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ORI GIN AL PA PER
Emissions’ reduction of a coal-fired power plantvia reduction of consumption through simulationand optimization of its mathematical model
G. Tzolakis Æ P. Papanikolaou Æ D. Kolokotronis ÆN. Samaras Æ A. Tourlidakis Æ A. Tomboulides
Received: 15 November 2008 / Revised: 14 April 2009 / Accepted: 12 May 2009 /
Published online: 29 May 2009
� Springer-Verlag 2009
Abstract One of the main sources of carbon dioxide emissions is the electrical
power production by fossil fuels (coal). 84% of the electrical power generated in
Greece (source:Regulatory Authority for Energy) comes from lignite combustion
and therefore optimized operation of the conversion system will result in higher
efficiencies of the combustion and the water/steam circle. Thus, more electrical
power can be generated with less fuel and less emissions. That forms our moti-
vation for the modeling, simulation and optimization of a lignite fired power plant.
An electrical power production unit, with 300 MW maximum output, has been
chosen to model (similar to Greece KARDIA IV unit). For this purpose two
software programs, using iterative method solvers, have been used. One is the
open source code D.N.A. (Dynamic Network Analysis) and the other is gPROMS
by the Process System Enterprise. The advantage of the former is that it consists
G. Tzolakis � P. Papanikolaou � D. Kolokotronis � A. Tourlidakis � A. Tomboulides
Department of Engineering and Management of Energy Resources, University of Western
Macedonia, Kozani, Greece
G. Tzolakis
e-mail: [email protected]
P. Papanikolaou
e-mail: [email protected]
D. Kolokotronis
e-mail: [email protected]
A. Tourlidakis
e-mail: [email protected]
A. Tomboulides
e-mail: [email protected]
N. Samaras (&)
Department of Applied Informatics, University of Macedonia, 156 Egnatia Str., 54006 Thessaloniki,
Greece
e-mail: [email protected]
123
Oper Res Int J (2010) 10:71–89
DOI 10.1007/s12351-009-0053-7
of a library with the models of the components of a power plant and the steam/
water properties but it does not include an optimizer, while in the latter, the user
has to code the component models and the steam/water properties but it includes a
non-linear optimizer, which is necessary due to the non-linearity of the problem.
Simulation of the steady state operation of the power plant was successful and the
optimization software showed an increase of *1.42% in the efficiency of the
water/steam cycle by regulating the steam mass flow rates at the extractions from
the different stages of the turbines. Simulation of the boiler of the unit had also
been performed with satisfactory results, in comparison with the measurements
done in the control room of the unit.
Keywords D.N.A. � gPROMS � Power plants � Optimization � Efficiency
List of symbolsV Volume area (m3)
T Temperature (K)
c Ratio of specific heat Cp/Cv
E3 Pumps consumed electrical energy (kW)
Ut Overall heat transfer coefficient (kW/m2 K)
DTl Mean logarithmic temperature (K)
A Radiative surface (m2)
agas Gas heat transfer coefficient (kW/m2 K)
Fc Cross-flow correction factor
rA Radiative surface radius (m)
W Mechanical power (kW)
m1:
Inlet flow rate (kg/s)
P Pressure (bar)
E1 Generators produced electric power (kW)
Q3 Heat consumption (kJ/s)_Q Heat transfer (kW)
rin Inside radius (m)
rout Outside radius (m)
kwat Thermal conductivity of water (kW/mK)
ass Steam heat transfer coefficient (kW/m2 K)
gi Efficiency of the i component [-]
1 Introduction
The effects of global climate change due to greenhouse gas emissions, including
carbon dioxide, are beginning to become obvious throughout the world. One of the
main sources of carbon dioxide emissions is electrical power generation by fossil
fuels (coal). Additionally the operation of this kind of power plants results to
Nitrogen Oxide (NOx) and Sulphur Oxide (SOx) emissions which are also harmful
72 G. Tzolakis et al.
123
for the environment. 84% of the electrical power generation in Greece is produced
from lignite combustion and thus optimized operation of the conversion system will
result in higher efficiency of the whole process, with the same electrical power
generated, consuming less fuel and producing lower emissions. This forms our
motivation for the modeling, simulation and optimization of a lignite fired power
plant.
The first step for the optimization is the simulation of the power plant operation.
Elmegaard (1999), extended the capabilities of the Dynamic Network Analysis
(D.N.A.) software in order to simulate the dynamic behavior of the steam boilers
used in such power plants. In this way the boiler of a coal fired electric generation
unit in Denmark was simulated with satisfactory results. Rodrigues et al. (2005),
simulated the combustion chamber of the boiler by creating a 1-dimensional
pseudo-homogeneous mathematical model, using the physical properties of the fuel
as variables. The model was based on energy and mass conservation, and was added
to the gPROMS software. The results showed that the flue gas synthesis predicted
with satisfactory accuracy.
Perrin (2007) proceeded to the optimization of the operation of a 500 MW power
plant. After modeling the different components in Matlab, they simulated the whole
power plant and the results were satisfactory apart from the mass flow rate of the
steam at the exit of the high pressure turbine, where, for the specific plant simulated,
a discrepancy of 11% was observed between the calculated and the measured value.
