1 3 handschy sandia solar persistence
TRANSCRIPT
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SERIAL CORRELATION ... andOVERCONFIDENCE
Sandia-EPRI 2016 PV Systems Symposium5th PV Performance Modeling Workshop
Mark HandschySolarRetina, LLCMay 9, 2016
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CONTEXT: MODEL PURPOSE
• Such models are used to ... determine the future value of PV generation projects (expressed as the predicted energy yield).... Greater confidence in the accuracy of performance models will lead to lower financing costs and an increase in the number of projects that are built.
• Historical data is typically used to predict output of proposed systems.
— https://pvpmc.sandia.gov/
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P50 ESTIMATION3
time
prediction error
(here, the mean of the 20 pre-construction annual resource averages)
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PREDICTION ERROR DISTRIBUTION4
assumptions:• resource values are statistically independent• resource values are normally distributed• variability is the same pre- and post-construction
definition:
then: • t has Student’s t-distribution with n1 + n2 – 2 degrees of
freedom
2121
212
222
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21
)2()]()1()1[(
nnnnnnnn
XXt
−++−+−
−≡
σσ
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Long Records
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SUNSHINE DURATION: CAMPBELL-STOKES6
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ARMAGH OBSERVATORY7
daily sunshine hours01/01/1881–12/31/2014
48,942 days (134 y)140 bad: 0.3%
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BLUE HILL OBSERVATORY8
monthly sunshine hours01/1886–12/2015
1560 months (130 y)
www.bluehill.org
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KTH (STOCKHOLM)9
Moll-Gorczynski pyranometer (ca. 1936)
monthly avg. irradiance01/1923–12/2013
1092 months (91 y)
data from: Global Energy Balance Archive
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Results
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TIME SERIES11
avg. irradiance (W/m2)avg. daily sunshine (h)
Armagh Blue Hill Stockholm
randomly permuted versions of time series
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P50 ESTIMATION
Procedure:• “predict” average of each decade, using...
• mean of previous decade as estimator
• 12 cases for 130-y records: Armagh, Blue Hill; 8 cases for 90-y record: Stockholm
• difference means; divide by “σ ,” giving tOutputs:
• distribution of t-statistic
• distribution of # of years out 10 exceeding P50Control:• same outputs for randomly permuted inputs
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P50 ERROR DISTRIBUTIONS: t-STATISTIC13
Armagh Blue Hill Stockholm
randomly permuted version of time series
theory 1.4 1.4 1.4interquartile
ranges fort-statistic
chronological 1.4 2.9 4.2
random 1.0 1.3 0.8
chrono/theory 1.0 2.1 3.1
energy error spreads are larger than expected
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P50 EXCEEDANCE DISTRIBUTIONS (# years/10)14
Armagh Blue Hill Stockholm
randomly permuted version of time series
theory 2.0 2.0 2.0interquartile
ranges for P50 exceedance
chronological 2.5 4.0 7.5
random 2.5 1.5 2.5
chrono/theory 1.3 2.0 3.8
exceedance spreads are larger than expected
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INTERANNUAL VARIABILITY (σ𝒿𝒿/μ)15
Armagh Blue Hill Stockholm
record length 𝒿𝒿 (y)
IAV
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CONCLUSIONS
• assumption of statistical independence is NOT warranted:
• resource levels exhibit year-to-year correlation over decades
• IAV appears to grow with record length, out to 130-y limit of available records
• assumption of independence will lead to material understatement of risk:– 2–3× understatement of energy production prediction interval – 2–3× understatement of exceedance-range prediction interval
(based on interquartile ranges).
THANK YOU
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