Modeling Solar Variability Effects on Power Plants

Matthew Lave and Jan KleisslSolar 2011

Variability Reduction through Aggregation

Rela

tive

Out

put

Large ramps are detectable real-time by satellite and ground stationsVariability models primarily needed for large central power plants / microgrids

• Method to estimate aggregated PV plant output variability given a single point sensor measurement

• Model requirements:• Universal: work for plants of any size, at any location, with any

arrangement of PV panels• Account for different variability at different timescales

• Applications:• Estimate variability of output from distributed and central PV plants to

determine grid impacts• Generate virtual PV output for renewable grid integration studies• Estimate benefits of various capacities of energy storage in reducing

ramp rates

Variability Model

3

Data

GHI recorded once per second using LICOR Li-200SZ silicon pyranometers.

4

Model Development

5

• Decompose GHI timeseries into variability at different time scales using the top hat wavelet

• Determine correlation of GHI fluctuations as a function of distance and timescale between different sites

• Use correlation relationship to model variability for a variety of solar PV plant types: distributed/central, large/small

• Setup a simple user interface: draw polygons around PV on Google map; input point sensor time series; output DC power for PV plant.

Model Development

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Top Hat Wavelet Transform

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• Wavelet decomposition using a “top hat” wavelet

• Shows fluctuations away from mean at each timescale

• Strong peaks (high variability) of duration 2048 sec (~34min) are detected at 10:30 and 11:00.

• Clear sky: No fluctuations from 12:00 to 15:30.

Correlation Between Sites

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.2

0

0.2

0.4

0.6

0.8

1

corr

elat

ion

()

UCSD DEMROES year 2010

exp(-x/tavg)

= 0.73 exp(-x/tavg

)

2-sec/4-sec8-sec/16-sec32-sec/64-sec128-sec/256-sec512-sec/1024-sec2048-sec/4096-sec

+0.27 exp(-x/tavg

)200

8*presentation by Tom Hoff at DOE/CPUC High Penetration Solar Forum, March 2, 2011

Large distance or small time

Small distance or large time

• Correlation at each timescale found by comparing the wavelet modes for two sites at a certain timescale• Normalized distance divided by time scale (Hoff, 2011*)

Case Study

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UCSD1.2 MW

Distributed PV

UCSD1.2 MW

Central PV

Henderson, NV 48 MW

Central PV

Compare variability of PV plants:

Correlation -> Variability Ratio (VR)

• VR can be computed between each set of points (“containers”) for an entire plant over all timescales

• After a wavelet transform, each wavelet mode from a point sensor is divided by the VR at that timescale to create wavelet modes for the PV plant. An inverse transform creates the PV plant output.

N

i

N

jji

sitesallavg

sitex

dxt

Nt

ttVR

1 1,

2

2__

2_1

ˆ

),()()(

)(

10

UCSD distributed

PV plant

central PV plant of

same MW size

1.2 MW UC San Diego PV plant

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48MW Henderson, NV PV plant

UCSD: 1.2 MW; 0.4 kW containersHenderson: 48 MW; 90 kW containers

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UCSDDistributed PV

Henderson, NV Central PV

PV plant variability expressed in GHI units

• Power output smoothed compared to point sensor• UCSD distributed has noticeably smaller fluctuations than UCSD central.13

Acknowledgements•We very much appreciate funding from the DOE High PV Penetration Program

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• Questions?• Please come visit us at solar.ucsd.edu• Contact: mlave@ucsd.edu

Backup Slides

Model Assumptions

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• Correlations are solely a function of distance and timescale: no consideration for anisotropic variations

• PV is spaced evenly throughout the plant area

• “Containers” of varying size are appropriate to model PV plants

• PV plant average GHI can be converted into plant power output

Power Content of Fluctuations

• Power content = integral of wavelet mode at a certain timescale – shows variance at each timescale• Power content of one highly variable day (left) is much larger than the average power content of 48 days • Power content of average of 6 sites always less than power content of EBU2

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Variability Ratio

NVRrVR

2__

21_

tesavg_all_si

site_1

fpifpi

VRsitesallavg

site

1 vs. 48 days various N

to allow for easy visual comparison on same plot

VR is a function of timescale and number of sites (or, rather, correlation between sites)

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Future Improvements

•Compare correlations found at UC San Diego to other locations

• Verify correlation relation at very short distances

•Compute power output with PV performance model

•Validate against actual power plant data

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