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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

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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

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Outline

  • Motivation
  • Geographic Diversity
  • Methodology
  • Case Studies
  • Conclusions

2

  • Dr. Louie
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SLIDE 3

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
  • Dr. Louie

3

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SLIDE 4

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
  • perational time scales
  • Dr. Louie

4

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SLIDE 5

Motivation

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

5

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SLIDE 6

Geographic Diversity

  • Types of geographic diversity
  • Spatial
  • Topographical
  • Dr. Louie

6

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SLIDE 7

Geographic Diversity

  • Wind plants in close proximity in homogeneous

terrain likely exhibit strong correlation in their power output

  • Dr. Louie

7

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SLIDE 8

Geographic Diversity

  • Dr. Louie

8

system

2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%)

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Geographic Diversity

  • As distance increases, the linear correlation

between the power output decreases

  • Dr. Louie

9

system

large distance

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SLIDE 10

Geographic Diversity

  • Dr. Louie

10

system

large distance

2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%)

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SLIDE 11

Geographic Diversity

  • Dr. Louie

11 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.

Increasing Operational Timescale

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SLIDE 12

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

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Geographic Diversity

  • Dr. Louie

13

system

2 4 6 8 10 12 14 16 18 20 22 24 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%) 2 4 6 8 10 12 14 16 18 20 22 24 0.2 0.4 0.6 0.8 1 Time (hr) Power (%)

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SLIDE 14

Wind Resources in the U.S.

  • Dr. Louie

14

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SLIDE 15

Geographic Diversity: Theoretical Basis

  • Consider wind plant n in an N-wind plant system
  • Normalized power output of wind plant
  • : representative wind speed at the wind plant
  • : wind plant power curve
  • Dr. Louie

15

 

n n n

P g v

n v

n

g 

n

P

5 10 15 20 25 0.33 0.67 1 Normalized Power (%) Wind Speed (m/s) Power Curve 5 10 15 20 25 30 5 10 15 20 Frequency (%) Wind Speed (m/s) Wind Speed Distribution

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20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%)

N = 1

Geographic Diversity: Theoretical Basis

  • Example distribution
  • 1 year hourly (8760)
  • GE 1.5 XLS wind turbine
  • Contains information on uncertainty
  • Dr. Louie

16

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20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%)

N = 1

Geographic Diversity: Theoretical Basis

  • Case of no geographic diversity
  • If we have identical N wind plants with the

assumption

  • Histogram remains the same (after normalization)
  • Dr. Louie

17

1

    

n N

v v v

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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?

  • Dr. Louie

18

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SLIDE 19

Geographic Diversity

  • Dr. Louie

19

20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%) Density

3 6 9 12 N = 10

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SLIDE 20

Geographic Diversity: Theoretical Basis

  • Since are independent will also be independent
  • Aggregate power distribution is found from:
  • Dr. Louie

20

1 agg

     

n N

P P P f P f f f N N N

n

v 

n

P 

agg

P 

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Geographic Diversity: Theoretical Basis

  • Central Limit Theorem applies
  • As N => infinity
  • Variance changes as
  • Dr. Louie

21

2 2

2

1 2

x

f x e

 

2 2 2 1

1

agg N n n

N

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Geographic Diversity: Theoretical Basis

  • Dr. Louie

22

4 8 12 16 20 24 scheduling: day Power (MW) regulation: seconds-minutes

sec

load-following: minutes-hours

min

Time (hr)

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Geographic Diversity: Theoretical Basis

  • Variations
  • : variation
  • : power output at hour h
  • k: variation period
  • Dr. Louie

23

agg agg agg

P h P h k P h   

agg

P 

agg

P 

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SLIDE 24

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

  • Dr. Louie

24

  • 75
  • 50
  • 25

25 50 75 10 20 30 40 Frequency (%) N=1 Hourly Power Variation (%)

  • 75
  • 50
  • 25

25 50 75 10 20 30 40 Frequency (%) N=10 Hourly Power Variation (%)

