fynsværket, fv07 · 2018. 3. 22. · future earnings of fynsværket blok 7, based on a client’s...

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Fynsværket, FV07 Modelling potential future earnings at Fynsværket

Semester project - Energy Technology, ET-EKO-U2, 2. Semester,

Southern University of Denmark, May 29th 2015

Supervisor:

Christian T. Veje

Written by:

Mathias C. Gjøl (16-12-1992) Kristoffer Christensen (03-03-1995)

Jonathan M.R.-Hemmingsen (07-04-1993) Mads Odsgaard Olesen (13-10-1992)

Jonas Korsgaard (27-09-1993) Karl Meyer (10-04-1993)

Fynsværket, FV07 Semester project, Energy Technology May 29th 2015 Southern University of Denmark

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1 Abstract

The focus of this project has been producing a mathematical model that is able to calculate

future earnings of Fynsværket Blok 7, based on a client’s own expectations of electricity and

fuel prices. FV07 is as CHP-plant and the only large power plant on Fyn. In this report, FV07 is

described and hereafter analysed from a political and economic point of view. A

thermodynamic assessment of the plant is made and, as the project outline states, a

mathematical model is established, in order to give a potential buyer a better overview of the

plant and its related costs and revenues.

Furthermore, the optimal electricity production is estimated alongside with the total revenue

of sales, total costs and in the end the optimal annual profit of FV07.


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2 Table of contents

1 Abstract ...................................................................................................................................... 2

2 Table of contents ........................................................................................................................ 3

3 Introduction................................................................................................................................ 4

4 Price regulations ......................................................................................................................... 6

4.1 Regulations of the energy prices ......................................................................................... 6

4.2 Marginal cost ....................................................................................................................... 6

4.3 Net electricity price ............................................................................................................. 7

4.4 Financial challenges associated with running a CHP ........................................................... 7

4.5 Interconnections of European electricity ............................................................................ 9

5 Political regulations .................................................................................................................. 10

5.1 Cooling water .................................................................................................................... 10

5.2 Air pollution ....................................................................................................................... 10

5.3 Security of supply .............................................................................................................. 11

5.4 Economy ............................................................................................................................ 12

6 Optimising the electric efficiency ............................................................................................. 13

6.1 The Rankine cycle .............................................................................................................. 13

6.2 Thermal efficiency ............................................................................................................. 13

6.3 The Rankine cycle at FV07 ................................................................................................. 14

6.4 Assumptions ...................................................................................................................... 15

6.5 Electric efficiency .............................................................................................................. 16

6.6 Conclusion ......................................................................................................................... 18

7 Fuel input calculation ............................................................................................................... 19

8 Model development ................................................................................................................. 21

8.1 Model assessment ............................................................................................................. 23

9 Simulations ............................................................................................................................... 25

9.1 Simulation 1....................................................................................................................... 25

9.2 Simulation 2....................................................................................................................... 26

9.3 Simulation 3....................................................................................................................... 28

10 Discussion ............................................................................................................................... 31

11 Conclusion .............................................................................................................................. 33

12 References .............................................................................................................................. 35

13 Appendix list ........................................................................................................................... 37


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3 Introduction

Fynsværket (FV) is a combined heat and power plant (CHP) located, as the only central plant, in

Odense, Fyn. It consists of two operating blocks, block 7 and 8. Block 8 is a biomass-fired unit

that is able to run on both straw and wood pellets, producing exclusively district heat, whilst

block 7 is coal fired.

Fynsværket Blok 7 (FV07) is the main production unit at FV and the subject of the research of

this report. In full condensing mode FV07 can produce as much as 416 MW and has a lower

capacity limit of 74 MW. When producing district heat the lower limit reaches 62.2 MW with a

district heat capacity of up to 582 MJ/s. For electricity production, FV07 utilises five steam

turbines, two one-sided and three two-sided symmetric turbines connected to a generator.

The produced electricity is then supplied to the main transmission network at 400 kV. Some of

the discharge from the second medium pressure turbine is used to produce district heat in a

heat exchanger; this amount can be regulated at will. For a full schematic of the plant, please

see Appendix 8.

Considering the Danish 2050 emission targets, coal fired power plants such as FV are to be

scuttled by the year 2050. Due to financial doubts concerning the future feasibility of FV,

Vattenfall put it up for sale in 2010. This report aids a potential buyer in the evaluation of

whether purchasing FV is still an attractive investment, by both analytically and

mathematically, investigating the issues and advantages of operating FV.

The report outlines the production and verification of a mathematical model, which calculates

the future earnings of FV07 based on data supplied by Vattenfall. It contains a description of

how the cooling water temperature influences the electrical efficiency of a Rankine cycle. An

outline of the method used to calculate the fuel input to the boiler from measurements of the

flue-gas composition and knowledge of the fuel-composition. In addition, an assessment of

said method’s accuracy, as well as a description of the political and economic factors that

govern the production of electricity and district heat at a CHP-plant. The stem data used in this

report is depicted in Figure 3-1.


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Figure 3-1: Measured electricity and district heat production in 2010 at FV07.

To make the report easy to read, FV is described with the most significant information in the

introduction. Every section starts with its own introduction to each subject, followed by the

main text with references highlighted in brackets for easy access to literature and a numerated

structure for each paragraph and figure. The main results of each paragraph are summed up in

a partial conclusion that leads up to a discussion and final conclusion.

-100

0

100

200

300

400

500

600

700

Electricity production [MW] District heat production [MJ/s]


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4 Price regulations

The energy market, NordPool, is the exchange where energy prices are determined. It is

elaborated further in this chapter, both how the market price for electricity is determined and

how the marginal cost (MC) of a power plant is established. Some of the tariffs and taxes on

electricity are discussed and the net price for the consumer is determined.

4.1 Regulations of the energy prices

On the exchange the different production reports are sorted by their MC, cheapest first. The

energy consumption determines which and how many of the energy producing plants that

have to produce and deliver electricity. Then the plant with the highest MC of the producing

plants sets the overall market price, as the price will be equal to the highest MC of the

producing plants. The price of electricity is found where demand meets production in Figure 4-

1, and the MC of the last plant that produces the energy that the demand requires, will then

be the electricity price. In the case of Figure 4-2, a coal condensation power plant will set the

market price.

If a large fraction of the demand is covered by e.g. wind energy because of good conditions,

producers with higher MC cannot cover their costs through the market price and so, cannot

compete given that the electricity price will now be lower than the power plant’s MC.

Figure 4-1: Determination of market prices, found from the demand curve.

4.2 Marginal cost

The marginal production cost is found from an equation where the following basic information

about the plant is needed:

o Fuel prices (FP)

o Fuel consumption (FC)

o Variable operation cost (VC)


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o CO2 price (CO2P)

o CO2 emission (CO2E)

With these costs, the marginal cost is found from this equation [1]:

𝑀𝐶 = 𝐹𝑃 ∙ 𝐹𝐶 + 𝑉𝐶 + 𝐶𝑂2𝑃 ∙ 𝐶𝑂2𝐸

4.3 Net electricity price

Consumers of electricity are imposed some taxes and tariffs when using the electricity grid.

Appendix 9 shows taxes and tariffs for households, small companies and large companies.

Three, and the highest of the tariffs, are the Grid-tariff, System-tariff and PSO-tariff. The Grid-

and the System-tariff are used to maintain the grid. The PSO is used to fund the expansion of

the Danish renewable energy sector. The Danish Climate- and Energy-ministry established the

state owned company Energinet.dk in 2005 [2]. Energinet.dk manages the tariffs. Energinet.dk

is the Transmission System Operator (TSO) and is responsible for the Danish transmission

system and the security of supply. Due to the added taxes and tariffs, including System- and

Grid-tariffs to Energinet.dk, the net electricity price is relatively high even with a low spot

electricity price.

