2. Combined
Cycle
Gas
Turbine What is the CCGT?
A combined cycle gas turbine power plant,
frequently identified by CCGT shortcut, is
essentially an electrical power plant in which
a gas turbine and a steam turbine are used in
combination to achieve greater efficiency than
would be possible independently. The gas
turbine drives an electrical generator. The gas
turbine exhaust is then used to produce steam
in a heat exchanger (steam generator) to
supply a steam turbine whose output provides
the means to generate more electricity.
However the Steam Turbine is not necessarily,
in that case the plant produce electricity and
industrial steam which can be used for heating
or industrial purpose.
3. Combined
Cycle
Gas
Turbine Basic Gas Turbine Information
•Main Gas Turbine Manufactures:
General Electrics, Simens Westinghouse &
Alstom
•Approximately Cost per MW – 0.7mln E
•Efficiency approx 40% for gas turbine
however in the CCGT plant the efficiency is
50-60% (even higher for cogenerated plant)
•Low Green Gas Emission C02, NOx & SOx
•Chepear comparing to other technology e.g.
CCS
•Lifetime 30-40 years
5. Combined
Cycle
Gas
Turbine CCGT Fuel Available in KSA
Natural Gas. Resources available in KSA
Synthetic Gas from coal.
Resources not available in KSA
Fuel Oil. Resources available in KSA
Biogas from forestry, domestic and
agricultural waste.
Resources not available in KSA
6. Combined
Cycle
Gas
Turbine CCGT Plants Conventional or Cogeneration
Variable CCGT High Efficiency
Cogeneration
Transmission Network Lower Impact Higher Impact
Power Losses Less power losses Higher Power Losses
Heat Market Required Not Required
Fuel consumption -33% +33%
CO2 Emission -67% +67%
Water Consumption -30% +30%
Capital Cost per kW delivered 630 1200
7. Combined
Cycle
Gas
Turbine grid Grid Code
Grid Code contains general conditions and rules for general application.
The specification and conditions for each application are adjust individually.
Those information are included in Grid Connection Offer & Agreement
between developer and Transmission Operator TSO.
•Client (Requires connection) and TSO must implement Grid Code specification
during each stages of the project, for project above 10MW
•TSO may be disconnected or terminated the Grid Connection Agreement
if the Grid Code is not implemented by client.
•The Implementation of the Grid Code may have significant impact on the cost of the
Grid Connection
•ESB Networks Electrical Safety Rules must be implemented
8. Combined
Cycle
Gas
Turbine Grid Constraints
•Capacity of the transmission lines
• Small Infrastructures of the High Voltage Lines
•Distance from Energy Load Centres (West Coast)
• High Cost of Design and planning permission for Shallow Connection,
significantly for OHL 220kV
•Planning Restrictions regarding OHL Construction
9. Combined
Cycle
Gas
Turbine Grid Connection Costs
Variable Cost
Gas & Steam Turbine Generator 210’000’000
2 bay 110kV/220kV Substation 4’420’000
220kV OHL 710’000/km (12km)
110kV OHL 320’000/km (15km)
Buried Cable 500MVA (optional) 2’150’000/km
Total Cost 227’740’000
12. Combined
Cycle
Gas
Turbine
12
Types of Gas Turbine Plants
• Simple Cycle
– Operate When Demand is High – Peak
Demand
– Operate for Short / Variable Times
– Designed for Quick Start-Up
– Not designed to be Efficient but Reliable
• Not Cost Effective to Build for Efficiency
• Combined Cycle
– Operate for Peak and Economic Dispatch
– Designed for Quick Start-Up
– Designed to Efficient, Cost-Effective Operation
– Typically Has Ability to Operate in SC Mode
13. Combined
Cycle
Gas
Turbine
13
The energy contained in a flowing ideal gas
is the sum of enthalpy and kinetic energy.
Pressurized gas can store or release energy.
As it expands the pressure is converted to
kinetic energy.
Principles of Operation
• Open Cycle
Also referred to as simple cycle)
Link to picture
17. Combined
Cycle
Gas
Turbine
17
Principles of Operation
Compressor
• As air flows into the compressor, energy is transferred from its
rotating blades to the air. Pressure and temperature of the air
increase.
• Most compressors operate in the range of 75% to 85%
efficiency.
Combustor
• The purpose of the combustor is to increase the energy stored
in the compressor exhaust by raising its temperature.
Turbine
• The turbine acts like the compressor in reverse with respect to
energy transformation.
• Most turbines operate in the range of 80% to 90% efficiency.
18. Combined
Cycle
Gas
Turbine
18
Principles of Operation
Overall Energy Transformations (Thermal Efficiency)
• Useful Work = Energy released in turbine minus energy
absorbed by compressor.
The compressor requires typically approximately 50% of
the energy released by the turbine.
• Overall Thermal Efficiency =
Useful Work/Fuel Chemical Energy *100
Typical overall thermal efficiencies of a combustion
turbine are 20% - 40%.
22. Combined
Cycle
Gas
Turbine
22
Combined Cycle Plant Design
GT PRO 13.0 Drew Wozniak
1512 10-13-2004 23:27:31 file=C:Tflow13MYFILES3P 0 70.gtp
Net Power 95959 kW
LHV Heat Rate 7705 BTU/kWh
p[psia], T[F], M[kpph], Steam Properties: Thermoflow - STQUIK
4.717 m
Fogger
1X GE 6581B 2 X GT
33781 kW
12.54 p
90 T
30 %RH
944 m
4327 ft elev.