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Methodology

  • Parametric evaluation:
  • Examine statistical moments
  • Non-parametric evaluation:
  • Compare PDFs (empirical histograms) to known

distributions

  • Dr. Louie

25

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Methodology: Uncertainty

  • Observations
  • Bounded between 0 and 1
  • Diverse shapes as N increases
  • Asymmetric for most levels of geographic diversity
  • Dr. Louie

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20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%)

N = 1

20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%) Density

3 6 9 12 N = 10

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SLIDE 27

20 40 60 80 100 1 2 3 4 5 6 7 8 Power (%) Density

Methodology: Uncertainty

  • Beta Distribution:
  • Dr. Louie

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1 1 1 1 1

1 1 , , x x f x B B x x dx      

20 40 60 80 100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Power (%) Density

: 0.5 : 2 : 2 : 2

20 40 60 80 100 1 2 3 4 5 6 7 8 Power (%) Density

: 2 : .05

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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
  • Dr. Louie

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agg

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20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%) Density

3 6 9 12 N = 1

Methodology: Uncertainty

  • Dr. Louie

29

: 0.27 : 0.46

agg: 0.13

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SLIDE 30

Methodology: Uncertainty

  • Dr. Louie

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20 40 60 80 100 10 20 30 40 Frequency (%) Power Output (%) Density

3 6 9 12 N = 10

: 5.38 : 10.75

agg: 0.013

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SLIDE 31

Methodology: Variability

  • Laplace (double exponential) distribution:
  • 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

  • Dr. Louie

31

1 2

x a b

f x e b

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Methodology: Variability

  • Variance: 0.0128
  • Skewness ( 1): -0.112
  • Kurtosis ( 2): 5.64
  • Dr. Louie

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  • 50
  • 25

25 50 10 20 30 40 Frequency (%) 5 10 15 Hourly Power Change (% Total Capacity) Density N=1

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Case Studies

  • How does the statistical signatures of uncertainty

and variability change with penetration?

  • How would long-distance transmission affect the

uncertainty and variability?

  • Dr. Louie

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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

  • Dr. Louie

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SLIDE 35

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
  • Dr. Louie

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Case Study: BPA

  • Capacity increased by 220 percent
  • 722 MW to 1599 MW
  • 15 wind plants
  • Dr. Louie

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Jan. Apr. Jul. Oct. Jan. Apr. Jul. Oct. Jan. 500 1000 1500 2000 Power (MW)

Month

2007 2008

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SLIDE 37
  • Dr. Louie

37

200 km

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20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 BPA 2007 Power Output (% Total Capacity)

Density

Case Study: BPA

  • Year-to-year comparison of uncertainty
  • Similar distributions
  • Variance increased in 2008
  • Dr. Louie

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: 0.47 : 1.13

20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 Power Output (% Total Capacity) BPA 2008

Density

: 0.51 : 1.09

agg: 0.084 agg: 0.088

BPA 2008 BPA 2007

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Case Study: BPA

  • Year-to-year comparison of variations
  • 1-hour variation period
  • Dr. Louie

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  • 50
  • 25

25 50 10 20 30 40 50 Hourly Power Change (% Total Capacity) Frequency (%)

2007 2008

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Case Study: BPA

  • Statistical moments of the 1-hour variations
  • Skewness ( 1):
  • Positive in 2007, 2008
  • Increased in 2008
  • Kurtosis ( 2):
  • Leptokurtic in 2007, 2008
  • Increase in 2008
  • Dr. Louie

40

Case

agg agg agg agg

BPA 2007 0.0000203 0.0030 0.514 6.85 BPA 2008

  • 0.0000191

0.0032 0.638 8.19

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Case Study: ERCOT

  • Capacity increased by 290 percent
  • 2790 MW to 8111 MW
  • Approx. 50 wind plants

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Jan Apr Jul Oct Jan Apr Jul Oct Jan 2000 4000 6000 8000 10000 capacity (MW) Jan Apr Jul Oct Jan Apr Jul Oct Jan 2000 4000 6000 8000 10000 capacity (MW) 2008 2007 2009

PTC Deadline

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Case Studies: ERCOT

  • Dr. Louie

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200 km

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Case Study: ERCOT

  • Year-to-year comparison
  • Similar distributions
  • Variance unchanged
  • Dr. Louie

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20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 ERCOT 2007

