a fractal based cumulus cloud shadow model for power
TRANSCRIPT
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A Fractal Based Cumulus Cloud Shadow ModelFor Power System Analysis With High
Penetration Photovoltaics (PV)
Chengrui CaiDr. Dionysios Aliprantis (major professor)
Iowa State UniversityDepartment of Electrical and Computer Engineering
Sept. 11, 2013
C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 1 / 41
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Introduction Outline
Outline
Introduction to photovoltaicsMotivationLiterature reviewCloud shadow modelFuture work
C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 2 / 41
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Introduction Solar energy
Types of solar energy
Concentrating solar power (CSP)
Photovoltaics (PV)
C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 3 / 41
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Introduction Solar energy
PV development in US
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 20120
1000
2000
3000
4000
5000
6000
7000
8000
Year
MW
7383
US Photovoltaics Capacity
Country Capacity (MW)Germany 32,509
Italy 16,987China 8,043
US 7,383Japan 6,704Spain 4,543
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Introduction Solar energy
PV potential in US v.s. Germany and Spain
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Model development Motivation
MotivationImpact of PV: variability and uncertaintyModeling PV generation considering cloud shadowsPoint measurement v.s. areal averageNo high resolution data (power or irradiance)
Cumulus clouds 25 MW DeSoto PV Plant, FL
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Model development Motivation
Problem definition
Develop a package of solar irradiance models that can realisticallygenerate solar irradiance time series for an area of interest underdifferent weather conditions.
Sunlight: clear, partially cloudy or overcast.Cloud coverage ratio: fixed or changing.Wind: speed and direction.
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Model development Literature review
Literature review
Measurement grid: very expensive.Satellite images: no sequential images with good spatialresolution.Numerically generate cloud patterns.
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Model development Literature review
Literature reviewW. T. Jewell et al. (1987 to 1990)
C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 9 / 41
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Model development Literature review
Literature reviewD. L. Garrett et al. (1989)
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Model development Literature review
Literature reviewH. G. Beyer et al. (1994)
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Model development Literature review
Literature review
W. T. Jewel and D. L. Garrett:Simple and rigid shape of clouds.No consideration of cloud coverage ratios.
H. G. BeyerSingle frame of cloud pattern.Fixed meteorology conditions, e.g. wind speed and cloudcoverage.
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Model development Contribution
Contribution
Extend Beyer’s work in:Arbitrary number of frames of cloud pattern to enablelonger-term simulation studies.The global irradiance is modeled by two separate components,e.g. beam and diffuse irradiance.The effect of variable cloud thickness is reproduced;Statistics from measured data are qualitatively applied in thesynthesis of the solar irradiance to obtain a realistic variation.The model can represent variable wind speed and cloud coverageratio.
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Model development Overview
Overview
Irradiance Model During Days with Cumulus Clouds:
Solar irradiance characteristics.Basics of fractal-based cloud generation.Meteorological and geographic parameters.Cloud pattern Generation.Synthesis of the irradiance pattern.
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Model development
Solar irradiance characteristicsExperimental station at Iowa State University.
270 Wp DC-off grid PVstation.
MPPT.
NI ENET 9205 samplingcard.
Logging data at 1-secinterval.
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Model development
Solar irradiance characteristics
Key questions:
How to model the beam and diffuse component in thecloud-based irradiance model?
What is the duration of shading?
How severe is the shading?
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Model development
Solar irradiance characteristics
100 200 300 400 500 600 700 800 9000
500
1000
(a) / secondW
/m
2
100 200 300 400 500 600 700 800 90051.5
52
52.5
53
(b) / second
Degrees
100 200 300 400 500 600 700 800 9000
500
1000
1500
(c) / second
W/m
2
100 200 300 400 500 600 700 800 900
0
0.5
1
(d) / second
High/L
ow
(a) Global horizontal irradiance (solid) and the estimated diffuse horizontal irradiance (dotted).(b) Zenith angle. (c) Beam normal irradiance (solid) and the digitization threshold (dotted).
(d) Digitized shading condition.C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 17 / 41
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Model development
Solar irradiance characteristics
Answers:
The beam irradiance will be directly affected by the cloudshadow.
A constant value or a slowly changing profile is used for thediffuse irradiance.
Apply this process to all data collected to get the statistics ofthe beam irradiance.
C. Cai, D. C. Aliprantis (ECpE, ISU) ECpE Graduate Seminar Sept. 11, 2013 18 / 41
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Model development
Basics of fractal-based cloud generation
What is a fractal?
Mandelbrot:A fractal is defined as a rough or frag-mented geometric shape that can be splitinto parts, each of which is, at least ap-proximately, a reduced-size copy of thewhole.
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Model development
Basics of fractal-based cloud generation(1,1) (1,5)
(5,1) (5,5)(a) (b)
(c) (d)
stage 1
stage 2
5x5 grid example (N = 4)
Midpoint displacement algorithm.
