Investment in Electricity Markets – a Market and Model Perspective

8/11/2019 Investment in Electricity Markets a Market and Model Perspective

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Selected topics in energy economics

Exercise 3

Investment in Electricity Markets a market and model

perspective

Student's name ID

Marin Galic -

Vienna, January 2014


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1. The problem to solve

Exercise3.1: Full load hours, contribution margin vs. fix costs

a)

Calculate the theoretical full load hours of the given power plants (Coal plant,

Combined Cycle Gas turbine (CCGT), Open Cycle Gas turbine (OCGT)) for the years 2006

to 2012. (see figure 1). The market prices for those years can be found in spotprices.xlsx.

Assume that the power plants will only produce, if the price is greater than the short run

marginal costs of production. Assume that the short run marginal costs are defined by the

fuel costs and CO2 costs. Data on monthly average costs of those inputs can be found in the

file Fuel_CO2_costs.xlsx. (You can also use yearly average costs for your calculations but

that should be stated in your report). All other relevant parameters are given in table 1.

Present your results graphically!

b)

Calculate the contribution margin in each year. We define the contribution margin as

gross income minus variable costs for each year. (see figure 1) Compare the contribution

margin to the yearly fix costs. The yearly fix costs consist of operation and maintenance costs

(O&M) and the yearly capital costs (annuity of investment = I). Note that both components

are independent of the actual production within a year. To calculate the annuities use a

discount rate of 5% and the technical life time given in table 1.

Present your results graphically! What is your interpretation of the results? Where those

power plants profitable between 2006 and 2012?

c)

What is the minimal yearly contribution margin at which you would decide to go in

operation for each power plant if you assume that the plant is already built? What is the

minimal expected yearly contribution margin at which you would decide to invest in a new

power plant? Which decision would you take in year 2012 for each type of power plant?

Interpret your results!

(We assume that the O&M costs are not to be paid if the plant does not operate throughout a

whole year)


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Exercise 3.2: Investment model Scenario analyses of minimal system costs

a)

Convert the generation dispatch model (I nvestmodel_Exerci se.gms) to an investment

model. Add an investment term (annuity of the investment) and the O&M costs to the

objective function (Cost). Those additional costs are considered to be yearly fixed

capacity costs. As we only simulate one typical day in the model we divide those costs by

365 which approximately yields daily capacity costs (Ccapacity [/kWday]).

[MW] is the additional capacity for each power plant (j) and is to found by the

optimization model together with the optimal dispatch tjP, for each hour (t) and power plant

(j)

The constraint Output which limits the power output of each plant has to be adjusted to

consider new installed capacity.

Addition:

Definition of daily capacity costs for model calculations:

With Ias specific investment costs, as annuity factor and Opexas fixed yearly operation

and maintenancecosts (O&M) for each power plantj. Of course this is a simplification. Here

we assume the load pattern to be constant in all days of a year. We also assume the same

patterns and costs over the whole life time of the power plants. Think of possible implications.


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b)

Find the optimal solution for the following base scenario:

Base scenario:

CO2 price: 20 /t

Gas price: 25 /MWh

Coal price: 10 /MWh

PV installed capacity (Cap_PV): 0.1 GW

No existing capacity: Capold=0 for all power plants.

What is the optimal installed capacity of each power plant?

c)

Shadow prices and the costs of capacity:

Take a look at the shadow prices of demand. They can be found in the Gamsoutput file (*.lst)

or in the Gdxviewer. The shadow price of demand for each hour can be found under

equation (or SolEQU in the .lst file) and the demand equation. It is the value in the

column marginal. It reflects the marginal additional or reduced costs if the right hand side

of the equation is increased by the value 1. In this case it reflects the additional costs of a

demand increase of one MWh in hour t.

In theory this can be interpreted as the price of one MWh in hour t.

Try to explain the shadow price of demand in hour 3 and in hour 19. Why is the shadow price

of hour 19 so high? What are the components of this price?

d)

Scenario analysesthe influence of Photovoltaic and CO2 costs:

Calculate the optimal capacity mix for the following scenarios:

PV scenario: Installed capacity of PV from 0 to 1 GW with 0.2 GW steps

CO2 scenario: CO2 price from 0 to 30 /tCO2 with 5 steps (Installed capacity of PV

stays at 0.1 GW as in Base scenario.)