As explained earlier, the spot price is determined from the demand. With a high demand the

price will rise, as producers with higher MC will need to deliver electricity. The TSO manages

the funds to maintain and extend the grid. Therefore, all the consumers give financial help to

push the Danish grid towards a green revolution.

4.4 Financial challenges associated with running a CHP

In Figure 4-2, the production at FV07 is illustrated for a period of 36 hours, starting on

December 10th. There is a close correlation between the production in Figure 4-2 and the DK1

spot price vs. the marginal cost of FV07 depicted in Figure 4-3.

Figure 4-2: Production at FV07 vs. Minimum production over a 36-hour period from 10/12-2010 11.00 pm to 12/12-2010 11.00 am.

0

100

200

300

400

23 1 3 5 7 9 11 13 15 17 19 21 23 1 3 5 7 9 11

MWh

Hours

Electricity production min. electricity production


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Figure 4-3: Marginal cost vs. DK1 spot price over a period of 36 hours from 10/12-2010 11.00 pm to 12/12-2010 11.00 am.

The decline of the price is caused by the large percentage of wind energy in the Danish energy

system. Because electricity in Denmark is bought from the producers with the lowest short-

term MC, as explained in section 4.1, CHP-plants running on coal, like FV, cannot compete with

wind, as wind energy uses no fuel and emits no CO2, which is a large fraction of the MC of e.g.

coal fired power plants.

Since wind turbines have no expenses for fuel, very low maintenance cost and are by

legislation ensured a minimum price per MWh, they report a MC to Nord Pool of 0 DKK/MW to

be sure to sell all the electricity they produce.

This poses a problem for power plants like FV as they are forced to stop production in periods

with sufficient wind. This ads expenses because they have to start and stop, increasing fuel

consumption for start-ups. This is visible in Figure 4-2 and 4-3. As the price declines in Figure 4-

3 and goes below the MC line it can be seen from Figure 4-2 that the production falls below 74

MW, which is the technical minimum production of electricity. Thus, it is assumed that

production ceases completely. With more wind energy, this happens more frequently and

lowers the amount of MWh’s produced. As a result, FV has fewer units to divide the overall

cost by. This is the challenge FV is facing. As more sustainable production, favoured by the

government, is connected to the grid, they risk having to shut down the plant.

If some of the CHP-plants stop producing for good, because of their bad economy, it will lower

the security of supply in the grid, due to the fact that the fluctuating wind production does not

have a backup alternative to CHP plants, that can deliver sufficient regulatory capacity. To

counteract this, unless alternative regulateable energy sources are found or large-scale energy

storage becomes an option, the government will be forced to come up with a way of

supporting the plants. Such a way could be a large power transmission-grid across Europe, so

that electricity can be distributed to areas were it is needed, when production in other areas is

higher than needed.

Vattenfall applied for an approval to shut down FV07 by 2016 [3] because the cost of

operation was too high compared to the revenue. The request was denied due to the risk of

-200

-100

0

100

200

300

400

500

23 1 3 5 7 9 11 13 15 17 19 21 23 1 3 5 7 9 11

kr/MWh

Hours

Maginal cost Spotprice DK1


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unbalancing the electricity supply on Fyn, as FV is the only major power plant on Fyn. To

ensure that Denmark will have plants in the future to supply a fluctuation backup and peak

load, some form of financial incentive for keeping the plants running is needed. Alternatively

Denmark could experience blackouts or be forced to import the electricity at a very high price.

4.5 Interconnections of European electricity

When the production of wind energy in Denmark is low, the countries surrounding it, like

Sweden and northern Germany, with a lot of wind energy, will also have a low wind energy

production, making the electricity price rise. The large amount of hydro energy in Norway

could be put into action, but as they will be connected to England and Holland, the demand

will rise and so will the price. Denmark’s own connection to Holland through the Cobra cable

can ensure a higher security of supply but still at a higher price as Holland also has a large

number of connections to other countries, which would most likely be in need of electricity

when Denmark is, as adjacent countries such as Germany have large amounts of wind energy

as well. This demand will in itself raise the price of electricity. The reason for Holland having

capacity to adjust the production if needed, is because of their many gas turbines, which have

higher marginal costs than renewable energy systems and even coal fired power plants as

FV07. Therefore, the price of electricity will rise as a function of these higher costs.

The uncertainty of what the spot price will be set at is the price a country pays for not being

energy-self-sufficient. That is why it is necessary to maintain the CHP-plants. If larger

interconnections of European electricity are not completed, CHP-plants might be the cheapest

alternative in the long term to keep the security of supply at an acceptable level, until a

sufficient alternative has been found.


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5 Political regulations

To manage FV correctly, it is necessary to ensure that the political aspects are considered. In

this section, the main political aspects for FV are mentioned and discussed. The main aspects

are the cooling water emission, the air pollution, the security of supply and the economy.

5.1 Cooling water

The cooling water used in the condenser comes from Odense New Canal, and the discharged

water goes into Odense Old Canal. The limit value for the temperature-rise of the water from

intake to outlet of the cooling system is 8°C. The chosen value is set to protect the flora and

fauna in the old canal. Even with the limit value, the temperature differences have a minor

effect on the flora and fauna. Miljøstyrelsen is trying to find an alternative to the discharged

cooling water, because of these effects [4].

5.2 Air pollution

Figure 5-1 shows the average emission of SO2, NOx and dust. The limit value of SO2 and NOx is

200 mg/Nm3. For dust, the limit value is 30 mg/Nm3 in 2013. In 2015 the limit value for dust is

20 mg/Nm3, and the limit value for SO2 and NOx is still 200 mg/Nm3 [5]. FYV7 has an average

emission far below the limit values.

Figure 5-1: Review of the limit values and the average emission of FV07 for 2013 [4]

The different power and district heat producing companies, including FV, are imposed a CO2-

quota law, as a part of the third package of liberalisation. This means that they have to pay for

their CO2 emission by buying quotas as well as being obligated to report their GHG-emissions.

The entire purpose of this law is to reduce the emissions by encouraging development of less

polluting technologies through an increased running-cost for conventional technologies [6].


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Emission Unit 2009 2010 2011 2012 2013

CO2 ton 1,956,875 1,996,064 1,329,548 1,636,993 1,659,811

CO2 g/kWh 461 414 379 415 417

SO2 g/kWh 0.11 0.09 0.08 0.06 0.07

NOX g/kWh 0.17 0.16 0.14 0.11 0.10

Dust g/kWh 0.03 0.02 0.02 0.03 0.01

Table 5-1: Table of GHG emissions from FV [4].

5.3 Security of supply

As FV supplies electricity and district heat to the Danish energy sector, they are obligated to

act in accordance with certain laws and regulatory statements put forth by the respective

authorities and the Danish government.

5.3.1 Law of electricity supply

FV is assigned to the law of electricity supply [7] under chapter 3, §10. They are licenced to run

an electricity producing plant with a capacity over 25 MW [8]. By signing the licence that

allows them to produce electricity, they are assigned to fulfil the duties and conditions

mentioned in the law of electricity supply, the law about advancing renewable energy [9] and

the law of CO2 quotas [6]. Energistyrelsen can, with a one-year notice, order FV to deliver a

minimum electricity capacity, according to §50 [7].

The purpose of the law of electricity supply is, according to §1, to secure that the Danish

electricity supply is organized in agreement with the security of supply. Its target is to deliver

cheaper electricity to the consumers and advance the sustainability of the energy use.

5.3.2 Law of heat supply

The purpose of the law of heat supply [10] is expressed in §1 and is to advance the economic

use of energy to heat indoor areas and supply them with hot water. The district heat supply

should be in agreement with the purpose from §1 to advance the co-generation of electricity

and district heat as much as possible. The municipalities are responsible for the approval of

projects for collective heat supply. With the licence to sell electricity they have the duty to

supply district heat to the plant’s district heat consumers, in accordance with §12 [7].


