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Energy Systems - Analysis, Design and Optimization (41416)

Mini Project 1 – Mathematical Models

Zosia Sobiech (s104645@student.dtu.dk)

Daniele Sciannandrone (s104813@student.dtu.dk)

Carlos Quiroz Melgar (s104589@student.dtu.dk)

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

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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:

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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.

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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

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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.

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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.

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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.

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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%.

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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.

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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.

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