Thermal Economy of the Drive of Feed Pumps of Power Stations

V. A. Bragin

(Presented by Honored Worker of Science and Technology Prof. I. N. Butakov)

At the present time, much attention is being given to the question of comparing the economy of electric and turbine drives for feed pumps of thermal power stations. This interest is not accidental, since the transition of stations to high and superhigh steam parameters places feed pumps under such operating conditions which, in a whole series of cases, favor the use of a turbine drive. These operating conditions are described in detail in the literature.

When comparing the thermal economy of an electric drive with that of a turbine drive, it is considered that the latter will be more advantageous if the following relation is satisfied \[1\]:

\[ \eta_{oi}^{pr} \cdot \eta_{m}^{pr} > a \cdot \eta_{oi}^{\prime} \cdot \eta_{m} \cdot \eta_{g} \cdot \eta_{ep} \cdot \eta_{ed} \cdot \eta_{r}, \tag{1} \]

where \(\eta_{oi}^{pr}\) and \(\eta_{m}^{pr}\) are the internal relative and mechanical efficiencies of the drive turbine;

\[ \eta_{oi}^{\prime} \]

is the internal relative efficiency of that part of the main turbine which is replaced, in terms of steam, by the turbine drive;

\[ \eta_{m} \text{ and } \eta_{g} \]

are, respectively, the mechanical efficiency of the turbine and the efficiency of the generator;

\[ \eta_{ep},\ \eta_{ed} \text{ and } \eta_{r} \]

are, respectively, the efficiencies of the electric transmission (including the transformer), the electric motor, and the speed-increasing reduction gear;

\[ a \]

is the ratio between the pump powers with turbine and electric drive \((a < 1.0)\), caused by throttling during feed regulation.

The indicated relation and similar ones \[2, 3\] are derived from the balance of energy required for rotating the feed pumps by electric and turbine drive. In doing so, it is assumed that the steam flow rate from the boilers and the internal relative efficiency of the main turbine remain unchanged.

Such a comparison of the thermal economy of the indicated types of drive is approximate and in many cases may lead

to incorrect results. Indeed, taking into account, in the comparison, only the difference in the efficiencies of the drive turbine and of the corresponding part of the main turbine leads to the fact that the following are excluded from consideration: first, the possibility of utilizing the exhaust steam of the turbine drive; second, if this possibility is realized in the regenerative feedwater-heating scheme of the main turbine, the deterioration in the economy of the latter.

All the noted shortcomings can be avoided if, when comparing the economy of an electric drive and a turbine drive, one considers the heat balance of the system: main turbine—feed-pump drive.

If \(N\) denotes the power of the turbogenerator required to satisfy all consumers, with the exception of the feed pump, kW; \(N_{\mathrm{em}}\) and \(N_{\mathrm{tm}}\), respectively, the shaft power of the pump with electric and turbine drive, kW; \(\eta_k^{e}\) and \(\eta_k^{n}\), the efficiency of energy production by the turbogenerator with electric and turbine drive; \(\eta_{\mathrm{pr}}^{e}\) and \(\eta_{\mathrm{pr}}^{n}\), respectively, the efficiencies of the electric and turbine drive, then the heat consumption in the case of electric drive of the feed pump will be equal to

\[ Q_{e}=\frac{860N}{\eta_k^{e}}+\frac{860N_{\mathrm{em}}}{\eta_{\mathrm{pr}}^{e}}, \tag{2} \]

and with turbine drive with utilization of exhaust steam in the regeneration scheme of the main turbine:

\[ Q_{n}=\frac{860N}{\eta_k^{n}}+\frac{860N_{\mathrm{tm}}}{\eta_{\mathrm{pr}}^{n}}. \tag{3} \]

Here

\[ \eta_{\mathrm{pr}}^{e}=\eta_k^{e}\cdot \eta_{\mathrm{el}}\cdot \eta_{\mathrm{ed}}\cdot \eta_p \quad\text{and}\quad \eta_{\mathrm{pr}}^{n}=\eta_{\mathrm{ku}}\cdot \eta_l\cdot \eta_{\mathrm{oi}}^{\mathrm{pr}}\cdot \eta_m^{\mathrm{pr}}, \]

where \(\eta_{\mathrm{ku}}\) and \(\eta_l\) are the efficiencies of the boiler installation and of the heat flow.