This model setup gave an optimized point of operation that minimized fuel cost,
with variables being the mass flow rate of the fuel and the air. Zhang et al. (2006)
performed a thermo-economic analysis of a power plant in China with interesting
outcome for the designers and operators of this kind of power plant. The authors
claim that thermo-economic analysis is more advantageous than analysis based on
the first and second law of thermodynamics.
The great importance of the simulation and optimization of fossil fuels power
plants is shown by the fact that the Department of Trade and Industry of the United
Kingdom is sponsoring the creation of a virtual power plant model so that they can
test innovative cycles of energy production and optimize the operation of existing
units (Patel and Wang 2008).
Our work has focused on the thermodynamic analysis of the combustion and
the water/steam cycle of such kind of units. Our objectives were the following:
(1) To model and simulate the steam/water cycle components of an existing
fossil fuel power plant, (2) to model and simulate the combustion in the same
unit and (3) to apply an optimization algorithm to these models in order to
maximize the total efficiency of the unit by using as variables the mass flow
rate of the steam from the turbine extractions. The layout of the paper is as
follows: Methods and analysis section includes a detailed description of the
unit modeled, the software used and the individual model used for each
component. In the results section, from the simulation and optimization results
are presented. The final part of the paper contains the main conclusions of the
presented work.
Emissions’ reduction of a coal-fired power plant 73
123
2 Methods and analysis
2.1 Modeled components
2.1.1 Water/steam cycle model
A flow chart of the water/steam cycle model is given in Fig. 1.
The liquid water, from the storage tank-deaerator (DEA), is directed through the
feed heaters (R5, R6), which exchange heat between the extraction steam of the
turbines and the water, to the boiler. The water is then converted to steam inside the
boiler and then, through 3 superheaters which here are presented as a single
component, high quality steam is directed to the high pressure turbine (HP). After
that, the steam is reheated inside 2 reheaters also represented by one component and
is directed to the intermediate pressure and low pressure turbines (IP1, IP2, IP3, IP4,
LP1, LP2, LP3). At the exit of each turbine stage, except the LP3, steam is extracted
to the feed heaters and the Deaerator. The steam is then condensed in the cooling
tower (COND) and through preheaters R1, R2, R3, R4 is directed to the storage
again.
Simplification of the boiler and the combustion chamber has been applied at this
point, due to the current focus on the water/steam cycle. At this stage, the boiler has
been simplified as a superheater (S/H) and a reheater (R/H) and energy input is
specified at a value instead of making use of a burner. Spraying between the
superheaters and the reheaters is used to control the steam temperature in order for
Fig. 1 Flow chart of the simulation of the steam/water cycle of the examined lignite fired electricalpower production unit (GEN Generator, HP High pressure turbine stage, IP Intermediate pressure turbinestage, LP Low pressure turbine stage, DEA Deaerator, COND Condenser, R Feed heaters, S/HSuperheater, R/H Reheater)
74 G. Tzolakis et al.
123
the steam not to exceed the limit temperature of 547�C as higher temperature could
lead to the turbine damage due to the materials used for its manufacturing.
In general this setup converts the chemical energy of the fuel to electric energy
since the turbines are connected with electric power generators. The extractions of
the turbines are represented through a splitter component where the exit of the stage
is the input to the splitter and the steam is then separated to the extracted steam
which goes to the feed heaters and the remaining steam going to the next stage. The
mass flow rates of the extracted steam are the control variables of our optimization
problem.
The components of the electrical power production unit that have been modeled
in gPROMS were the following:
• Feed water pumps
• Valves
• Boiler (simplified as simple superheater and reheater)
• Generators
• Extraction splitters from the turbines
• High pressure, intermediate pressure and low pressure turbines
• Condenser
• Feed heaters
• Deaerator
For the modeling of the unit, the conservation of mass and energy equations were
applied at each component and each node that connects them. In addition,
characteristic equations of individual components were used in order to give a more
realistic expression of the unit. Therefore:
1. A pressure drop equation is applied to the boiler and the feed heaters. The boiler
has been modeled as a simple superheater and a simple reheater and the feed-
heaters as heat exchangers. For the boiler, the conditions of pressure drop and
steam being the only product at the exit have been assumed; therefore there is
no need for use of a drum component in the simplified model of the boiler. The
maximum temperature was set to 535�C at the entrance of the turbine stages
after the superheater and reheater component. Also, for the heat exchangers,
assurance of no-cross of temperature profiles as well as cooling of the hot flow
and pressure drop has been established by applying the necessary restrictions to
the corresponding variables. Since the model is concentrated to the overall
water/steam cycle, no pinch analysis to the heat exchangers has been applied.
2. An overall efficiency equation is applied to the pumps and the generators.
3. A polytropic efficiency equation has also been applied to turbines.
The polytropic efficiency gpol is defined from the following equation
T2
T1
¼ P2
P1
� �gpolc�1c
ð1Þ
and connects the output pressure (P2) with the input pressure (P1), temperature (T1)
and c, the specific heat ratio of the steam.