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5.4 Economy

Energinet.dk has to perform the listed duties in §28 in the law of electricity supply. In §8 of the

law of electricity supply, it is stated the consumers of electricity have to cover a part of the

expenses, caused by Energinet.dk’s obligation to maintain the public duties listed in §8.

Denmark has a goal to achieve a large reduction in CO2 emissions, and have made a political

plan towards 2020 and 2050. To achieve the goals set by the plan Denmark has to make a big

investment in renewable energy. The financial resources for the plan come from the PSO tariff.

The PSO tariff is imposed on all electricity consumers, and finances all new renewable projects

that apply for support.

Figure 5-2: PSO with planned politics and alternatives without subsidies to power production. The left figure shows the renewable energy sector if the political plan proceed with their subsidies.

The right figure shows if they do not proceed. [11]

Figure 5-2 shows two different scenarios regarding the 2020 and 2050 plan. Negative aspects

of the planned politics include that even if the electricity spot price declines, the net price for

electricity rises because of the high PSO tariff, and the fact that wind turbines and farms are

guaranteed a fixed price when selling their electricity for a fixed amount of time or produced

energy, regardless of the spot price. The difference between the spot price and the guaranteed

price is covered by the PSO tariff. This subsidisation puts other renewable technologies at risk

of being without a financial incentive.

The Danish goals for reducing CO2 emissions are more ambitious than the goals of the

European Union (EU) as shown in Appendix 10. FV is licenced to produce electricity and is

assigned to the law of electricity supply, the law of heat supply and different environmental

laws. The environmental laws make it difficult for FV07, as a coal fired CHP, to survive in the

future, because of the 2020 and 2050 plans for EU and Denmark. Until then FV is bound to

deliver heat and electricity when needed.


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6 Optimising the electric efficiency

In this section, the Rankine cycle used at FV07 is reviewed. The relation between cooling water

temperature used in the condenser and the overall electricity efficiency is examined with the

purpose of optimising the net work output of FV07.

At FV, the condenser uses cooling water from Odense New Canal and discharges the heated

water into Odense Old Canal, joining Odense Stream and Odense Fjord. Since the canal has

inconsistent water temperatures throughout the year, the temperature varies and therefore

the overall net work output at FV07 varies. This relation is elaborated later on, however first

an ideal Rankine cycle is reviewed.

6.1 The Rankine cycle

In the T-s diagram in Figure 6-1, an ideal Rankine cycle is illustrated. The cycle consists of four

steps. Step 1 to 2 is an isentropic compression in the pump, step 2 to 3 is a constant pressure

heat addition in the boiler, step 3 to 4 is an isentropic expansion in the turbine, and step 4 to 1

is a constant pressure and heat rejection in the condenser. The grey area in the illustration

represents the net work produced in the cycle.

Figure 6-2: Illustration of an ideal Rankine cycle in a T-s diagram. The grey area represents the Wnet. [13]

6.2 Thermal efficiency

The thermal efficiency is determined using Equation 6-1 [12]. To obtain a higher efficiency, it is

necessary to increase the net work output relatively more than the heat input, obtaining an

efficiency as close to unity as possible.

𝜂𝑡ℎ =

𝑊𝑛𝑒𝑡𝑄𝑖𝑛

(6 - 1)


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The optimal thermal efficiency of a Rankine cycle is approximately 15-20 %. Several factors

affect the efficiency of the cycle and thus the actual power output. Both friction and heat loss

in the various components of the power plant will cause the pressure to drop. To maintain the

required net work output, more heat addition in the boiler is required causing the thermal

efficiency to decrease. These factors are difficult to improve. One way to regulate the

efficiency is to control the temperature of the cooling water used in the condenser.

Considering Figure 6-2, the points 1’, 2’ and 4’ are introduced to the illustration of an ideal

Rankine cycle. Reducing the temperature in the condenser will create point 4’ and therefore

point 1’, since both the temperature and pressure are held constant in the ideal process in the

condenser. Reducing the temperature in the condenser will increase the Wnet, being the grey

area enclosed by the points 1, 4, 4’ and 1’ in Figure 6-2. The required heat input, Qin, is also

increased but the change in heat addition is relatively small compared to the change in net

work output and considering Equation 6-1, the thermal efficiency of the entire cycle is, by

doing so, increased. The increase in required heat input is the red area enclosed by the points

1, 1’, 2’ and 2 in Figure 6-2.

Figure 6-3: Illustration of an ideal Rankine cycle in a T-s diagram. The grey area illustrates the increase of Wnet by lowering the temperature in the condenser and the red area illustrates the increase in Qinput. [13]

There is a deviation from the ideal Rankine cycle and the actual cycle at FV07 due to

irreversibilities in the various components throughout the cycle. The common reasons for

irreversibilities occur in the piping due to heat loss and friction in the piping connecting the

various components.

6.3 The Rankine cycle at FV07

In order to determine the thermal efficiency and how it fluctuates at FV07, the software

Engineering Equation Solver (EES) is used. All the relevant information, such as temperature,

pressure, mass flow etc., used in the thermodynamic model to determine the enthalpies and

the work- and heat-output, is extracted from the data sheet Kopi af Billeder fra turabs til


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studerende 2012-04-10 [14]. The model and its specific results can be examined further in

Appendix 11.

In Figure 6-3, the P-h diagram of the Rankine cycle at FV07 is illustrated. In the diagram, the

process 1 to 2 is the heat addition in the boiler. Process 2 through 8 is the turbine cycle. In a

Rankine cycle, it is possible to reheat the steam by conducting it back through the boiler. By

reheating the steam in the cycle, a higher optimal thermal efficiency than 15-20 % is achieved

due to e.g. reducing moisture content in the steam and increased enthalpies.

At FV07, the steam is reheated twice; from the high-pressure turbine to the first medium-

pressure turbine and from the second medium-pressure turbine to the low-pressure turbines,

causing the overall net work output to rise. The rise in enthalpy from the reheat is illustrated in

the P-h diagram in Figure 6-3, from point 3 to 4 and from point 6 to 7.

Figure 6-4: P-h diagram illustrating the Rankine cycle at FV07.

The process from 8 to 9 is the heat extraction in the condenser, implying that point 8 is

regulated by the cooling water temperature. The final process to complete the cycle from the

pump, through the feedwater tank and the pre-heaters and into the boiler again is process 9

through 1.

6.4 Assumptions

Some assumptions have been made in order to define the cycle and to determine the thermal

efficiency at FV07. It is important to state that the thermodynamic model in this report

assumes FV07 to produce no district heat. This assumption causes the thermal efficiency of the

cycle to be calculated completely from electricity production; that is, the electric efficiency


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solely depends on the generator efficiency. The specific generator used at FV is unknown;

however, due the scope of the production requirement at FV07, it is assumed that it is a highly

productive and modern generator suggesting an efficiency of about 98% [15].

The turbines have outlets to the pre-heaters, to Stobudako and to other parts of FV. These

outlets have been neglected in the model due to a lack of information in the data sheet. By

simplifying the model in such a way, the calculated enthalpies throughout the cycle will differ

from the actual energy output making the model rather inaccurate. However, since the subject

of inquiry in this section is the relation between the efficiency and the cooling water

temperature, the actual energy output will only affect the outcome by resulting in a higher

theoretical efficiency than the actual one at FV07 preserving the relation between rise in

efficiency per degree Celsius, %

°𝐶.

When considering the relation between the inlet cooling water temperature and the inlet

temperature of the steam into the condenser, a relation of 10°C is used. It has not been

possible to determine the actual relation between the two streams and therefore this relation

is considered a reasonable assumption.

When calculating the thermal efficiency at FV07, the cycle is considered an ideally reversible

process; that is, the thermal efficiency of the heat engine is considered equal to the reversible

thermal efficiency [12].

𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙 = 𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙,𝑟𝑒𝑣 (6 - 2)

Since the heat engine at FV07 is considered reversible, the efficiency is determined as,

𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙 = 1 −

𝑇𝐿𝑇𝐻

(6 - 3)

By doing so, the TL is regulated by the cooling water temperature in the condenser causing the

overall thermal efficiency to fluctuate.

