ee w07.1 w_ 2. electricity generation _ part 4 (missing money & capacity payments)

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Energy Economics

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• theenergycollective.com– Schalk Cloete– Robert Wilson – Jeff St. John – Michael Davidson – Nathan Wilson – Severin Borenstein – Willem Post

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• Homework

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• 1. What is the main difference between Alternating Current (AC) and Direct Current (DC) transmission lines?

• 2. Why cant an AC transmission be built to connect Finland and Russia (or Poland and BeloRus)?

• 3, What is the frequency of the electricity grid in Europe, what in the USA and what in Japan?

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Table 1 Fixed cost per MWh Variable cost per MWh

Baseload 40 0 Midload 20 30 Peaker 10 50

4. The (levelized) fixed and variable costs of 3 types of plants are given in Table 1 above. In the system, the maximum price is capped by Pcap = 1050, and we assume perfect competition.

a) Determine the ranges of duration (in %) that will be used for the 3 types in an optimal investment and dispatch. (first draw a figure with the total (levelized) costs of the 3 types as a function of duration. As a hint, use the figure below from the lecture and make the modifications for the case when investment can also be done in Midload generators).

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Table 1 Fixed cost per MWh Variable cost per MWh

Baseload 40 0 Midload 20 30 Peaker 10 50

4. The (levelized) fixed and variable costs of 3 types of plants are given in Table 1 above. In the system, the maximum price is capped by Pcap = 1050, and we assume perfect competition.

b) assume that the daily load curve is as given in Figure 2. The maximal price in the system is set at Pcap = 1050. How much capacity (in MW) would be invested of each of the 3 types of generation in the case of optimal investment and dispatch?

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DURATION (%)100500

1

2

3

Daily Demand in MW

Daily Load Curve LC:Duration[y] = Pr[Demand > y]D=3-2* Duration

  Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Midload 20 40Peaker 10 50

8

0

60

40

Duration

Baseload

Peaker

100%66%

10

(=8760 hours/year)0%

Cost/MWh

Use baseload when capacity factor > 66%

Use peakers when capacity factor <50%

  Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Midload 20 30Peaker 10 50

50%

Midload

Use Midload when 50%< capacity factor < 66%

Demand Response

1%

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Table 1 Fixed cost per MWh Variable cost per MWh

Baseload 40 0 Midload 20 30 Peaker 10 50

4. The (levelized) fixed and variable costs of 3 types of plants are given in Table 1 above. In the system, the maximum price is capped by Pcap = 1050, and we assume perfect competition.

c) What is the duration of shortage? (the percentage of time that supply will be lower than demand)

d) Show that the average price per MWh for a consumer is now

E41.8/MWh.

e) The regulator is very unhappy about any shortage. What would you recommend him to do?

E40.1/MWh

10DURATION (%)

10050

1

2

3

Daily Demand in MW

Daily Load Curve LC:Duration[y] = Pr[Demand > y]

D=3-2* Duration

672

2.98

1.67

baseload

Midload

Peaker

Shortage

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Table 1 Fixed cost per

MWh Variable cost per

MWh Baseload 40 0 Midload 20 30 Peaker 10 50

5. The generation types are the same as in question 1. Also the demand-duration curve is the same. The regulator now has– secretly – written a contract for extra backup capacity in the amount of 0.4 MW with a foreign generator. The regulator uses this capacity only when there is a shortage. It allows the regulator to avoid the shortage and also to keep the electricity price at 50 (the marginal cost of the Peaker).

a) Once the contract has stopped being a secret, how will Peaker generator investors react? What is now the equilibrium number of MW invested in Peaker generator capacity?

b) What if the regulator would follow the procedure of NordPool: when there is a

shortage, the regulator uses the backup capacity to avoid blackouts, but it sets the electricity price at the cap (E1050/MWh). How would Peaker generator investors react? What is now the equilibrium number of MW invested in Peaker generator capacity?

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Table 1 Fixed cost per

MWh Variable cost per

MWh Baseload 40 0 Midload 20 30 Peaker 10 50

c) The regulator now decides to make a Capacity Payment (CP) to all generation

of E5/MWh. The costs of the capacity payment will be added to the electricity bill of consumers. What will be the duration of the different types of generation? What is the duration of the shortage?

