#### 4.1.1 Thermodynamic optimisation

The power developed by a steam turbine supplied with a constant mass flow rate varies on the exhaust pressure changes for the following reasons:

(a) As the exhaust pressure is reduced, the isentropic heat drop across the last stage increases and so additional work is done in the turbine.

(b) The additional work is not as large as it could be because the volumetric flow rate, and therefore the velocity of the steam, increases as the exhaust pressure is reduced. An increase in velocity means an increase in kinetic energy of the steam at the turbine exhaust and therefore a loss of power due to the increased leaving loss.

(c) As the exhaust pressure is reduced, the corresponding saturation temperature is reduced. Therefore, more steam is extracted from the turbine to heat the condensate in the first feedwater heater, so that less steam passes through the last

stages of the turbine, giving a further loss in output.

These conflicting points mean that there is an 'optimum exhaust pressure' where the greatest net power is produced. This occurs when the effect of point (a) is equal to points (b) and (c). At exhaust pressures lower than optimum, the increase in power due to (a) is less than the decrease due to (b) and (c), so a net reduction in power generation and increase in heat rate will occur as exhaust pressure is lowered further. At exhaust pressures higher than optimum, the opposite effects occur. This is shown graphically in Fig 1.57, where the percentage increase in heat rate has been plotted against (exhaust pressure/optimum exhaust pressure).

Figure 1.58 shows the corresponding characteristic for the change in power output.

The variation of turbine heat rate with exhaust pressure, shown in Fig 1.57, is obtained from the basic turbine design data relating to the turbine exhaust area, exhaust mass flows and the heat rejected. The term 'optimum' is used here with respect to the power generated and heat rate. Economic factors are also involved in the choice of design exhaust pressure, resulting in the exhaust pressure being somewhat greater than the thermodynamic optimum.