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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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Example: Midwest ISO expanding must estimate “backup” capacity for wind power

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0.69 GW

Historical data for total wind power in Midwest ISO

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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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LDT is a better model of the tails than Central Limit Theorem (Normal)

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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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Long-Term Variability Example: Financing a new wind farm

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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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Group wind sites based on correlation of annual energy generation

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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)