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Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Measurement and Modeling of 

Solar and PV Output Variability 

Preprint

M. Sengupta

To be presented at SOLAR 2011

Raleigh, North Carolina

May 17–21, 2011

Conference Paper

NREL/CP-5500-51105

April 2011
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1 

MEASUREMENT AND MODELING OF SOLAR AND PV OUTPUT VARIABILITY

Manajit Sengupta 

National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden CO 80401 

Manajit.Sengupta@nrel.gov 

ABSTRACT

This paper seeks to understand what temporal and 

spatial scales of variability in global horizontal 

radiation are important to a PV plants and what 

measurements are needed to be able to 

characterize them. As solar radiation measuring 

instruments are point receivers it is important to 

understand how those measurements translate to 

energy received over a larger spatial extent. Also 

of importance is the temporal natural of variability 

over large spatial areas. In this research we use 

high temporal and spatial resolution 

measurements from multiple sensors at a site in 

Hawaii to create solar radiation fields at various 

spatial and temporal scales. Five interpolation 

schemes were considered and the high resolution 

solar fields were converted to power production 

for a PV power plant. It was found that the 

interpolation schemes are robust and create ramp 

distributions close to what would be computed if 

the average solar radiation field was used. We 

also investigated the possibility of using time 

averaged solar data from 1 sensor to recreate the 

ramp distribution from the 17 sensors. It was 

found that the ramping distribution from using 

appropriately time averaged data from 1 sensor 

can reasonably match the distribution created 

using the 17 sensor network. 

Solar energy reaching the earth’s surface is 

influenced by clouds, aerosols, water vapor and 

other atmospheric constituents thereby 

introducing variability in the amount of solar 

radiation reaching the earth’s surface. Each of 

these constituents influences solar radiation at its 

own inherent time and space scale. Therefore 

modeling solar variability becomes an inherently 

complicated problem. 

1. INTRODUCTION

The issue of variability in PV plant output has 

become important in the last couple of years as 

utility scale PV plants go online [1, 2]. 

Understanding variability in PV plant output 

requires an understanding of (a) the spatial and 

temporal variability of solar radiation; (b) the 

influence of solar variability on PV plant output. 

Some studies have been conducted in Spain to 

relate PV plant power output and measured 

Global Horizontal Irradiance [3, 4]. 

Pre-feasibility and feasibility studies for utility 

scale PV plants involve, among other things, the 

determination of solar resource at potential 

deployment sites. While a plant may be feasible 

based on the availability of solar resource at a 

location the impact of deploying a large quantity 

of variable renewable generation on the grid 

requires additional studies. For such studies it is 

important that realistic, high temporal resolution 

PV production estimates for various size plants be 

available over large regions. As such studies need 

to be done in advance of putting large quantities 

of power on the grid, actual PV production data 

will not generally be available to conduct such 

studies. In the absence of actual production data it 
2 

is important that a capability for simulating such 

scenarios be developed. One way to create such 

simulations is to deploy a large number of solar 

sensors in highly dense grids. Such highly dense 

solar grids are expensive to deploy and maintain 

and are therefore not feasible at multiple 

locations. Another option is the possibility of 

using single solar sensors that can measure at high 

resolution and filtering the data to create datasets 

resembling sensor networks. This data can then be 

used to create PV plant out for various size plants.

Figure 1: GHI distribution from 17 GHI 

measurements at a site in Hawaii. The sensors, 

represented by dots, are distributed over an 

approximately 1 square kilometer area and 

measurements are made every second.

To test the viability of using single sensors to 

model utility scale PV plants a dense solar sensor 

network was set up in Oahu, HI. This dense 

sensor network contains 17 sensors spread over a 

1 square kilometer area. GHI is measured at 1 

second resolution using Licor Model LI200SB 

Pyranometer , Campbell CR800 data loggers with 

GPS time synchronization capability.Data has 

been continuously available since March 2010. 