12.39 p
68 T
948.7 m
Natural gas 18.58 m
96 T
77 T
LHV 369671 kBTU/h
149.2 p
684 T
143.2 p
2072 T
967.3 m
12.93 p
1034 T
1934.6 M
73.85 %N2
13.53 %O2
3.233 %CO2+SO2
8.497 %H2O
0.8894 %Ar
1031 T
1934.6 M
1031
897
569
568
538
534
481
419
326
268
268 T
1934.6 M
30813 kW
0.1296 M
FW
1.694 p
120 T
222.1 M
120 T
Natural gas
0 M
122 T
292.6 M
122 T 17.19 p
220 T
29.58
M
17.19 p
220 T
29.65 M
LPB
29.65
M
292.6
M
203.6 p
373 T
292.6 M
IPE2
203.6 p
383 T
36.75 M
IPB
199.7 p
460 T
36.75 M
IPS1
195.8 p
500 T
36.75 M
IPS2
924.2 p
472 T
251.1 M
HPE2
910.5 p
523 T
251.1 M
HPE3
910.5 p
533 T
248.6 M
HPB1
879.8 p
954 T
248.6 M
HPS3
850 p
950 T
248.6 M
879.8
p
954
T
6.89 M
183 p 375 T 70 M V4
26.36 M
195.8
p
597
T
V8
6.89 M
46. Combined
Cycle
Gas
Turbine
46
Aero-derivative Versus Heavy Duty
Combustion Turbines
• Aero-derivatives
– Higher Pressure Ratios and Firing
Temperatures Result in Higher Power Output
per Pound of Air Flow
– Smaller Chilling/Cooling Systems Required
– Compressor Inlet Temperature Has a
Greater Impact on Output and Heat Rate
– Benefits of Chilling/Cooling Systems are
More Pronounced
47. Combined
Cycle
Gas
Turbine
47
Typical Simple Cycle CT Plant Components
• Prime Mover (Combustion Turbine)
• Fuel Supply & Preparation
• Emissions Control Equipment
• Generator
• Electrical Switchgear
• Generator Step Up Transformer
• Starting System (Combustion
Turbines)
• Auxiliary Cooling
• Fire Protection
• Lubrication System
49. Combined
Cycle
Gas
Turbine
49
Combining the Brayton and Rankine Cycles
• Gas Turbine Exhaust used as the heat source for the
Steam Turbine cycle
• Utilizes the major efficiency loss from the Brayton cycle
• Advantages:
– Relatively short cycle to design, construct & commission
– Higher overall efficiency
– Good cycling capabilities
– Fast starting and loading
– Lower installed costs
– No issues with ash disposal or coal storage
• Disadvantages
– High fuel costs
– Uncertain long term fuel source
– Output dependent on ambient temperature
52. Combined
Cycle
Gas
Turbine
52
Combined Cycles Today
• Plant Efficiency ~ 58-60 percent
– Biggest losses are mechanical input to the compressor and heat in the
exhaust
• Steam Turbine output
– Typically 50% of the gas turbine output
– More with duct-firing
• Net Plant Output (Using Frame size gas turbines)
– up to 750 MW for 3 on 1 configuration
– Up to 520 MW for 2 on 1 configuration
• Construction time about 24 months
• Engineering time 80k to 130k labor hours
• Engineering duration about 12 months
• Capital Cost ($900-$1100/kW)
• Two (2) versus Three (3) Pressure Designs
– Larger capacity units utilize the additional drums to gain efficiency at the
expense of higher capital costs
54. Combined
Cycle
Gas
Turbine
54
Gas Turbine Generator Performance
Factors that Influence Performance
– Fuel Type, Composition, and Heating Value
– Load (Base, Peak, or Part)
– Compressor Inlet Temperature
– Atmospheric Pressure
– Inlet Pressure Drop
• Varies significantly with types of air cleaning/cooling
– Exhaust Pressure Drop
• Affected by addition of HRSG, SCR, CO catalysts
– Steam or Water Injection Rate
• Used for either power augmentation or NOx control
– Relative Humidity
57. Combined
Cycle
Gas
Turbine
57
Cogeneration Plant
• A Cogeneration Plant
– Power generation facility that also provides thermal
energy (steam) to a thermal host.
• Typical thermal hosts
– paper mills,
– chemical plants,
– refineries, etc…
– potentially any user that uses large quantities of steam
on a continuous basis.
• Good applications for combined cycle plants
– Require both steam and electrical power
58. Combined
Cycle
Gas
Turbine
58
Major Combined Cycle Plant Equipment
• Combustion Turbine (CT/CTG)
• Steam Generator (Boiler/HRSG)
• Steam Turbine (ST/STG)
• Heat Rejection Equipment
• Air Quality Control System (AQCS)
Equipment
• Electrical Equipment
61. Combined
Cycle
Gas
Turbine Primary to Secondary to End-Use Energy
Secondary
Energy
Utilization
Deviceor
System
Final
Useful
Energy
Transformation
Transportation
Distribution
Primary
Energy
Losses Losses
63. Combined
Cycle
Gas
Turbine Electricity Basics
• Electricity can be either direct current (DC) or alternating current
(AC)
• In AC current, the voltage and current fluctuate up and down 60
times per second in North America and 50 times per second in the
rest of the world
• The power (W) in a DC current is equal to current (amps) x voltage
(volts): P=VI
• The power in an AC current is equal to the product of the root mean
square (RMS) of the fluctuating current and voltage if the current
and voltage are exactly in phase (exactly tracking each other):
P=Vrms x Irms
• The standard electricity distribution system consists of 3 wires with
the current in each wire offset by 1/3 of a cycle from the others, as
shown in the next figure
66. Combined
Cycle
Gas
Turbine • Electricity demand continuously varies, and power utilities have to
match this variation as closely as they can by varying their power
production. The following distinctions are made:
• Base_load power plants: these are plants that run steadily at full
load, with output equal to the typical minimum electricity demand
during the year. Plants (such as coal or nuclear) that cost a lot to
build but are cheap to operate (having low fuel costs) are good
choices
• Peaking powerp lants: these are plants that can go from an off
state to full power within an hour or so, and which can be
scheduled based on anticipated variation in demand (natural gas
turbines or diesel engines would be a common choice)
• Spinning reserve: these are plants that are on but running at part
load – this permits them to rapidly (within a minute) vary their
output, but at the cost of lower efficiency (and so requires greater
fuel use in the case of fossil fuel power plants).
67. Combined
Cycle
Gas
Turbine Electricity from Fossil Fuels
• Pulverized coal
• Integrated Gasification/Combined Cycle
(IGCC)
• Natural gas turbines and combined cycle
• Diesel and natural gas reciprocating
engines
• Fuel cells
68. Combined
Cycle
Gas
Turbine Technical issues related to electricity
from fossil fuels
• Full load efficiency
• Part-load efficiency
• Rates of increase of output
• Impact of temperature on output
• Auxiliary energy use
69. Combined
Cycle
Gas
Turbine Generation of electricity from a conventional,
pulverized-coal power plant
steam
High-Pressure Boiler
Generator
electricity out
to cooling tower
or cold river water
and/or
cogeneration
cooling water return flow
Condenser
Pump
Steam
Turbine
water
condensate
sequestered CO
out
2
CO up the stack
2
CO2
air (O )
2
fossil fuel in
Source: Hoffert et al (2002, Science 298, 981-987)
70. Combined
Cycle
Gas
Turbine The upper limit to the possible efficiency of a
power plant is given by the Carnot efficiency:
η = (Tin-Tout)/Tin
So, the hotter the steam supplied to the steam
turbine, the greater the efficiency.
