41416 miniproj1 math models_ver01
TRANSCRIPT
1
Energy Systems - Analysis, Design and Optimization (41416)
Mini Project 1 – Mathematical Models
Zosia Sobiech ([email protected])
Daniele Sciannandrone ([email protected])
Carlos Quiroz Melgar ([email protected])
Technical University of Denmark (DTU), Copenhagen, Spring Semester 2011
1. Abstract
The purpose of this project is to create a mathematical model for the unit 1 of Avedøreværket
(AVV) Cogeneration plant in Denmark, determine the efficiency and utilization factors as
functions of load, and to determine the relationship between heat used for district heating and
nominal electric power. The P-Q curves of the plant were plotted, defining the operation limits
and the region of operation of the plant. Also, changes in efficiency and utilization factor of
the plant were calculated, plotted and analyzed.
Finally, we analyzed two possible scenarios for replacing the boiler of the plant with gas
turbines. An appropriate arrangement of turbines was selected in order to transform the plant
from the actual simple steam cycle configuration to a combined cycle plant, showing the
increases in efficiency and power output.
2. Introduction
In 21st century civilization is so developed that we can’t imagine life without electricity and hot
water, it’s a basic facility for people from developed countries. One of the methods of heat and
electricity production is to use Cogeneration plants. This kind of plants allows to produce both
electricity and heat in one cycle.
Cogeneration plants, also known as combined heat and power plant (CHP) are used for
simultaneous production of electricity and heat from one fuel. The first CHP plant was
designed and built by Thomas Edison in the end of 19th century in New York [COGEN].
Cogeneration is an environmentally-friendly method. It frequently uses waste heat and waste
products, while the emission of CO2 and NOx is decreasing as technology permits to reach
efficiencies near to 60% [COGEN_TERM]. Because of the production of heat additionally to
electricity, Cogeneration plants reach better efficiency compared with traditional power
plants. Common power plants waste about 65% of the fuel through heat loss [COGEN_TERM],
so CHP plants result clearly much better according to the economical and efficiency points of
view.
This report’s aim is to show up the characteristics of the AVV 1 power plant, based on
simulated operational data. The other important task is to select new with gas turbines to
repower the plant by building up a combined cycle. In the report, we explain the process for
selecting the appropriate gas turbines of the future combined cycle and finally, show the
2
improvements in efficiency and electrical power for the repowered plant. As a background for
our work, we include in Table 2.1 [BEE] a summary of the advantages and disadvantages of
various types of co-generation systems.
Table 2.1 Advantages and disadvantages of various cogeneration systems
Variant Advantages Disadvantage
Back pressure -High fuel efficiency rating -Little flexibility in design and
operation
Steam turbine & fuel firing in
boiler
-simple plant
-well- suited to low quality fuels
-more capital investment
-low fuel efficiency rating
Gas turbine with waste heat
recovery boiler
-Good fuel efficiency
-simple plant
-low civil const. cost
-less delivery period
-moderate part load efficiency
-limited suitability for low
quality fuels
Combined gas & steam turbine
with waste heat recovery boiler
-Optimum fuel efficiency rating
-low relative capital cost
-less gestation period
-quick start up & stoppage
-less impact on environment
-high flexibility in operation
-average to moderate part-load
efficiency
-limited suitability for low
quality fuels
Diesel Engine & waste heat
recovery
Boiler & cooling water heat
exchanger
-high power efficiency
-better suitability as stand power
source
-low overall efficiency
-limited suitability for low
quality fuels
3. Method
3.1. P-Q diagram
P-Q diagram is a characteristic diagram of a Cogeneration plant. On the x-axis there is the ratio
between the actual and the nominal heat power used for district heating; on the y-axis it is
represented the ratio between the actual and the nominal electrical power transferred to the
net. Usually it is represented by an area of all possible operational conditions of the plant.
The behavior of the plant in particular conditions was analyzed, in order to obtain the four
main curves that delimit the operation region. The behavior of the plant in all intermediate
points inside the operation region was not analyzed, since it was assumed that all points inside
are possible to be reached by specific combinations of values for P and Q.
The lines that limit the operation region represent:
3
a. Plant in full condensing asset with variation of the heat load in the boiler from
minimum to maximum value;
b. Plant with maximum heat load in the boiler with variation of the asset from full
condensing to full back pressure;
c. Plant in full back pressure asset with variation of heat load in the boiler from minimum
to maximum value;
d. Plant with minimum heat load in the boiler with variation of the asset from full
condensing to full back pressure.