Then the sign of the difference \(\Delta Q=Q_n-Q_e\) will show which type of drive, under the given specific conditions, is more economical in the thermal respect. Subtracting from the right- and left-hand sides of equation (3) the corresponding parts of equation (2), and after simple transformations, we obtain

\[ \Delta q=\frac{1}{\eta_k^{e}}\cdot \left[ \varepsilon_t-n_e\cdot \frac{ \eta_{\mathrm{oi}}^{\mathrm{pr}}\cdot \eta_m^{\mathrm{pr}} -a\cdot \eta_{e}^{e}\cdot \eta_{\mathrm{el}}\cdot \eta_{\mathrm{ed}}\cdot \eta_p }{ \eta_{\mathrm{oi}}^{\mathrm{pr}}\cdot \eta_m^{\mathrm{pr}}\cdot \eta_{\mathrm{el}}\cdot \eta_{\mathrm{ed}}\cdot \eta_p } \right]. \tag{4} \]

Here \(\Delta q\) is the saving or overconsumption of heat for each kcal released in the form of electric power to consumers when one or another type of drive is used;

\[ \varepsilon_t=\frac{\eta_t^{e}-\eta_t^{n}}{\eta_t^{n}} \]

is the relative deterioration of the thermal efficiency of the main turbine when the exhaust steam of the turbine drive is introduced into the regeneration scheme;

\(\eta_e^{e}\) is the absolute electrical efficiency of the turbogenerator with electric drive;

\[ n_e=\frac{N_{\mathrm{em}}}{N}; \]

\(\eta_t^{e}\) and \(\eta_t^{p}\) are the thermal efficiency of the main turbine with electric drive and turbine drive.

In deriving expression (4), the deterioration in the economy of the main turbine due to the increase in terminal losses was not taken into account, as being insignificant.

From equation (4) it is seen that the turbine drive will be more advantageous only if

\[ n_{e}\cdot \frac{ \eta_{oi}^{pr}\cdot \eta_{m}^{pr} - a\cdot \eta_{e}^{3}\cdot \eta_{el}\cdot \eta_{eo}\cdot \eta_{p} }{ \eta_{oi}^{pr}\cdot \eta_{m}^{pr}\cdot \eta_{el}\cdot \eta_{eo}\cdot \eta_{p} } > \varepsilon_t, \tag{5} \]

A similar relation is easily obtained also for the case where the turbine drive is supplied with steam from an extraction of the main turbine.

From inequality (5) it is seen that the advantage of the turbine drive in comparison with the electric drive will increase: a) as \(\eta_{oi}^{pr}\cdot \eta_m^{pr}\) increases, which causes the left-hand side of the inequality to grow, since the numerator of the fraction grows faster than the denominator, and the right-hand side decreases as a result of a smaller reduction in the thermal efficiency of the installation; b) with deterioration of all efficiencies relating to the turbogenerator and the electric drive; c) with an increase in the power of the drive; d) with the choice of the most rational scheme for connecting the turbine drive into the scheme of the main machine, since in this case the difference between \(\eta_t^{e}\) and \(\eta_t^{p}\) will be smoothed out, which will correspondingly reduce the value of \(\varepsilon_t\).

Equality (4) shows that, when designing a turbine drive, it is not sufficient to obtain satisfaction of inequality (1); it is also necessary to take into account the influence of the turbine drive on the economy of the main turbine.

Fig. 1.

Therefore, the equality sign in expression (1) does not correspond to equal economy of the types of drive under consideration. For this, according to (5), it is necessary to have a higher value of \(\eta_{oi}^{pr}\), the internal relative efficiency of the drive turbine. In Fig. 1, for the particular case of the BK-50 turbogenerator, a comparison is made of an electric drive with a turbine drive (of the OVPT-270 type) at various values of \(\eta_{oi}^{pr}\), with the exhaust steam entering regenerative heater No. 2 \((p \simeq 1.6\ \text{ata})\). According to expression (1), for these conditions the turbo-

the drive will be more economical if \(\eta^{\mathrm{pr}}_{0i} \ge 0.64\). According to equality (4), however, for this it is necessary to have \(\eta^{\mathrm{pr}}_{0i} \ge 0.677\).

REFERENCES

1. Krushel, G. E. Turbine drive of feed pumps of unit power stations. Teploenergetika, No. 3, 1958.

2. Krushel, G. E. On the drive of feed pumps of power stations. Teploenergetika, No. 11, 1954.

3. Luknitskii, V. V. Thermal electric power stations of industrial enterprises. GEI, 1953.