Hotter steam requires greater pressure, which
requires stronger steel and thicker walls.
so there is a practical limit to the achievable
Carnot efficiency (and actual efficiencies are
even lower)
71. Combined
Cycle
Gas
Turbine Coal power plant operating
temperatures and efficiencies
• Typical: 590ºC, 35% efficiency
• Best today:
> 600ºC, 42-44% efficiency
• Projected by 2020:
720ºC, 48-50% efficiency
72. Combined
Cycle
Gas
Turbine
Integrated Gasification
Combined Cycle (IGCC)
• This is an alternative advanced coal power
plant concept
• Rather than burning pulverized solid coal,
the coal is heated to 1000ºC or so at high
pressure in (ideally) pure oxygen
• This turns the coal into a gas that is then
used in a gas turbine, with heat in the
turbine exhaust used to make steam that is
then used in a steam turbine
• Efficiencies of ~ 50% are expected, but are
much lower at present
73. Combined
Cycle
Gas
Turbine Generation of electricity with natural gas
• Simple-cycle power generation
• Combined-cycle power generation
• Simple-cycle cogeneration
• Combined-cycle cogeneration
74. Combined
Cycle
Gas
Turbine Simple-cycle turbine
• Has a compressor, combustor, and
turbine proper
• Because hot gases rather than steam
are produced, it is not restricted in
temperature by the rapid increase in
steam pressure with temperature
• Thus, the operating temperature is
around 1200ºC
75. Combined
Cycle
Gas
Turbine Simple-cycle gas turbine and electric
generator
FUEL
EXHAUST
SHAFT
COMPRESSOR TURBINE
INTAKE AIR
GENERATOR
ELECTRICITY
COMBUSTOR
Source: Williams (1989, Electricity: Efficient End-Use and New Generation Technologies and Their Planning Implications, Lund University Press)
76. Combined
Cycle
Gas
Turbine Efficiency of generating electricity using
natural gas
• One might expect a high efficiency from
the gas turbine, due to the high input
temperature (and the resulting looser
Carnot limit)
• However, about half the output from the
turbine has to be used to compress the air
that is fed into it
• Thus, the overall efficiency is only about
35% in modern gas turbines
78. Combined
Cycle
Gas
Turbine Efficiency and cost of a simple-cycle gas
turbine with and without water injection
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60
Turbine Power (MW)
Turbine
Efficiency
(%)
0
100
200
300
400
500
600
Cost
(euros/kW)
Without water injection
With water injection
Cost
79. Combined
Cycle
Gas
Turbine Due to the afore-mentioned high operating
temperature of the gas turbine, the temperature
of the exhaust gases is sufficiently hot that it
can be used to either:
Make steam and generate more electricity in a
steam turbine (this gives combined cycle power
generation). Or:
provide steam for some industrial process that
can use the heat, or to supply steam for district
heating (this gives simple cycle cogeneration)
80. Combined
Cycle
Gas
Turbine Combined-cycle power generation using
natural gas
INTAKE AIR
STEAM TURBINE
ELECTRICITY
CONDENSER
COOLING TOWER
STEAM
EXHAUST
WATER
PUMP
HEAT RECOVERY
STEAM GENERATOR
FUEL
SHAFT
COMPRESSOR TURBINE
GENERATOR
ELECTRICITY
COMBUSTOR
Source: Williams (1989, Electricity: Efficient End-Use and New Generation Technologies and Their
Planning Implications, Lund University Press)
81. Combined
Cycle
Gas
Turbine Simple-cycle cogeneration
EXHAUST
WATER
PUMP
HEAT RECOVERY
STEAM GENERATOR
PROCESS STEAM
FUEL
SHAFT
COMPRESSOR TURBINE
INTAKE AIR
GENERATOR
ELECTRICITY
COMBUSTOR
Source: Williams (1989, Electricity: Efficient End-Use and New Generation Technologies and
Their Planning Implications, Lund University Press)
82. Combined
Cycle
Gas
Turbine The energy can be cascaded even further,
as follows:
• Gas turbine → steam turbine → useful
heat as steam from the steam turbine
(combined cycle cogeneration), or
• Gas turbine → steam turbine → steam
→ hot water (also combined cycle
cogeneration), or
• Gas turbine → steam → hot water
83. Combined
Cycle
Gas
Turbine Combined-cycle cogeneration
STEAM TURBINE
ELECTRICITY
CONDENSER
COOLING TOWER
STEAM
EXHAUST
WATER
PUMP
HEAT RECOVERY
STEAM GENERATOR
FUEL
SHAFT
COMPRESSOR TURBINE
INTAKE AIR
GENERATOR
ELECTRICITY
COMBUSTOR
PROCESS STEAM
Source: Williams (1989, Electricity: Efficient End-Use and New Generation Technologies and
Their Planning Implications, Lund University Press)
84. Combined
Cycle
Gas
Turbine Cogeneration system with
production of steam and hot water
FUEL
ELECTRICITY
GAS
TURBINE GENERATOR
EXHAUST GAS
STEAM
HEAT
RECOVERY
STEAM
GENERATOR
HEAT
EXCHANGER
HOT WATER
EXHAUST GAS
Source: Malik (1997, M. Eng Thesis, U of Toronto)
85. Combined
Cycle
Gas
Turbine • State-of-the-art natural gas combined-cycle
(NGCC) systems have electricity generation
efficiencies of 55-60%, compared to a typical
efficiency of 35% for single-cycle turbines
• However, NGCC systems are economical only
in sizes of 25-30 MW or greater, so for smaller
applications, only the less efficient simple-cycle
systems are used
• Thus, a number of techniques are being
developed to boost the electrical efficiency of
simple gas turbines to 42-43%, with one
technique maybe reaching 54-57%
86. Combined
Cycle
Gas
Turbine
In cogeneration applications, the overall
efficiency (counting both electricity and
useful heat) depends on how much of the
waste heat can be put to use. However,
overall efficiencies of 90% or better have
been achieved
87. Combined
Cycle
Gas
Turbine
Reciprocating engines
• These have pistons that go back and
forth (reciprocate)
• Normally they use diesel fuel – so these
are the diesel generators normally used
for backup or emergency purposes
• However, they can also be fuelled with
natural gas, with efficiencies as high as
45%
88. Combined
Cycle
Gas
Turbine Fuel cells
• These are electrochemical devices – they
generate electricity through chemical
reactions at two metal plates – an anode
and a cathode
• Thus, they are not limited to the Carnot
efficiency
• Operating temperatures range from 120ºC
to 1000ºC, depending on the type of fuel
cell
• All fuel cells require a hydrogen-rich gas as
input, which can be made by processing
natural gas or (in the case of high-
temperature fuel cells) coal inside the fuel
cells
89. Combined
Cycle
Gas
Turbine Fuel cells (continued)
• Electricity generation efficiencies using
natural gas of 40-50% are possible, and
90% overall efficiency can be obtained if
there is a use for waste heat
• In the high-T fuel cells, the exhaust is hot
enough that it can be used to make steam
that can be used in a steam turbine to
make more electricity
• An electrical efficiency of 70% should be
possible in this way – about twice that of a
typical coal-fired.
