On the Question of Calculating the Technical-and-Economic Indicators of CHP Plants

Z. F. Nemtsev

In the method for calculating the technical-and-economic indicators of CHP plants proposed by the Ministry of Electric Power Stations \[1, 2, 3\], there is a fundamental inaccuracy, a discrepancy with the actual picture of the processes taking place at CHP plants.

Fig. 1. Diagram of the energy flows of a CHP plant

It appears possible to represent the processes of a CHP plant by the energy-flow diagram shown in Fig. 1. (In the diagram, recirculating heat has been omitted, since it does not change the substance of the question under consideration but complicates the diagram. The losses of the recirculating heat flow are included in \(\dot Q^{\mathrm{tp}}_{\mathrm{pot}}\).)

Notation:

\[ Q_{\mathrm{topl}} \]
— heat of the fuel burned;

\[ Q^{\mathrm{kot}}_{\mathrm{pot}} \]
— boiler losses;

\[ Q^{\mathrm{tp}}_{\mathrm{pot}} \]
— losses of the heat flow;

\[ Q^{\mathrm{obl}}_{\mathrm{pot}} \]
— losses of the district-heating installation;

\[ Q^{\mathrm{ee}}_{\mathrm{tur}} \]
— heat received by the turbines and expended on the generation of electric power;

\[ Q^{\mathrm{te}}_{\mathrm{tur}} \]
— the same, expended on the supply of heat energy;

\[ Q^{\mathrm{ee}}_{\mathrm{kot}},\; Q^{\mathrm{te}}_{\mathrm{kot}} \]
— the same, but supplied by the boiler;

\[ Q^{\mathrm{mekh}}_{\mathrm{pot}} \]
— heat equivalent to mechanical losses;

$Q_{pot}^{gen}$ — heat equivalent to generator losses;

$Q_{otp}$ — heat supplied to consumers;

$860\,E$ — heat equivalent to the generation of electric power;

$Q_{pot}^{con}$ — heat losses to the turbine condenser (condensing).

According to the MES method, all losses of the heat flow occurring between the boilers and the turbines are attributed to the generation of electric power, while the efficiency of the heat flow $\eta_{tp}$ with respect to heat supply is taken as equal to 100%, as is evident from the formula [1, p. 10].

\[ B_{ta}= \frac{ \left(\sum Q_{otp}^{n}+\sum Q_{otp}^{g.v.}-\sum Q_{voz}+\sum Q_{pot}\right)10^3 }{ \eta_{k}^{nt}\,7000 }\,t, \tag{1} \]

where (p. 21) “the quantity $\sum Q_{pot}$ includes the following losses: heat losses in extraction steam pipelines, from the turbine to the point of measurement of heat supplied to consumers; heat losses in the main and peak water heaters; heat losses in pressure-reducing and cooling installations, in steam pipelines to them and from them to the point of measurement of heat supply; heat losses connected with the preparation of additional chemically treated water used to make up for condensate not returned from production and to prepare make-up water for heat networks; losses connected with increased boiler blowdown caused by nonreturn of condensate from production.”

Thus, these losses do not include the losses of the heat flow occurring between the boilers and the turbines, which, consequently, are attributed to the generation of electric power (taking into account the MES formula $B_{ee}=B-B_{ta}$). Consequently, with unchanged heat-flow losses, the efficiency $\eta_{tp}$ calculated by the MES method will decrease substantially as the share of cogeneration output increases. This occurs because the same losses are then attributed to a smaller part of the heat expended in cogeneration for the generation of electric power (Fig. 1).

