A basic steam power plant consists of four interconnected components, typically as shown in the figure below. These include a steam turbine to produce mechanical shaft power, a condenser which uses external cooling water to condense the steam to liquid water, a feedwater pump to pump the liquid to a high pressure, and a boiler which is externally heated to boil the water to superheated steam. Unless otherwise specified we assume that the turbine and the pump (as well as all the interconnecting tubing) are adiabatic, and that the condenser exchanges all of its heat with the cooling water.

**A Simple Steam Power Plant Example -** In this example we wish to determine the performance
of this basic steam power plant under the conditions shown in
the diagram, including the power of the turbine and feedwater
pump, heat transfer rates of the boiler and condenser, and thermal
efficiency of the system.

In this example we wish to evaluate the following:

- Turbine output power and the power required to drive the feedwater pump
- Heat power supplied to the boiler and that rejected in the condenser to the cooling water
- The thermal efficiency of the power plant
(η
_{th}), defined as the net work done by the system divided by the heat supplied to the boiler. - The minimum mass flow rate of the cooling water in the condenser required for a specific temperature rise

Do not be intimidated by the complexity of
this system. We will find that we can solve each component of
this system separately and independently of all the other components,
always using the same approach and the same basic equations. We
first use the information given in the above schematic to plot
the four processes (1)-(2)-(3)-(4)-(1) on the
** P-h diagram**. Notice that the fluid entering and exiting the boiler
is at the high pressure 10 MPa, and similarly that entering and
exiting the condenser is at the low pressure 20 kPa. State (1)
is given by the intersection of 10 MPa and 500°C, and state
(2) is given as 20 kPa at 90% quality, State (3) is given by the
intersection of 20 kPa and 40°C, and the feedwater pumping
process (3)-(4) follows the constant temperature line, since T4
= T3 = 40°C, .

Notice from the *P-h* diagram plot how
we can get an instant visual appreciation of the system performance,
in particular the thermal efficiency of the system by comparing
the enthalpy difference of the turbine (1)-(2) to that of the
boiler (4)-(1). We also notice that the power required by the
feedwater pump (3)-(4) is negligible compared to any other component
in the system.

(*Note:* We find it strange that the only
thermodynamics text that we know of that even considered the use
of the *P-h* diagram for steam power plants is
**Engineering
Thermodynamics - Jones and Dugan** (1995). It is widely
used for refrigeration systems, however not for steam power plants.)

We now consider each component as a separate
control volume and apply the energy equation, starting with the
steam turbine. The steam turbine uses the high-pressure - high-temperature
steam at the inlet port (1) to produce shaft power by expanding
the steam through the turbine blades, and the resulting low-pressure
- low-temperature steam is rejected to the condenser at port (2).
Notice that we have assumed that the kinetic and potential energy
change of the fluid is negligible, and that the turbine is adiabatic.
In fact any heat loss to the surroundings or kinetic energy increase
would be at the expense of output power, thus practical systems
are designed to minimise these loss effects. The required values
of enthalpy for the inlet and outlet ports are determined from
the **steam tables**.

Thus we see that under the conditions shown the steam turbine will produce 8MW of power.

The very low-pressure steam at port (2) is now directed to a condenser in which heat is extracted by cooling water from a nearby river (or a cooling tower) and the steam is condensed into the subcooled liquid region. The analysis of the condenser may requre determining the mass flow rate of the cooling water needed to limit the temperature rise to a certain amount - in this example to 10°C. This is shown on the following diagram of the condenser:

Notice that our steam tables do not include
the subcooled (or compressed) liquid region that we find at the
outlet of the condenser at port (3). In this region we notice
from the *P-h* diagram that over an extremely high pressure
range the enthalpy of the liquid is equal to the saturated liquid
enthalpy at the same temperature, thus to a close approximation
h_{3} =
h_{f@40°C},
independent of the pressure.

Thus we see that under the conditions shown, 17.6 MW of heat is extracted from the steam in the condenser.

I have often been queried by students as to
why we have to reject such a large amount of heat in the condenser
causing such a large decrease in thermal efficiency of the power
plant. Without going into the philosophical aspects of the Second
Law (which we cover later in **Chapter
5**, my best reply was provided to me by Randy Sheidler,
a senior engineer at the **Gavin Power
Plant**. He stated that the **Fourth Law of Thermodynamics**
states: **"****You
can't pump steam!"**, so until we condense all the steam into liquid water
by extracting 17.6 MW of heat, we cannot pump it to the high pressure
to complete the cycle. (Randy could not give me a reference to
the source of this amazing observation).

In order to determine the enthalpy change Δh
of the cooling water (or in the feedwater pump which follows),
we consider the water to be an **Incompressible Liquid**, and
evaluate Δh as follows:

From the **steam
tables** we find that the specific heat capacity for liquid
water C_{H2O}
= 4.18 kJ/kg°C. Using this analysis we found on the condenser
diagram above that the required mass flow rate of the cooling
water is 421 kg/s. If this flow rate cannot be supported by a
nearby river then a cooling tower must be included in the power
plant design.

We now consider the feedwater pump as follows:

Thus as we suspected from the above *P-h*
diagram plot, the pump power required is extremely low compared
to any other component in the system, being only 1% that of the
turbine output power produced.

The final component that we consider is the boiler, as follows:

Thus we see that under the conditions shown the heat power required by the boiler is 25.7 MW. This is normally supplied by combustion (or nuclear power). We now have all the information needed to determine the thermal efficiency of the steam power plant as follows:

Note that the feedwater pump work can normally be neglected.

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**Problem
4.3 - A Geothermal Hybrid Steam Power Plant**

**Problem
4.4 - Solar Pond Hybrid Steam Power Plant**

**Problem
4.5 - A Cogeneration Steam Power Plant**

**Problem
4.6 - An Open Feedwater Heater added to
the Cogeneration Steam Power Plant**

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Engineering Thermodynamics by Israel Urieli is licensed under a
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Alike 3.0 United States License