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Illustrate your results graphically!

Interpret your results!

What do you observe?

What are your conclusions for future developments of the installed capacity?

What kind of problems could arise if the market price is limited to the short run marginal cost

of the conventional power plants?

Sources:

GAMS download:http://www.gams.com/download/

All other files including the GAMS license can be found in TISS
http://www.gams.com/download/http://www.gams.com/download/http://www.gams.com/download/http://www.gams.com/download/


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3. Solution

3.1. Full load hours, contribution margin vs. fix costs

a)Theoretical full load hours have been calculated using spot prices of electrical energy,

fuel costs and CO2costs. CO2costs can be calculated using fuel emission factor (Table 1) and

CO2costs (in Excel, Fuel_CO2_costs.xl sx). Looking at the Table 1 it can be seen that fuel

emission factors are 0,2for CCGT and OCGT and 0,35for Coal Power Plant.

CO2costs have been calculated multiplying fuel emission factorand CO2_spot. For

example, in period January 2006, price of CO2 was 21,58 /t CO2:

In this period (for coal power plant):

Using Price of CO2, fuel costs and efficiency, we can calculate short run marginalcosts (SMC):

For example (coal power plant, same period):

Table 2. Example of CO2 and SMC costs calculation (January 2006)

Power plant fuel emission

factor

Price of CO2[/MWh]

fuel costs

[/MWh]

Short marginal

costs (SMC)

[/MWh]

CCGT 0,2 4,32 20,13 41,43

OCGT 0,2 4,32 20,13 61,11

Coal 0,35 7,55 7,74 38,24


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It has been assumed that each power plant will produce electrical energy only if spot

price of electrical energy will be higher than short run marginal costs. It is also assumed that

daily fuel price in a specific month is equal to the average monthly price of that month. Full

load hours of each power plant have been calculated comparing production costs with spot

prices. Results are presented on the Picture 1and in the Table 3.

Picture 1. Full load hours of each power plant in a specific year

Table 3. Full load hours for 2006 and 2012

Power plant full load hours

(2006) [h]

full load hours

(2012) [h]

CCGT 4769 3857

OCGT 2233 268

Coal 5963 6289

b)

Contri bution marginis defined as a gross incomeminus variable costsfor each year.

The final value of contribution margins are given in the table below. The whole calculation

can be found in the Excel file.

4769

2233

5963

3860

269

6289

0

1000

2000

3000

4000

5000

6000

7000

2006 2006 2006 2012 2012 2012

CCGT OCGT HC CCGT OCGT HC

Full load hours of each power plant in 2006 and 2012


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Table 4. Total contribution margin of each power plant in every year [/MWh]

2006 2007 2008 2009 2010 2011 2012

CCGT 119490,37 74154,82 154448,85 50203,09 70359,44 60657,11 39153,44

OCGT 51078,86 38304,74 49875,08 11171,92 7467,65 1581,22 4714,84

HC 152341,72 78536,88 146277,02 70356,62 80009,81 86733,62 92704,19

Picture 2. Contribution margin, variable costs and spot price of CCGT power plant in 2006


0

200

400

600

800

1000

CCGT 2006

MC contribution margin spot price

0

200

400

600

800

1000

OCGT 2006



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Picture 4. Contribution margin, variable costs and spot price of HC power plant in 2006


Picture 6. Contribution margin, variable costs and spot price of OCGT power plant in 2012

0

200

400

600

800

1000

HC 2006


0

50

100

150

200

CCGT 2012

Short run marginal cost (MC) Contribution margin Spot price

0

50

100

150

200

OCGT 2012



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Picture 7. Contribution margin, variable costs and spot price of HC power plant in 2012

Compari son of contr ibuti on margin and yearly fi x costs

The yearly fix costs consist of operation and maintenance costs (O&M) and the yearly

capital costs (annuity of investment = I). Both components are independent of the actual

production within a year. To calculate the annuities there have been used a discount rate of

5% and the technical life time given in Table 1.