90. Combined
Cycle
Gas
Turbine
Several such cells
would be placed next
to each other to form
a fuel cell stack.
DC Power
Eelectron flow
Nitrogen
Oxidized
Fuel (H O)
Fuel
distribution
plate
Negative ions
Positive ions
CA
THO
DE
ELECTRO
LYTE
Fuel (H )
2 Air (Mostly
N + O )
2 2
2
or
Cross section of
a single fuel cell.
91. Combined
Cycle
Gas
Turbine United Technologies Company 200-kW phosphoric
acid fuel cell that uses natural gas as a fuel.
Source: www.utcfuelcells.com
1=fuel processor,
2=cell stack,
3=power conditioner,
4=electronics and controls
92. Combined
Cycle
Gas
Turbine Solid Oxide Fuel Cell / Gas Turbine System
SOFC = Solid Oxide Fuel cell
AC,FC = Air & Fuel compressor
CB = Catalytic burner
GT = Gas turbine
HRSG = Heat recovery steam generator
HE = Heat exchanger
847 C
o
GT-2
1079 C
o
GT-1
CB
1290 C
o
SOFC 985 C
o
Turbine
Exhaust
To heat load
From heat load
HE-3
Pump
25 C
o
224 C
o
509 C
o
440 C
o
468 C
o
HRSG
M
448 C
o
526 C
o
HE-2
738 C
o
HE-1
25 C
o
Air
Fuel
FC AC
301 C
o
236 C
o
25 C
o
95. Combined
Cycle
Gas
Turbine Summarizing the preceding slides and other
information,
• Natural gas combined-cycle has the highest full-load
efficiency (55-60%) and holds its efficiency well at part
load
• Reciprocating engines have intermediate full-load
efficiencies (40-45%) and load their efficiencies well at
part load
• Gas turbines and micro-turbines have low full-load
efficiencies (typically 25-35%, but ranging from 16% to
43%) and experience a substantial drop at part load
• Fuel cells using natural gas have intermediate full-load
efficiency (40-45%) but this efficiency increases at part
load
96. Combined
Cycle
Gas
Turbine
Capital Costs Today
• Pulverized coal power plant with state-of-
the-art pollution controls: $1200-1400/kW
• Natural gas combined cycle: $400-600/kW
in mature markets, $600-900/kW in most
developing countries
• Reciprocating engines: $600-1200/kW
• Fuel cells: $3000-5000/kW
98. Combined
Cycle
Gas
Turbine
Cogeneration is the simultaneous
production of electricity and useful heat –
basically, take the waste heat from
electricity generation and put it to some
useful purpose. Two possible uses are to
feed the heat into a district heating
system, and to supply it to an industrial
process
99. Combined
Cycle
Gas
Turbine Figure 3.12 Proportion of electricity produced
decentrally (overwhelmingly as cogeneration)
0 10 20 30 40 50 60
Denmark
Netherlands
Finland
Russia
Germany
Canada
China
Chile
Portugal
USA
Percent Decentralized Electricity Generation
100. Combined
Cycle
Gas
Turbine
Technical issues
• Impact of withdrawing useful heat on the
production of electricity
• Ratio of electricity to heat production
• Temperature at which heat is supplied
• Electrical, thermal and overall efficiencies
• Marginal efficiency of electricity generation
101. Combined
Cycle
Gas
Turbine
Four efficiencies for cogeneration:
• The electrical efficiency – the amount of
electricity produced divided by the fuel use
(later I’ll need to call this the direct electrical
efficiency)
• The thermal efficiency –
the amount of useful heat provided divided
__by the fuel use
• The overall efficiency – the sum of the of two
• The effective or marginal efficiency of
electricity generation – explained later
102. Combined
Cycle
Gas
Turbine
Impact of withdrawing heat
• In simple-cycle cogeneration, capturing some
of the heat in the hot gas exhaust does not
reduce the production of electricity, but the
electrical production is already low
• In cogeneration with steam turbines, the
withdrawal of steam from the turbine at a
higher temperature than would otherwise be
the case reduces the electricity production
• The higher the temperature at which we want
to take heat, the more that electricity
production is reduced
103. Combined
Cycle
Gas
Turbine Example of the tradeoff between production of useful heat
and loss of electricity production
using steam turbine cogeneration
0.05
0.10
0.15
0.20
0.25
0.30
0.35
80 100 120 140 160 180 200 220 240
Steam Temperature (o
C)
Loss
of
electricity
as
a
fraction
of
heat
withdrawn
Source: Bolland and Undrum (1999, Greenhouse Gas Control Technologies, 125-130, Elsevier
Science, New York)
104. Combined
Cycle
Gas
Turbine
Thus, to maximize the electricity production,
we want to be able to make use of heat at
the lowest possible temperature.
If the heat is to be provided to buildings, that
means having well insulated buildings that
can be kept warm with radiators that are not
very hot
105. Combined
Cycle
Gas
Turbine
The alternative to cogeneration is the
separate production of heat and electricity.
The effective efficiency in generating
electricity is the amount of electrical energy
produced divided by the extra fuel used to
produce electricity along with heat compared
to the amount of fuel that would be used in
producing heat alone. The extra amount of
fuel required in turn depends on the
efficiency with which we would have
otherwise have produced heat with a boiler
or furnace.
