NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

2009 Colorado 

Renewable Energy 

Conference

Seung-Jae Lee1

,

Ray George2,

Brian Bush1

,

29 April 2009

NREL/PR-6A2-46208

Estimating Solar PV Output Using Modern Space/Time 

Geostatistics

1Strategic Energy Analysis Center

2Electric, Resources, and Building 

Systems Integration Center

sean_lee@nrel.gov
Project Description - Motivation

• PV output data for any location in SW US, 10 minute 

time step are required to assess the grid environment 

under high penetrations of wind, CSP, PV

• Solar measured PV data is spatially sparse but 

temporally dense

• Satellite (modeled) PV data is spatially dense but 

temporally sparse

• New measurement stations are needed, but they 

must be sited effectively, and data must be 

assimilated into applications

• There is no current research using geostatistics and 

atmospheric science on PV modeling

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Project Description

• Mapping Situations

- Hourly inaccurate modeled data on 10km solar grids + 10-minute 

measured data at several locations

• Goals

- Predict solar output at subhourly resolution at any spatial points 

(disaggregation & extrapolation) 

- Develop a methodology that is applicable to natural resources in 

general

- Demonstrate capability of geostatistical techniques to predict the 

output of a potential solar plant

• Technology-Transfer Opportunities

- Publication of the basic statistical methods in the open literature

- Distribution of the computation-intensive geostatistical software

- Application to “siting” for RE data collection

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Its main job is to 

provide an estimate at 

an unsampled

space/time coordinate

t

s1

s2

Space/time Geostatistics

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An Example of Geostatistics

PM2.5 data over the U.S. PM2.5 estimates over the U.S.

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Classical vs. Modern Geostatistics

Classical Approach

• Linear estimator

• Interpolation

• Integrates variability and 

randomness between samples

• Estimation error as a function of 

error-free measurements

• Gaussian assumption (mean & 

variance only)

• No incorporation of data 

uncertainty (hard only)

• Non-linear estimator

• Interpolation and extrapolation

• Integrates variability, 

randomness, and data 

uncertainty between samples

• Estimation error as a function of 

error-free or error-containing 

measurements

• No Gaussian assumption

• Incorporation of data uncertainty 

(hard and soft)

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Modern Approach
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Hard vs. Soft Data

Data uncertainty

U

Probabilistic soft data If U is neglected

hardened data;

deterministic values

If U is accounted for
Modern Geostatistics

Process various physical knowledge available

1. General knowledge

- statistical moments (autocorrelation in space and 

time) 

- physical laws (fate and transport, chemistry, etc.)

2. Site-specific knowledge

- exact measurements called hard data

- measurement with uncertainty called soft data 

Produce a complete stochastic characterization of 

variables at the estimation point in terms of the BME 

posterior probability density function (PDF)

Prob[xk<u] =

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National Renewable Energy Laboratory Innovation for Our Energy Future

Modern Geostatistics

We estimate x at unsampled

point across space and time 

t

error-free 

hard and 

uncertain 

soft data

mean and 

covariance

BME estimate of x

Posterior PDF at the estimation point

Geostat. fK(χk)

68 % BME confidence interval

s1

s2
Southwest Solar Resources

This slide from Strategic Energy Analysis Center, NREL

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11

Distributed Energy Interconnection Testing

This slide from Electric, Resources, Building Systems Integration Center, NREL

Distributed Energy 

Resources

Interconnection 

Technologies

Electric Power 

Systems

Fuel Cell PV

Microturbine Wind

Generator

Inverter 

Switchgear, 

Relays, & 

Controls

Functions

• Power Conversion

• Power Conditioning

• Power Quality

• Protection

• DER and Load Control

• Ancillary Services

• Communications

• Metering

Energy 

Storage

Loads

PHEV - V2G
Cloud Effect on PV output

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 7 9 11 13 15 17 19

Habitat House

Hab. House Ramp Rate

SUNY Hourly PV Output

Clear Sky Hourly PV Output

Synthetic 10 Minute PV Output

Synthetic Ramp Rate

Clear Sky Deviation

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Data Available for PV Modeling

Solar radiation – satellite modeled – hourly “snapshots”

Cloud cover – 10 minute measured from Automated 

Surface Observing System

Modeled PV output – uses PVWatts (calculator for gridconnected PV systems) for any collector orientation 

 hourly PV output on 10 km solar grids

Measured PV Output – AC power, 1 minute or 10 

minute averages  10-minute PV output at 5 

locations (4 in Arizona and 1 in Colorado)

All PV outputs are normalized to the standard DC 

output of the PV panels.

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Datasets We Used

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1-axis tracking Photovoltaic Plants over the Phoenix area

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Statistics to evaluate data uncertainty

Geostatistics

Project Procedure – Flow Chart

Soft data generated

Initial data

Phase I

Phase II

Real PV data Modeled PV data Atmospheric data

(cloud cover)

Inaccurate 10-min PV estimates

Accurate 10-min

PV estimates

Accurate 10-min PV estimates

for further use

Modern geostatistics

Re-estimated in Phase II

Final product
Validation Procedure

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Real dataset for the other

Method 2

Real time-series data

at 5 locations

Modeled PV data

Calculate Mean Square Error (MSE) for each method

and reduction in MSE from Methods 1 to 2 & 1 to 3

10-min

PV estimates

Pick two sites

Validation set for one site

Method 3

Cloud cover

Method 1

Correlation structure

from Phase II

10-min

PV estimates

10-min

PV estimates
A Case of Validation (Case 1)

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49.4 km
Validation Results

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5% improvement

24% improvement

33% improvement

Phase I 

Phase II
PV Output Estimation Maps

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Conclusions

• The incorporation of real measurements into model-based PV 

estimates (Phase I) improves those estimates relative to model-only 

estimates within radii of approximately 15 km

• The accurate Phase I results can be extended spatially and temporally 

through the use of statistical models based on the correlation between 

Phase I results and atmospheric data (Phase II)

• Accounted for data uncertainty in PV model data that contain more 

biases than real measurements

• This technique can be used to quantify the value of measured data and 

provide guidance on the choice of new measurement sites

• This technique can be readily applied to wind and other RE resources 

(PV is actually a more difficult case than other RE resources because 

of fewer constraints on PV output and poorer data quality)

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