Mastodon Power plant and calculations: How do you calculate the Power generation in steam Turbines??

### How do you calculate the Power generation in steam Turbines??

Power in the steam Turbines produces at every stage where the steam is taken out, whether it may be bleed, extraction or exhaust steam. As the steam out from the turbine increases the power developed on that particular stage will increase.
Power generation phenomenon.
Power generation in steam Turbines is calculated based on difference between the heat content of inlet steam & extracted steam.

Factors affecting the power generation:
• Power generation at particular stage increases, when there is more steam flow &vice versa
• Power generation at particular stage increases when there is more difference between inlet & extraction steam & Vice versa
• Power develop at particular stage decreases if its extraction pressure increases & vice versa
• Power developed at particular stage decreases if its extraction temperature increases & vice versa
• Power developed in steam Turbine decreases if inlet live steam pressure & temperature decrease
• If steam vacuum decreases power generation reduces or else Turbine will consume more steam to develop same power
• If exhaust steam temperature increases then the power power generation reduces or else Turbine will consume more steam to develop same power
• If wheel chamber pressure increases, then the power generation capacity of the Turbine decreases
HOW DO YOU CALCULATE POWER GENERATION COST??

In which part of the Turbine higher power can be produced at lower steam consumption? And why?
It is at the exhaust stage. Because at the exhaust stage pressure & temperature of the steam is very lesser than bleed &extraction stages.
In which part of the Turbine lowest power is produced at higher steam consumption? And why?
It is at the bleed stage. Because at bleed steam pressure & temperatures are higher than extraction & exhaust stages
Calculation part:
1-Calculate the power generated in a back pressure steam Turbine, where 50 TPH steam enters the Turbine at 66 kg/cm2 & temperature 485 Deg C.And steam exhausts to process at pressure 2 kg/cm2 & temperature 180 Deg C.
For calculation of power we need to know the enthalpy of inlet & exhaust steam.
Refer steam table
Enthalpy of inlet steam at rated parameters H1 = 806.5 kcal/kg
Enthalpy of inlet steam at rated parameters H2 = 677 kcal/kg
Now power developed in steam turbine P = Q X (H1-H2) / 860
Where Q is steam flow
P = 50 X (806.5-677) / 860
P = 7.52 MW
Note: 860 kcal = 1 KWH
2. Calculate the power developed by a steam turbine by using following data
 Sl No. Particular UOM Value 1 Turbine inlet steam flow TPH 145 2 Turbine inlet steam pressure Kg/cm2 88 3 Turbine inlet steam temperature C0 515 4 Bleed steam flow TPH 20 5 Bleed steam pressure Kg/cm2 12 6 Bleed steam temperature C0 250 7 Extraction flow TPH 100 8 Extraction steam pressure Kg/cm2 1.8 9 Extraction steam temperature C0 145 10 Exhaust flow to condenser TPH 25 11 Exhaust pressure Kg/cm2 0.08 12 Exhaust temperature C0 44 13 Dryness fraction % 90

Also calculate the specific steam consumption of this Turbine
Solution:
Note down the enthalpy of steam at various stages
Turbine inlet steam enthalpy H1 = 818 kcal/kg
Bleed steam enthalpy H2 =700 kcal/kg
Extraction steam enthalpy H3 = 657.2 kcal/kg
Exhaust enthalpy =Liquid heat + Dryness fraction X Vapour enthalpy = 41.77 + 0.9 X 615.5 = 595.72 kcal/kg
Also steam flow is given
Inlet steam flow Q1 = 145 TPH
Bleed steam flow Q2 = 20 TPH
Extraction steam flow Q3 =100 TPH
Exhaust steam flow Q4 = 25 TPH
Power generation at 1st stage (Bleed) P1 = Q2 X (H1-H2) / 860
P1 = 20 X (818-700) / 860 = 2.74 MW
Power generation at 2nd stage (Extraction) P2 = Q3 X (H1-H3) / 860
P2 = 100 X (818-657.2) / 860 = 18.69 MW
Power generation at 3rd stage (Exhaust) P3 = Q4 X (H1-H4) / 860
P3 = 25 X (818-595.72) / 860 = 6.46 MW
SO total power developed at Turbine shaft P = P1+P2+P3 = 2.74+18.69+6.46 = 27.89 MW
Specific steam consumption SSC = Turbine inlet steam flow / Power generation = 145 / 27.89 =5.19 MT/MW