Data used was provided by simulations with DNA software.
The variation of the asset is done by (i) opening valves of district heating heat exchangers and
(ii) closing valves at the inlet of low pressure turbine. In this way part of the steam flow starts
to flow in the heat exchangers until it reaches the maximum value when low pressure turbine
valves are completely closed.
3.2 Thermal efficiency and utilization factor
A typical diagram for power plants is the variation of the thermal efficiency against the
variation of load (electrical power transferred to the net).
In the case of a cogenerative plant it is difficult to define a unique load; actually they are
designed to provide electrical energy to the net and heat to district heating. There are two
variables almost independent (limits exist for minimum and maximum electrical power
produced for a given heat transferred to district heating, see section 5.1) so a 3D plot should
be used to obtain a surface of thermal efficiency.
To avoid the use of hard-to-view plots, the chosen procedure was to draw different curves of
thermal efficiency with different heat loads. From data provided by DNA simulations of the
plant, configurations in which the same amount of heat was transferred to district heating
were chosen and the behavior of the thermal efficiency against the electrical power
transferred to the net was drew.
The same procedure was adopted to draw curves of utilization factor. In case of Q=0 thermal
efficiency and utilization factor curves coincide; this can be shown by simple consideration of
definitions of two parameters:
H
Q+P=ε
H
P=η equation 3.1
Where, P is the electrical power transferred to the net, Q is the heat for district heating and H
is heat consumption in the boiler.
4
3.3. Gas Turbine Selection
Upgrading the Unit 1 in Avedøreværket with the use of gas turbines makes it necessary to
analyze which parts should or should not be replaced. The actual configuration shows the use
of high pressure steam for preheating of water, which is a considerable lose of energy that in
other way could be used for increasing the energy production. These preheaters are located
out from the boiler, so we decided to analyze two possible scenarios that involve these
installations:
a. The gas turbines will replace only the boiler of the plant, while the four (4) water
preheaters (FH1, FH2, FH3, FH4) will still be used.
b. The gas turbines will replace the boiler AND the four water preheaters.
In the case “a”, maintaining the preheaters means that the water entering to the new HRSG(s)
will still have a temperature of 274.7 °C (from data file AVC.DAT), so the temperature in the
chimney of the HRSG will have to be higher than that value. For defining the appropriate gas
turbines to be used, we defined 285°C as the temperature in the chimney.
In the case “b”, the energy transferred from the hot gases of the gas turbine(s) has to deliver
enough energy to replace the fuel used in the boiler, and also to replace the heat transferred
to the water in the four preheaters. It means that the total energy to transfer is equal to
602.907 MJ/s plus 91.525 MJ/s (energy transferred to the water in the four preheaters), to
make a total of 694.432 MJ/s. Also, due to the fact that the preheaters are not going to be
used, then the water pumped from the feedwater tank will enter directly to the new HRSG
with a temperature of 180.18°C, which means that the temperature in the chimney has to be
above it. We defined 200°C as the temperature in the chimney for making the selection of the
gas turbines.
In order to choose the appropriate type and number of gas turbines for replacing the
installations indicated, we followed the next procedure:
- Define the value of HEAT to replace with the heat transferred from the hot gases of
the gas turbine(s). For the case “a”, we selected the highest value of HEAT
CONSUMPTION of the boiler, among the information provided in all the data files. This
value represents the energy transferred from the fuel combustion to the steam
produced. The value is 602.907 MJ/s and was found in the data file AVC.DAT. For the
case “b”, we included the heat that is transferred to the water in the preheaters,
which as indicated previously is 694.432 MJ/s.
- Find an appropriate combination of gas turbines with enough temperature of their
outlet hot gases for transferring the energy indicated in the previous step. This energy
will be transferred to the steam cycle in the HRSG that will form the combined cycle.
The energy transferred from the hot gases to the steam is calculated according to
equation 4.1:
Qhg = mhg * Cp * (Thg – Tout) equation 3.2
5
Where: mhg is the hot gases mass flow, Thg is the temperature of hot gases after the
turbine (°K), Tout is the temperature of the hot gases in the chimney of the HRSG (°K ),
and Cp is the specific heat of the average temperature of hot gases in the HRSG
(kJ/kg°K).
For calculating Cp, we used the curves for hot gases from combustion as function of
temperature [KTH,2010], shown in Figure 3.3.
Figure 3.1 Specific heat for gases from combustion as function of temperature
Being known the amount of energy necessary from the HRSG, we selected among all the
available models, the appropriate gas turbines whose hot exhaust gases could transfer to the
steam the energy indicated in both cases defined.