6.5 Electric efficiency

To examine how the inconsistent water temperatures in the cooling water flow affects the

lowest temperature in point 4’ in Figure 6-2, the turbine cycle at FV07 is divided into two parts,

part A and part B, to make sure that the reheat process from the high-pressure turbine to the

medium-pressure turbine is taken into account. Part A covers the high-pressure turbine and

part B covers the rest of the turbines combined. The reheat process before the low-pressure

turbines is neglected in this model because the change in enthalpy in this process is relatively

small and because otherwise the complexity of the model exceeds the scope of this report.

At a cooling water temperature of 1°C, the model results in the following thermal efficiency.

𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙, 𝑨 = 1 −

341.4°𝐶 + 273.15

541.1°𝐶 + 273.15= 0.2453 (6 - 4)


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𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙, 𝑩 = 1 −

(1 + 10)°𝐶 + 273.15

509.1°𝐶 + 273.15= 0.6368 (6 - 5)

Thus, the overall thermal efficiency at FV07 is determined to be:

𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙 =

𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙, 𝑨 + 𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙, 𝑩2

= 0.441 (6 - 6)

This thermal efficiency is to be multiplied with the efficiency of the generator used at FV07,

which is set to be 98 %, to determine the electricity efficiency of FV07:

𝜂𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦 = 𝜂𝑇ℎ𝑒𝑟𝑚𝑎𝑙 ∙ 𝜂𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟 (6 - 7)

𝜂𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦, (1°𝐶) = 0.441 ∙ 0.98 = 0.4322 = 43.22 % (6 - 8)

By using the model in EES, the fluctuating efficiencies according to the respective cooling water

temperatures are calculated. The model shows that the average rise in efficiency per decrease

in cooling water temperature is 0.0625 %

°𝐶. In Figure 6-4, the relation between temperature and

efficiency is illustrated. The outlet cooling water temperature at FV07 is also illustrated.

Figure 6-4: The relation between cooling water temperature and electricity efficiency.

By using EES to create a T-s diagram, the difference in net work output is illustrated. In Figure

6-5 the temperatures and entropies of the Rankine cycle at FV07 are inserted. The difference

between point 9a and 9b represents the change in net work output. The point 9a represents a

cooling water temperature of 1°C and 9b represents 25°C.

41

41.5

42

42.5

43

43.5

0 5 10 15 20 25 30 35 40

Elec

tric

ity

effi

cien

cy [

%]

Cooling water temperature [°C]

Inlet temperature

Outlet temperature


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Figure 6-5: T-s diagram of the Rankine cycle at FV07. 9a represents a cooling water temperature of 1°C and 9b represents a temperature of 25°C.

6.6 Conclusion

The theoretical electricity efficiency calculated is estimated to be higher than the actual

efficiency at FV07, due to the isolated enthalpy system throughout the Rankine cycle as

elaborated in section 6.3. The assumption that the turbine cycle at FV07 is considered a

reversible heat engine will also result in a higher theoretical efficiency than the actual.

However, the relation between temperature and electricity efficiency is considered

unaffected. For every degree the temperature rises, the efficiency will decrease 0.0625

percentage points leading to the conclusion that the electricity efficiency at FV07 will be at its

highest during the winter, when the temperature in Odense New Canal is at its lowest.


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7 Fuel input calculation

The fuel input is calculated from the composition of the flue gas and knowledge of the fuel

composition via an oxygen balance calculation [16]. The data used for a comparison of the

results is a direct measurement of the hourly average fuel input to the boiler for 24 hours from

the 10th of February 2011 to the 11th of February 2011.

C 63.40 % 0.6340 kg/kg

H 3.55 % 0.0355 kg/kg

S 0.60 % 0.0060 kg/kg

O2 8.16 % 0.0816 kg/kg

N 1.39 % 0.0139 kg/kg

H2O 10.40 % 0.1040 kg/kg

Ashes 12.50 % 0.1250 kg/kg

Table 7-1: Table of the composition of coal on a mass basis.

When the coal is burned, the water evaporates and is therefore negligible. The composition of

the ash is not known and it is therefore impossible to do any calculations on this part of the

fuel, hence, it is not included in the calculations. Assuming a complete combustion of the fuel

due to an oxygen surplus, the following six reactions occur:

𝐶 + 2𝑂 → 𝐶𝑂2 𝑆 + 2𝑂 → 𝑆𝑂2

𝑁 + 𝑂 → 𝑁𝑂 𝑁 + 2𝑂 → 𝑁𝑂2

𝑁 + 3𝑂 → 𝑁𝑂3 2𝐻2 + 2𝑂 → 2𝐻2𝑂

Now the molar composition and the oxygen required for full combustion is calculated from the

respective molar masses of the elements and the stoichiometric coefficients of the reactions:

Molar composition Required O2

C 0.05278495 kmol/kg 0.052784947 kmol

H 0.03522035 kmol/kg 0.008805088 kmol

S 0.00018712 kmol/kg 0.000187120 kmol

O2 0.00510319 kmol/kg -0.002551595 kmol

N 0.00099238 kmol/kg 0.001240478 kmol

Table 7-2 Molar composition and amount of O2 required for a full combustion.


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The oxygen is negative because it is already present in the coal and it must therefore be

subtracted from the oxygen input to the combustion. The oxygen required for the nitrogen

combustion is calculated based on an assumption of an equal distribution of NO, NO2 and NO3.

The oxygen factors are now summarised to achieve a factor of how much oxygen is needed to

fully combust 1 kg of the coal-type used in this case: 0.060466038 kmol O2/kg coal.

Assuming a dry-air-basis the air-input-flow is now converted to oxygen input flow in kmol/s

using the density of air at 20°C, an assumed air composition of 79 % N and 21 % O2, and the

molar mass of dry-air. The oxygen content of the flue gas is now subtracted from the input

flow in order to calculate the amount of oxygen used in the combustion in kmol/s. This is then

divided by the amount of oxygen needed to fully combust 1 kg of coal found earlier, to give a

fuel input in kg/s. Multiplying this with the energy content of the coal-type used at the plant

and converting to the correct unit yields an estimate of the energy supplied to the boiler and

can now be compared to the measured value supplied by Vattenfall. The estimated deviation

from the actual supplied value is now calculated for all 24 hours and averaged; this yields an

average deviation of 5.09 %, which, considering the assumptions made earlier can be deemed

a satisfactory result and the method can therefore be assessed to be accurate. For a full

schematic of the calculations, refer to Appendix 12.


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8 Model development

The mathematical model simulates an optimal operation of FV07 and ensures that power

production is always above the lowest possible electricity production capacity, while fulfilling

the requirements for minimum district heat production. The model also ensures that FV07 only

produces power where the marginal cost is lower than the electricity price.

The model is constructed in MatLab [17] [18], so that a potential buyer of FV07 can simulate

an optimal operation. Given other expectations of electricity and fuel prices, the vectors Coal

which is the price of coal in 2010, ElectricityPrice which is the DK1 spot price in 2010 and

Oil_Price_pr_tonne, which will be the price for a tonne of oil in 2010, can be changed at will, to

simulate other scenarios. Furthermore, all other costs, as well as expectations for electricity

and district heat production, are replaceable. The model can therefore be used to simulate any

outcome based on any given assumption of costs, prices and so on.

First, all the expenditures of FV07 are estimated, in order to make an estimate of the marginal

cost of FV07.

The model uses the input to perform various calculations. First, calculating the extra start-up-

fuel consumption of oil in the hours where FV07 has been taken out of production. If FV07

stands still for one to five hours, the start-up fuel consumption is categorized as a warm-start

and will consume 800 GJ of fuel oil, and if the number of hours of standstill exceeds five hours,

the oil consumption will be a cold-start and consume 1500 GJ fuel oil.