In reality, however, all the steam travels the path from the boilers to the turbines, and, of course, the entire heat flow loses heat, not only the part intended for the generation of electric power (Fig. 1). Accordingly, the heat-flow losses should be distributed between electric power and heat in proportion to the capacities of the corresponding energy flows. Then

\[ B_{ta}= \frac{ \left(Q_{otp}+Q_{pot}^{boil}\right)10^3 }{ \eta_{kot}^{nt}\,\eta_{tp}\,7000 }\,t \tag{2} \]

and

\[ \eta_{tp}= \frac{ Q_{kot}^{nt}-Q_{pot}^{tp} }{ Q_{kot}^{nt} } = \frac{ Q_{tur} }{ Q_{kot}^{nt} }. {}^{1)} \tag{3} \]

$^{1)}$ If heat is supplied from the boiler house through a pressure-reducing and cooling unit (or a thermocompressor), with some approximation,

\[ \eta_{tp}= \frac{ Q_{tur}+Q_{pou} }{ Q_{kot}^{nt} }, \]

where $Q_{pou}$ is the heat entering the pressure-reducing and cooling unit and intended for heat supply. More accurately, it may be calculated by the formula

\[ B_{ta}= \frac{ \left( \frac{Q_{otp}-Q_{otp}^{pou}}{\eta_{tp}^{tur}\,\eta_{boil}} + \frac{Q_{otp}^{pou}}{\eta_{tp}^{pou}\,\eta_{boil}} \right)10^3 }{ 7000\,\eta_{kot}^{nt} }\,t. \]

In this case, if necessary, $\eta_{boil}$ may also be distinguished for the specific conditions of each CHP plant.

The inclusion, proposed by Professor I. N. Butakov [4, 5] (p. 22 and p. 137), of the losses of the district-heating installation in the losses of the heat flow (apparently for the sake of simplification) appears inexpedient, since the losses of the boiler house are connected only with the supply of heat and therefore must be assigned entirely to heat supply.

It should be noted that there has been no critical analysis in the literature of the MES methodology in this respect. Meanwhile, the noted discrepancy between the MES methodology and the actual processes at a CHP plant leads to substantial distortions of the principal technical-and-economic indicators of CHP operation, as illustrated by Table 1.

Table 1

Designations in the table:

$Э$ and $Э_m$ — total and district-heating generation of electricity;
$q^{mn}_{nom}$ — percentage of heat-flow losses;
$b_e$ — specific consumption of reference fuel per generated kWh of electricity;
$b_t$ — the same per supplied million kcal of heat;
the index “MES” means that the indicator has been calculated by the MES methodology.

The table was compiled on the basis of calculations made for the simplest scheme, consisting of a boiler and two turbines: a condensing turbine ($p_1 = 18$ ata, $t_1 350^\circ C$, $p_2 = 0,048$ ata, $\eta_{oi} = 0,625$) and one with a deteriorated vacuum ($p_2 = 0,6$ ata, $\eta_{oi} = 0,596$); $\eta_{mex}\eta_{gen} = 0,9$; $\eta^{kt}_{kot} = 0,83$. The steam consumption from the boiler house and the absolute magnitude of the heat-flow losses, equal to 4% in the condensing mode, were taken as constant.

It is evident from the table that, for a condensing power plant, the MES methodology produces no distortions. The distortions become the greater, the more electricity is generated by the district-heating method. The maximum distortions are obtained for a back-pressure installation, for which the percentage of heat-flow losses $q^{mn}_{nom}$ is overstated by the MES methodology by 5.6 times, and the error in determining $b_e$ is 20%. With an insignificant district-heating generation of electricity of 13.7%, the error in determining $q^{mn}_{nom}$ already amounts to 18.5%. The fuel consumption for heat is in all cases understated by the percentage of heat-flow losses.

Confirmation of what has been set forth may be provided by the reporting data of one of the Siberian CHP plants, given in Table 2.

Table 2

From the table it can be seen that in October, owing to the fact that almost all electric-power generation was for heat consumption, the efficiency $\eta_{\text{tp}}$ fell to the unprecedented value of $78.64\%$. In Fig. 2 it is seen that the reported points lie close to the theoretical curve constructed from the data of Table 1. Some scatter of the points is explained by the incomplete correspondence of the CHP plant scheme and parameters with those adopted in the calculation.

