Statistical Analysis of the Effects of Geographic Diversity on Wind - PowerPoint PPT Presentation

Statistical Analysis of the Effects of Geographic Diversity on Wind Plant Integration Professor Henry Louie Seattle University Energy and the Environment Seminar University of Washington November 5, 2009

Outline • Motivation • Geographic Diversity • Methodology • Case Studies • Conclusions 2 Dr. Louie

Motivation • Wind generation in US: >25,000 MW • Research interest increases: 3450 articles in IEEE Xplore database as of Sept. 2009 • Federal Production Tax Credit (PTC) renewed • State Renewable Portfolio Standards (RPS)  30 states  WA: 15% by 2020 3 Dr. Louie

Motivation • What are the operational consequences of high levels of wind power penetration? • Must understand the wind resource as characterized by  Uncertainty: inability to perfectly forecast weather  Variability: changing of the wind resource across operational time scales 4 Dr. Louie

Motivation • Uncertainty and variability are influenced by  Penetration level  Geographic diversity  Transmission constraints 5 Dr. Louie

Geographic Diversity • Types of geographic diversity  Spatial  Topographical 6 Dr. Louie

Geographic Diversity • Wind plants in close proximity in homogeneous terrain likely exhibit strong correlation in their power output 7 Dr. Louie

Geographic Diversity 1 0.8 Power (%) 0.6 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 1 1 Time (hr) 0.8 0.8 Power (%) 0.6 Power (%) 0.6 0.4 0.4 0.2 0.2 0 0 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Time (hr) Time (hr) system 8 Dr. Louie

Geographic Diversity • As distance increases, the linear correlation between the power output decreases system large distance 9 Dr. Louie

Geographic Diversity 1 0.8 Power (%) 0.6 1 0.4 0.8 0.2 Power (%) 0.6 0 1 2 4 6 8 10 12 14 16 18 20 22 24 0.4 Time (hr) 0.8 0.2 0 Power (%) 0.6 2 4 6 8 10 12 14 16 18 20 22 24 Time (hr) 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 Time (hr) system large distance 10 Dr. Louie

Geographic Diversity Increasing Operational Timescale Source:B . Ernst, Y. Wan, and B. Kirby, “Short -term power fluctuation of wind turbines: Analyzing data from the German 250- MW measurement program from the ancillary services viewpoint,” Tech. Rep. NREL/CP- 500-26722, Jul. 1999. 11 Dr. Louie

Geographic Diversity • Terrain influences geographic diversity • Examples  Shore lines: sea breezes caused by land/water temperature differentials  Mountain valleys or gorges: flow channeling  Mountain tops/down slope: mountain wave events (Chinook winds) 12

Geographic Diversity 1 0.8 Power (%) 0.6 1 0.4 0.9 0.8 0.2 Power (%) 0.7 0 2 4 6 8 10 12 14 16 18 20 22 24 0.6 1 Time (hr) 0.5 0.8 0.4 Power (%) 0.6 2 4 6 8 10 12 14 16 18 20 22 24 Time (hr) 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 22 24 Time (hr) system 13 Dr. Louie

Wind Resources in the U.S. 14 Dr. Louie

Geographic Diversity: Theoretical Basis • Consider wind plant n in an N -wind plant system  • Normalized power output of wind plant P n   P g v n n n v  n : representative wind speed at the wind plant  : wind plant power curve g  n Wind Speed Distribution Power Curve 20 1 Normalized Power (%) 15 Frequency (%) 0.67 10 0.33 5 0 0 0 5 10 15 20 25 30 0 5 10 15 20 25 Wind Speed (m/s) Wind Speed (m/s) 15 Dr. Louie

Geographic Diversity: Theoretical Basis • Example distribution  1 year hourly (8760)  GE 1.5 XLS wind turbine • Contains information on uncertainty 40 N = 1 30 Frequency (%) 20 10 0 0 20 40 60 80 100 Power Output (%) 16 Dr. Louie

Geographic Diversity: Theoretical Basis • Case of no geographic diversity • If we have identical N wind plants with the assumption v  v  v    n N 1 • Histogram remains the same (after normalization) 40 N = 1 30 Frequency (%) 20 10 0 0 20 40 60 80 100 Power Output (%) 17 Dr. Louie

Geographic Diversity: Theoretical Basis • Now assume that the wind speeds at each plant are independent random variables for each hour • How does the histogram change as the number of independent wind plants are added? 18 Dr. Louie

Geographic Diversity 40 12 N = 10 30 9 Frequency (%) Density 20 6 10 3 0 0 0 20 40 60 80 100 Power Output (%) 19 Dr. Louie

Geographic Diversity: Theoretical Basis  • Since are independent will also be independent v  P n n  • Aggregate power distribution is found from: P agg    P P P  f P f f f   n N 1 N N N agg 20 Dr. Louie