The total fuel consumption, not including oil, is calculated on the basis of the fuel consumption

model supplied by Vattenfall:

𝐹𝑢𝑒𝑙 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛 (𝑝, 𝑞) = 𝑎2 ∙ 𝑝2 + 𝑎1 ∙ 𝑝 + 𝑏2 ∙ 𝑞

2 + 𝑏1 ∙ 𝑞2 + 𝑐

The inputs of this model include different coefficients, where a-coefficients are coefficients of

the electricity production vector P, b-coefficients are coefficients of district heat production

vector Q and the coefficient c is a baseline consumption coefficient. The coefficient values are:

a2 0.00291999985879979

a1 1.86501347204465∙10-4

b2 6.429118241647

b1 1.04197700742527

c 426.593857573076

Table 8-1: Coefficients to the fuel consumption formula

Hereafter fuel and CO2-emission costs are found on the basis of both coal and fuel-oil prices, as

the two fuels have different prices, heating-values and CO2-emissions pr. unit. The cost of fuel

oil for start-ups is calculated on the basis of the consumption found above, the price of oil in

2010 and heating-value of the oil. Similarly the cost of coal-based consumption is calculated


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from the heating-value of coal and price of coal in 2010 and the fuel-consumption model

supplied by Vattenfall.

In a similar manner, the cost of CO2 emissions is found based on different coefficients of

emission for both oil and coal and the fuel-consumption of each type of fuel calculated above.

Now additional production cost such as cost of chalk, water, catalysers, operating and

maintenance cost, filter bags and disposal of waste products are summed up. Also, fixed costs

such as cost of staff, handling of fuel oil, annual handling of coal, transport, harbour cost and

annual investment of the plant are summed-up to give the total annual cost of the plant. The

sum of these costs is now corrected for inflation, as the data is from 1993.

Now the extra effect, and in relation to this the extra oil-consumption in times of peak-

productions is calculated and added to the total fuel consumption. The cost is divided by the

total fuel-consumption, to give the cost per fuel.

The marginal fuel consumption is now found by differentiating the fuel-consumption model

supplied by Vattenfall expressed in terms of electricity-production with respect to P.

This marginal fuel-consumption is now multiplied with the cost per fuel to give the MC of

electricity production for FV07 as a function of P.

When the marginal cost has been derived, the optimization loop itself simulates an optimal

operation of FV07 by ensuring that no electricity is produced when the marginal cost MC is

higher than the electricity price by setting the values of district heat production in these points

as zero. In these points no electricity production will be simulated either, as power production

in the model is a function of district heating production Q, Cm and Cv-values.

The estimated electricity-production is calculated from a Cv-value, which indicates how much

electricity production is lost due to additional district heating production, and a starting value

equal to the maximum possible electricity production of 416.225 MW. The minimum required

electricity productions are found as the Cm-values: Cm1 and Cm2, with starting values found

by choosing end values, supplied by Vattenfall, of the Cm1 and Cm2 lines and estimating the

point where the line intersects with the second axis in the area of possible production. These

two lines intersect each other at the minimum possible electricity production of 74 MW, which

is included in the loop. The loop ensures that electricity production on these lines beneath 74

MW is not incorporated in the calculations. Therefore production outside the area of possible

production is not incorporated in order to yield a more accurate result. The total minimum

production will be the sum of minimum required electricity production and minimum required

electricity production2, as minimum electricity will be calculated from the Cm2 value until

district heat production exceeds 110 MJ/s. Hereafter the minimum electricity production will

be calculated from the Cm-value. If these values are added, they will yield the total minimum

electricity production. A plot of the Cv, Cm1 and Cm2 functions is created to illustrate the area

of possible production. The plot can be seen in Figure 8-1.

The model also ensures that the production of electricity is higher than the lowest possible

production of 74 MW, again by setting the district heating production Q to zero in points


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where the measured electricity production values supplied by Vattenfall are beneath 74 MW.

Also, if district heat values, Q, and condensing mode values, C, are beneath zero, the electricity

production will be set to zero. When all criteria above is fulfilled, the model will simulate an

optimal operation of FV07.

Figure 8-1: Cv, Cm1 and Cm2 curves as a function of electricity production and district heat production, showing the area of possible production.

8.1 Model assessment

The estimated fuel consumption is calculated on the basis of the model supplied by Vattenfall

and estimates the measured fuel consumption with a percentile difference of 1.37 %. Reasons

for the small differences include that the values of P and Q are hourly measurements of FV07´s

electricity and district heat production. FV07 can alter the production of electricity and district

heat rather quickly and since the measurements are hourly averages, this will be a reason for

discrepancies as some data is lost by averaging.

Estimated fuel consumption 21,208,700 GJ

Measured fuel consumption 20,921,700 GJ

Percentile differences in fuel consumption 1.37142 %

Maximum Electricity Production 1,740,100 MWh

Exact Electricity production 2,241,970 MWh


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Surplus Power -501,873 MWh

Percentile difference in Electricity production 22.3853 %

Minimum required Electricity production 752,011 MWh

Minimum required Electricity production2 143,089 MWh

Minimum required district heat 1,269,360 MJh

Table 8-2: Mathematical model, operation of FV07, results.

Some measured values supplied by Vattenfall are negative, which will also be a reason for

discrepancies between measured fuel consumption and the estimated fuel consumption.

Negative hourly values of electricity and district heat will yield a negative hourly, estimated

fuel consumption. It is impossible to have negative values for fuel consumption leading to

further discrepancies in the model.

The potential buyer of FV07 can with confidence use the mathematical model as a guideline

for the fuel consumption of FV07 in future years because of the small percentile difference

from the simulation to the actual production. The model can also be used to calculate costs

related to the operation of FV07, as seen in simulation 3, where the potential buyer can use

own expected values for e.g. electricity and fuel prices.


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9 Simulations

The mathematical model simulating optimal operation of FV07 is tested in three different

simulations each estimating different aspects of operation such as production, cost and profit

from selling electricity.

The first simulation estimates the electricity production of FV07 hour by hour in 2010. The

second simulation estimates an annual deficit of inefficient production when FV07 is forced to

produce electricity in times where the marginal cost exceeds the DK1 spot price for electricity,

due to district heat requirements. The third simulation optimises the operation of FV07 and

calculates the annual profit when producing and selling electricity only. That is when district

heat productions and requirements are neglected.

9.1 Simulation 1

Simulation 1 simulates the production and operation of FV07 in the year 2010 hour by hour

and compares the calculated electricity production, with the actual electricity production at

FV07. Any discrepancies are explained. Until the point of deriving the MC, simulation 1 is

identical to the overall model explained above.

The simulation loop itself, ensures that electricity production values of P, lower than the

minimum possible electricity production capacity of 74 MW are disregarded so that there in

these hours is no electricity production, as such a production would be impossible in actual

operation. Actual operation is approximated further as the model ensures that to electricity-

production takes place when the values of district heat Q and operation in condensing mode C,

are below zero, as no electricity production can take place if there is neither district heat

production, nor condensing mode production.

In simulation 1, the total minimum production will be the sum of minimum required electricity

production and minimum required electricity production 2, as explained in the overall model.

Table 9-1 contain the results from simulation 1.

Maximum Electricity Production 2,396,010 MWh

Exact Electricity production 2,241,970 MWh

Surplus Electricity 154,041 MWh

Percentage Error in Percent 6.87077 %

Table 9-1: Simulation 1, operation of FV07 in 2010

9.1.1 Assessment of simulation 1

Reasons for discrepancies between the actual operation and simulation 1 include negative

values of P in the actual measured values of FV07 in 2010. Such negative values are not


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technologically possible, and are therefore not included in simulation 1, which will be a reason

why electricity production will be higher.

Another similar reason for discrepancies would be that measured values of district heating

production, at times, are negative. Such values are avoided by the optimization values of

simulation 1, and as electricity production is a function of district heating, the summed up

electricity production will as a result become higher for the simulation.

