4.1.3 Economic optimisation of exhaust pressure, condenser and CW system
Up to now we have only considered the design of the turbine. The economic optimisation is highly dependent upon the Cooling Water (CW) system as well. The general economic considerations given in the previous section will now be developed to examine the combination of the turbine, condenser and CW system.
Figure 1.60 shows a typical 'direct cooled system', using sea water as a coolant. The system is called direct cooled because the water is used once and then discharged. A circulating pump forces water through screens, which removes any debris large enough to block the condenser. There are valves at inlet and outlet to the condenser to ensure flexibility of operation during changes in climatic conditions. Flexibility is developed further by increasing the number of circulating pumps available. The CW system therefore makes a significant contribution to the capital cost of the plant. On inland stations, using indirect cooling with large cooling towers, the costs can be higher still.
The task is to optimise the overall design so as to minimise the lifetime generation costs. This means minimising the capital and running costs over the lifetime of the plant. The capital costs usually considered for a direct cooled system are:
- The capital cost of the turbine and of the building to house it (this will vary if longer last-stage blades or a different number of turbine cylinders are chosen).
- The capital cost of the CW culvert system (this will vary with CW flow).
- The capital cost of the CW pump (rated to suit the CW flow).
- The capital cost of the condenser surface (an independent variable, subject to constraints).
The running costs are:
- The cost of additional pumping power (this will vary with CW flow).
- The cost of a small change in turbine efficiency.
Plant operating and maintenance costs are ignored unless there are exceptional circumstances.
It is clear that there are many variables to be considered and it is therefore necessary to fix certain turbine design parameters (the number and area of the LP exhausts) so that the characteristic relationship between the power output and exhaust pressure can be maintained. With the turbine exhaust design fixed, constraints are automatically imposed on the size of the condenser.
The condenser surface can vary in two ways:
- Increasing the number of tubes (and adjusting the flow to give the same velocity).
- Increasing the length of the tubes.
Having fixed the turbine design, for a typical transverse underslung condenser, the maximum tube length will also be fixed (Fig 1.61). The condenser tube surface area can only be changed by varying the number of tubes used up to limits imposed by the available height. Since these are basically heat transfer calculations, the condenser tube materials, diameter and thicknesses must all be fixed according to the principles set out in Chapter 4.
A site study is undertaken to obtain the temperature of the water source over a period of a year, so that an estimate of the average annual CW inlet temperature can be made. The specific heat and density of the water are also measured.
Using these fixed parameters, the heat transfer calculations can be made. As well as the effect of the exhaust pressure on output and heat rate, there are other variables needing optimisation. Increasing the number of tubes in the condenser, for a given CW flow rate, results in a reduction in CW velocity, and hence a reduction in friction losses and pumping power costs. However, low CW velocity needs a larger heat transfer surface, which could be achieved by increasing the length of the condenser tubes. This is not possible because, as stated earlier, the length of the tubes is usually constrained.
Increasing condenser outlet temperature reduces the mass flow of CW but increases the turbine exhaust pressure, resulting in a rise in heat rate, a fall in power and therefore a drop in efficiency.
Figure 1.62 shows the results from the heat transfer calculations. Lines of constant CW velocity and turbine exhaust pressure are displayed. If we consider increasing the condenser tube surface area by increasing the number of tubes, then as discussed above, at constant CW flow, both CW velocity and turbine exhaust pressure decrease. The effect on output of the changing exhaust pressure, may be determined from the output/exhaust pressure characteristic (Fig 1.58).
It is customary to consider a reference or nominal design having a given surface area and CW flow rate, and to compute the change in cost from the reference.
The effect of the variables on the following economic data can now be considered:
- Increments of CW flow will affect CW pump costs.
- Increments of CW flow will affect CW system costs.
- Increments of condenser surface will affect condenser costs.
- Changes in output will affect the running costs.
- Increments of CW flow and head will affect the consumed CW pump power and will therefore affect the running costs.
If the individual costs are calculated for the grid of points on Fig 1.62 and then summated to give the total cost at each point, we can plot contours of constant cost, as shown in Fig 1.63.
Computer programs have been devised which will evaluate the best design combination of parameters for minimum total cost and Fig 1.63 is a typical graphical output. From Fig 1.63 it can be seen that the smaller the contour, the lower the total cost. The most economic design parameters therefore exist at the centre of the smallest contour. It is, however, quite possible that these will not be used, because there are further constraints on the design yet to be considered.
The most significant constraints, after the turbine exhaust area and condenser length previously mentioned, are the limits on CW velocity. There is a maximum velocity permissible to prevent tube erosion and a minimum velocity to avoid silting. Environmental considerations enforce a limit on the maximum temperature of the CW discharge into the river or sea so that fishing is not affected.
The exercise can be repeated with one of the fixed parameters changed to a new value. In this way, the change in costs using different exhaust annulus areas can be found. A similar analysis can be undertaken for a tower-cooled system, where CW is cycled between the condenser (where it receives heat from the steam), and the cooling tower where it transfers the heat to the rising air. (For a full explanation of the 'indirect cooling' system see Chapter 4.)
The economic optimisation calculations are based on a constant CW inlet temperature and the assumption that all the condenser tubes will be available. In reality, the seasonal changes in temperature in the UK produce a range of CW inlet temperature of between 5-17°C, corresponding to a variation from the ideal turbine exhaust pressure of ±15 mbar. This could be responsible for a change in turbine efficiency of around 0.7%.
It cannot be assumed, either, that all the condenser tubes will be operational throughout the lifetime of the condenser. Material too small to be trapped by the screens may build up in the tubes, restrict the flow and eventually block it entirely (known as fouling). The problem can be alleviated either by regular maintenance or through the provision of automatic cleaning by circulating foam rubber balls that clean away the dirt and scale formation. The effects of erosion at the higher velocities can be practically eliminated by the use of hard materials such as Titanium for the condenser tubes. Changes in tube material and in fouling factor, are evaluated during the design to confirm the most economic choice for the full range of operating conditions.