106. Combined
Cycle
Gas
Turbine
For example, suppose that we have a cogeneration
system with an electrical efficiency of 25% and an
overall efficiency of 80%. Then, the thermal
efficiency is 80%-25%=55% - we get 55 units of
useful heat from the 100 units of fuel. If the
alternative for heating is a furnace at 80%
efficiency, we would have required 68.75 units of
fuel to produce the 55 units of heat. Thus, the extra
fuel use in cogeneration is 100-68.75=31.25 units,
and the effective electricity generation efficiency is
25/31.25=80%. I call this the marginal efficiency,
because it is based on looking at things on the
margin (this is a concept from economics).
107. Combined
Cycle
Gas
Turbine
With a little algebra, it can be shown that
the marginal efficiency is given by
nmarginal = nel/(1-nth/nb)
where nel and nth are the electrical and
thermal efficiencies of the cogeneration
system, and nb is the efficiency of the
boiler or furnace that would otherwise be
used for heating
108. Combined
Cycle
Gas
Turbine Marginal efficiency of electricity generation in cogeneration
(ηel = efficiency of the alternative, central power plant for
electricity generation)
0.0
0.5
1.0
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Thermal Efficiency
Marginal
Efficiency
of
Electricity
Generation
Boiler efficiency = 0.8
Boiler efficiency = 0.9
ηel=0.25
ηel=0.40
ηel=0.55
109. Combined
Cycle
Gas
Turbine
Key points
• For a given thermal efficiency, the
effective electrical efficiency is higher the
higher the direct electrical efficiency
• However, very high effective electrical
efficiencies can be achieved even with
low direct electrical efficiencies if the
thermal efficiency is high – that is, if we
can make use of most of the waste heat
• To get a high thermal efficiency requires
being able to make use of low-
temperature heat (at 50-60ºC), as well as
making use of higher temperature heat
110. Combined
Cycle
Gas
Turbine
Electricity:heat ratio
• Because the marginal electricity generation
efficiency in cogeneration is generally much higher
than the efficiency of a dedicated central
powerplant, there is a substantial reduction in the
amount of fuel used to generate electricity when
cogeneration is used
• Thus, we would like to displace as much inefficient
central electricity generation as possible when
cogeneration is used to supply a given heating
requirement
• This in turn requires that the electricity-to-heat
production ratio in cogeneration be as large as
possible
• (Remember – none of the gains that we’ve talked
about occur if we can’t use the waste heat produced
by cogeneration)
111. Combined
Cycle
Gas
Turbine Electricity : heat output ratio in cogeneration
0.0
0.5
1.0
1.5
2.0
Electricity:Useful-Heat
Ratio
Back-
pressure
steam
turbine
Micro-
turbine
Gas turbine/
heat recovery
steam
generator
Fuel cell/
heat recovery
steam
generator
Gas turbine/
back-pressure
steam turbine
Fuel cell/
gas turbine/
back-pressure
steam turbine
Reciprocating
engine/
heat recovery
steam
generator
112. Combined
Cycle
Gas
TurbineFigure 3.17 Dependence of overall savings through cogeneration
on the electricity:heat ratio and on the central powerplant
efficiency, assuming a 90% overall efficiency for cogeneration and
90% efficiency for the alternative heating system
0
10
20
30
40
50
60
0.0 0.5 1.0 1.5 2.0
Electricity:Heat Ratio
Per
cent
Overall
Savings
η=0.6
η=0.5
η=0.4
114. Combined
Cycle
Gas
Turbine Issues related to the cost of
electricity:
• Capital cost, interest rate, lifespan
• Fuel cost (impact of depends on
efficiency)
• Fixed and variable operation &
maintenance costs
• Baseload vs peaking costs
• Transmission line costs and
transmission losses
• Amount of backup capacity
115. Combined
Cycle
Gas
Turbine Capital cost of natural gas combined cycle
cogeneration plants
0
400
800
1200
1600
0 100 200 300 400 500
Electrical Capacity (MW)
Cost
(US$/kW)
116. Combined
Cycle
Gas
Turbine
Amortization of capital cost:
CRF x Ccap / (8760 x CF) units: $/kWh
where CRF = i /(1-(1+i)-N) is the cost recovery
factor
_i = interest rate
_N = financing time period
Ccap = capital cost ($/kW)
8760 is the number of hours in a year
CF= capacity factor (annual average output as a
fraction of capacity)
117. Combined
Cycle
Gas
Turbine
Fuel contribution to the final cost:
Cfuel ($/GJ) x 0.0036 (GJ/kWh) / efficiency
The cost of electricity from less efficient
power plants will be more sensitive to the
cost of fuel than the cost of electricity from
efficient power plants, but more efficient
power plants will tend to have greater capital
cost
118. Combined
Cycle
Gas
Turbine
Typical overnight capital costs and best
efficiencies
• Pulverized coal: $1200-1400/kW,η= 0.45-0.48
• IGCC: $1400-2600/kW today, η= 0.41-0.55
$1150-1400/kW hoped for, future
• NGCC: $400-600/kW, η = 0.55-0.60
• Reciprocating engine: $600-1200/kW,η=0.40-0.46
• Micro-turbine: $1800-2600/kW, η= 0.23-0.27
• Fuel cells: $3000-5000/kW, η= 0.35-0.45
$1000-1500/kW hoped for, future
• NGCC/FC hybrid: $2000-3000/kW, η= 0.70-0.80
119. Combined
Cycle
Gas
Turbine Cost of electricity from coal and natural gas
0
2
4
6
8
10
12
14
16
0.2 0.4 0.6 0.8 1
Capacity Factor
Electricity
Cost
(cents/kWh)
Coal, $1500/kW, η=0.5, $4/GJ
Coal, $1000/kW, η=0.4, $4/GJ
NG, $2000/kW, η=0.7, $10/GJ
NG, $500/kW, η=0.4, $10/GJ
120. Combined
Cycle
Gas
Turbine Cost of heat from boilers, electricity with or without
cogeneration, and heat from cogeneration
0
1
2
3
4
5
6
7
8
9
2 4 6 8 10
Fuel Cost ($/GJ)
Heat
or
Electrictiy
Cost
(cents/kWh)
Heat cost
Electricity cost, dedicated facility
Gross electricity cost, cogen facility
Net electricity cost, cogen facility
121. Combined
Cycle
Gas
Turbine Cost of electricity from central coal (at $2/GJ)
and from natural gas (at $10/GJ)
0 2 4 6 8 10 12 14
Central baseload
coal
Central peaking coal
Central peaking NG
Onsite peaking NG
Peaking NG cogen
Cost of Electricity (cents/kWh)
122. Combined
Cycle
Gas
Turbine
Water requirements
• Most thermal power plants use water to cool