CCGT

Investment costs (I0) = 950 000 /MW

O&M costs (IO&M) = 28 000 /MWa

Calculating the yearly capital costs (annuity of investment = I) we have:

Ccapital costs

= I0*

Where is given by:

where: r = interest rate (5%)

L = lifetime of the power plant (Table 1.)

In this case: L = 35 years and = 0,06

So, we have:

Ccapital costs

= 58 018 /MWa

IO& M= 28 000 /MWa

0

50

100

150

200

HC 2012



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Using the same formulas and data from Table 1, we can calculate fix costs for OCGT

and HC power plants:

OCGT

Ccapital costs

= 26 040 /MWa

IO& M= 17 000 /MWa

HC

Ccapital costs

= 96 159 /MWa

IO& M= 36 000 /MWa

Final fix costs can be calculated using formula:

where Tis full load hours (Table 3).

Total fix costs [/MWh] are given in the table below.

Table 5. Fix costs of each power plant according to full load hours

2006 2007 2008 2009 2010 2011 2012

CCGT 18,03691 30,80874 14,75437 21,8764 14,58427 15,891 22,28446

OCGT 19,27452 37,65529 17,06582 45,21008 37,42609 122,9714 160

HC 22,16317 40,94145 23,48658 25,33237 21,07463 19,90047 21,01431

Table 6. Comparison (difference) of contribution margin in each year and yearly fix costs

2006 2007 2008 2009 2010 2011 2012

CCGT 33 472,37 -11863,18 68430.85 -35 814,91 -15658,56 -25360,89 -46864,56

OCGT 8038,86 -4735,26 6835,08 -31868,08 -35572,35 -41458,78 -38325,16

HC 20 182, 72 -53 622,12 14 118,02 -61802,38 -52149,19 -45 425,38 -39 454,81

Looking at the Table 6, it can be seen difference between contribution margin and

yearly costs. As we can see, CCGT power plant is profitable only in 2006. OCGT and HC

power plants are profitable in 2006 and 2008. Summing total money flow in these 7 years, it

can be seen that all three power plants are not profitable1.

If we assume that there are no O&M costs (because power plant does not operate

through the whole year), we get new results shown in the table below:

1If we are calculating with the constant fix costs (investment costs and O&M costs) for each year


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Table 7. Total money flow withouth O&M costs (only contribution marge and investment costs)

2006 2007 2008 2009 2010 2011 2012

CCGT 61 472 16 136 96 430 - 7 815 12 341 2639 -18 865

OCGT 25 038 12 264 23 835 -14 869 -18 573 -24 459 -21 326

HC 56 182 -17 623 50 118 - 25 803 -16 150 -9 426 -3 455

Excluding O&M costs, HC power plant is becoming profitable during these 7 years

(with the welfare of 33 843 ), but CCGT and OCGT power plants are still unprofitable.

Picture 8. Contribution margin and fix costs of CCGT power plant in 2006

Picture 9. Contribution margin and fix costs of OCGT power plant in 2006

0

5

10

15

20

25

30

35

2006 2007 2008 2009 2010 2011 2012

contribution margin and fix costs for CCGT

Contribution margin Fix costs

0

50

100

150

200

2006 2007 2008 2009 2010 2011 2012

contribution margin and fix costs for OCGT



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Picture 10. Contribution margin and fix costs of HC power plant in 2006

c)

If power plants are already built and if we want to go in operation, minimum total

welfare should cover at least investment costs. Because of the non-operating power plant has

more costs than a power plant that operate and cover at least investment costs. But let us

assume that we want to go in operation if all costs (variable costs, investment and O&M

costs) are being covered. Min imum contr ibution margins in th is case should be at least

equal or greater than fi x yearl y costs.

Thinking about the building of new power plant, we must have yearl y contr ibuti on

margin that covers investment and O&M costs. We also must consider the in terest rate.

Making a calculation using the interest rate and Net present value, we will decide to invest in

new power plant if the NPV is higher than 0.

