1. 2 1 Modeling Extreme Low-Wind-Speed Events for Large-Scale Wind Power Stephen Rose, Mark Handschy, Jay Apt June 23, 2014

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3. 2 3 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

4. 2 4 Example: Midwest ISO expanding must estimate “backup” capacity for wind power

5. 2 5 0.69 GW Historical data for total wind power in Midwest ISO

6. 2 6 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

7. 2 7 LDT is a better model of the tails than Central Limit Theorem (Normal)

8. 2 8 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

9. 2 9 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?

10. 2 10 Long-Term Variability Example: Financing a new wind farm

11. 2 11 Variability of annual energy generation affects project financing Loans sized so payments = revenue in 1 st percentile year (“P99”) –Assuming annual energy is normally-distributed Bigger loan = higher “leverage” = higher profits Combine several uncorrelated wind farms to reduce total variability

12. 2 12 Group wind sites based on correlation of annual energy generation

13. 2 13 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

14. 2 14 Administrative barriers to geographic diversity for long-term variability Bank rules against jointly-financing projects? Different legal jurisdictions (e.g. countries) Greater legal liability

15. 2 15 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)