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0

60

35

Duration

Baseload

Peaker

100%66%

5

(=8760 hours/year)0%

Cost/MWh

Use baseload when capacity factor > 66%

Use peakers when capacity factor <50%

  Fixed cost per MWh(Net of capacity payments)

Variable cost per MWh

Baseload 35 0Midload 15 30Peaker 5 50

50%

Midload

Use Midload when 50%< capacity factor < 66%

Demand Response

0.5%

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Table 1 Fixed cost per

MWh Variable cost per

MWh Baseload 40 0 Midload 20 30 Peaker 10 50

c) The regulator now decides to make a Capacity Payment (CP) to all generation

of E5/MWh. The costs of the capacity payment will be added to the electricity bill of consumers. What will be the duration of the different types of generation? What is the duration of the shortage?

d) Show that the average price for consumers (including the capacity payment) is still equal to 41.8.

E40.1/MWh

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Table 1 Fixed cost per

MWh Variable cost per

MWh Baseload 40 0 Midload 20 30 Peaker 10 50

e) The regulator now decides – to save money – to follow the Spanish example

and make the Capacity Payment (CP) of E5/MWh only to Peakers. Show that Midload will now leave the market.

f) What will be the duration of the different types of generation? g) What is the duration of the shortage? Show that the average price is now

43.49/ MWh. Why has the system become more expensive?

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0

60

40

Duration

Baseload

Peaker

100%67%

5

(=8760 hours/year)0%

Cost/MWh

Use baseload when capacity factor > 66%

Use peakers when capacity factor <50%

  Fixed cost per MWh(Net of capacity payments)

Variable cost per MWh

Baseload 40 0Midload 20 30Peaker 5 50

75%

Midload

Use Midload when 50%< capacity factor < 66%

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17

• Previous lecture

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• Is the “energy-only” model valid?

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•Source: ERU•Jiří Krejsa

•Yearly Load-Duration Curve:•Duration[y] = Pr[Demand > y]

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Installed power capacity 2011 (MW)Steam 10787,5 53,27%Nuclear 3970 19,60%PV 1971 9,73%Pumped-storage 1146,5 5,66%Hydro 1054,6 5,21%Gas 1101,7 5,44%Wind 218,9 1,08%Total 20250,2 100,00%

Source: ERU Jiří Krejsa

About 2x more capacity than peak demand!!!

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• Remains of the good old times of electricity being run as state-owned Vertically Integrated Utilities (VIUs) (up to 2000)– Civil engineers “gold-plate” the system: excess generation

reserves for “just-in-case” disregarding the costs– Prices calculated as average costs + an uplift for capital

expenses• 1990-2000: Onset of liberalization, privatization and

competition – Prices are marginal prices– Due to the excess capacity they are relatively low– Thus: no investment in new capacity

• Now: “sweating” the assets

• Source: Helm, D. 2005. The assessment: the new energy paradigm. Oxford review of economic policy, vol. 21, no. 1

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• This lecture

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Missing Money & Capacity Payments

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24

0

60

40

Capacity factor

Baseload

Peaker

100%60%

10

(=8760 hours/year)

Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

0%

Cost/MWh

Use baseload when capacity factor > 60%

Use peakers when capacity factor < 60%

-8

-8

Capacity payment of $8 per MWh for all producers

Technology Costs Table

25

25

0

60

40

Capacity factor

Baseload

Peaker

100%60%

10

(=8760 hours/year)

Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

0%

Cost/MWh

Use baseload when capacity factor > 60%

Use peakers when capacity factor < 60%

-8

-8

Capacity payment of $8 per MWh for all producers

Technology Costs Table

26

26

0

60

32 Baseload

Peaker

100%60%

2

Fixed cost per MWh

Variable cost per MWh

Baseload 32 0Peaker 2 50

0%

Cost/MWh

Use baseload when capacity factor > 60%

Use peakers when capacity factor < 60%

Capacity payment of $8 per MWh for all producers

Technology Costs Table

Capacity factor(=8760 hours/year)