the condenser of a steam turbine and for
other, minor, purposes
• There are two approaches:
a once-through cooling system
a recirculating system in a cooling tower
• Water use by power generation represents the
largest or second largest use of water in most
countries (with irrigation sometimes being a
larger use)
123. Combined
Cycle
Gas
Turbine • In once-through systems, the water is
returned to the source (but at a warmer
temperature). Large volumes of water are
needed – not available in arid regions
• In a recirculating systems, water that has
removed heat from the condenser is sprayed
through a cooling tower, where it is cooled by
evaporation, then returns to the condenser
• This consumes water, but the amount that is
withdrawn from the water source (lakes, rivers
or groundwater) is smaller than in once-
through systems
124. Combined
Cycle
Gas
Turbine
Typical water requirements
• Steam turbines (as in coal power plants)
Once through: 80-190 liters withdrawn per kWh of
__generated electricity, ~ 1 liter / kWh consumed
Recirculating: 1-3 liters/kWh withdrawn
1-2 liters/kWh consumed
• Natural gas combined cycle
Once through: 30 liters/kWh withdrawn
~ 0.4 liters/kWh consumed
Recirculating: 0.9 liters/kWh withdrawn
0.7 liters/kWh consumed
125. Combined
Cycle
Gas
Turbine
Bottom line:
• More efficient power plants, such as
natural gas combined cycle power
plants, use less water per kWh of
generated electricity than less efficient
power plants
• The water requirements can be a
constraining factor in arid regions
• It is possible to use air rather than water
to cool the condenser, but then the
efficiency drops
126. Combined
Cycle
Gas
Turbine
126
Section 3.1 – Steam Turbine Fundamentals
Overview
• Hero Reaction Turbine – 120 B.C.
• First Practical Turbine – 1884, C. Parsons
• First Power Plant – 7.5 kw – 1890
• Reaction, Impulse and Velocity-Compounded
• Reheat Steam – 1930’s
• Last 100 years Turbine is the key element in
generating electricity
• Turbines run Generators, Pumps, Fans, etc.
• Today up to 1,500 MW
129. Combined
Cycle
Gas
Turbine
129
Section 3.1 – Steam Turbine Fundamentals
Reaction Turbines
Newton’s third law of motion – For every action
there is an equal and opposite reaction.
Narrowing
Steam Path Narrowing
Steam Path
Steam Turbine Fundamentals
132. Combined
Cycle
Gas
Turbine
132
Section 3.1 – Steam Turbine Fundamentals
Velocity-Compounded Turbine
Velocity compounding is a form of staging which
by dividing the work load over several stages
results in improved efficiency and a smaller
diameter for the blade wheels due to a reduction in
Ideal blade speed per stage.
Inlet Pressure
Inlet
Velocity
P =
1
V
Steam Turbine Fundamentals
143. Combined
Cycle
Gas
Turbine A steam turbine is a device that extracts thermal
energy from pressurized steam and uses it to
do mechanical work on a rotating output shaft.
Its modern manifestation was invented by Sir
Charles Parsons in 1884.
Steam Turbine may also be define as a device
which converts heat energy of to the steam to
the mechanical energy which finally converted
into electrical energy.
143
144. Combined
Cycle
Gas
Turbine Because the turbine generates rotary motion, it is
particularly suited to be used to drive an
electrical generator – about 90% of all electricity
generation in the United States, is by use of
steam turbines. The steam turbine is a form of
heat engine that derives much of its improvement
in thermodynamic efficiency through the use of
multiple stages in the expansion of the steam,
which results in a closer approach to the ideal
reversible process.
144
145. Combined
Cycle
Gas
Turbine
The modern steam turbine was invented in
1884 by Sir Charles Parsons, whose first
model was connected to a dynamo that
generated 7.5 kW (10 hp) of electricity. The
Parsons turbine also turned out to be easy to
scale up. Parsons had the satisfaction of
seeing his invention adopted for all major world
power stations, and the size of generators had
increased from his first 7.5 kW set up to units
of 500MW capacity.
145
146. Combined
Cycle
Gas
Turbine Steam turbines are made in a variety of sizes
ranging from small <0.75 kW units used as
mechanical drives for pumps, compressors and
other shaft driven equipment, to 1,500 MW
turbines used to generate electricity. There are
several classifications for modern steam
turbines.
146
148. Combined
Cycle
Gas
Turbine Further the steam turbine is based
upon Rankine cycle
• An ideal Rankine cycle operates between
pressures of 30 kPa and 6 MPa. The
temperature of the steam at the inlet of
the turbine is 550°C. Find the net work for
the cycle and the thermal efficiency.
– Wnet=Wturbine-Wpump OR Qin-Qout
– Thermal efficiency hth=Wnet/Qin
– Net work done is converted into power output
of turbine.
148
149. Combined
Cycle
Gas
Turbine
Ideal Rankine Cycle
This cycle follows the idea of the Carnot cycle but can be
practically implemented.
1-2 isentropic pump 2-3 constant pressure heat addition
3-4 isentropic turbine 4-1 constant pressure heat rejection
149
150. Combined
Cycle
Gas
Turbine
CLASSIFICATION OF STEAM TURBINE
Classification of steam turbines may be done as
following:
1. According to action of steam
(a) Impulse turbine
(b) Reaction turbine
(c) Combination of both
2. According to direction of flow:
(a) Axial flow turbine
(b) Radial flow turbine
3. According to number of stages
(a) Single stage turbine
(b) Multi stage turbine
150
151. Combined
Cycle
Gas
Turbine
(4). According to number of cylinders
(a) Single cylinder turbine
(b) Double cylinder turbine
(c) Three cylinder turbine
(5) According to steam pressure at inlet of Turbine:
(a) Low pressure turbine
(b) Medium pressure turbine.
(c) High pressure turbine
(d) Super critical pressure turbine.
151
152. Combined
Cycle
Gas
Turbine Description of common types of Turbines.
The common types of steam turbine are
1. Impulse Turbine.
2. Reaction Turbine.
The main difference between these two turbines lies in
the way of expanding the steam while it moves through
them.