Emissions’ reduction of a coal-fired power plant 75
123
Concerning the overall water/steam cycle we assume that all energies and mass
flows entering a component are positive and those exiting the component are
negative, therefore additional constraints are given for the direction of the mass
flows.
Finally, the thermal efficiency of the unit, which is the objective function used for
the non-linear optimization was defined as follows:
gthermal ¼P
E1 �P
E3PQ3
ð2Þ
which is the fraction of the difference of the sum of the produced electric power
from the generator stages (E1) and the sum of the consumed electric power from the
pumps (E3) to the sum of the consumed thermal energy of the superheater and
reheater (Q3).
Analytically, E1 is given from:
nG ¼E1
W3
ð3Þ
where nG is the constant generator efficiency and W3 the mechanical power input
from the corresponding turbine stage and is calculated from the energy conservation
equation:
_m1T � h1T þ _m2T � h2T þW3 ¼ 0 ð4ÞAdditionally, the mass conservation equation of the turbine extractions relates the
turbine and the extraction:
_m1E þ _m2E þ _m2 Pr e ¼ 0 ð5Þ
where _m1E is the mass flow rate at the outlet of the corresponding turbine and _m2E is
the mass flow rate at the inlet of the following turbine or the reheater, if it is the
extraction of the HP turbine.
E3 is given as:
np � E3 ¼ _m1P � u1P P2P � P1Pð Þ � 102 ð6Þ
where np is the constant pump efficiency, u the specific volume of the water and pthe pressure which is known at the pump outlet.
Finally, Q3 is given from the energy conservation equation at the superheater and
the reheater:
_m1H � h1H þ _m2H � h2H þ Q3 ¼ 0 ð7Þ
where subscript 1 stands for the inlet and 2 for the outlet of each component.
The water/steam cycle model is a steady-state model in the sense of specific
working conditions which have been reached after the whole system has been
stabilised. Therefore, we are not talking about a static system but a dynamic one
where all the time dependent values (mass flows, energy flows, pressure,
temperature) have been stabilised therefore all the parameters that depend on those
values are now constant (such as heat transfer coefficient, water/steam properties
values, mechanical parts efficiencies). Optimization is also applied in that manner.
76 G. Tzolakis et al.
123
The optimized control variables are calculated for a different steady-state working
point close to the original one since we are interested in the full-load scenario,
therefore again the dependent variables will be constant.
2.1.2 Boiler model
In Fig. 2 the flow chart of the complete boiler model is presented.
Preheated water is coming from the preheater (R6) into the furnace where
combustion takes place. Inside the furnace, combustion flue gases heat is transferred
to the water which is flowing through the pipes located at the furnace walls.
Radiation and convection are the heat transfer mechanisms taking place in this
process. Heat transfer is calculated by making use of the following formula
_Q ¼ UtADTl ð8Þ
where Ut is the overall heat transfer coefficient based on the overall inside surface
area and is calculated as
Ut ¼1
ri� 1
10:5�agas�rout
þ 10:75�kwat
� ln rout
rinþ 1
0:9�ast�rin
ð9Þ
where ri and rout are the internal and external radius of the water pipes. The three
terms summed at the denominator are the thermal resistances of the gases, the pipe
walls and the steam, respectively. DSl is the mean logarithmic temperature which is
given from the following equation:
IP 1
R6
Cool water
feed
Components
from the
water/steam cycle
SH 3 RH 2 SH 1b RH 1b SH 1a RH 1a
BOILER
FU
RN
AC
E
SH 2
Reheated
steam
Flue gases
Attemp. RH 1b
HP
Attemp. SH 1b
Superheated
water/steam
Attemp. SH 2
AIR
FUEL
Fig. 2 Flow chart of the simulation of the boiler of the examined lignite fired electrical power productionunit. (FURNACE Water evaporator, SH Superheater, RH Reheater, R6 Feed heater 6, HP High pressureturbine, IP1 First intermediate turbine)
Emissions’ reduction of a coal-fired power plant 77
123
DTl ¼T1 � T4ð Þ � T2 � T3ð Þ
ln T1�T4
T2�T3
ð10Þ
Subscripts 1 and 2 denote the inlet and outlet of the gas side, while 3 and 4 denote
the inlet and outlet of the steam side, respectively. For the same component,
pressure loss in the water side and the flue gas side was calculated by using a
friction factor for the pipes.
After the furnace, the steam goes into the superheater S/H 1a as shown in Fig. 2.
This superheater has been simplified to a heat source and a heat sink, on the
assumption of superheated steam. The rest of the heat exchangers were modeled
according to the superheater model used in D.N.A. (Elmegaard 1999) and are
considered to be cross-flow tube bundle heat exchangers. This model handles both
radiative and convective heat transfer. The heat exchange is governed by a heat
transfer coefficient and a surface area. An assumption that needed to be made was
related to the superheater S/H 1b (Papanikolaou 2008). The superheater component
model of D.N.A. assumes that the tube banks are in-line, while in the examined unit,
the specific superheater is staggered. For that reason, we used this D.N.A.
component model with alternative dimensions of depth and width of the channel.
