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1st International Workshop on the 

Integration of Solar Power into Power 

Systems

October 24, 2011

Bri-Mathias Hodge

Marissa Hummon

Kirsten Orwig

Transmission and Grid Integration 

Group

National Renewable Energy Laboratory

Golden, Colorado USA

NREL/PR-5500-53409

Solar Ramping Distributions 

over Multiple Timescales and 

Weather Patterns

Photo from Tom Hall, NREL/PIX 06588

Photo by Warren Gretz, NREL/PIX 10926
Topics 

• Introduction

• Statistical Background

• Datasets Utilized

• Ramp Distributions by 

Timescale

• Ramp Distributions by 

Weather Pattern

• Conclusions

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Photo from Native Energy, 

Inc., NREL/PIX 17593
Renewable Energy Portfolio Standards

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Renewable Generation Integration Background

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Statistical Background

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4

4

)(

σ

ε

κ

E

=















 



 



 − =

3

σ

μ γ

X E

• Skewness – 3rd

Statistical 

Moment

• Kurtosis – 4th

Statistical 

Moment
Datasets Utilized

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Site Location ‘05 ‘06 ‘07 ‘08 ‘09 ‘10

SRRL Golden, CO X X X X X X 

NWTC Boulder, CO X X X X X X 

NPCS Las Vegas, NV X X X X 

UNLV Las Vegas, NV X X X X X 

HSU Arcata, CA X X 

LMU Los Angeles, CA X X 

SSO Monte Vista, CO X 

• 26 Datasets – one minute data for one year

• 7 different sites throughout the western United States

• 6 different years
Solar Variability

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One-Minute GHI Ramps – Site #20

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γ = -0.199; κ = 70.12
15-Minute GHI Ramps – Site # 19

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γ = 0.368; κ = 11.42
Normal Q-Q Plot – Site # 5 1-Min Ramps

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Normal Q-Q Plot – Site # 23 60-Min Ramps
Skewness Values – Multiple Timescales

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Site 1-Min 5-Min 15-Min 30-Min 60-Min

1 -0.064 -0.228 -0.323 -0.331 -0.234

2 -0.907 -0.150 -0.453 -0.384 -0.331

3 -0.328 -0.013 -0.109 -0.251 -0.175

4 -0.166 -0.022 0.143 -0.195 -0.333

5 -0.069 -0.063 -0.262 -0.586 -0.584

6 -1.517 -0.105 -0.264 -0.188 -0.190

7 0.039 0.053 -0.071 0.071 -0.198

8 0.068 -0.188 -0.072 0.097 -0.057

9 -0.158 -0.312 -0.417 -0.712 -0.635

10 -0.394 -0.284 -0.408 -0.513 -0.382

11 -0.098 -0.137 -0.472 -0.523 -0.193

12 0.164 0.305 0.378 0.578 0.451

13 0.001 -0.1117 -0.474 -0.411 -0.379

14 -0.065 -0.261 -0.444 -0.408 -0.262

15 -1.373 -0.299 -0.192 -0.351 -0.643

16 -0.118 -0.145 -0.280 -0.304 -0.316

17 0.050 -0.264 -0.462 -0.624 -0.725

18 -0.161 0.156 0.074 0.330 0.308

19 0.034 -0.035 0.368 0.447 0.427

20 -0.167 -0.180 -0.617 -0.746 -0.859

21 -0.149 -0.118 -0.532 -0.868 -0.948

22 -2.248 -0.073 -0.221 -0.131 -0.172

23 -0.115 -0.145 -0.369 -0.442 -0.345

24 0.231 0.399 0.868 0.311 0.180

25 -0.046 -0.120 0.054 -0.145 0.003

26 -0.004 -0.124 -0.068 -0.270 -0.365
Kurtosis Values – Multiple Timescales

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Site 1-Min 5-Min 15-Min 30-Min 60-Min

1 50.11 22.53 13.54 11.02 7.46

2 146.38 22.86 13.46 9.96 6.18

3 101.99 42.56 24.59 13.15 5.30

4 108.44 40.38 24.69 14.64 6.85

5 47.04 21.49 12.89 9.41 7.24

6 246.96 22.27 13.45 9.46 6.73

7 105.14 40.16 26.79 22.58 18.48

8 87.49 39.77 23.19 19.41 17.02

9 51.18 23.87 15.75 15.49 8.96

10 75.88 20.74 13.66 10.12 7.80

11 89.74 43.33 26.89 14.36 9.32

12 51.87 22.82 11.87 7.21 2.48

13 78.95 39.81 24.35 21.64 20.30

14 59.83 26.74 16.12 9.75 3.97

15 217.24 22.53 12.82 9.93 6.50

16 48.77 19.52 12.92 9.47 6.93

17 69.67 30.45 19.88 14.90 12.11

18 94.74 40.28 22.28 13.10 6.77

19 49.33 24.82 11.42 5.85 2.53

20 70.64 30.602 20.41 16.97 13.52

21 50.15 22.50 16.52 14.90 11.72

22 336.15 22.68 13.12 10.11 6.94

23 43.20 20.21 12.50 8.99 7.05

24 60.27 42.91 21.87 4.20 0.22

25 79.89 34.88 21.87 11.75 5.53

26 45.32 21.76 13.36 9.98 6.97
Distribution Fitting – Site #12 1-Minute

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The blue line represents a 

normal distribution with the

same mean and standard

deviation. 

The black line represents a 

hyperbolic distribution fit to

the data with: π = 0.0050, 

ζ = 0.0001, δ = 0.0015, 

μ = -0.1305. 
Distributions by Weather Patterns – Clear Sky

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Site # 26

5-Minute GHI ramps

γ = 9.17; κ = 119.89
Overcast Conditions

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Site # 26

5-Minute GHI ramps

γ = -5.74; κ = 36.64
Intermittent Cloud Activity

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Site # 26

5-Minute GHI ramps

γ = -1.05; κ = 5.99
Acknowledgements

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• Dr. Debra Lew and Yih-huei Wan– NREL

• U.S. DOE – Solar program

Photo by Warren Gretz, NREL/PIX 11188 Photo by Todd Spink, NREL/PIX 14961
Questions?

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Photo from Iberdrola

Renewables, NREL/PIX 16105

Photo by Patrick Corkery, 

NREL/PIX 17731