Richard Green Iain Staffell The economics of energy...
Transcript of Richard Green Iain Staffell The economics of energy...
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Richard GreenIain StaffellThe economics of energy markets, Toulouse, January 2013
How large should a portfolio of wind farms be?
© Imperial College Business School1
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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
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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
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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
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Wind farms around the UK
Wind resource mapSource: GL Garrad Hassan
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Wind turbine power curve
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Wind speed (metres per second)
Output relative to capacity
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Wind Output - Probability distribution
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30 GW of capacity in January
Source: Green and Vasilakos (2009)
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Wind Output - Probability distribution
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Source: Green and Vasilakos (2009)
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Correcting wind speeds – annual average
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Correcting wind speeds – Spring
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Correcting wind speeds – Summer
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Correcting wind speeds – Autumn
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Correcting wind speeds – Winter
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Validation: monthly load factors
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65-95%
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5-35%
Max
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Simulated:
Actual:
Actual load factors from Elexon and Ofgem ROC Register
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Mean and Standard Deviation of Annual Outputs
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Standard deviation of annual outputs (full-load hours/year)
Mean annual output (full-load hours/year)
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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
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Wind output and market prices
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Wind Output (GW)
Correlation coefficient = -0.17
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Risk and return from portfolios of wind farms
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Standard deviation of annual profits (£/kW-year)
Mean annual profits (£/kW-year)
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Optimal portfolios of wind farms
Mean Profit (£/kW-year)
Standard deviation
(£/kW-year)
291 43215 26139 19
93 1562 1340 13
-13 12
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Measuring the efficiency of a portfolio
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Standard deviation of annual profits (£/kW-year)
Mean annual profits (£/kW-year)
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Is output efficiency informative?
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Efficiency measured in terms of annual output
Efficiency measured in terms of annual profits
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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
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Extensions
• Study portfolios of on- and off-shore wind farms• Weed out unprofitable farms from the model• Consider a more sophisticated price-setting process
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Comparison of pricing models
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meritorderstack
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(Capacities adjusted to equilibrium levels within each model)
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