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P=0

S50

0

0 1.81 32

P P=50Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 5040%

58%

PCAP=5502%

πPEAKER= 0 πPEAKER= 0 πPEAKER=0.02 * 500= 10

Capacity payment of $8 per MWh for all producers

Total πPEAKER=8+10=18

Zero-profit condition

Supply & demand curve Technology Costs TableDMAXDMIN

28

28

P=0

S50

0

0 1.81 32

P P=50Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 5040%

59.6%

PCAP=5500.4%

πPEAKER= 0 πPEAKER= 0 πPEAKER=0.004 * 500= 2

Capacity payment of $8 per MWh for all producers

Total πPEAKER= 8 + 2 = 10

Zero-profit condition

Supply & demand curve Technology Costs TableDMAXDMIN

29

29

S50

0

0 1.81 32

P P=50Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

59.6%

PCAP=5500.4%

Total πPEAKER=8+2=10πPEAKER= 0 πPEAKER= 0 πPEAKER=0.004 * 50= 2

Capacity payment of $8 per MWh for all producers

P¯=P¯=8* (0.996) + 0.4* 0 + 0.59.6* 50 + 0.004* 550P¯=8* (0.996) + 0.4* 0 + 0.59.6* 50 + 0.004* 550

=8 + 0 + 29.8 + 2.2 = 40

Zero-profit condition

Supply & demand curve Technology Costs TableDMAX

P=040%

DMIN

30

30

0

60

40

Capacity factor

Baseload

Peaker

100%60%

10

(=8760 hours/year)

Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

0%

Cost/MWh

Use baseload when capacity factor > 60%

Use peakers when capacity factor < 60%

-8

Capacity payment of $8 per MWh only for Peakers

Technology Costs Table

31

31

0

60

Capacity factor

Baseload

Peaker

100%76%

2

(=8760 hours/year)

Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 2 50

0%

Cost/MWh

Use baseload when capacity factor > 76%

Use peakers when capacity factor < 76%

Capacity payment of $8 per MWh only for Peakers

Technology Costs Table

60%

40

32

32

Use baseload when capacity factor > 76%

Use peakers when capacity factor < 76%

0

60

40

Capacity factor

Baseload

Peaker

100%76%

10

DURATION (%)100500

1

2

3

BASELOAD

D=3-2* Duration

1.48

PEAKER

Daily Demand in MW

60

Daily Load-Duration Curve:Duration[y] = Pr[Demand > y]

Screening curve(Capacity-cost based)

76

33

33

P=550

DURATION (%)100500

1

2

3

BASELOAD

D=3-2* Duration

1.48

PEAKER

Daily Demand in MW

60

Daily Load-Duration Curve:Duration[y] = Pr[Demand > y]

76

Supply & demand curve

Uniformly distributed

50

0

0 1.481 32

P

P=0

P=50

24%

76%-x%Supply & demand curve

DMAXDMIN

X%

34

34

P=0

S50

0

0 3

P P=50Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

76-x

P=550X=0.4%

Total πPEAKER=πPEAKER= 0 πPEAKER= 0 πPEAKER=x * 500= 2

2 0.004500

x

Capacity payment of $8 per MWh only for Peakers

Total πPEAKER= 8+0+0+2=10

Zero-profit condition

Supply & demand curve Technology Costs TableDMAX

24%

DMIN

1.481

35

35

P=0

S50

0

0 3

P P=50Fixed cost per MWh

Variable cost per MWh

Baseload 40 0Peaker 10 50

76-x

P=550X=0.4%

P=0.24 * 0= 0

P=0.756* 50=37.8

P=0.004* 550= 2.2

P=0.76* 8= 6.08

Capacity payment of $8 per MWh only for Peakers

P=6.08 +37.8+2.2=46.08>40!Zero-profit condition

Supply & demand curve Technology Costs TableDMAX

24%

DMIN

1.481

36

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• Capacity payments:- Is a subsidy that allows the system to

- Lowers the price spikes and the duration of spikes

- Can distort generation technique choice if capacity payments are not equal for all techniques - Example: Spain

