mode of the CHP plant and practically may be accepted, as in the current methodology of the former Ministry of Power Plants,

\[ \frac{1}{\eta_t} = \frac{1}{\eta_{\text{loss}}\cdot \eta_{\text{ku}}}, \]

where \(\eta_{\text{ku}}\) is the net efficiency of the boiler plant and \(\eta_{\text{loss}}\) is the efficiency of the heat flow within the CHP plant. As for the efficiency \(\eta_k\), this value changes depending on the operating mode

CHP plant, in particular, on changes in steam extractions in a machine with intermediate steam extraction. It is necessary to determine the change in efficiency \(\eta_k\) due to the influencing factors. For this purpose, let us write the heat-balance equation of the CHP plant in the form:

\[ B Q_p^n = \frac{860 E + Q_{ku} + Q_{otb}}{\eta} = \]

\[ = \frac{860 \cdot E_t + Q_{otb}}{\eta_t} + \frac{Q_{ku}}{\eta_{pot}\cdot \eta_{ku}} + \frac{860(E-E_t)}{\eta_k} \ldots \tag{1} \]

Hence, taking approximately, as in the method of the former MPS, that
\(\eta_t \simeq \eta_{ku}\cdot \eta_{pot}\), transferring all terms except the last to the left-hand side of the balance and dividing both parts of equation (1) by \(860(E-E_t)\), we obtain

\[ \frac{1}{\eta_k} = \frac{ B\cdot Q_p^n - \dfrac{1}{\eta_{ku}\cdot \eta_{pot}} \cdot \left[Q_{ku}+Q_{otb}+860E_t\right] }{ 860(E-E_t) }. \tag{2} \]

In the formulas we denote: \(B\) is the quantity of fuel, in kg, consumed at the CHP plant over the time interval under consideration; \(Q_p^n\) is its calorific value (kcal/kg); \(Q_{ku}\) is the quantity of heat, kcal, supplied to heat consumers directly from the CHP boilers; \(Q_{otb}\) is the same from turbine extractions. By \(E_t\) are meant not only the kWh obtained on heat consumption \(Q_{otb}\), but also the kWh generated on the basis of unregulated regenerative steam extractions of the back-pressure section, so that

\[ E_t = E_t^{otb} + E_t^r . \]

The value \(E_t\) for turbines with back pressure is obtained directly on the CHP plant busbars for each turbine, and hence, for all these turbines, as the active generation \(\sum E_t\) of electric power for these turbines over the time interval under consideration (§ 634 and § 804a of the RTO). For machines with intermediate steam extraction, however, the power on heat consumption is proportional to \((i_1-i_n)D_{otb}\), and in condensing operation to \((i_1-i_2)(D-D_{otb})\), so that

\[ \frac{E_k}{E_t} = \frac{i_1-i_2}{i_1-i_n} \cdot \frac{D-D_{otb}}{D_{otb}} = a\left(\frac{D}{D_{otb}}-1\right). \]

Hence the generation of kWh on the station busbars of a machine with intermediate steam extraction is

\[ E^{prom.\,otb} = E_t+E_k = E_t + a\left(\frac{D}{D_{otb}}-1\right)E_t \]

and, consequently,

\[ E_t = \frac{E^{prom.\,otb}} {1+a(D/D_{otb}-1)} \ \text{kWh}. \]

The value \(E_t\) includes both the generation on heat consumption \(Q_{otb}\) and \(E_t^r\) kWh on unregulated regenerative extractions of the back-pressure section of the machine. Here \(D\), kg, is understood as the total steam flow to the turbine, recorded over the time interval under consideration by a self-recording instrument with which each turbine unit must be equipped (§ 330, item 6 of the RTO); for all turbines with intermediate steam extraction we obtain \(\sum E_t\).

The consumption of reference fuel for heat subscribers will therefore be

\[ \left( \frac{Q_{\mathrm{cu}}}{\eta_{\mathrm{ot}}\cdot\eta_{\mathrm{y}}} + \frac{Q_{\mathrm{otb}}}{\eta_{\mathrm{pot}}\cdot\eta_{\mathrm{cu}}} - Q_{\mathrm{econ}} \right)\frac{1}{7000} = B_{\mathrm{t}}\ \text{kg of reference fuel}, \]

i.e., per one Gcal,

\[ b_{\mathrm{t}}= \frac{B_{\mathrm{t}}\cdot 10^{6}}{Q_{\mathrm{cu}}\cdot Q_{\mathrm{otb}}}\ \text{kg}. \]

After all that has been said, determining the fuel saving

\[ Q_{\mathrm{econ}}=860\cdot E_{\mathrm{t}} \left( \frac{1}{\eta_{\mathrm{k}}} - \frac{1}{\eta_{\mathrm{t}}} \right) \ \text{kcal} \]

no longer presents any difficulty.

Then for electric consumers there remains \(B-B_{\mathrm{t}}=B_{\mathrm{e}}\) kg, and per one kWh there will be \(b_{\mathrm{e}}=\dfrac{B_{\mathrm{e}}}{E}\) kg.

Thus, the methodology of the former Ministry of Electric Power Stations, in the part concerning the allocation of fuel expenditures to Gcal and kWh, is preserved, with the only difference that the initial erroneous premise of this methodology is eliminated and replaced by a new premise corresponding to the actual process at a CHP plant. As a result of such a replacement, the cost of a Gcal at a CHP plant is reduced, while that of a kWh is increased. It is clear that the need to calculate, according to Shitsman, the generation of electric power at regenerative extractions is eliminated.