Yet another reason for the difference in electricity production between simulation 1 and the

actual operation of FV07, would be the hourly measurements of the electricity and district

heat production of the actual operation of FV07. By averaging the output hourly, data is lost

due to the large regulatory capacity of FV07. Had the measurements been available by minutes

or even seconds, the discrepancies would lessen. It can be concluded that the simulation is

somewhat accurate and can be used to simulate production at FV07 for a potential buyer of

the plant.

9.2 Simulation 2

If FV07 is forced by the district heat requirement to have any electricity production to cover

the requirement, even when the production is economically inefficient, the deficit in DKK must

be estimated and paid by the district heat company in order to be fair.

Until the point of deriving the MC, simulation 2 is identical to the overall model explained

above.

Figure 9-1: Electricity-price vs. marginal cost at FV07 in 2010

-400.00

-200.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

[kr/

MW

h]

Electricity-price [kr/MWh] Marginal cost [kr/MWh]


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Figure 9-1 is an illustration of why simulation 2 is relevant. The marginal cost is a limitation of

when production renders any profit. The simulation finds all the production hours where the

spot price is below the marginal cost. For each of these hours, it determines the difference

between price and cost and sums it up giving the deficit from producing electricity in the

periods with unattractive prices. Using the MC-function, production with a negative surplus

occurs 2,136 hours in 2010. Yet because of the law of heat supply, FV07 is forced to produce

electricity. This is because the plant has a minimum required production of electricity of 74

MW for it to keep running and produce district heat. The district heat company is required to

cover the increased expenses associated with the ineffective production, paying FV the

calculated extra price/GJ produced district heat in the hours of unattractive electricity prices.

The optimization loop of simulation 2 ensures that FV07 never produces electricity below the

minimum electricity production capacity. The model also ensures that FV07 only produces

power in times, where there is district heat and full condensation-mode production and

therefore these values of Q and C, are above zero. Given these limitations, the electricity

productions are calculated, as in simulation 1.

The point of this simulation is to simulate a non-optimal operation of FV07, where electricity is

produced even though marginal cost is higher than the price of electricity.

The efficient electricity production from the mathematical model is now subtracted from the

maximum electricity production in order to find the inefficient production, which is found as

production deficit in Table 9-2.

Hereafter the deficit in DKK is calculated in a loop that ensures that every time the marginal

cost of production is higher than electricity production, the deficit of that hour is calculated as

the marginal cost subtracted from the price of electricity. The sum of these deficits is

multiplied with the production deficit in MWh to yield the total deficit of inefficient production

in DKK from Table 9-2. The sum is also divided with 3.6 in order to convert the deficit from

DKK/MWh into DKK/GJ, and hereby estimating the extra cost of producing inefficient power in

order to fulfil district heating requirements in DKK per produced district heating unit.

Maximum Electricity Production, simulation 2 2,396,010 MWh

Efficient Electricity production 1,740,010 MWh

Production Deficit 655,914 MWh

Minimum required District Heating 1,913,650 MJh

Total deficit of inefficient production -22,206,500 DKK

Suggested compensation 9.40438 DKK/GJ

Table 9-2: Results from simulation 2


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The production deficit and therefore the inefficient electricity production of simulation 2 yields

655,914 MWh, which is the production forced by district heat, when marginal cost of

production is higher than the price of electricity. Such a production is inefficient and should be

avoided if possible. Yet it is unavoidable given the laws concerning a required amount of

district heat deliverance from FV07.

The inefficient production will cause a deficit in DKK which should be paid by the district heat

company, as their demand for district heat causes the inefficient production at FV07. The price

of district heat varies from technology to technology. A general rule is that it lies between 20

DKK/GJ and 80 DKK/GJ [19]. An extra payment of the estimated deficit of 9.40 DKK/GJ is rather

realistic.

9.3 Simulation 3

In this simulation the mathematical model is tested by calculating the total profit of FV07,

assuming that FV07 runs exclusively in condensing mode and therefore only produces

electricity.

The potential buyer can simulate the total profit of FV07, when producing electricity only,

based on any fuel and electricity prices by simply replacing the Coal, which is the price of Coal

in 2010, ElectricityPrice which are DK1 spot prices in 2010 and Oil_Price_pr_tonne, which is the

price for a tonne of oil in 2010. Generally all values in simulation 3 are replaceable with own

expectations of future prices and costs.

Until the point after calculating the marginal cost of the operation of FV07, simulation 3 is the

same as simulation 1 and 2, with the only difference being that the fuel-consumption in

simulation 3 is expressed only in terms of electricity production P. Naturally this affects the

cost of operation of FV07, as both CO2-emission cost, Fuel-cost (both oil and coal), cost of

docking and transportation costs are functions of the fuel consumption. Therefore, the MC-

function in simulation 3 will be different from the other simulations.

With the marginal cost of FV07, all data needed to simulate an optimal operation are in place.

The optimisation loop now ensures that FV07 does not produce electricity when the MC is

higher than the price and that the production of electricity is never lower than the minimum

capacity of 74 MW in order to ensure that cold and warm start fuel consumption and thereby

additional fuel cost can be avoided. The optimal electricity production is found and

consequently the fuel-consumption will change as the model supplied by Vattenfall is a

function of the electricity production, P. The new, optimal P is substituted into the model,

which yields lower fuel consumption and hence lowers cost, which gives a higher total profit.

As seen from Figure 9-2 though, some hours of the year FV07 will have to shut down due to

MC being higher than the price of electricity, the model has accounted for the fuel

consumption during these hours.


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Figure 9-2: Optimal production of FV07 in 2010

The optimal power production P is now summarised to yield the optimal power production of

the plant for 2010. On the basis of the hourly production of this optimal production, the total

sales are calculated by multiplying the optimal production with the hourly price of electricity.

Total revenue in an optimal operation of FV07 is now calculated by subtracting the total cost

from the electricity sales.

Optimal Electricity Production 1,830,130 MWh

Total revenue of electricity sale 694,729,000 DKK

Total Cost 576,048,000 DKK

Total Profit 118,681,000 DKK

Table 9-3: Simulation 3 results


As seen from the results listed in table 9-3 the power production in this simulation 3 does not

come close to the actual measured power production of FV07 in 2010. The main reason for the

difference would be that the simulation takes its point of departure of estimating the optimal

power production, only when such a production is economically feasible. Another reason for

the inaccuracy could be the assumption that FV07 only produces electricity and no district heat


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and is therefore not forced to produce inefficient electricity along with the minimum required

district heat, even though MC is higher than the spot price. In other words, in simulation 3,

FV07 produces the electricity that yields the largest profit, which is not necessarily the case for

the actual operation.

The revenue of 694,729,000 DKK in simulation 3 is made from selling the simulated power

production for each hour of the year 2010 at the spot price at that given hour. The cost

fluctuates with the power production, as e.g. fuel cost and CO2-emission cost are functions of

the power and heat production, due to the fuel-consumption model being a function of these

productions.

Reasons for the profit being as high as it is, includes the fuel-consumption and CO2-emission

cost saved, due to the fact that FV07 only produces electricity in simulation 3 and hence does

not incorporate additional cost for district heat production. Additional costs and negative

revenues are avoided further in simulation 3 as power is only produced when the spot price is

higher than the MC and therefore no non-optimal electricity is produced due to the minimum

district heat requirements mentioned above, which lowers the cost and therefore maximises

the total profit.


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10 Discussion

There are multiple things that need to be discussed, they can be divided into two categories;

internal- and external factors.

First the external factors that influence FV will be discussed. The largest influence on the plant

comes from the political decisions of the government. Their 2020-plan for throttling back a

large part of the coal fired power production and replace it with energy from wind turbines will

harm the revenue for the CHP-plants, especially in the long run, as the Danish goal for 2050 is

to have a 100 % green energy production [20]. Yet more than half of energy engineers believe

that it is not achievable [21]. A positive thing is that FV also produces district heat; the risk of

the investment is therefore spread, as there is no alternative that can cover an equal amount

of district heat production. In addition, the plant is guaranteed a compensation for the hours

they produce ineffectively, because of the district heat requirement as shown in simulation 2.