This resulted to a change of the mean beam wave length of radiation between the
two surfaces of the superheater, which is expressed as
L ¼ 3:5V
Að11Þ
with A and V being the surface and volume area of the enclosure. Thus, the amount
of heat transferred through radiation was tuned appropriately, so that the values of
the temperatures and pressures, of the steam and the flue gases, were in agreement
with the measured values in the examined unit.
Exchange of heat between the flue gas side and the steam side is calculated in the
same way as in the furnace, differing only in the use of a cross-flow correction
factor as following:
_Q ¼ Fc � U � A � DTl ð12ÞOverall heat transfer coefficient is given as
U ¼ 1
rA� 1
1
rout� agasþarð Þ þ1
kwat� ln rout
rinþ 1
ast�rin
ð13Þ
Fc depends on temperatures from both sides of the tube bundle.
In Fig. 2, it can be observed that there are 3 attemperator components (one
after SH1b, one after SH 2 and one after RH 1b). Those are spraying setups used
for the cooling of the live steam so that it will not exceed the temperature of
547�C which is the limit set by the turbine manufacturer. Temperature can in
principle exceed design limits if there is pollution in the furnace in the form of
solidified ash, on the surface of the exchanger’s tubes. In this paper we assume
that all surfaces are clean but in future work we plan to investigate the effect of
fouling of the heat exchangers, due to that solidified plaque on the pipe walls, on
the thermal efficiency of the unit.
78 G. Tzolakis et al.
123
The above model is to be used in future work for the optimization of the whole
power plant. It will replace the simple superheater and reheater components, which
is currently being used for the optimization.
2.2 Simulation and optimization software
Initially for the simulation we used the D.N.A. software which uses an iterative
Newton method for the solution of the non-linear problem. We made this choice as
this software was specifically designed for the simulation of fossil fuel power plants
and has libraries with most component models. Also the properties of steam and
water as well as fuel properties are calculated through the use of libraries included
in the same software. All the simulation parameters of D.N.A. can be found at the
model_name.data file which is generated with the execution of the simulation. All
of them can be parameterized. In addition, it is an open-source Fortran 77 and C
code; however, it does not include any optimization algorithm.
For the optimization part we used gPROMS where we had to re-model all the
components in this software environment, based on the mathematic formulas
presented in the previous section. The gPROMS software has a variety of solvers
for the simulation as well as the optimization of a given problem. In this non-
linear steady-state case, solvers ‘‘BDNLSOL’’ and ‘‘SPARSE’’ were used for the
simulation of the model. ‘‘BDNLSOL’’(Block Decomposition NonLinear SOLver)
is a general solver for solving sets of dynamic nonlinear equations rearranged to
block triangular form. It can handle reversible symmetric discontinuities (IF
statements) ‘‘SPARSE’’, which is a Newton-type method solver without decom-
position has been parameterized to have a convergence tolerance of 10-7 instead of
10-5 which is the default value and allowing 3 iterations without calculating a new
Jacobian matrix contrary to the default, zero iterations so that the results would be
more accurate but the calculation time would not increase greatly. The rest of the
solver’s parameters have been used with their default values. The ‘‘MA48’’ linear
solver is used for the calculation of the linear equations which uses direct LU
decomposition algorithms. ‘‘SPARSE’’ is implemented for the solution of the blocks
of the ‘‘BDNLSOL’’. All three are included in the DAE (Differential Algebraic
Equation) solver ‘‘DASOLV’’ which can be applied for dynamic and steady-state
simulations with use of a variable time step BDF method (Backward Differentiation
Formula). gPROMS is also capable to handle discontinuities which can arise. In our
case, those can occur due to the change of the state of the water. That is done with
the State-Transition Networks (STNs) which provide a general way to describe
discontinuous systems (‘‘gPROMS Introductory User Guide’’, Chapter 4).
For the general optimization problem, gPROMS makes use of the Control
Vector Parameterization approach, either with Single or Multi-shooting algorithms
(Spangelo, 1994). These are parts of the gPROMS modeling system with the
‘‘CVP_SS’’ and ‘‘CVP_MS’’ solvers, respectively. In our case model, ‘‘CVP_SS’’ is
used due to the ability it has to solve steady-state problems. This can be achieved
due to the fact that the numerical calculations are applied to the whole time horizon
contrary to the multi-shooting where the time is splitted to control intervals.
A dynamic problem can be considered steady-state with the time dependent
Emissions’ reduction of a coal-fired power plant 79
123
variables being constant. Therefore, single-shooting is ideal since the whole time
horizon is uniquely defined. ‘‘DASOLV’’ is used for the solution of the underlying
DAE (Differential Algebraic Equations) system and its sensitivities. The equations
that describe the model are produced by gPROMS as residual equations and as
symbolically generated partial derivatives (Jacobian) and used as input to the
optimization code. The latter employs a mixed integer non-linear programming
code implementing a reduced sequential quadratic programming algorithm (RSQP)
through the use of the ‘‘SRQPD’’solver.
Details about all of the above solvers as well as for their parameterization which
is possible for all of the solvers are described in the gPROMS Introductory and
Advanced User Guides.