But with such a solution the dualism of the methodology is preserved, whereas we must strive for dialectical monologicity, following V. I. Lenin’s indication (Philosophical Notebooks, p. 322) that “the separate does not exist otherwise than in the connection that leads to the general. The general exists only in the separate, through the separate. Every general only approximately embraces all separate objects. Every separate incompletely enters into the general. Every separate is connected by thousands of transitions with separate objects of another kind.” Hence it is evident that, for full knowledge of reality, it is necessary to know not only particular indicators for individual kinds of CHP-plant products, but also the general indicator of the operation of the CHP plant as a whole. In practice such a general indicator is necessary for scientific and design-and-survey work, since the presence of two particular indicators, mutually uncoordinated, having different dimensions and different changes over time in the fuel consumption per unit of measure, greatly hampers investigations. In addition, the entire energy community must know with what efficiency each CHP plant operates, their aggregate in power systems, and in the country as a whole. Such a general indicator may be the overall efficiency of the CHP plant, whose value is easily determined as the quotient from (1):

\[ \eta= \frac{860E+Q_{\mathrm{otb}}+Q_{\mathrm{cu}}}{B\cdot Q_{\mathrm{r}}^{\mathrm{n}}}. \]

This indicator, whose originator was Prof. Grinevetskii, has had very poor fortune in our practice. Until 1943 the indicator was accepted as the sole and mandatory one for power stations of the USSR. In 1943 it was discarded and replaced by the operating methodology of the Ministry of Electric Power Stations, as being unable to satisfy the need for analysis of the economic activity of CHP plants, which is possible, as indicated, through the “separate,” through indicators of the particular processes at the CHP plant. But by this act, monologicity, the dialectical principle of the connection between the whole and its parts, was violated. The time has come

the time of “negation” and synthesis of Prof. Grinevetsky’s method with corrected “separate” indicators of the partial processes of a CHP plant on the basis of the latter’s heat balance, if we truly wish to base our practice and state planning on science, which is obligatory under the conditions of our country after the decisions of the Twenty-Second and Twenty-Third Congresses of the CPSU. The introduction of a general indicator should not present difficulties for power plants, since experience in its application has already existed in the past.

A serious obstacle that interfered with the correct understanding of Prof. Grinevetsky’s proposal was the statements of thermodynamic scholars (Prof. D. P. Gokhshtein, Prof. G. I. Fuks, and others), who asserted that such heterogeneous terms as expenditures of electric power and heat cannot be added together. This created a fear of applying formulas of the Grinevetsky type as being fundamentally erroneous. Such fear among a number of workers, unfortunately, has not yet been overcome, as can be seen from a review I recently received of my article, which gave the editorial board grounds for rejecting it for publication. The error of the thermodynamic scholars’ point of view is evident from the following considerations. The basement of the Rankine diagram denotes, on the one hand, the latent heat of vaporization of the exhaust steam at its temperature \(T_{\text{exh}}\), directed to heat consumers. On the other hand, it is the work performed by the working body in the temperature interval \(T_{\text{exh}}\) and \(T = 0\). The latter is expressed, of course, in the same units as the Rankine cycle, so that adding this work to the work of the Rankine cycle cannot raise objections. But since the work of the basement is equal in area to the latent heat of vaporization at the temperature \(T_{\text{exh}}\), this work can always be replaced by the latent heat of vaporization supplied to heat consumers, bearing in mind that the problem of the basement work process in the temperature interval \(T_{\text{exh}}\) and \(T = 0\) at the present stage of the development of science and technology has not been solved. The use of the latent heat of vaporization for heat consumers, however, is a process widely mastered by technology, equivalently replacing the indicated process of basement work; for this reason Prof. Grinevetsky’s formula is correct, but it must, of course, be used in connection with the “separate” partial processes at the CHP plant in the form of a heat balance that links the general with the partial, serving here at the same time as a kind of controlling authority.

Erroneous theoretical provisions in the methodology of the former Ministry of Power Plants must lead to erroneous practice. To provide the population with fresh vegetables throughout the year, greenhouses under glass or film are now being built; they are major heat consumers capable of seriously strengthening the role of CHP plants in the power system. Heat consumption here must be year-round, since in vegetable-growing combines it is necessary, even in the non-heating period, to warm the soil of open ground in order to make possible the cultivation of heat-loving plants. The high cost of \(\text{Gcal}\) from CHP plants greatly increases the cost of vegetables. To reduce the cost of a unit of heat in greenhouses, local power associations are forced to resort to various contrivances having nothing in common with the current methodology of the former Ministry of Power Plants, and to resort to the construction of separate boiler houses, since this methodology does not distinguish the valuation of heat from turbine extractions and directly from boilers.

A logical development of the erroneous premise in the methodology of the former Ministry of Power Plants is also the trend, becoming apparent among some power engineers, to abandon CHP plants altogether, this remarkable achievement of Soviet power engineering, and to supply electric-power consumers from systems with powerful condensing power plants, and heat consumers from large boiler houses at

at the points of heat consumption. If, however, one proceeds from a correct assessment of reality, the use of CHP plants can ensure fuel savings, as indicated above, as well as savings in initial capital investments. The latter is evident from the fact that, with year-round heat consumption due to the presence of large vegetable-growing complexes with substantial areas of open heated ground, and with the broad development of residential heat consumption involving direct water withdrawal from heat networks, CHP plants can be equipped to a significant extent with back-pressure turbogenerators, which are relatively cheaper, while consumers can obtain the lacking electric power from power systems; this will mitigate the increase in the cost of the kWh associated with back-pressure turbines.

The use of back-pressure turbogenerators will also facilitate the solution of the often difficult problem of supplying CHP plants with water.