Turbines, both steam and gas (internal combustion) versions, create large amounts of shaft horsepower in a small physical package, especially compared to piston engines. Steam turbines are by far the most common way to drive electrical power generators in utility companies because of their reliability and high efficiency, especially compared to internal combustion methods of producing electrical power. Calculating turbine efficiency is possible with knowledge of how much power the turbine produces and how much energy it needs to produce it.
Step 1
Define the steam turbine calculation. In this example, a 1.2-megawatt-hour power generator in a sugar mill is driven by a steam turbine that receives 52,462 pounds per hour of superheated steam at 450 pounds per square inch absolute (psia) pressure with a temperature of 556.28 degrees Fahrenheit. The steam exits the turbine saturated at 30 psia (about 15-psi/gauge) and used elsewhere in the plant. If the electrical generator has a conversion efficiency of 82 percent, you can calculate the turbine efficiency.
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Step 2
Calculate the actual power used by the generator to produce the 1.2 megawatt-hours of electricity: 1.2 megawatt-hours divided by 0.82 (82 percent) generator efficiency = 1.4634 megawatt-hours of power.
Step 3
Convert the to shaft horsepower for the turbine: 1.4634 megawatt-hours / (0.746-kilowatt-hours/horsepower X 1,000 kilowatt-hours/megawatt-hours) = 1,962 horsepower.
Step 4
Convert the 1,962 horsepower produced by the turbine into BTU/hour. Multiplying 1,962.45 by 2,545 BTU/Hour results in a total of 4,993,323 BTU/hour consumed by the turbine.
Step 5
Look up the enthalpy values of the entering and exiting steam. The superheated steam has an enthalpy of 1275.42 BTU/pound. The exiting steam has an enthalpy of 1164.1 BTU/pound. The net value of power supplied to the turbine by the steam is 111.32 BTU/pound of steam.
Step 6
Calculate the theoretical pounds of superheated steam at the above conditions to supply 4,993,323 BTU/hour by dividing by the 111.32 BTU/pound of net steam enthalpy consumed in the turbine. This works out to 4,993,323 / 111.32 = 44,855.58 pounds/hour of steam.
Step 7
Calculate steam turbine efficiency by dividing the theoretical pounds per hour of steam by the steam actually consumed. This is 44,855.58 pounds (theoretical) / 52,462 pounds actual = 0.855 or 85.5 percent operating efficiency.
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