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# Power Generation: Efficiency

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Question 1 

In a coal fired power plant the output from the steam turbine is 500 MW in the form of shaft power. This is connected to an electric turbine with an efficiency of 96 %. The output voltage from the electric generator is 2000 V.

What is the power output from the electric generator? What is the electric current output from the electric generator.

An electric power transformer is connected to the electric generator. The transformer has an efficiency of 99% and is used to step up the voltage from the electric generator to 400 kV.

What is the electric current that flows in the transmission line?

Question 2 

Steam at a temperature of 400 °C is used by a steam turbine. The outlet of the steam turbine is connected to a dry cooled air condenser with an average temperature of 35 °C.

What is the Carnot efficiency of this turbine?

In real life it was found that the real turbine efficiency is 90 % of the Carnot efficiency due to heat loss and irreversibilities within the turbine.

If 200 MJ/s of steam enters the turbine, what is the shaft output of the turbine? How much heat is rejected to the environment via the condenser?

The condenser is replaced with a wet cooling tower with a temperature of 15 °C. If the steam turbines efficiency remains 90 % of the Carnot efficiency, what is the new output from the turbine?

Question 3 

A coal fired power station has the following:
? Boiler steam temperature TH = 400 °C
? Condenser steam temperature of TL = 35 °C
? Energy rate into boiler = 3000 MJ/s
? Boiler efficiency = 85 %
? The real turbine efficiency is 90% of Carnot efficiency
? A dry cooled condenser uses 3% of the electrical output
? The boiler pump uses 0.8% of the electrical output
? Other electrical needs total 0.5% of the electrical output
? The electric generator has an efficiency of 95 %

What is the power station's final electrical output?

If you have trouble with this, follow these steps:
Calculate the boiler energy output rate. Remember 1 J/s = 1 W
Calculate the Carnot efficiency
Calculate the real turbine efficiency
Calculate the turbine shaft output using the real turbine efficiency
Calculate the output from the electric generator
Calculate the power used by all the auxiliaries (pumps etc) and subtract this from the electric generator's output to obtain the final electric output

Question 4 

A nuclear power station of 1800 MW (final output into transmission lines) is situated on the coast. Ocean water is used in the once-through condenser.

This pressurised water reactor (BWR) generates steam at 320 °C. The condenser temperature is 17 °C.

The pump that circulates the ocean water through the condenser uses 10.8 MW. Other electrical devices on the plant use a total of 20 MW. What is the output from the electric generator?

If the generator has 95 % efficiency, what is the output from the steam turbine?

What is the turbines Carnot efficiency?
The steam entering the turbine has a heat flow of 4287 MW. What is the turbines real efficiency?

What percentage of the Carnot efficiency does the turbine operates on?

Question 5 

Make a list of the different types of condensers used in conventional power stations (there should be five). What is their application, installation and running costs (water and electricity). What is their environmental impact?

You might need to use additional sources on the internet for this. Keep it short and compact.

Textbook: AUBRECHT, 2006, 'ENERGY'

Read through  Chapter 6 p 187 - 222