In this study we use 1 month of 1 second data. As 

1 second solar measurements are equivalent to 

instantaneous point measurement the data was 

averaged to a minimum of 10 seconds to create a 

representative measurement for a small region 

surrounding the measurement point. Other 

averaging periods such as 1 minute and 5 minutes 

were also considered for this study. 

There are two parts to this study. The first part of 

the study is to determine whether the high-density 

solar network is capable of producing a robust 

high resolution solar field using interpolation 

methods. The second part of the study investigates 

the possibility of using data from a single sensor 

to model variability in the high-resolution solar 

field created using the high-density network. 

2. METHODOLOGY

Four interpolation schemes were chosen to create 

50 m resolution data. Averages of all the sensors 

were also considered. The interpolation methods 

considered were – 

2.1 High-resolution solar fields

(1) Nearest Neighbor: Effectively the nearest 

observation to the interpolated grid is considered

after Delauney triangulation [6] of the 

measurement points. 

(2) Natural Neighbor: This spatial interpolation 

method is based on Voronoi tessellation [7] of a 

discrete set of spatial points created using the 

Delauney triangulation method. This method 

provides a smoother approximation to the 

underlying distribution than other methods such 

as the nearest neighbor method. Effectively the 

method uses a weighted average of members 

(3) Linear: This method again uses Delauney 

triangulation and then linearly interpolates to 

create the high-resolution solar datasets.

(4) Cubic: This method too uses Delauney 

triangulation and then uses a cubic fit to the data 

to produce smoother surfaces than the nearest 

neighbor or linear method. 
3 

(5) Average: The data is averaged to produce a 

single radiation value for the whole area. 

After creation of high resolution solar fields the 

GHI data is used to compute PV output using the 

PV Watts model. The PV output is then used to 

create ramps or changes in output production from 

one time to the next. The ramp distributions are 

then analyzed to determine the sensitivity of those 

distributions to the interpolation scheme used. 

The goal of this work is to investigate the possible 

of creating solar and PV output datasets that have 

similar ramp characteristics to those produced by 

the dense sensor network. The simplest way to 

produce the characteristics of a large solar field 

using a single sensor is to temporally average the 

data over various time intervals. Other 

sophisticated schemes that consider cloud height 

winds and weight the temporal data can be 

devised but in our case we use simply box filters. 

2.2 Single sensor comparisons

3. RESULTS

Data from the month of July 2010 was used in this 

study. While the measurements were taken at 1 

second the analysis was done at resolutions of 10 

seconds, 60 seconds and 300 seconds. The GHI 

data from the 17 sensors were averaged to the 3 

time resolutions. The time-averaged datasets were 

then used to create 50 m resolution GHI fields 

using the 5 schemes described in Section 2.1. The 

GHI field was then used in PVWatts [5] to create 

power out from a PV plant. The rated capacity of 

the PV plant was calculated to be 42 MW under 

the assumption that a 1 MW plant covers 20,000 

square meters in area. The PV panels were 

assumed to be at fixed horizontal tilt for this 

analysis. 

Ramps or changes in power production per 

relevant time interval (10, 60 or 300 seconds) 

were calculated and the distributions of those 

ramps are shown in Figures 2, 3 and 4. Note that 

only ramps greater than 1 MW in magnitude are 

considered as our primary goal is to be able to 

capture ramps that occur due to cloud passage.

Figure 2: Cumulative Probability distribution of 

ramps in MW for power output at 10 second 

resolution. Note the robustness of the schemes 

shown by the relative insensitivity of ramp rate 

statistics to the interpolation method used. 

Figure 3: Cumulative Probability distribution of 

ramps in MW for power output at 60 second 

resolution 

It is observed that the ramp distributions are 

relative insensitive to the interpolation method 

used to create the solar fields. We can therefore 

assume that any of the interpolation schemes 

considered can be used to create PV output from 

GHI measurements and the results will be similar 

to the other methods. 
4 

Figure 4: Cumulative Probability distribution of 

ramps in MW for power output at 300 second 

resolution.