The reason why coal fired power plants are still needed is that there are simply no alternatives

when it comes to supplying a steady base load that can be regulated easily depending on the

fluctuations of the wind production. A possible way to achieve 100% independence from fossil

fuels is by storing the energy from wind turbines; however, there are no units with a capacity

large enough to store sufficient amounts of energy.

Moving away from CHP-plants will jeopardise the security of supply as discussed in section 4.4,

and therefore the government will have to support them until an alternative can be found. To

safeguard the plant against the transition to a more green energy system, the production can

be converted to run on biomass as the primary fuel, as has been partially done with block 8.

This can be cause for further discussion as even though there is a large portion of biomass in

the Danish system, further utilisation will take up land that could be used for food production,

so there is an ethical question here and it will alter the balance between nature and human

territory. Also, if a large part of the coal production should be substituted with biomass, import

of said fuel will be necessary [22]. All these are factors that will cause an increase in the price

per unit compared to coal, which will further decrease a plants competitiveness.

The internal factors that need to be discussed, regard the model. The first and most striking

cause of uncertainties is the fact, that the model is based on financial data for FV07 from 1993,

when the block was commissioned. A lot of the data, such as expenses for staff and waste

management will most likely have changed more than just the inflation, which is already taken

into account. This gives a distorted picture on the actual expenses of running the plant and can

be the cause of a skewed result.

Another factor that can alter the accuracy of the calculations is the fact that the data given for

the power production in MW, which is the base of the calculations, is a measured average

value within the production hour. FV07 has substantial regulatory capacity, meaning that it can

change its production on very short notice and by a large amount. These fluctuations in

production are not reflected in the average value and have an influence of the accuracy of the

model.


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Since the data that is the base of the model is from 2010, changes have occurred to the

composition of how the producers share the deliverance to the grid. Especially as Anholt wind

farm with a capacity of 400 MW was connected to the grid in 2013. Yet this will be reflected in

the spot price, because a larger production of wind energy with more fluctuation will yield

lower prices in some periods and higher in others. Therefore, future calculations using the

model will incorporate this change as production can be set up to only occur when the spot

price is favourable.

The relation between cooling water temperature and electricity efficiency of FV07 can be used

as a point of departure to evaluate whether or not it is feasible to speculate in artificially

lowering the cooling water temperature as much as possible throughout the year or if using

the water from Odense New Canal to regulate the efficiency, optimises the performance

enough. These calculations are not considered in the report. However, comparing the costs of

the current process and a process, where cooling towers are used to lower the temperature

instead, might be interesting when optimising the energy output in accordance with a feasible

economy.


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11 Conclusion

The electricity spot price is set as the MC of the last and most expensive unit that delivers

electricity to the grid. However, it is a lesser part of the price that the consumers pay for

electricity, due to tariffs and taxes such as Grid-tariff, System-tariff and PSO-tariff, which make

up the largest fraction of the electricity bill. The PSO tariff subsidises the renewable

development of the Danish energy sector, and pays e.g. the gap between a guaranteed

electricity sales price of an offshore wind farm, and the spot price in the electricity market.

Financial challenges for coal fired power plants such as FV07 include the production cost of

such plants compared to e.g. production units such as wind turbines, that deliver electricity to

the grid at a very low MC due to no costs for fuel and CO2 emission quotas. Another financial

challenge for coal fired power plants is that renewable systems such as wind turbines are

subsidised heavily by the PSO tariff, despite the fact that e.g. large-scale offshore wind farms

are not yet financially compatible with e.g. coal fired power plants such as FV07, which creates

a financial challenge in the future for CHP-plants even though they are more compatible with

the electricity grid of today.

The Danish law of electricity supply regulates power plants such as FV, as the unit is above 25

MW and therefore assigned to fulfil the duties and conditions mentioned in the law. The

purpose of units above 25 MW being regulated by the law of electricity supply is to secure

Danish security of supply in the most economical and environmentally friendly way while

protecting the customer. The responsibility of ensuring Danish security of supply is the TSO of

Denmark, Energinet.dk, who´s responsibilities are mentioned in §28 in the law of electricity

supply. Part of the additional price for electricity, which the consumer has to pay, is the system

tariff paid to Energinet.dk, which is a tariff paid to ensure the security of supply.

FV is also regulated by the law of heat supply as the FV is a cogeneration plant and is therefore

obligated to deliver district heat while producing electricity, in accordance with §1, which

states that cogeneration of district heat and power should be utilized as much as possible.

The electrical efficiency of FV07 is calculated to be 43.22 % at a cooling water temperature of

1°C under ideal conditions and the assumption that the generation process at FV07 resembles

an ideal reheating Rankine cycle and therefore a reversible heat engine. The calculations show

that the electrical efficiency increases as a result of decreasing cooling water temperatures, as

the extra heat extracted in the condenser causes the net work output to increase, as the

cooling water temperature decreases. Even though the increase in efficiency per degree drop

in cooling water temperature is 0.0625 %

°𝐶, it should be taken into account when producing,

because of the difference in water temperature with changing seasons.

The mathematical model of FV07 simulates an actual operation of electricity and district heat

production on the basis that production only occurs when the MC is lower than the spot price,

when the electricity production is above the minimum and when district heat requirements

are fulfilled. The model also estimates the fuel consumption of FV07 in 2010, as 21,208,700 GJ

with a percentile difference from the measured fuel consumption of 1.37 %. Also, the


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electricity production is estimated as 2,289,050 MWh which yields a percentile difference from

the measured electricity output of 2.1 %.

Simulation 1 simulates the operation of FV07 in the year 2010 hour by hour and compares the

calculated electricity production, with the actual electricity production at FV07. The electricity

production is estimated to 2,396,010 MWh with a percentile difference of 6.87 % to the actual

electricity production in 2010.

Simulation 2 simulates a scenario where FV07 is forced by district heating requirements to

have some inefficient production, when the marginal cost is higher than the spot price. The

deficit of the inefficient production is found, and an amount of loss per unit heat produced,

which should be paid by the district heat company, in order to compensate for financial losses,

is calculated. The electricity production of 2010, including inefficient production is estimated

as 2,396,010 MWh compared to an efficient production in 2010 of 1,740,100 MWh. The

difference is 655,914 MWh. The total deficit of inefficient production in DKK, found as the sum

of hourly marginal cost – the hourly spot electricity price times the inefficient production, is -

22,065,000 DKK and the deficit per unit of produced district heating, which should be paid by

the district heat company, is 9.40 DKK/GJ.

In simulation 3 the mathematical model is tested by calculating the total profit of FV07,

assuming that FV07 runs exclusively in condensing mode and therefore only produces

electricity.

The optimal electricity production is estimated to be 1,830,130 MWh, the total revenue of

sales is estimated as 694,729,000 DKK, total costs 576,048,000 DKK and thus a total profit of

118,681,000 DKK.


Page 35 / 75

12 References

1. Material from ELVA course.

2. Wikipedia, 09/01/2015. Energinet.dk. [Website] Available from:

http://da.wikipedia.org/wiki/Energinet.dk [05/14/2015]

3. Wittrup, S., 11/17/2014. Vattenfall får nej til at skrotte Fynsværket i 2016. [Website

(Ingeniøren)] Available from: http://ing.dk/artikel/vattenfall-faar-nej-til-skrotte-

fynsvaerket-i-2016-172352 [05/21/2015]

4. Vattenfall, 2013. Fynsværket- Grønt regnskab 2013.

5. The ministry of environment, 02/16/2015. Bekendtgørelse om begrænsning af visse

luftforurenende emissioner fra store fyringsanlæg. [Website (schulz lovportaler)]

Available from: http://miljoe-

offentlig.lovportaler.dk/ShowDoc.aspx?activesolution=http%3a%2f%2fwww.lovportale

r.dk&q=grænseværdier&t=%2fV1%2fNavigation%2fKoncept+kommune%2fKoncept+Te

knik%2fLT+Miljoe+offentlig%2fEmneindgang%2fLuft%2f&docId=bek20150162-full

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Available from: https://www.retsinformation.dk/Forms/R0710.aspx?id=144102

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7. Ministry of Climate, Energy & Building, 01/01/2013. Lovbekendtgørelse 2013-11-25 nr.