3.4. Combined Cycle Electrical Power
The inclusion of the gas turbines in place of the boiler (and feedwater preheaters) makes of
the Avedøreværket plant a combined cycle power plant. For both of our cases of study, we
have assumed that the electric power produced in the steam cycle doesn’t change.
Then the total power of the upgraded plant is calculated by equation 3.3.
Ptotal = PST + n * PGT equation 3.3
Where, PST is the power of the steam turbine (invariable in all cases, 261.5 MW), n is the
number of gas turbines, PGT is the power of the selected gas turbine.
6
4.5. Efficiency of the Combined Cycle
The efficieny of a combined cycle is calculated according to the equations 3.4 and 3.5.
ncc = (PGT + PST) / Qf equation 3.4
Qf = PGT/nGT equation 3.5
Where: PGT is the electrical power produced by the gas turbine(s), PST is the power generated
by the steam turbine, Qf is the heat in the fuel fed to all the gas turbine(s) and nGT is the
efficiency of the gas turbine(s).
4. Results
4.1. P-Q diagram
In Figure 4.1 is represented the P-Q diagram for the considered plant.
Figure 4.1 P-Q diagram for the Unit 1 of Avedøreværket CHP plant
The bold black lines represent the operational limits of the plant. All the region inside those
limits are possible points of operation (as a combination of values por P and Q). The black and
white squares shown represent data obtained from the base simulations.
4.2 Thermal efficiency and utilization factor
In figure 4.2 are represented thermal efficiency and utilization factor for the considered plant.
7
Figure 4.2 Thermal efficiency and Utilization factor for AVV Unit 1
4.3. Gas Turbine Selection
As detailed in section 3.3, from all the proposed available gas turbines, we tried different
combinations of units that could meet the need of energy transferred to the steam in the
HRSG. For case “a”, we found that the combination of 03 gas turbines ANSALDO V94.3A (285
MW) is the most suitable for this application. The data of the selected turbines is showed in
Table 4.1.
Table 4.1 Specifications for Ansaldo gas turbines (source: 2009 GTW Simple Cycle Specs)
The hot gases of this arrangement of gas turbines transfer 664.233 MJ/s to the steam in the
HRSG(s), which is enough to cover the requirement of 602.907 MJ/s. The excess of energy
could be used to produce more power in the steam cycle, or if it is not possible, it could be
controlled by limiting the temperature in the outlet of gas turbines or by increasing drainages
in the steam cycle.
For case “b”, we found that the combination of 02 gas turbines SIEMENS SGT5-8000H (340
MW) is the most suitable for this application. The data of the selected turbines is showed in
Table 4.2.
8
Table 4.2 Specifications for Siemens gas turbines (source: 2009 GTW Simple Cycle Specs)
As explained before, the hot gases of this arrangement of gas turbines should transfer enough
energy to replace the boiler and the four preheaters that use high pressure steam. The energy
transferred to the steam in the HRSGs is 773.998 MJ/s, which covers the necessary 694.432
MJ/s. Again, the excess of energy from the gas turbines could be used to increase the power
production in the steam cycle, or if it is not possible, it could be controlled by limiting the
outlet temperature of the gas turbines or by increasing the drainages in the steam cycle.
4.4. Combined Cycle Electrical Power
Using equation 3.3 and the results from section 4.3, the new power of the upgraded plant is
determined for both cases proposed.
For case “a”: Steam Turbine Power: 261.5 MW
Gas Turbine Power (ANSALDO V94.3A): 3 x 285 MW
Total power of the new combined cycle is 1116.5 MW.
For case “b”: Steam Turbine Power: 261.5 MW
Gas Turbine Power (SIEMENS SGT5-8000H): 2 x 340 MW
Total power of the new combined cycle is 941.5 MW.
For calculating the auxiliary services consumption, we assume that the steam cycle maintains
its consumption of 11964.705 kW (obtained from data file AVC.DAT) even after the installation
of the combined cycle, while for the gas turbines we assume an auxiliary consumption of 1000
kW for each turbine, which is an acceptable value according to the existant experiences.
Therefore, the total auxiliary consumption of the new plant will be approximately 13.965 MW.
4.5. Efficiency of the Combined Cycle
With previous results, and using equations 3.4 and 3.5, the thermal efficiency for the upgraded
plant for both analyzed cases is shown.
For case “a”: PGT = 3 x 285 MW PST = 261.5 MW nGT = 0.396
The calculated efficiency for the new combined cycle is 51.70%.
