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
Recommend
More recommend
