One Possible Option for a Simplified Determination of the Prime Cost of MGC at a CHP Plant

I. N. Butakov

The heat balance of a number of CHP plants can be represented in the form

\[ \frac{860\mathcal{E}+Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{\eta} = \frac{860\mathcal{E}_{\mathrm{t}}+Q_{\mathrm{ext}}}{\eta_{\mathrm{t}}} + \frac{860(\mathcal{E}-\mathcal{E}_{\mathrm{t}})}{\eta_{\mathrm{k}}} + \frac{Q_{\mathrm{boil}}}{\eta_{\mathrm{ku}}\cdot \eta_{\mathrm{loss}}\cdot \eta_{\mathrm{aux}}} \ldots \tag{1} \]

Here the output of the given CHP plant is given in annual cal, as is the corresponding fuel consumption (cal/year); \(\mathcal{E}\) is the total annual generation of kWh; \(\mathcal{E}_{\mathrm{t}}\) is the same for heat consumption; \(Q_{\mathrm{ext}}\) is the quantity of cal/year from turbine extractions; \(Q_{\mathrm{boil}}\) is the same directly from the boilers.

From (1) we determine \(1/\eta\), i.e., the number of calories in the fuel attributable to 1 calorie of CHP output. Note that

\[ \frac{Q^{*}_{\mathrm{ot}}+Q_{\mathrm{ext}}}{860\mathcal{E}} \Bigg/ \left( 1+\frac{Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{860\mathcal{E}} \right) = 1- \frac{1}{ 1+\dfrac{Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{860\mathcal{E}} } \ldots \tag{2} \]

Substituting expression (2) into the heat-balance equation (1), we finally obtain

\[ \begin{aligned} 1/\eta &= \frac{1}{ 1+\dfrac{Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{860\mathcal{E}} } \cdot \frac{1}{\eta_{\mathrm{t}}} \left[ \eta_{\mathrm{t}}/\eta_{\mathrm{k}} - \frac{\mathcal{E}_{\mathrm{t}}}{\mathcal{E}} \left( \frac{\eta_{\mathrm{t}}}{\eta_{\mathrm{k}}}-1 \right) + \frac{1}{860\mathcal{E}} \left( Q_{\mathrm{ext}} + \frac{\eta_{\mathrm{t}}}{ \eta'_{\mathrm{ku}}\cdot \eta'_{\mathrm{loss}}\cdot \eta'_{\mathrm{aux}} } Q_{\mathrm{boil}} \right) \right] \\ &= 1+ \frac{1}{ 1+\dfrac{Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{860\mathcal{E}} } \cdot \frac{1}{\eta_{\mathrm{t}}} \left[ \eta_{\mathrm{t}}/\eta_{\mathrm{k}} - \frac{\mathcal{E}_{\mathrm{t}}}{\mathcal{E}} \left( \eta_{\mathrm{t}}/\eta_{\mathrm{k}}-1 \right) -1 \right] \\ &= 1+ \frac{1}{ 1+\dfrac{Q_{\mathrm{ext}}+Q_{\mathrm{boil}}}{860\mathcal{E}} } \cdot \frac{1}{\eta_{\mathrm{t}}} \left[ \left( \eta_{\mathrm{t}}/\eta_{\mathrm{k}}-1 \right) \left( 1-\frac{\mathcal{E}_{\mathrm{t}}}{\mathcal{E}} \right) \right] \ldots \tag{3} \end{aligned} \]

From equation (3) it is evident that the dependence of \(1/\eta\) on the energy coefficient

\[ \frac{Q_{\text{sel}} + Q_{\text{boil}}}{860\,Э} \]

is hyperbolic; moreover, the values of \(1/\eta\) for the annual output of a CHP plant and the corresponding fuel expenditures vary very little, since the hyperbola approaches its horizontal asymptote independently of the initial steam parameters and the pressures in the turbine extractions (Fig. 1). In constructing Fig. 1 according to equation (3), the particular case \(Э_{\text{t}}/Э = 0.1\) was adopted.

Fig. 1

Taking the annual output of the CHP plant in kilocalories, and, on the other hand, the annual monetary expenditure of the CHP plant in rubles, obtained with the inclusion of profitability, and dividing the total monetary expenditures by the output of the CHP plant, we easily obtain the cost of one Mgc, which should be lower than at condensing stations. Thus, the cost of an Mgc at a CHP plant will be the same regardless of whether it is obtained in the form of kWh or for heat consumers. This will correct the incorrectness in the existing MES methodology, according to which the entire benefit from the CHP plant went in favor of electric consumers, increasing the cost of heat for heat subscribers and, in particular, making vegetables from greenhouse gardens inaccessible in price.

Not to mention that the heat benefit from a CHP plant is determined precisely by the presence of heat consumers.

The proposal made greatly simplifies the reporting of CHP plants and the monitoring of the state of affairs at each CHP plant.

After the decisions of the XXIII Congress of the CPSU, the question of the development of district heating in cities and even villages must acquire special significance, since this will satisfy the improvement of the living conditions of the broad masses. The demand for pipes will be met thanks to the large planned assignments to plants. As a result of the commissioning of a number of large power stations, at old stations part of the condensing units will be used as district-heating units, by conversion to a degraded vacuum or to back pressure. The uniformity of the cost of an Mgc at CHP plants will be convenient for settlements with external consumers.