Density

Power Output (% Total Capacity) 20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 ERCOT 2008

Density

Power Output (% Total Capacity)

: 0.81 : 2.42 : 0.96 : 2.38

agg: 0.043 agg: 0.043

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Case Study: ERCOT

  • Year-to-year comparison of variations
  • 1-hour variation period
  • Dr. Louie

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  • 50
  • 25

25 50 10 20 30 40 50 Frequency (%) Hourly Power Change (% Total Capacity)

2007 2008

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Case Study: ERCOT

  • Statistical moments of the 1-hour variations
  • Skewness ( 1):
  • Positive in 2007, 2008
  • Increased in 2008
  • Kurtosis ( 2):
  • Leptokurtic in 2007, 2008
  • Decrease in 2008
  • Dr. Louie

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Case

agg agg agg agg

ERCOT 2007 0.0000028 0.0027 0.095 6.59 ERCOT 2008 0.0000168 0.0031 0.224 5.91

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Case Study: Interconnected System

  • Hypothetical connection of BPA and ERCOT during

the data sets

  • Approximately: 2500 km of transmission
  • Dr. Louie

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Case Study: Interconnected System

  • Significantly different from BPA or ERCOT
  • Dr. Louie

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20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 Interconnected 2008

Density

Power Output (% Total Capacity) 20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 Interconnected 2007

Density

Power Output (% Total Capacity)

: 1.20 : 3.36 : 1.40 : 3.21

agg: 0.084 agg: 0.088

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SLIDE 49
  • Dr. Louie

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20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 ERCOT 2007

Density

Power Output (% Total Capacity)

: 0.81 : 2.42

agg: 0.043

20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 Interconnected 2007

Density

Power Output (% Total Capacity)

: 1.20 : 3.36

agg: 0.084

20 40 60 80 100 5 10 15 20 25 Frequency (%) 2 4 6 8 BPA 2007 Power Output (% Total Capacity)

Density

: 0.47 : 1.13

agg: 0.084 BPA 2007

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Case Study: Interconnected System

  • Year-to-year comparison
  • Dr. Louie

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  • 50
  • 25

25 50 10 20 30 40 50 Hourly Power Change (% Total Capacity) Frequency (%)

2007 2008

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Summary of Variations

Case

agg agg agg agg

BPA 2007 0.0000203 0.0030 0.514 6.85 BPA 2008

  • 0.0000191

0.0032 0.638 8.19 ERCOT 2007 0.0000028 0.0027 0.095 6.59 ERCOT 2008 0.0000168 0.0031 0.224 5.91 Interconnected 2007 0.0000103 0.0019 0.137 6.10 Interconnected 2008 0.0000064 0.0021 0.207 5.62

  • Dr. Louie

51

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24 48 72 96 120 144 168

  • 0.1

0.1 0.2 0.3 0.4

2007

  • Corr. Coeff.

Time Shift (Hours) 24 48 72 96 120 144 168

  • 0.1

0.1 0.2 0.3 0.4 2008

  • Corr. Coeff.

Time Shift (Hours)

Case Study: Interconnected System

  • Check correlation (linear)
  • Dr. Louie

52

24 hours

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SLIDE 53

Conclusions

  • Recent, substantive increases in wind capacity

(penetration) in BPA and ERCOT did NOT significantly alter the statistical characteristics of uncertainty and variability

  • Aggregate power of ERCOT wind plants have

favorable characteristics when compared with BPA

  • Interconnection had noticeable affect on

uncertainty and variability

  • Correlation likely caused by solar influences exist

even in distant systems

  • Dr. Louie

53

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Related Research

  • Extending analysis to Midwest ISO and year 2009

data sets

  • Goodness-of-fit analysis
  • Variations across longer time scales
  • Diurnal pattern analysis
  • Benefits of geographic diversity
  • Dr. Louie

54

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Questions?

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SCIENCE AND ENGINEERING

Henry Louie, PhD

Assistant Professor Department of Electrical and Computer Engineering 901 12th Avenue, Bannan 219 P.O. Box 222000 Seattle, WA 98122-1090

www.seattleu.edu Tel: (206) 398-4619 Fax: (206) 296-5962 louieh@seattleu.edu

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