In the impulse turbine, the steam expands in the nozzles
and it's pressure does not alter as it moves over the
blades. In the reaction turbine the steam expanded
continuously as it passes over the blades and thus there
is gradual fall in the pressure during expansion below the
atmospheric pressure.
152
154. Combined
Cycle
Gas
Turbine Simple impulse Turbine.
It the impulse turbine, the steam expanded within the
nozzle and there is no change in the steam pressure as it
passes over the blades
154
NOZZLE
STEAM
CHEST
ROTOR
156. Combined
Cycle
Gas
Turbine PRESSURE-VELOCITY DIAGRAM FOR
A MOVING IMPULSE BLADE
VELOCITY
PRESSURE
TURBINE
SHAFT
DIRECTION OF SPIN
ENTRANCE
HIGH VELOCITY
STEAM INLET
REPRESENTS MOVING
IMPULSE BLADES
EXIT
LOW VELOCITY
STEAM EXHAUST
156
157. Combined
Cycle
Gas
Turbine Reaction Turbine
In this type of turbine, there is a gradual pressure drop
and takes place continuously over the fixed and moving
blades. The rotation of the shaft and drum, which carrying
the blades is the result of both impulse and reactive force
in the steam. The reaction turbine consist of a row of
stationary blades and the following row of moving blades.
The fixed blades act as a nozzle which are attached
inside the cylinder and the moving blades are fixed with
the rotor as shown in the figure.
157
158. Combined
Cycle
Gas
Turbine When the steam expands over the blades there is
gradual increase in volume and decrease in pressure.
But the velocity decreases in the moving blades and
increases in fixed blades with change of direction.
Because of the pressure drops in each stage, the
number of stages required in a reaction turbine is much
greater than in a impulse turbine of same capacity.
It also concluded that as the volume of steam increases
at lower pressures therefore the diameter of the turbine
must increase after each group of blade rings.
158
163. Combined
Cycle
Gas
Turbine
.Compounding in Steam Turbine.
The compounding is the way of reducing the wheel or
rotor speed of the turbine to optimum value. It may be
defined as the process of arranging the expansion of
steam or the utilization of kinetic energy or both in several
rings.
There are several methods of reducing the speed of rotor
to lower value. All these methods utilize a multiple system
of rotors in series keyed on a common shaft, and the seam
pressure or jet velocity is absorbed in stages as the steam
flows over the blades.
163
164. Combined
Cycle
Gas
Turbine
Different methods of compounding are:
1.Velocity Compounding
2.Pressure Compounding
3.Pressure Velocity Compounding.
These are explained in detail as given below:
164
165. Combined
Cycle
Gas
Turbine Velocity Compounding:
There are a number of moving blades separated by rings
of fixed blades. All the moving blades are keyed on a
common shaft. When the steam passed through the
nozzles where it is expanded to condenser pressure, it's
Velocity becomes very high. This high velocity steam
then passes through a series of moving and fixed blades
When the steam passes over the moving blades it's
velocity decreases. The function of the fixed blades is to
re-direct the steam flow without altering it's velocity to the
following next row moving blades where a work is done
on them and steam leaves the turbine with a low velocity
as shown in diagram.
165
168. Combined
Cycle
Gas
Turbine
These are the rings of moving blades which are keyed on a
same shaft in series, are separated by the rings of fixed
nozzles.
The steam at boiler pressure enters the first set of nozzles
and expanded partially. The kinetic energy of the steam thus
obtained is absorbed by moving blades.
The steam is then expanded partially in second set of nozzles
where it's pressure again falls and the velocity increase the
kinetic energy so obtained is absorbed by second ring of
moving blades.
This process repeats again and again and at last, steam
leaves the turbine at low velocity and pressure. During entire
process, the pressure decrease continuously but the velocity
fluctuate as shown in diagram.
168
Pressure Compounding:
171. Combined
Cycle
Gas
Turbine
This method of compounding is the combination of two
previously discussed methods. The total drop in steam
pressure is divided into stages and the velocity obtained
in each stage is also compounded. The rings of nozzles
are fixed at the beginning of each stage and pressure
remains constant during each stage as shown in figure.
The turbine employing this method of compounding may
be said to combine many of the advantages of both
pressure and velocity staging By allowing a bigger
pressure drop in each stage, less number stages are
necessary and hence a shorter turbine will be obtained
for a given pressure drop.
171
Pressure velocity compounding
174. Combined
Cycle
Gas
Turbine
These types include condensing, non-condensing, reheat,
extraction and induction.
Condensing turbines are most commonly found in
electrical power plants. These turbines exhaust steam in
a partially condensed state, typically of a quality near 90%,
at a pressure well below atmospheric to a condenser.
Non-condensing or back pressure turbines are most
widely used for process steam applications. The exhaust
pressure is controlled by a regulating valve to suit the
needs of the process steam pressure. These are
commonly found at refineries, heating units, pulp and
paper plants, and desalination facilities where large
amounts of low pressure process steam are available.
174
Steam supply and exhaust conditions
175. Combined
Cycle
Gas
Turbine Reheat turbines are also used almost exclusively in
electrical power plants. In a reheat turbine, steam flow
exits from a high pressure section of the turbine and is
returned to the boiler where additional superheat is
added. The steam then goes back into an intermediate
pressure section of the turbine and continues its
expansion.
Extracting type turbines are common in all applications.
In an extracting type turbine, steam is released from
various stages of the turbine, and used for industrial
process needs or sent to boiler feedwater heaters to
improve overall cycle efficiency. Extraction flows may be
controlled with a valve, or left uncontrolled.
Induction turbines introduce low pressure steam at an
intermediate stage to produce additional power.
175
176. Combined
Cycle
Gas
Turbine
These arrangements include single casing, tandem
compound and cross compound turbines. Single casing
units are the most basic style where a single casing and
shaft are coupled to a generator. Tandem compound are
used where two or more casings are directly coupled
together to drive a single generator.
A cross compound turbine arrangement features two or
more shafts not in line driving two or more generators that
often operate at different speeds. A cross compound
turbine is typically used for many large applications.
176
Casing or shaft arrangements
177. Combined
Cycle
Gas
Turbine
A two-flow turbine rotor. The steam enters in the middle of
the shaft, and exits at each end, balancing the axial force.
