A Fractal Based Cumulus Cloud Shadow Model For Power ...

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

Introduction Outline

Outline

Introduction to photovoltaicsMotivationLiterature reviewCloud shadow modelFuture work


Introduction Solar energy

Types of solar energy

Concentrating solar power (CSP)

Photovoltaics (PV)



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



PV potential in US v.s. Germany and Spain


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


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.


Model development Literature review

Literature review

Measurement grid: very expensive.Satellite images: no sequential images with good spatialresolution.Numerically generate cloud patterns.



Literature reviewW. T. Jewell et al. (1987 to 1990)



Literature reviewD. L. Garrett et al. (1989)



Literature reviewH. G. Beyer et al. (1994)



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.


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.


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.


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.


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?


Model development


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

Model development


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.


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.


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.


Model development

Basics of fractal-based cloud generationGenerate a 33 x 33 fractal surface:

Stage 0 (Initialization)


Model development


Stage 1


Model development


Stage 2


Model development


Stage 3


Model development


Stage 4


Model development


Stage 5


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%


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


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.


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.


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.


Model development


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.


Model development


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


Model development


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.


Model development


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 .


Model development


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.


Model development


1260 m

1260 m

Magnified cloud shadow pattern.


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.


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.


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.


Q & A

Thank you!Questions?

Chengrui [email protected]

http://home.eng.iastate.edu/˜ccai


mailto:[email protected]

http://home.eng.iastate.edu/~ccai

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