The objective function of the non-convex, non-linear optimization problem we
have was the thermal efficiency of the steam/water cycle described before and the
control variables were the mass flow rates of the extractions from the various turbine
stages, which are the only variables of interest at this moment. Our problem consists
of 3361 algebraic variables (decision variables) and 3326 equality constraints. In a
later model where the full boiler system will be implemented in the current steam/
water cycle model, more variables will be taken into consideration. Constrains had
to do with restrictions on the temperatures of the steam entering the turbines
(\535�C), the electric power output of the unit should not fall below the design
value as well as the conditions described before for the exchangers and the boiler
(steam at the exit, pressure drop, no-cross of temperature profiles, cooling of the hot
flow).
3 Results and discussion
3.1 Results of the simulation and optimization of the water/steam cycle
3.1.1 Simulation
This simulation resulted to satisfactory agreement between the measured data (in the
control room of the examined unit) and the calculated data of D.N.A. and gPROMS
for the steady state operation scenario of power output of 300 MW. Table 1
compares the measured data with the simulated results of D.N.A. and gPROMS
models. Negative values mean that the flow exits the component while positive
mean that the flow enters the component. Simulation and measured results agree
fairly well since the relative error of the values calculated, is lower than 4.39%, in
gPROMS, and lower than 3.04%, in D.N.A., for all components. The higher relative
error in the case of gPROMS is because of the restricted control that we have in the
solution of the power plant model, by using this software. Simulation times for both
programs are in the area of seconds, which make them especially useful tools for
examining a variety of cases in a small amount of time.
The simulation results led us to useful conclusions about the choice of
optimization software. First of all, we showed that the power plant can be modeled
and simulation can give satisfactory results compared to the control room
80 G. Tzolakis et al.
123
measurements of the unit. Second, modeling based on gPROMS (which is not open-
source) gave similar results with D.N.A. Since gPROMS also contains optimization
algorithms for such applications it was chosen for the optimization study.
3.1.2 Optimization
As mentioned in previous section optimization has been performed by using the
software gPROMS. Our objective function was to maximize the thermal efficiency
of the steam/water cycle by regulating the mass flow rate of the steam at the
extractions from the different turbine stages. It can be observed, from Table 2, that
significant changes in the mass flow rates of the extractions resulted to an increase
of 1.42% to the efficiency of the steam/water cycle of the unit. The increase of the
thermal efficiency is due to the lower amount of thermal energy that is necessary to
be given to the water in the S/H component (Superheater) as a result of the
optimized preheating of the water, thus lower fuel consumption.
The reader can see in Fig. 3 the values of the steam mass flow rate at the
extractions from the different stages of the turbines. It shows that for the extractions
from the high pressure turbine and the first stage of the intermediate pressure
turbine, we need to reduce the steam mass flow rate 23.14 and 16.29%, respectively;
Table 1 Comparison of the measured data with the simulation results of D.N.A. and gPROMS for
operational scenario of 300 MW
Components Measured data D.N.A. gPROMS Difference (%)
D.N.A. gPROMS
Generators Electric power production (kW)
GEN1 -81428 -80760 -79977 -0.82 -1.78
GEN2 -30873 -30400 -30185 -1.53 -2.23
GEN3 -30505 -30880 -30773 1.23 0.88
GEN4 -23849 -24190 -24175 1.43 1.37
GEN5 -40035 -39380 -39459 -1.64 -1.44
GEN6 -29468 -29530 -29541 0.21 0.25
GEN7 -32259 -33560 -33344 4.03 3.36
GEN8 -21390 -22040 -22329 3.04 4.39
Pumps Electric power consumption (kW)
Cond. Pump 421 420 420 -0.24 -0.24
Deaer. Pump 5525 5521 5522 -0.07 -0.05
Heaters Heat consumption (kW)
S/H 603600 603800 603492 0.03 -0.02
R/H 105350 105700 104998 1.29 0.62
Condenser Heat losses (kJ/s)
Cond. -421640 -421700 -421723 0.01 0.02
Unit Thermal efficiency [-]
g 0.4010 0.4014 0.4006 0.11 -0.09
Emissions’ reduction of a coal-fired power plant 81
123
while for the rest of the extractions we need to increase the steam mass flow rates.
Of course this is possible to be done if the technical stuff of the power generation
unit installs regulating valves with proper diameter of pipes to control the mass flow
rates from the extractions.
Figure 4 shows the required thermal energy for the superheater (S/H) and the
reheater (R/H), necessary to convert the water into superheated steam. The sum
of the thermal energy required before optimization, for both components, was
708490 KJ/s and after applying the optimization algorithm it was reduced to
684864 KJ/s. This is a reduction to the consumed energy of 3.33%, which is
very significant for such applications. Less consumed energy means less fuel and
that results to lower emissions without reducing the electric power output of the
unit.