Fig. 2. Dependence of the heat-flow efficiency $\eta_{\text{tp}}^{\mathrm{MES}},\%$, calculated by the MES method, on the share of cogeneration electric-power output.
$\bigcirc$ — points of the theoretical curve
$\bullet$ — reported data

Calculations carried out for various conditions show:

1) the use of regeneration increases the distortion of the technical and economic indicators of CHP plants calculated by the MES method, since in this case $Q_{\text{tur}}^{e}$ decreases;

2) the use of extraction instead of a worsened vacuum also increases the distortions, since in this case $Q_{\text{tur}}^{e}$ decreases per kilogram of steam;

3) the use of high pressure reduces the distortions: thus, for example, for the back-pressure part of a high-pressure turbine (VPT-25-3), the heat-flow losses are overestimated by the MES method by a factor of 4 (from $4\%$ to $14 \div 18\%$);

4) with an increase in heat-flow losses to 6%, the error in determining \(b_e\) for an installation with impaired vacuum will be \(+32\%\).

Accordingly, under the procedure described, the cost of electric energy is also overstated.

A very important practical point is that such a substantial distortion of the technical-and-economic indicators by the MES methodology disorients the operating personnel of a CHP plant, makes it difficult to analyze operating indicators, and reduces the effectiveness of the struggle for high technical-and-economic indicators by directing efforts in the wrong direction.

Thus, in the operating practice of the CHP plant under consideration, for no apparent reason, in recent years the reported efficiency \(\eta_{mp}\) systematically fell, from 91.32% in 1952 to 90.2% in 1953. Decisive measures were taken at the CHP plant to raise the efficiency \(\eta_{mp}\). Extensive thermal-insulation work was carried out, and the minimum number of steam lines under pressure was used. Despite this, when the annual report for 1954 was compiled it turned out that the efficiency \(\eta_{mp}\) had fallen by another 0.9%. The matter proved to be not an actual increase in losses, but a systematic increase in the share of cogeneration output, which, in calculations by the MES methodology, led to a reduction in the efficiency.

The second puzzle in the operation of the CHP plant was the high value of \(b_e\) when operating in the impaired-vacuum mode, on the order of 220 g/kWh, whereas all theoretical calculations led to the conclusion that \(b_e\) should be 170–180 g/kWh. The reason for this proved to be the same.

CONCLUSIONS

1. In the methodology for calculating the technical-and-economic indicators of CHP plants recommended by the Ministry of Electric Power Stations, contrary to the actual process of CHP plants, the efficiency of the heat flow for heat-energy supply is taken as equal to 100%. This leads to substantial distortions of the principal technical-and-economic indicators, hampers analysis and control of the operating results of CHP plants, disorients the operating personnel in the struggle for high operating indicators, and reduces the effectiveness of this struggle.

2. It appears advisable to legalize formula (2) instead of formula (1), and to calculate the efficiency of the heat flow by formula (3), leaving the other formulas in their previous form, which ensures the elimination of distortions of the principal technical-and-economic indicators.

For the specific consumption for heat supplied, the following checking formula may be recommended:

\[ b_t=\frac{10^6}{7000\,\eta_{kom}^{nt}\,\eta_{mp}\,\eta_{boil}}\ \text{kg/million kcal} \]

LITERATURE

1. Instructions for compiling the technical report on the operation of thermal power stations. L. M. Mittelman, G. S. Lifshits, V. P. Moiseev, Gosenergoizdat, 1955.

2. Instructions for compiling the monthly report on the operation of thermal power stations. Gosenergoizdat, 1949.

3. Instructions for compiling the monthly production report of NKES thermal power stations (form E-4-RT). Published by the Planning and Economic Department of NKES, March 31, 1944, No. 35–512.

4. Questions of Determining the Efficiency of Combined Heat and Power Plants, collected articles. Gosenergoizdat, 1953.

5. Butakov I. N. Thermal Power Installations. Part I. Publication of the Tomsk Polytechnic Institute. Tomsk, 1954.