The moving steam imparts both a tangential and axial
thrust on the turbine shaft, but the axial thrust in a simple
turbine is unopposed. To maintain the correct rotor position
and balancing, this force must be counteracted by an
opposing force.
Either thrust bearings can be used for the shaft bearings,
or the rotor can be designed so that the steam enters in
the middle of the shaft and exits at both ends. The blades
in each half face opposite ways, so that the axial forces
negate each other but the tangential forces act together.
This design of rotor is called two-flow or double-exhaust.
177
Two-flow rotors
179. Combined
Cycle
Gas
Turbine
An ideal steam turbine is considered to be an isentropic
process, or constant entropy process, in which the entropy of
the steam entering the turbine is equal to the entropy of the
steam leaving the turbine
No steam turbine is truly isentropic, however, with typical
isentropic efficiencies ranging from 20–90% based on the
application of the turbine.
The interior of a turbine comprises several sets of blades,
or buckets as they are more commonly referred to. One set of
stationary blades is connected to the casing and one set of
rotating blades is connected to the shaft.
The sets intermesh with certain minimum clearances, with the
size and configuration of sets varying to efficiently exploit the
expansion of steam at each stage.
179
Principle of operation and design
180. Combined
Cycle
Gas
Turbine
Schematic diagram outlining the difference between an
impulse and a reaction turbine
To maximize turbine efficiency the steam is expanded, doing
work, in a number of stages. These stages are characterized
by how the energy is extracted from them and are known as
either impulse or reaction turbines.
Most steam turbines use a mixture of the reaction and
impulse designs: each stage behaves as either one or the
other, but the overall turbine uses both. Typically, higher
pressure sections are impulse type and lower pressure
stages are reaction type.
180
Turbine efficiency
181. Combined
Cycle
Gas
Turbine
An impulse turbine has fixed nozzles that orient the steam flow
into high speed jets. These jets contain significant kinetic
energy, which is converted into shaft rotation by the bucket-like
shaped rotor blades, as the steam jet changes direction.
A pressure drop occurs across only the stationary blades, with
a net increase in steam velocity across the stage. As the steam
flows through the nozzle its pressure falls from inlet pressure to
the exit pressure (atmospheric pressure, or more usually, the
condenser vacuum). Due to this high ratio of expansion of
steam, the steam leaves the nozzle with a very high velocity.
The steam leaving the moving blades has a large portion of the
maximum velocity of the steam when leaving the nozzle. The
loss of energy due to this higher exit velocity is commonly
called the carry over velocity or leaving loss.
181
Impulse turbines
182. Combined
Cycle
Gas
Turbine
In the reaction turbine, the rotor blades themselves are
arranged to form convergent nozzles. This type of turbine
makes use of the reaction force produced as the steam
accelerates through the nozzles formed by the rotor.
Steam is directed onto the rotor by the fixed vanes of the stator.
It leaves the stator as a jet that fills the entire circumference of
the rotor. The steam then changes direction and increases its
speed relative to the speed of the blades.
A pressure drop occurs across both the stator and the rotor,
with steam accelerating through the stator and decelerating
through the rotor, with no net change in steam velocity across
the stage but with a decrease in both pressure and
temperature, reflecting the work performed in the driving of the
rotor.
182
Reaction turbines
183. Combined
Cycle
Gas
Turbine
When warming up a steam turbine for use, the main steam
stop valves (after the boiler) have a bypass line to allow
superheated steam to slowly bypass the valve and
proceed to heat up the lines in the system along with the
steam turbine. Also, a turning gear is engaged when there
is no steam to the turbine to slowly rotate the turbine to
ensure even heating to prevent uneven expansion.
After first rotating the turbine by the turning gear, allowing
time for the rotor to assume a straight plane (no bowing),
then the turning gear is disengaged and steam is admitted
to the turbine, first to the astern blades then to the ahead
blades slowly rotating the turbine at 10–15 RPM (0.17–
0.25 Hz) to slowly warm the turbine.
183
Operation and maintenance
184. Combined
Cycle
Gas
Turbine Any imbalance of the rotor can lead to vibration, which in
extreme cases can lead to a blade breaking away from
the rotor at high velocity and being ejected directly
through the casing. To minimize risk it is essential that the
turbine be very well balanced and turned with dry steam -
that is, superheated steam with a minimal liquid water
content.
If water gets into the steam and is blasted onto the blades
(moisture carry over), rapid impingement and erosion of
the blades can occur leading to imbalance and
catastrophic failure. Also, water entering the blades will
result in the destruction of the thrust bearing for the
turbine shaft.
184
185. Combined
Cycle
Gas
Turbine To prevent this, along with controls and baffles in the
boilers to ensure high quality steam, condensate drains
are installed in the steam piping leading to the turbine.
Modern designs are sufficiently refined that problems with
turbines are rare and maintenance requirements are
relatively small.
The steam turbine operates on basic principles
of thermodynamics using the part of the Rankine
cycle. Superheated vapor (or dry saturated vapor,
depending on application) enters the turbine, after it having
exited the boiler, at high temperature and high pressure.
The high heat/pressure steam is converted into kinetic
energy using a nozzle. Once the steam has exited the
nozzle it is moving at high velocity and is sent to the
blades of the turbine.
185
186. Combined
Cycle
Gas
Turbine A force is created on the blades due to the pressure of
the vapor on the blades causing them to move. A
generator or other such device can be placed on the
shaft, and the energy that was in the vapor can now be
stored and used.
The gas exits the turbine as a saturated vapor (or liquid-
vapor mix depending on application) at a lower
temperature and pressure than it entered with and is
sent to the condenser to be cooled
186
187. Combined
Cycle
Gas
Turbine
To measure how well a turbine is performing we can look
at its isentropic efficiency. This compares the actual
performance of the turbine with the performance that
would be achieved by an ideal, isentropic, turbine. When
calculating this efficiency, heat lost to the surroundings is
assumed to be zero.
The starting pressure and temperature is the same for
both the actual and the ideal turbines, but at turbine exit
the energy content ('specific enthalpy') for the actual
turbine is greater than that for the ideal turbine because
of irreversibility in the actual turbine.
187
Isentropic turbine efficiency
188. Combined
Cycle
Gas
Turbine
The isentropic efficiency is found by dividing
the actual work by the ideal work.
where
•h1 is the specific enthalpy at state one
•h2 is the specific enthalpy at state two for
the actual turbine
•h2s is the specific enthalpy at state two for
the isentropic turbine
188