Table 2 Optimization results of gPROMS and relative difference from the simulation for operational
scenario of 300 MW
Components Simulation Optimization Difference (%)
Extractions Turbine extraction mass flow rate (kg/s)
HP -23.29 -17.9 -23.14
IP1 -15.41 -12.9 -16.29
IP2 -5.02 -7.27 44.82
IP3 -14.91 -18.5 24.07
IP4 -5.78 -10.2 76.47
LP1 -10.55 -15.85 50.24
LP2 -0.47 -1.35 187.23
Generators Electric power production (kW)
GEN1 -79977 -79987 0.01
GEN2 -30185 -30917 2.43
GEN3 -30773 -31938 3.79
GEN4 -24175 -24843 2.76
GEN5 -39459 -39883 1.07
GEN6 -29541 -29154 -1.31
GEN7 -33344 -31856 -4.46
GEN8 -22329 -21217 -4.98
Pump Electric power consumption (kW)
Cond. Pump 420 420 0.00
Deaer. Pump 5522 5592 1.27
Heater Heat consumption (kW)
S/H 603492 577340 -4.33
R/H 104998 107524 2.41
Condenser Heat losses [kJ/s]
Cond. -421723 -397906 -5.65
Unit Thermal efficiency [-]
g 0.4006 0.4148 3.54
82 G. Tzolakis et al.
123
Change of the control variables
-15.41
-12.9
-7.27
-18.5
-10.2
-15.85
-1.35
-14.91
-0.47
-10.55
-5.78
-23.29
-5.02
-17.9
-25
-20
-15
-10
-5
0HP IP1 IP2 IP3 IP4 LP1 LP2
Turbine of the coresponding extraction
Mas
s fl
ow
rat
e [k
g/s
]
SimulationOptimisation
Fig. 3 Change of the control variables through optimization leading to a 1.42% increase of the thermalefficiency of the 300 MW scenario. (HP: -23.14%, IP1: -16.29%, IP2: 44.82%, IP3: 24.08%, IP4:76.47%, LP1: 50.24%, LP2: 187.23%)
Change of the consumed thermal energy
107524104998
603492 577340
0
100000
200000
300000
400000
500000
600000
700000
H/RH/S
Heat exchanger
Co
nsu
med
th
erm
al e
ner
gy
[kJ/
s]
SimulationOptimisation
Fig. 4 Resulting change of the consumed thermal energy after application of optimization which led to a1.42% increase of the thermal efficiency. (S/H: -4.33%, R/H: 2.41%)
Emissions’ reduction of a coal-fired power plant 83
123
This is clearly seen in Fig. 5 where the electric power output corresponding to the
generator of each turbine stage is shown. There is a small difference between
the values of the electric power output before and after the application of the
optimization but the sum of the generated electric energy of all generators before
and after the application of the optimization algorithm is the same, approximately to
290 MW. We have mentioned that the operating scenario that we investigated was
for a load of 300 MW. This is the maximum load for the specific unit and by using
the operating conditions given by the technical stuff of the unit we have both in
D.N.A. and gPROMS simulations an electrical power output of 290 MW. This is
why the sum of the values (Fig. 5) of the electrical power output—from the
generator—of each turbine stage is 290 MW.
Boundary conditions needed to be assigned also. In addition to the mass flow
rates of the extractions which are given in Table 2, the constant mass flow rate of
the water/steam which circulates into the water/steam cycle needs to be known (it
was fixed at 247.35 kg/s). In addition, steam temperatures at the entrance of HP and
IP1 turbines which are located after the superheater and reheater need to be known.
This temperature (535�C) is close to the maximum acceptable temperature (547�C)
set by the manufacturer of the turbines for the protection of the metallic parts.
Pressure at the entrance of the HP Turbine is specified at 170 bar and the electric
power needed for the condenser pump was specified at 420 kW.
One of the advantages of gPROMS is the direct connection of the simulation
model to the optimization one. What needs to be done is to identify the implicit
Change of the produced electric power
-21217-22329
-29541
-24175
-79977
-33344
-39459
-30773-30185-31856
-29154
-39883
-24843-31938-30917
-79987-90000
-80000
-70000
-60000
-50000
-40000
-30000
-20000
-10000
0GEN1 GEN2 GEN3 GEN4 GEN5 GEN6 GEN7 GEN8
Generator
Ele
ctri
c P
ow
er [
kW]
Simulation
Optimisation
Fig. 5 Change of the produced electrical power after application of optimization which led to a 1.42%increase of the thermal efficiency. (GEN1: 0.01%, GEN2: 2.43%, GEN3: 3.79%, GEN4: 2.76%, GEN5:1.07%, GEN6: -1.31%, GEN7: -4.46%, GEN8: -4.98%)
84 G. Tzolakis et al.
123
variable that needs to be maximized or minimized and set it as the objective
function and then identify the control variables from the explicit ones. Therefore,
the thermal efficiency is set as the objective function to be maximized and the
extractions’ mass flow rates are the control variables.
Although to a general optimization problem such an improvement (1.42%
absolute) might seem marginal, for a power plant is considered to be extremely
good, considering the sizes we are talking about. Next, we are going to see the effect
of the control variables on the maximization of the thermal efficiency in order to
prove that such increase is not marginal.