In the year 2012 all power plants are not making any profit. Their looses (L) are:

LCCGT= 18 865 /MW

LOCGT= 21 326 /MW

LHC= 3 455 /MW

But if we decide not to operate with these three power plants in 2012, looses will be

higher because we will not be able to cover investment costs. So, if power plants are shuttled

0

10

20

30

40

50

2006 2007 2008 2009 2010 2011 2012

contribution margin and fix costs for HC



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down in 2012, they will not have any O&M or variable costs but they will have investment

costs for that year:

ICCGT= 58 018 /MW

IOCGT= 26 040 /MW

IHC= 96 159 /MW

These uncovered investment costs are higher than costs that we have during the

operation, so we think it is better for these three power plants to operate during 2012.

Exercise 3.2: Investment model

Scenario analyses of minimal system costs

a)

This part of exercise has been done in the GAMS-code. The result is given in the folder below.

* suggestion: copy this file on the computer and then open it using WordPad orNotePad.

Exercise3_part_a.lst

Solution a). File that constrain solution 3.2.a (Solution and the code can be seen in this file)

b)

Optimal install ed capacity

Accordint to the base scenario, we have determined the optimal capacity of each

power plant. The results are given in the file below.

Exercise_3_b.lst

Ex_3_b_.gms

Solution b). Files that constrain solution 3.2.b

c)

Shadow price at the hour 3 is 42.500/MWhand at the hour 19 is 48.356 /MWh.

Looking at the demand, we can see that in hour 3 it was 640 MWh and in the hour 19it was 1550 MWh. During these two hours we didnt have any electrical energy from the PV


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modules. Wind power plants were producing 210 MWh (at the hour 3) and 150 MWh (at the

hour 19).

Because of the higher demand at the hour 19, we must have higher electricity

production, what means that we have to operate with the more expensive power plants to

cover whole demand during that period (production of an additional MWh determine the price

of the electrical energy (marginal cost)).

Components of this price are production costs (fuel costs, CO2costs and O&M costs).

d)

PV scenar io

Tabela 8. Output of each power plant in 12th hour [MWh]

Output of each power plant [MWh] in 12th

hour

Power plant for PV = 0.2 for PV = 0.4 for PV = 0.6 for PV = 0.8 for PV = 1

HC 600 600 600 480 320

CCGT 360 200 40 0 0

OCGT 0 0 0 0 0

PV 160 320 480 650 800

Wind 100 100 100 100 100

Picture 11. Output of each power plant in 12th hour [MWh]

Increasing the power of PV modules, less amount of energy produced by HC, CCGT

and OCGT is needed. This also effects at the price of electrical energy. As the price of an

additional MWh determines the price of electrical energy, we can conclude that increasing the

PV power, price of electrical energy will be crashed. For example in the case with PV = 0,2

0

100

200

300

400

500

600

700

800

900

PV = 0,2 GW PV = 0,4 GW PV = 0,6 GW PV = 0,8 GW PV = 1 GW

Outpu

tofeachpowerplant[MWh]

Output of each power plant in hour 12

HC

CCGT

OCGT

PV

Wind


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GW, price was determinate by CCGT power plant (because this power plant is the most

expensive operating power plant in this hour). Increasing PV power (case with PV = 1 GW),

CCGT power plant does not operate any more, so the most expensive power plant in this case

is HC power plant which determines the price of electrical energy (energy is now cheaper

than in case with PV = 0,2 GW).

CO2scenar io

Table 9. Price of electrical energy in a specific hour according to the different CO2 price

hour

CO2_p=

0 /tCO2

CO2= 5

/tCO2

CO2= 10

/tCO2

CO2= 15

/tCO2

CO2= 20

/tCO2

CO2= 25

/tCO2

CO2= 30

/tCO2

6 25 29,375 33,75 38,125 42,5 46,875 51,25

12 42,373 44,068 45,763 47,458 49,153 50,847 52,542

19 62,5 65 67,5 70 72,5 75 77,5

Picture 12. Price of electrical energy in a specific hout according to the different CO2 costs

Increasing CO2price, short run marginal costs are also being increased. This effect on

marginal costs (they are getting higher), i.e. it effects on the price of electrical energy (it is

also getting higher).

0

10

20

30

40

50

60

70

80

90

Priceofelectricalenergyinaspecifichour

/MWh

Marginal costs of electrical energy in a specific hour

hour 6

hour 12

hour 19

Investment in Electricity Markets – a Market and Model Perspective

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