9
For case “b”: PGT = 2 x 340 MW PST = 261.5 MW nGT = 0.390
The calculated efficiency for the new combined cycle is 53.98%.
5. Discussion
5.1. P-Q Diagram
From the plot in figure 1 can be seen that the maximum electrical power is produced when the
total heat transferred to district heating is equal to zero (point [0,1]). This is obvious since in
this condition the plant works in full condensing mode and can completely exploit the pressure
jump between the high pressure turbine inlet and the condenser. When valves of district
heating are opened and valves of low pressure turbine are closed, the amount of steam
passing through the low pressure turbine decrease until it becomes equal to zero; in that
situation, with full heat load in the boiler, the maximum amount of heat to district heating is
transferred (point [1,0.86]).
By decreasing the heat load in the boiler similar curves could be drew, covering the whole
area. A lower limit exists in the heat load in the boiler since it isn't designed to operate too far
from nominal conditions.
One interesting observation is that it is impossible to work at maximum electrical load and
maximum heat provided to district heating: if part of the mass flow goes to the district heating,
a part of work is lost from the low pressure turbine; this explains why the upper line slightly
decrease with increasing of the heat load transferred to district heating.
Finally we can say that with a fixed Q, lower and upper limits exist of the total electrical power
transferred to the net and regulation range decrease for high value of Q: for 100% of heat to
the district heating there’s only one possible value of electrical power produced.
5.2. Thermal Efficiency and Utilization Factor
As it can be seen from figure 2, thermal efficiency increase with electric load and slightly
decrease with the heat load but its value doesn’t change a lot and settles on a value of 37%
with no big variations for high loads.
On the other hand the utilization factor has a different behavior: its value is high for low loads
and decreases with increasing of electrical output. Actually this behavior can be explained by
simple mathematical considerations on the definition of the utilization factor.
P
Q+η=
H
Q+η=
H
Q+P=ε 1.
From the formula it can be seen that utilization factor is the sum of the thermal efficiency and
another term which is the ratio of a constant term (Q is constant for each line) and a term
which increase with the load. For high electrical loads the utilization factor decreases and
tends to be equal to the thermal efficiency. The higher is the value of Q, the higher is the
importance of the second term.
10
For small value of produced electrical power, the utilization factor tends to be equal to
;H
Q=ε
the total heat transferred to the district heating over the heat consumption: the plant works
like a boiler used to produce only heat and the utilization factor becomes the efficiency of that
boiler, including all heat losses in the plant.
Those mathematical considerations are useful to understand if what has been got makes
sense; actually, there are technical limits of the produced electrical power and produced heat.
5.3. Gas Turbine Selection
The upgrading of a power plant implies to maintain or increase the previous power output or
any other characteristic decided by the owner, don’t use much more space than the previous
installation and also, as in any other project, one of the main objectives is to maintain the cost
of the works as low as possible.
We selected 02 cases of study. In case “a” we decided to replace only the boiler of AVV1, and
in case “b” we decided to replace also the feedwater preheaters. As mentioned in section 4.3,
for the case “a” we decided to select 03 gas turbines ANSALDO V94.3A (285 MW) as the
replace option, and 02 gas turbines SIEMENS SGT5-8000H (340 MW) for the case “b”. Even
though during the analysis of all the other gas turbines, we found some options that were
closer to match the heat needs from the hot gases, we decided not to take them because
some technical considerations. For example, for case “a” we had the option to use 09 turbines
Ansaldo V64.3A (75 MW) that could transfer 611 MJ/s of heat, very close to the requirement
of 602.907 MJ/s (for our selected option, the transferred heat is 664.233 MJ/s), but installing
09 small turbines instead of 02 big ones clearly takes more investment, space and
maintenance costs, among others. For case “b” we also had the option of the turbine Ansaldo
V64.3A (773.998 MJ/s of transferred heat, compared with the objective of 694.432 MJ/s), but
it would have been necessary to install 08 units, which as in the previous case, is a clear
disadvantage for an upgrading work.
Of course, due to the location of the plant in Denmark, and in order not to introduce extra and
unnecessary equipment with the upgrading, we were careful to select gas turbines that match
the nominal frequency of the Danish system, 50 Hz.
6. References
[COGEN] http://cogeneration.net/cogenerationexplained/
[COGEN_TERM] http://cogeneration.net/terms.htm
[BEE] http://www.bee-india.nic.in/
[KTH,2010] Sustainable Power Generation course, Fall 2010, KTH, Stockholm, Sweden.
11