In Fig. 6 we see the effect of the combined influence of the control variables by
increasing the allowable boundaries of each variable by 5, 10, 15, 20 and 50% and
re-applying the optimization algorithm. In all cases zero mass flow rates is the
minimum flow extracted from the turbine stages. Therefore, increase to the
boundaries implies further increase to the maximum value that the extraction mass
flow rate could have as an absolute value.
The tendency was increase of all the extraction mass flow rates except from the
HP extraction mass flow rate, which degreases. As expected, the increase is not
linear since increasing values alter the balances of the various implicit variables
non-linearly.
Figure 7 shows the effect of change of the mass flow rate for each extraction
separately, by keeping the rest unchanged to the simulated value. In all cases mass is
conserved so that the total amount of steam in the system remained constant to the
value assigned as boundary condition.
As it can be seen, going from the last extraction of the LP turbine to the first
extraction of the IP turbine, the influence decreases. Value a is the gradient of the
linear fit which can be assumed for each extraction mass flow rate.
Combined Influence by increasing the control variable boundaries
-25
-20
-15
-10
-5
0LP2 LP1 IP4 IP3 IP2 IP1 HP
Extractions
Mas
sflo
w r
ate
[kg
/s]
Initial simulation(nth=40.06%)
5%(nth=40.216%)
10%(nth=40.37%)
15%(nth=40.525%)
20%(nth=40.68%)
50%(nth=40.95%)
Fig. 6 Optimization cases for increased boundaries of the control variables
Emissions’ reduction of a coal-fired power plant 85
123
The reader can see that although the changes of the mass flow rates from the
extractions are significant relative to the initial values they had, the thermal
efficiency increased *1.4%. The above showed the extend in which the mass flow
rates from the extractions can affect the thermal efficiency of the water/steam cycle
of the unit and validates our results. This increase of the objective function is not
marginal and it is of great importance in such applications since it means less fuel
consumption and less emissions.
It should be noted that state of the art power generation units have started to
exclude extraction from the HP turbine stage and increase the mass flow rate of
them at the LP stages (Chaibakhsh and Ghaffari 2008). The results from Fig. 6
agree with this tendency.
For the optimization gPROMS needed 3 s to execute the algorithm with three
Non Linear Problem (NLP) iterations and three NLP Line Search steps and achieved
an accuracy of 1.75 9 10-10. The wanted accuracy and speed have been also
achieved for the optimization. Expected increase to the number of control variables
constrains and variables will lead to an increase of the time, NLP iterations and NLP
Line Search steps.
3.2 Results of the D.N.A. simulation of the boiler
The results of the D.N.A. simulation of the boiler, in terms of steam pressure and
temperature and flue gases temperature of the different components, are presented in
Table 3. It can be observed that the values measured in the specific power
generation unit and the values calculated with the D.N.A. software are in very good
agreement, with the highest discrepancy being the 3.65% difference observed in the
inlet temperature of the steam at the furnace. As we are in the process of developing
further the boiler model, by taking into account the solid plaque that is created on
Sensitivity of thermal efficiency to the individual massflow rate of the extractions
a = 0.0011
a = 0.001 a = 0.0009
a = 0.0007
a = 0.00065
a = 0.0001
0.398
0.4
0.402
0.404
0.406
0.408
0.41
0.412
0.414
0.416
0 10 20 30
Absolute difference of massflow rate from the initial simulated value [kg/s]
Th
erm
al E
ffic
ien
cy
LP2_Extraction(Init.=0.47 [kg/s])
LP1_Extraction(Init.=10.55 [kg/s])
IP4_Extraction(Init.=5.78 [kg/s])
IP3_Extraction(Init.=14.91 [kg/s])
IP2_Extraction(Init.=5.02 [kg/s])
IP1_Extraction(Init.=15.41 [kg/s])
Fig. 7 Optimization cases for individual increase of each of the control variables
86 G. Tzolakis et al.
123
the tube surfaces, we have not yet modeled this in gPROMS to apply the
optimization algorithm using fuel and air related control variables. This is subject of
future work but, at this point, we managed a successful simulation of the boiler
something which is the first step for the further optimization of the unit.
It should be noted that in this model the boiler is considered to operate at steady-
state conditions; thus all the mass flow rates are constant. These flow rates were
fixed to 574.96 kg/s for the flue gases and 248.05 kg/s for the water/steam at the
furnace inlet. The mass flow rate of the steam after the high pressure turbine
extraction was also fixed to -232.22 kg/s in addition to the temperatures and
pressures which are given in Table 3 as input values of the furnace. The above data
as well as heat losses from the heat exchangers and the mass flow rates and
temperatures of the cooling water from the attemperators, given in Table 4, were
also required.