Geographic Diversity: Theoretical Basis • Central Limit Theorem applies  As N => infinity 2 x  1 f x  e  2 2 2 • Variance changes as N 1 2 2 agg n N 2 n 1 21 Dr. Louie

Geographic Diversity: Theoretical Basis regulation: load-following: seconds-minutes minutes-hours sec Power (MW) min scheduling: day 4 8 12 16 20 24 Time (hr) 22 Dr. Louie

Geographic Diversity: Theoretical Basis • Variations    P h P h k P h agg agg agg  P : variation  agg  P : power output at hour h  agg  k : variation period 23 Dr. Louie

Geographic Diversity: Theoretical Basis • Consider 1-hour variation period • Empirical histogram contains information on variability • Influence of independence of wind speeds has an analogous influence on distribution of variability 40 40 N=10 N=1 30 30 Frequency (%) Frequency (%) 20 20 10 10 0 0 -75 -50 -25 0 25 50 75 -75 -50 -25 0 25 50 75 Hourly Power Variation (%) Hourly Power Variation (%) 24 Dr. Louie

Methodology • Parametric evaluation:  Examine statistical moments • Non-parametric evaluation:  Compare PDFs (empirical histograms) to known distributions 25 Dr. Louie

Methodology: Uncertainty • Observations  Bounded between 0 and 1  Diverse shapes as N increases  Asymmetric for most levels of geographic diversity 40 40 12 N = 10 N = 1 30 30 9 Frequency (%) Frequency (%) Density 20 20 6 10 10 3 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Power Output (%) Power Output (%) 26 Dr. Louie

Methodology: Uncertainty • Beta Distribution: 8 : 2 7 1 x  x  6 1 : .05 1  f x 5 Density B , 4 3 1 2 1 B , x  x  dx  1 1 1 0 0 20 40 60 80 100 0 Power (%) 8 1.6 : 2 : 0.5 7 1.4 : 2 6 1.2 : 2 5 1 Density Density 4 0.8 3 0.6 2 0.4 1 0.2 0 0 0 20 40 60 80 100 0 20 40 60 80 100 Power (%) Power (%) 27 Dr. Louie

Methodology: Uncertainty • Qualitative interpretation of parameters: < 1 increasing density toward 0  > 1 decreasing density toward 0  < 1 increasing density toward 1  > 1 decreasing density toward 1  • Convenient calculation of capacity factor agg 28 Dr. Louie

Methodology: Uncertainty 40 : 0.27 12 N = 1 : 0.46 30 agg : 0.13 9 Frequency (%) Density 20 6 10 3 0 0 0 20 40 60 80 100 Power Output (%) 29 Dr. Louie

Methodology: Uncertainty 40 12 N = 10 : 5.38 : 10.75 30 9 agg : 0.013 Frequency (%) Density 20 6 10 3 0 0 0 20 40 60 80 100 Power Output (%) 30 Dr. Louie

Methodology: Variability • Laplace (double exponential) distribution:  x a 1 f x  e b b 2 • Statistical moments of observation interpretation  Variance: spread of values  Skewness ( 1 ): asymmetry • Positive: large increases in power • Negative: large decreases in power  Kurtosis ( 2 ): peakedness, thickness of tails • >3, leptokurtic — greater peak, thicker tails than Normal distribution 31 Dr. Louie

Methodology: Variability • Variance: 0.0128 • Skewness ( 1 ): -0.112 • Kurtosis ( 2 ): 5.64 40 15 N=1 30 Frequency (%) 10 Density 20 5 10 0 0 -50 -25 0 25 50 Hourly Power Change (% Total Capacity) 32 Dr. Louie

Case Studies • How does the statistical signatures of uncertainty and variability change with penetration? • How would long-distance transmission affect the uncertainty and variability? 33 Dr. Louie

Case Studies: Approach • Consider two distant systems with rapid capacity additions over a two year period • Perform year-to-year comparisons • Consider a hypothetical connection between the two systems 34 Dr. Louie

Case Studies: Data Considerations • Published data from:  Bonneville Power Administration (BPA)  Electric Reliability Council of Texas (ERCOT) • Data Range:  January 1, 2007 to December 31, 2008*  Hourly granularity • Limitations of data  Curtailment not reported  Transmission constraints  Wind turbine outages  Losses 35 Dr. Louie

Case Study: BPA • Capacity increased by 220 percent  722 MW to 1599 MW • 15 wind plants 2000 2007 2008 1500 Power (MW) 1000 500 0 Jan. Apr. Jul. Oct. Jan. Apr. Jul. Oct. Jan. Month 36 Dr. Louie

200 km 37 Dr. Louie