Takes logN2 stages to generate a
(N + 1)× (N + 1) fractal surface.
2 steps in each stage.
Added noise ε ∼ N (0, σ2).
In each step σ is reduced.
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 0 (Initialization)
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 1
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 2
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 3
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 4
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Model development
Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:
Stage 5
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Model development
Basics of fractal-based cloud shadow generation
From the fractal surface to the cloud pattern.
513-by-513 fractal surface
513 pixels513 p
ixel
s
Cloud shadow patternobtained with R = 33.4%
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Model development
Basics of fractal-based cloud shadow generation
Relationship between the cutting surface height (h) and the cloudcoverage ratio (R)
−10 −5 0 5 10 150
0.5
1
h
R
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Model development
Meteorological and geographic parameters
14:00 14:10 14:20 14:30 14:40 14:50 15:000
10
20
30
40
50
Clo
ud
co
ver
age
rati
o (
%)
(a)
14:00 14:10 14:20 14:30 14:40 14:50 15:000
5
10
15
Win
d s
pee
d(m
/s)
(b)Time
(a) Cloud coverage ratio.(b) Wind speed at cloud height.
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Model development
Meteorological and geographic parameters
0
500
1000
15000 500 1000 1500 2000
dis
tan
ce (
m)
distance (m)
N
Geographic layout of measurement points.
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Model development
Cloud pattern Generation
Steps to generate the cloud pattern:
Determine the number of frames to generate, based on the windspeed and simulation time.
Calculate the cutting surface, based on the cloud coverage ratio.
Represent the change of thickness of clouds by a multi-layertechnique.
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Model development
Cloud pattern Generation
Determine the number of frames:
F = ceil(∑ke−1
k=ks vw(tk) ∆t(N + 1)s
)+ 1 (1)
where:F is the number of frames to generate.ks and ke are the start and end index of the simulation time step.vw is the wind speed.∆t is the step size, here 1 second.s is the scale.
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Model development
Cloud pattern Generation
Calculate the cutting surface:
S1 S2 S3 S4 S5
frames of fractal surface1st window at time ts2nd window at time ts + 60∆t3rd window at time ts + 120∆t
Wind direction
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Model development
Cloud pattern Generation
Interpolate the cutting surface value:
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
−20
0
20
column index
h
Comparison of the cutting surface height before and after interpolation.
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Model development
Cloud pattern Generation
Represent the change of the thickness of cloud (multi-layertechnique):
Create K -1 more cutting surface below the original one.Each cutting surface is lowered by a factor l = (hmax − hmin)/α.Assign clouded pixels in k-th layer values using a uniformdistribution U(a, b), where a = (k − 1)/K , b = k/K , andk = 1, 2, ...,K .
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Model development
Cloud pattern Generation
Result of generated cloud shadow pattern.
Frame number
1 2 3 4 5 6 7 8 9 10 11
3591m
A
14:00 14:05 14:10 14:15 14:20 14:25 14:30 14:35 14:40 14:45 14:50 14:55 15:00
(Top) Generated binary cloud shadow pattern for time period between 2:00 and 3:00 PM. Thewind direction is SW. A is the study area.
(Bottom) Final cloud shadow pattern, using a multi-layer rendering technique. The pixels of thehatched area on the right were not needed in this simulation.
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Model development
Cloud pattern Generation
1260 m
1260 m
Magnified cloud shadow pattern.
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Model development
Synthesis of the irradiance pattern
14:00 14:10 14:20 14:30 14:40 14:50 15:00
0
0.5
1
1−
sp
(a)
14:00 14:10 14:20 14:30 14:40 14:50 15:00350
400
450
500
W/m
2
(b)
14:00 14:10 14:20 14:30 14:40 14:50 15:000
350
700
W/m
2
(c)
14:00 14:10 14:20 14:30 14:40 14:50 15:000
350
700
W/m
2
(d)
(a) Cloud transparency level.(b) Beam horizontal irradiance under clear sky condition.
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Model development
14:00 14:10 14:20 14:30 14:40 14:50 15:00
0
0.5
1
1−
sp
(a)
14:00 14:10 14:20 14:30 14:40 14:50 15:00350
400
450
500
W/m
2(b)
14:00 14:10 14:20 14:30 14:40 14:50 15:000
350
700W
/m2
(c)
14:00 14:10 14:20 14:30 14:40 14:50 15:000
350
700
W/m
2
(d)
(c) Synthesized global horizontal irradiance pattern.(d) Averaged irradiance pattern.
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Future work
Future work
Complete the solar irradiance package for three majorconditions:
I Fully clear day.I Partially cloudy day.I Overcast day.
Establish a PV panels model library.Improve the test feeder model by adding location of each house.Perform simulation studies to investigate the impact of highpenetration PV.Test the performance of control methods under different weatherconditions.
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Q & A
Thank you!Questions?
Chengrui [email protected]
http://home.eng.iastate.edu/˜ccai
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