Table 3 Comparison of the measured data with the simulation results of D.N.A. for the boiler opera-
tional scenario of 300 MW
Components Measured data Simulated data Difference (%)
Temp.
gas
(�C)
Temp.
steam
(�C)
Pres.
steam
(bar)
Temp.
gas
(�C)
Temp.
steam
(�C)
Pres.
steam
(bar)
Temp.
gas
(�C)
Temp.
steam
(�C)
Pres.
steam
(bar)
Inlet values
Furnace 1197 332.11 196.13 1197 320 196 0.00 -3.65 -0.07
S/H 1a 362 188.8 360.74 189.48 -0.35 0.36
S/H 1b 370 186.7 369.99 186.7 0.00 0.00
Atte. S/H 1b 443 183.2 445.13 183.35 0.48 0.08
S/H 2 422 181.7 422.95 183.35 0.23 0.91
Atte. S/H 2 510 177.9 509.99 177.9 0.00 0.00
S/H 3 494 176.6 494 177.9 0.00 0.74
R/H 1a 346 44.8 349.32 44.75 0.96 -0.11
R/H 1b 376 44.5 376 44.5 0.00 0.00
Atte. R/H 1b 470 44 471.19 44 0.25 0.00
R/H 2 431 43.8 432.79 44 0.42 0.46
Outlet values
Furnace 973 359.69 190 973.1 360.74 189.48 0.01 0.29 -0.27
S/H 1a 442 370 186.7 442 369.99 186.7 0.00 0.00 0.00
S/H 1b 590 443 183.2 590 445.13 183.35 0.00 0.48 0.08
Atte. S/H 1b 422 181.7 422.95 183.35 0.23 0.91
S/H 2 866 510 177.9 866.5 509.99 177.9 0.05 0.00 0.00
Atte. S/H 2 494 176.6 494 177.9 0.00 0.74
S/H 3 812 540 172.5 811.9 540 172.5 -0.01 0.00 0.00
R/H 1a 417 376 44.5 416.9 376 44.5 -0.03 0.00 0.00
R/H 1b 520 470 44 520 471.19 44 0.00 0.25 0.00
Atte. R/H 1b 431 43.8 432.79 44 0.42 0.46
R/H 2 728 540 43.1 728 539.74 42.6 0.00 -0.05 -1.16
Emissions’ reduction of a coal-fired power plant 87
123
The furnace model has the potential to be partitioned into several horizontal parts
where for each one of them, different thermodynamic conditions apply and the
outlet of each one is the input for the next. In that way, the changes of the various
variables depending on the thermodynamic conditions will be more accurately
described. At this point, use of the furnace as a single part is used. However, the
results are still satisfactory.
4 Summary and conclusions
The work described in this paper, mainly focused on the thermodynamic analysis of
the water/steam cycle along with the combustion modeling of the boiler of electrical
power generation units, with 300 MW maximum output (similar to Greece
KARDIA IV unit). Two software programs, D.N.A. and gPROMS were used for
the simulation with the later also being used for the optimization. The results were
satisfactory in relation to the measured data of the unit’s control room. The relative
error of the values calculated, were lower than 4.39% for all the components, in
terms of energy inlet and outlet at the different components. Application of the
optimization algorithm at the water/steam cycle simulation led to a 1.42% increase
of the absolute value of the overall thermal efficiency of the water/steam cycle,
having as control variables the steam mass flow rates at the extractions of the
different turbine stages. Such increase is notable for a power plant as the need for
lower fuel consumption and less emissions is imminent. It is worth pointing out that,
because of the use of local optimization algorithms for the solution of the NLP,
which is accepted since we are talking about a specific working point of the power
plant and specifically for the full-load scenario; the global optimum of any solution
obtained with our approach cannot normally be achieved. This is a common
deficiency of optimization-based design methods that can only be overcome by the
adoption of global optimization techniques. However, the increase of the efficiency
is yet again exceptional.
In addition, it is the first time that optimization of the operation of a fossil fuel
power plant was done, using as control variables the mass flow rates from the
extractions. Sensitivity analysis showed that although they can change significantly,
the thermal efficiency can be improved at *1.42%.
Table 4 Assigned values needed for the simulation of the boiler system
Heat exchangers’ heat losses (kW)
S/H 1a S/H 1b S/H 2 S/H 3 R/H 1a R/H 1b R/H 2
-58490 0 -6802 -6515 -2841 -1527.56 -6979.83
Cooling water’s temperature (�C) and mass flow rate (kg/s)
Attemp. S/H 1b Attemp. S/H 2 Attemp. R/H 2
Mass (kg/s) Temp. (�C) Mass (kg/s) Temp. (�C) Mass (kg/s) Temp. (�C)
9.61 152.63 6.22 275.05 7.78 132.61
88 G. Tzolakis et al.
123
The simulation of the boiler system gave similar results with the unit’s measured
data. This is the first step to apply optimization with control variables related to the
fuel and air flow rate and fuel quality.
Further work will include the modeling of the boiler system with gPROMS,
taking into account the solid plaque that is created on the tube surfaces due to ash
solidification. In addition, the boiler model should be connected with the water/
steam cycle model so that we have a more accurate representation of the electric
power generation unit as well as more detailed models of existing components so
that more control variables could be taken into account. Finally optimization
algorithm will be applied in this accurate model, using as control variables not only
the steam mass flow rate from the extractions of the different turbine stages, but the
mass flow rate of the fuel and the air, as well as the fuel humidity content.
Acknowledgments The authors would like to acknowledge financial support from the Greek Secretariat
of Research and Technology.
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