Richard GreenIain StaffellThe economics of energy markets, Toulouse, January 2013

How large should a portfolio of wind farms be?

© Imperial College Business School1

The issue

• The output from wind farms is risky• Hour-to-hour and year-to-year variation

• Correlations generally fall with distance• A portfolio should be better than a single wind farm• System operators worry about hour-to-hour variation

• Doherty et al (IEEE Trans. Power Systems, 2006) • Roques et al (Energy Policy, 2010)• Rombauts et al (Renewable Energy, 2011)

• Investors may have longer time horizons

Our approach

• Calculate annual profitability and risk for wind stations• Model hourly prices and outputs using 18 years of wind

and demand data• Merit order stack for price-setting• Capacity based on near-term forecasts• Plant costs from five recent studies (UK×3, EIA, IEA)• Constant fuel prices from UK government predictions • Demand level normalised (before weather) across years• Wind output estimated from BADC wind speed data, given

11 GW of onshore and 19 GW of offshore plant

Generators

Capacity (GW) Marginal Cost (£/MWh)Wind (onshore) 11.0 0.00Wind (offshore) 19.0 0.00Nuclear 6.0 5.00Coal (new) 0.0 42.02Coal (old) 11.5 53.25CCGT (new) 15.8 60.03CCGT (2000s) 8.0 66.82CCGT (1990s) 7.0 72.28Oil 0.0 120.49OCGT 1.0 167.73

Wind farms around the UK

Wind resource mapSource: GL Garrad Hassan

Wind turbine power curve

00.10.20.30.40.50.60.70.80.9

1

0 5 10 15 20 25

Wind speed (metres per second)

Output relative to capacity

Wind Output - Probability distribution

0

5

10

15

20

25

30

1 4 7 10 13 16 19 22

GW

Hour

Maximum90th percentile75th percentileMedian25th percentile10th percentileMinimum

30 GW of capacity in January

Source: Green and Vasilakos (2009)

Wind Output - Probability distribution

0

5

10

15

20

25

30

1 4 7 10 13 16 19 22

GW

Hour

Maximum90th percentile75th percentileMedian25th percentile10th percentileMinimum

30 GW of capacity in July

Source: Green and Vasilakos (2009)

Correcting wind speeds – annual average

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

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

Actualoutput

Initialsimulation

Hours

Correcting wind speeds – Spring

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

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

Actualoutput

Initialsimulation

Hours

Correcting wind speeds – Summer

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

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

Actualoutput

Initialsimulation

Hours

Correcting wind speeds – Autumn

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

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

Actualoutput

Initialsimulation

Hours

Correcting wind speeds – Winter

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

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

Actualoutput

Initialsimulation

Hours

Validation: monthly load factors

0%

10%

20%

30%

40%

50%

60%

70%

80%

2003 2004 2005 2006 2007 2008 2009 2010 2011

65-95%

35-65%

5-35%

Max

Mean

Min

Simulated:

Actual:

Actual load factors from Elexon and Ofgem ROC Register

Mean and Standard Deviation of Annual Outputs

0

50

100

150

200

250

300

0 1 000 2 000 3 000 4 000 5 000

Standard deviation of annual outputs (full-load hours/year)

Mean annual output (full-load hours/year)

Calculating profits

• Revenues come from prices equal to the marginal cost of thermal plant plus Renewables Obligation Certificates worth £50/MWh

• Annual cost assumed to be £208 per kW• Mostly capital costs; also fixed O&M costs

• Mean (super-normal) profit is £38/kW-year• Standard deviation (across the years for one station) has

a mean of £22/kW-year

Wind output and market prices

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30

£/MWh

Wind Output (GW)

Correlation coefficient = -0.17

Risk and return from portfolios of wind farms

05

1015202530354045

-30 0 30 60 90 120 150 180 210 240 270 300

Standard deviation of annual profits (£/kW-year)

Mean annual profits (£/kW-year)

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Optimal portfolios of wind farms

Mean Profit (£/kW-year)

Standard deviation

(£/kW-year)

291 43215 26139 19

93 1562 1340 13

-13 12

Measuring the efficiency of a portfolio

05

1015202530354045

-30 0 30 60 90 120 150 180 210 240 270 300

A

B

C

Standard deviation of annual profits (£/kW-year)

Mean annual profits (£/kW-year)

Is output efficiency informative?

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,4 0,5 0,6 0,7 0,8 0,9 1,0

Efficiency measured in terms of annual output

Efficiency measured in terms of annual profits

Conclusions

• Year-on-year changes in weather lead to economically important variations in wind farm profits

• A relatively small portfolio can dampen these• Studying the mean-variance properties of a portfolio’s

output will not tell you much about its profits

Extensions

• Study portfolios of on- and off-shore wind farms• Weed out unprofitable farms from the model• Consider a more sophisticated price-setting process

Comparison of pricing models

0

20

40

60

80

100 fulldispatchmodel

meritorderstack

£/MWh

Hours (1 week)

(Capacities adjusted to equilibrium levels within each model)

© Imperial College Business School