1329 om elforsyning.

8. The Energy Agency, 04/01/2015. Bevilling til elproduktion til Fjernvarme Fyn

Fynsværket A/S. Climate, Energy- and Buildingministry.

9. The ministry of Climate, Energy and Building, 04/16/2015. Bekendtgørelse af lov om

fremme af vedvarende energi. [PDF] [05/21/2015]

10. Ministry of Climate, Energy & Building, 02/02/2015. Bekendtgørelse af lov om

varmeforsyning.

11. The Econmic counsel, 02/03/2014. Økonomi og Miljø 2014: Kapitel I -Omkostninger

ved støtte til vedvarende energi. [PDF] Available from:

http://www.dors.dk/files/media/rapporter/2014/m14/m14_kapitel_1.pdf

[05/18/2015]

12. Çengel, Y. A. & Boles, M. A., 2015. Thermodynamics: an engineering approach. 8th ed.

in SI units ed. NewYork: McGraw-Hill Education.


Page 36 / 75

13. Rankine Cycle. [Website] Available from:

http://home.iitk.ac.in/~suller/lectures/lec29.htm [05/12/2015]

14. Data supplied with the task specification.

15. Electropaedia, 2005. Energy Effiency. [Website] Available from:

http://www.mpoweruk.com/energy_efficiency.htm [05/20/2015]

16. Felder, R. M. & Rousseau, R. W., 2005. Elementary Principles Of Chemical Processes.

3rd ed., 2005 ed. with integrated media and study tools. ed. Hoboken, NJ: Wiley.

17. Griffiths, D. F., October 2012. An Introduction to Matlab. [PDF] 3rd edition ed.

Scotland, UK: University of dundee.

18. Kreyszig, E., 2006. Advanced Engineering Mathematics. 9th ed. ed. Hoboken, NJ: John

Wiley.

19. Ea Energianalyse, 04/08/2014. Elproduktionsomkostninger -Samfundsøkonomiske

langsigtede marginalomkostninger for udvalgte teknologier. [PDF] Available From:

http://www.ea-energianalyse.dk/reports/1410_elproduktionsomkostninger.pdf

[05/21/2015]

20. The energy agency, Dansk klima- og energipolitik. [Website] Available from:

http://www.ens.dk/politik/dansk-klima-energipolitik [05/21/2015]

21. Wessel, L., Ingeniøren, 03/28/2012. Ingeniører tvivler på fossilfrit Danmark i 2050.

[Website] Available from: http://ing.dk/artikel/ingeniorer-tvivler-pa-fossilfrit-danmark-

i-2050-128001 [05/21/2015]

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http://www.ens.dk/undergrund-forsyning/vedvarende-

energi/bioenergi/biomasseressourcer [05/21/2015]

23. Christensen, N. B. & Poulsen, A., 2005. Mikroøkonomi. [PDF] bookboon.com. Available

From: bookboon.com

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25. Vanek, F. M., Albright, L. D. & Angenent, L. T., 2012. Energy Systems Engineering:

evaluation and implementation /. 2nd ed. ed. New York: McGraw-Hill.


Page 37 / 75

13 Appendix list

Appendix 1 - The group process .................................................................................................. 38

Appendix 2 - Methods ................................................................................................................. 39

Appendix 3 - Time schedule ........................................................................................................ 40

Appendix 4 - Brainstorms ............................................................................................................ 41

Appendix 5 - Supervisor contract ................................................................................................ 42

Appendix 6 - Group contract ....................................................................................................... 43

Appendix 7 - Belbin profiles ........................................................................................................ 44

Appendix 8 - Fynsværket illustration .......................................................................................... 46

Appendix 9 - Composition of electricity prices ........................................................................... 47

Appendix 10 - Energy and climate goals ..................................................................................... 48

Appendix 11 - EES model and results .......................................................................................... 49

Appendix 12 - Fuel consumption calculations ............................................................................ 53

Appendix 13 - The overall model ................................................................................................ 55

Appendix 14 - Simulation 1 ......................................................................................................... 60



Appendix 17 - Symbol list ............................................................................................................ 75


Page 38 / 75

Appendix 1 - The group process

The 6-phase model is composed of six isolated stages. The model is a work model that attempts

to ensure, that a subject is thoroughly examined and that the problems are solved optimally.

Problem analysis During the first phase, the Problem Analysis, the overall project outline and its demands were

analysed piece by piece with the purpose of establishing various sub tasks and an time schedule

as shown in Appendix 3 In this first phase, we also analysed these different sub tasks individually

by brainstorming which topics we should consider in detail.

Idea phase After considering all sub tasks, we could move on to the next phase, the Idea Phase. We took

notes of every part of the assignment and discussed how to solve them. We brainstormed the

various outlines and noted our ideas on how to solve them. Regarding our model we went

through the project outline and noted our ideas on how to solve them in the best way,

concerning both structure and complexity.

Planning phase In the next phase, the Planning Phase, we formed a detailed time schedule based on the general

time schedule and the specified sub tasks. This detailed time schedule is attached as Appendix

3. We discussed how we wanted to work with the individual tasks and concluded that we were

to choose between two options. The first option was to split the tasks up between us so that

each group member singlehandedly had responsibility of their respective tasks. By doing so, the

other group member’s understanding of a certain topic would depend completely on that one

person’s written product, which might lead to misinterpretations and misunderstandings within

the report. This could be avoided if the group worked on the topics in plenum. We chose a

middle way between the two options, which was that groups of 2 and three group members

worked on individual subtask in order to supplement each others knowledge, while at the same

time keeping every group member busy, and therefore getting sufficient amounts of work done,

in less time than working everything through in plenum. We choose to begin every topic by

harmonizing our understandings and expectations in plenum, where after we divided the tasks

between us regarding research for data, theory discussion and so on. This middle way of

working in plenum, and working individually ensured both a large amount of work being done in

little time, while ensuring an organized product in terms of every member having an idea, of

what the other members where doing, at all times.

Problem-solving phase The fourth phase, the Problem-solving phase, was the most time consuming phase since it was

here the report itself had to be worked out. The sub tasks were treated as described above and

in accordance with the detailed time schedule. Due to our well-organized work schedule, this

phase was carried out without complications, mainly because we at all times had an idea of how

far in the process we were and where we were headed in terms of how we wanted the product

to shape up. As mentioned in our Group contract, we agreed to meet at least one day a week to

focus on the project and to assure that we kept up with our time schedule. During the rest of

the week, we worked on our respective assignments and made sure to keep in touch with the

rest of the group. To do this we established an online Dropbox folder, in which we had a system


Page 39 / 75

to store every single part of written material. This was done both to ensure a back-up of our

work but also so that every group member at all times was kept up to date with what was going

on during the entire process.

Conclusion phase In this phase we summed up our results and discussed how we could have done things

differently and what results we might have come up with then. We defined the most important

results with regards to the model and the simulations and tried to validate them as much as

possible.

Product phase In this last phase we produced most of the written material and formulated all the sections

required by the project outline and guidelines. We made sure everything was written to address

the target group outlined in the project outline and formulated in a proper manner. The end of

the product phase was marked by a period of proofreading all the written material and making

sure the layout was set-up according to the guidelines as well as making sure all the references

were correct.

Appendix 2 - Methods The data has been analysed with a mixture of qualitative and quantitative methods. The

quality of the gi

fynsværket, fv07 · 2018. 3. 22. · future earnings of fynsværket blok 7, based on a client’s...

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