Figure 5: 60 second ramp probability distribution 

for a single sensor compared to the power output 

created from multi-sensor high-density solar field. 

The upper solid blue line represents the multisensor array. The lower black line is represents 

the single-sensor with 60 second averaging. The 

lower and upper dotted red and green lines 

represent 150 and 180 second averaging. 

The next step in the analysis involved using data 

from 1 sensor to create radiation fields that are 

representative of the distributions shown in 

Figures 2, 3 and 4. A sensor at the middle of the 

array was considered for creating the time 

averages.

Figures 5 and 6 show the results of averaging a 

single sensor measurement in order to create ramp 

distribution similar to that observed by multisensor arrays. For the 60 second ramps considered 

in Figure 5 it is seen that comparable distributions 

can be created by averaging the single sensor data 

to 150 – 180 seconds. When we consider the 5 

minute ramps, Figure 6 shows that the single 

sensor averages need to be close to 450 seconds.

It is found that interpolation schemes used to 

create high-resolution GHI fields from multisensor datasets are robust and relatively 

insensitive to the method used. It is therefore 

reasonable to assume that any of the schemes can 

be used to create high resolution GHI fields which 

can then be used to create power output from a 

PV plant under certain assumptions. 

4. CONCLUSIONS AND FUTURE WORK

Figure 6: 300 second (5 minute) ramp probability 

distribution for a single sensor compared to the 

power output created from multi-sensor highdensity solar field. The solid blue line represents 

the multi-sensor array. The black line is represents 

the single-sensor with 60 second averaging. The 

dotted red and green lines represent 450 and 600 

second averaging. 

As multi-sensor arrays are generally not available 

because of the inherent cost of setting up and 

maintaining such arrays it is useful to create 
5 

models that can simulate multi-sensor fields using 

single sensor output. It is found that simple lowpass filters such as those shown in Figures 5 and 6 

are capable of producing reasonably close 

approximations to the multi-sensor fields.

The current results were derived for a PV plant 

size of 42 MW. Various size PV plants as well as 

other ramping interval need to be considered in 

order to create comprehensive base level filters 

for potential scenarios. Other atmospheric 

parameters such as cloud height winds need to be 

considered as are seasonal impacts. Additional 

work to model single axis trackers is also needed.

1. Curtright, A., & Apt, J. (2008). The 

character of power output from utilityscale photovoltaic systems. Progress in 

Photovoltaics: Research and Applications, 

16 (3), 241-247 

5. REFERENCES

2. North American Electric Reliability 

Corporation (NERC). 2009. 

Accommodating High Levels of Variable 

Generation. White Paper. April 

3. Marcos, J., Marroyo, L., Lorenzo, E., 

Alvira, D. and Izco, E. (2010). Power 

output fluctuations in large scale PV 

plants: one year observations with one 

second resolution and a derived analytic 

model. Progress in Photovoltaics: 

Research and Applications. DOI: 

10.1002/pip.1016 

4. Marcos, J., Marroyo, L., Lorenzo, E., 

Alvira, D. and Izco, E. (2011). Fro 

irradiance to output power fluctuations: 

the pv plant as a low pass filter. Progress 

in Photovoltaics: Research and 

Applications. DOI: 10.1002/pip.1063 

5. Mennicucci, D. F. (1986). Photovoltaic 

Array Simulation Models. Solar Cells, 18, 

383-392 

6. B. Delaunay: Sur la sphère vide, Izvestia 

Akademii Nauk SSSR, Otdelenie 

Matematicheskikh i Estestvennykh Nauk, 

7:793–800, 1934 

7. Du, Q., Faber, V., Gunzburger, M. (1999), 

Centroidal Voronoi Tesselations: 

Applications and Algorithms, SIAM 

Review 41 (4): 637–676