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Modeling Extreme Low-Wind-Speed Events for Large-Scale Wind Power
Stephen Rose, Mark Handschy, Jay Apt
June 23, 2014
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Low-wind events are important for wind power
• Short (hours)– Affects planning of backup (conventional) power plants– I am modeling how probability of low-wind events changes
as new wind farms are added
• Long (months)– Affects financing and profitability of wind farms– I am modeling the benefits of financing several wind farms
together to reduce revenue uncertainty
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5 independent sites
0.69 GW firm power
6 independent sites
0.85 GW firm power
7 independent sites
0.98 GW firm power
8 independent sites
1.1 GW firm power
9 independent sites
1.2 GW firm power
Large Deviations Theory models the tails of aggregate power distribution
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Extend Large Deviations Theory for more realistic cases
• Non-i.i.d. random variables– Most wind farms are close enough to be correlated– Most wind farms don’t have identical power distributions– The Gartner-Ellis Theorem generalizes LDT
• Correlation with load– The grid operator really wants to know how much wind is
available during peak load hours
• Temporal autocorrelation– We can’t distinguish between 10 1-hour periods and 1 10-
hour period
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Several barriers to geographic diversity for short-term variability
• Economics – Wind farms cluster in areas with best wind resource– Transmission lines are expensive
• Administrative– Grid operators not allowed to consider generation outside
their area for reserve– Cross national boundaries?– Mechanism to compensate owner for collective benefits?
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Variability of annual energy generation affects project financing
• Loans sized so payments = revenue in 1st percentile year (“P99”)– Assuming annual energy is normally-distributed
• Bigger loan = higher “leverage” = higher profits
• Combine several uncorrelated wind farms to reduce total variability
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Use reanalysis data to estimate annual energy for each potential site
• Interpolates historical meteorological data using numerical weather prediction models– 1979 - today– 1-hour time resolution– 0.5º spatial resolution
• Not optimal for wind speed– Not calculated at wind turbine height– Questionable accuracy
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Administrative barriers to geographic diversity for long-term variability
• Bank rules against jointly-financing projects?• Different legal jurisdictions (e.g. countries) • Greater legal liability
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Acknowledgements
• Funding– U.S. National Science Foundation Grant 1332147– Doris Duke Charitable Foundation– R.K. Mellon Foundation– Electric Power Research Institute– Heinz Endowments– RenewElec Project at Carnegie Mellon University
• U.S. Department of Energy National Laboratories• Prof. Julie Lundquist (U. Colorado, Boulder)