4 Power Plant Efficiency
Learning Objectives
Operate the Plant at full generating capacity and compute the Power Plant Efficiency when the plant is operating:
- Under normal conditions,
- With the cooling water temperature very high (lake water temperature: 35°C),
- Without regeneration.
Theory
Excluding hydroelectric power plants, most power generating plants employ a type of boiler and steam turbine. A schematic diagram of a simple steam power plant is shown below:
High-pressure steam leaves the boiler and enters the turbine. The steam expands in the turbine and does work which enables the turbine to drive the electric generator. The exhaust steam leaves the turbine and enters the condenser where heat is transferred from the steam to cooling water. The pressure of the condensate leaving the condenser is increased in the pump thereby enabling the condensate to flow into the boiler. This thermodynamic cycle is known as the Rankine Cycle.
The Rankine Cycle Efficiency
As noted above, some heat is always lost from the steam to cooling water. In addition, feed pumps consume energy thus reducing the net work output. Rankine Cycle Efficiency then can be expressed as:
[latex]\eta_{Rankine} = \frac{Net\ work\ output}{Heat\ supplied\ in\ the\ boiler}[/latex]
or
[latex]\eta_{Rankine} = \frac{W_{Turbine}-W_{Pump}}{Q_{boiler}}[/latex]
referring to the diagram above and using the enthalpy values in the Rankine cycle, we can write:
[latex]\eta_{Rankine} = \frac{(h_{1}-h_{2})-(h_{4}-h_{3})}{(h_{1}-h_{4})}[/latex]
Improvements to the Rankine Cycle Efficiency
Effect of Pressure and Temperature on the Rankine Cycle
If the exhaust pressure drops from P4 to P4‘ with the corresponding decrease in temperature at which heat is rejected in the condenser the net work is increased by area 1-4-4′-1′-2’-2-1 (see diagram below)
In a similar way, if the steam is superheated in the boiler, it is evident that the work is increased by area 3-3′-4′-4-3 (see diagram below):
Superheating the steam is done by increasing the time the steam is exposed to the flue gases. The result of superheating is that for a given power output, the plant using superheated steam will be of smaller size than that using dry saturated steam.
The Reheat Cycle
Above we noted that the efficiency of the Rankine cycle is increased by superheating the steam. If metals could be found that would allow us to reach higher temperatures, the Rankine cycle could be more efficient. To improve the efficiency, the reheat cycle has been developed which is shown schematically below:
In this cycle, the steam is expanded to some intermediate pressure in the turbine and is then reheated in the boiler, after which it expands in the low-pressure turbine to the exhaust pressure. Rankine Cycle with reheat thermal efficiency can be expressed as:
[latex]\eta_{thermal} = \frac{W_{12}+W_{67}-W_{43}}{Q_{41}+Q_{26}}[/latex]
The Regenerative Cycle
Another variation from the Rankine cycle is the regenerative cycle, which involves the u