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Electricity generation and climate change

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40

41

42

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Renewables EfficiencyCarbon emissions

EU’s 20-20-20 strategy for 2020

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• 20-20-20 strategya) 20 reduction of CO2b) 20% increase in efficiencyc) 20% renewables

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b) 20% increase in efficiency

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• What is the effect of an increase in efficiency on fuel demand?– Substitution effect– Income effect

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Other consumption goods

Car Usage

Effect of a fall in the price of car fuel (here a normal good)

5 2010

Substitution effect

Income effect

Total effect

Fuel=12

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Other consumption goods

Car Usage

If car useage were an inferior good (it is not!), the income effect could undo a part of the substitution effect

5 2010

Substitution effect

Income effect

Total effect

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• Both substitution and income effect contribute to an increase in demand

• What can be done?• Price must increase too.

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Other consumption goods

Car Usage

Increase in price makes consumers use less.

Both income and substitution effect lower care useage

5 209

Income effect

Substitution effect

Total effect

Fuel=12

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Other consumption goods

Car Useage

Effect of a fall in the price of car fuel (here a normal good)

5 2010

Substitution effect

Income effect

Total effect

Fuel=12

PPizza=10

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c) 20% renewables

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Wind turbines

Solar panels

Renewable energies

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• Do subsidized renewables lower the price of electricity?

• Price versus charge

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10

50

P=10 P=50

DLDH

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50

prob DL DH

50% 50%10% 10 50

1 200

56

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50

prob DL DH

50% 50%10% 10 50

50% 10 50% 50 30P

10

50 DL

DH

P=10 P=50

Average electricity price

50% ( ) 50% ( )L HQR P MC P MC

50% 50%L HP P P

50% (0) 50% (40) 20QR

57

10

50

P=10 P=50

Wind outputUnits Probability

2 10%1 20%0 70%

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

DLDH

1 200

Heavily subsidize to get 30% electricity from wind

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P=10 P=50

10

50

0

P=0 P=0

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

DLDH

1 20

Wind outputUnits Probability

2 10%1 20%0 70%

59

P=10 P=50

10

50

0

P=0 P=10

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

DLDH

1 20

Wind outputUnits Probability

2 10%1 20%0 70%

60

P=10 P=50

10

50

0

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

DLDH

1 20

Wind outputUnits Probability

2 10%1 20%0 70%

61

Wind availability

prob DL DH

50% 50%2 10% 0 01 20% 0 100 70% 10 50

( ) 70% 10 20% 0 10% 0 7LP D

( ) 70% 50 20% 10 10% 0 37HP D

50% 7 50% 37 22P 0

Average electricity price

10

50

P=10 P=50

70%

DL

DH

10

50

P=0 P=10

20%

DL

DH

10

50

0

P=0 P=0

10%

DL

DH

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

Electricity price

62

Wind availability

prob DL DH

50% 50%2 10% 0 01 20% 0 100 70% 10 50

20% 50% (10 0)QR

10

Average earnings of Wind

10

50

P=10 P=50

70%

DL

DH

10

50

P=0 P=10

20%

DL

DH

10

50

0

P=0 P=0

10%

DL

DH

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

Electricity price

63

50% 7 50% 37 22P Average electricity price

23.5 1 22.5 1550% 1 50% 2 1.5

Uplift on electricity price

22 15 37

Average electricity charge

23% increase in charges for consumers!

10

50

P=10 P=50

70%

DL

DH

10

50

P=0 P=10

20%

DL

DH

10

50

0

P=0 P=0

10%

DL

DH

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 23.5 0

Average charge without wind: 30

64

Units Fixed cost

Variable cost

Baseload 1 20 10Peaker 1 0 50Wind 2 22.5 0

70% 50% (50 10)QR

70% 20 14 0

10

50

P=10 P=50

70%

DL

DH

10

50

P=0 P=10

20%

DL

DH

10

50

0

P=0 P=0

10%

DL

DH

Average Baseload earning (QR)

Wind availability

prob DL DH

50% 50%2 10% 0 01 20% 0 100 70% 10 50

Electricity price