3-By taking above example, explain how pure condensing steam Turbines have higher power generation & lower specific steam consumption (SSC)
Consider the above example, where Turbine inlet steam flow is 145 TPH & having 25 TPH exhaust steam flow to condenser.
If we condense 100% steam, then we will have reduced SSC
Let us see..
Q1=Q4=145 TPH..Where Q4 = Exhaust steam to condenser
Q2 & Q3 are considered zero (No flow)
Enthalpy of exhaust steam increases due to higher exhaust pressure
SO, Consider exhaust pressure = 0.1 kg/cm2 & Dryness fraction 0.9
Then, exhaust enthalpy becomes H1 = 46 + 0.9 X 617 = 601.9 kcal/kg
Total Power developed P= Q1 X (H1-H4) / 860
P =145 X (818-601.9) / 860 = 36.43 MW
So SSC = 145 / 36.43 = 3.98 MT/MW
This is very less as compared to bleed & extraction turbines

4-By taking an example No.2 explain how bleed steam flow will cause reduction in net power consumption
Solution:
We shall take the data of Example No.2
In this, we will increase bleed steam flow, pressure & temperature & parallel shall decrease extraction flow to match mass flow
 Sl No. Particular UOM Value 1 Turbine inlet steam flow TPH 145 2 Turbine inlet steam pressure Kg/cm2 88 3 Turbine inlet steam temperature C0 515 4 Bleed steam flow TPH 30 5 Bleed steam pressure Kg/cm2 15 6 Bleed steam temperature C0 285 7 Extraction flow TPH 90 8 Extraction steam pressure Kg/cm2 1.8 9 Extraction steam temperature C0 145 10 Exhaust flow to condenser TPH 25 11 Exhaust pressure Kg/cm2 0.08 12 Exhaust temperature C0 44 13 Dryness fraction % 90

Solution:
Note down the enthalpy of steam at various stages
Turbine inlet steam enthalpy H1 = 818 kcal/kg
Bleed steam enthalpy H2 =716.63 kcal/kg
Extraction steam enthalpy H3 = 657.2 kcal/kg
Exhaust enthalpy =Liquid heat + Dryness fraction X Vapour enthalpy = 41.77 + 0.9 X 615.5 = 595.72 kcal/kg
Also steam flow is given
Inlet steam flow Q1 = 145 TPH
Bleed steam flow Q2 = 30 TPH
Extraction steam flow Q3 =90 TPH
Exhaust steam flow Q4 = 25 TPH
Power generation at 1st stage (Bleed) P1 = Q2 X (H1-H2) / 860
P1 = 30 X (818-716.63) / 860 = 3.53 MW
Power generation at 2nd stage (Extraction) P2 = Q3 X (H1-H3) / 860
P2 = 90 X (818-657.2) / 860 = 16.82 MW
Power generation at 3rd stage (Exhaust) P3 = Q4 X (H1-H4) / 860
P3 = 25 X (818-595.72) / 860 = 6.46 MW
SO total power developed at Turbine shaft P = P1+P2+P3 = 3.53+16.82+6.46 = 26.81 MW
Specific steam consumption SSC = Turbine inlet steam flow / Power generation = 145 / 26.81 =5.41 MT/MW
So by increasing the bleed steam flow, the work done by the Turbine decreases & hence steam consumption will increase

5-A Turbine’s inlet steam enthalpy is 825 kcal/kg & Exhaust enthalpy is 590 kcal/kg. Calculate the work done by steam & specific steam steam consumption
We have,
H1 = 825 kcal/kg, H2 = 590 kcal/kg
Work done per kg of steam = (H1-H2) = 825-890 =235 kcal/kg
SSC = 860 / Work done = 860 / 235 =3.65 kg/kwh or 3.65 MT/MW
6-A steam Turbine inlet steam pressure & temperatures are 104 kg/cm2 & 540 C0 & exhausts at pressure 0.09 kg/cm2 & temperature 43 Deg C calculate the
a-      Work done per kg of steam
b-      Heat supplied per kg of steam
c-       Cycle efficiency
Enthalpy of inlet steam = 829 kcal/kg
Exhaust liquid enthalpy = 44 kcal/kg
Exhaust enthalpy by considering 90% dryness fraction = 44 + 0.9 X 616.44 =598.76 kcal/kg
A-Work done per kg of steam = (829-598.76) = 230.24 kcal/kg
B-Heat supplied per kg of steam = 829-44 = 785 kcal/kg
C-Cycle efficiency = Work done per kg of steam X 100 / Heat supplied per kg of steam
= 230.24 X 100 / 785 = 29.32%
Note:
Power developed at Generator terminals = Power developed at Turbine Shaft X Reduction gear box efficiency X Alternator efficiency
For example:
Calculate the net power developed at Generator terminal if 100 TPH steam enters the Turbine at 811 kcal/kg enthalpy & leaves the Turbine at enthalpy 565 kcal/kg .Assume Gear box efficiency as 98% & Generator efficiency as 95%
Power developed on Turbine shaft = 100 X (811-565) / 860 = 28.0 MW
Net power developed at Generator output terminals = 28.0 X 0.98 X 0.95 = 26.06 MW

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