NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5D00-75869

June 2020

Quantifying Solar PV Variability at 

Multiple Timescales for Power Systems 

Studies

Preprint

Himanshu Jain, Manajit Sengupta, Aron Habte, 

and Jin Tan

National Renewable Energy Laboratory

Presented at the 47th IEEE Photovoltaic Specialists Conference (PVSC 47)

June 15–August 21, 2020
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Conference Paper

NREL/CP-5D00-75869

June 2020

Quantifying Solar PV Variability at 

Multiple Timescales for Power Systems 

Studies

Preprint

Himanshu Jain, Manajit Sengupta, Aron Habte, 

and Jin Tan

National Renewable Energy Laboratory

Suggested Citation 

Jain, Himanshu, Aron Habte, Manajit Sengupta, and Jin Tan. 2020. Quantifying Solar PV 

Variability at Multiple Timescales for Power Systems Studies: Preprint. Golden, CO: 

National Renewable Energy Laboratory. NREL/CP-5D00-75869. 

https://www.nrel.gov/docs/fy20osti/75869.pdf.

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in 

any current or future media, including reprinting/republishing this material for advertising or promotional purposes, 

creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of 

this work in other works.
NOTICE

This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable 

Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding 

provided by U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Solar Energy 

Technologies Office. The views expressed herein do not necessarily represent the views of the DOE or the U.S. 

Government.

This report is available at no cost from the National Renewable 

Energy Laboratory (NREL) at www.nrel.gov/publications.

U.S. Department of Energy (DOE) reports produced after 1991 

and a growing number of pre-1991 documents are available 

free via www.OSTI.gov.

Cover Photos by Dennis Schroeder: (clockwise, left to right) NREL 51934, NREL 45897, NREL 42160, NREL 45891, NREL 48097, 

NREL 46526.

NREL prints on paper that contains recycled content.
1

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

Quantifying Solar PV Variability at Multiple 

Timescales for Power Systems Studies

Himanshu Jain, Manajit Sengupta, Aron Habte and Jin Tan

National Renewable Energy Laboratory

Golden, Colorado, USA

Himanshu.Jain@nrel.gov; Manajit.Sengupta@nrel.gov; Aron.Habte@nrel.gov; Jin.Tan@nrel.gov

Abstract—This paper presents two metrics – Fourier 

coefficients of irradiation ramps and average irradiation ramps to 

quantify solar photovoltaic (PV) variability at multiple temporal 

scales to improve the accuracy of power systems studies under 

high solar PV penetrations. The key findings based on these 

metrics are: (i) a single sensor significantly exaggerates the 

variability of a solar PV power plant at seconds to 1-minute

temporal resolution, but it can be fairly accurate at lower than 1-

minute resolutions, (ii) at each 1-minute and lower temporal 

resolution, largest solar irradiation ramps appear to be 

independent of the geographical location, and (iii) significant 

reduction in solar PV plant variability over a region with multiple 

plants is possible at all temporal scales, but more high temporal 

resolution data is needed to conclusively quantify the reduction.

Keywords—solar photovoltaics, variability of solar PV power 

plant, multi-timescale, global horizontal irradiation, rotating 

shadowband radiometer

I. INTRODUCTION

Reliable operation of power systems requires that 

interactions among various devices and equipment and the grid 

are studied at multiple timescales (sub-seconds to several 

hours). Electromechanical transient programs can be used to 

study these interactions using validated models of various 

equipment and controllers. Models of conventional generators 

are standardized, and it is assumed in electromechanical 

transient simulations that enough fuel is available at all times to 

meet the power demand put on these generators by the rest of 

the system. This assumption, however, breaks down with solar 

PV (and other variable renewable energy resources such as 

wind), where the plant operator has no control over the incident 

solar irradiation. Therefore, modeling solar irradiation is 

critical to accurately simulating the input power to the solar 

panels and inverters.

The main challenge in modeling solar irradiation and the 

resulting output of solar PV plants arises from the variability 

induced by clouds. The analytical solution to modeling cloudsinduced irradiation variability is to use numerical weather 

prediction models such as WRF-solar [1]. However, developing

models of solar irradiation and solar PV plant outputs at the 

temporal and spatial scales required in electromechanical 

transient simulations (sub-seconds to few minutes) is extremely 

computationally expensive and the data required to initialize the 

simulations is not publicly available today. The alternative is to 

use publicly available datasets to model the temporal and 

spatial variability, which is the approach that was adopted in 

this paper.

There have been several efforts in the past to quantify solar 

PV variability at various spatial and temporal scales [2]–[9]. 

The wide variety of approaches used in these studies points to 

the absence of a universally acceptable method of quantifying 

solar PV variability. From the point of view of power systems 

reliability, particularly for frequency response analysis, 

variabilities ranging from seconds to several minutes are of 

interest [10]. E.g., a single large-ramp during a day may be 

easier to manage than several large unexpected variations that 

occur throughout a day because reliability metrics such as the 

control performance standard (CPS) scores [11] may be more 

adversely impacted by the latter.

Therefore, in this paper we propose two metrics that enable 

solar PV variability to be captured across an entire day over 

timescales ranging from seconds to an hour. These metrics are 

(i) Fourier coefficients and (ii) average irradiation ramps. Data 

from NREL’s Measurement and Instrumentation Data Center 

(MIDC) [12] for 6 locations across the US is used to compare 

the performance of the two metrics and quantify and analyze

solar PV variability. 

II. METHODOLOGY TO CALCULATE THE VARIABILITY METRICS

A. Fourier Coefficients of Irradiation Spectrum

Fourier coefficients are obtained by using discrete Fourier 

transform. Fourier transform is applied on an entire day’s data 

resulting in a frequency resolution of 1/(H*3600) Hz, where 

“H” is the number of hours for which the data is collected 

during a day. The highest frequency that can be captured is 

“fs/2” Hz, where “fs” is the sampling frequency of the data set. 

E.g., if a dataset has 1-second resolution data, “fs” is 1 Hz and 

the minimum frequency that can be captured using the Fourier 

transform is 0.5 Hz. In other words, the maximum temporal 

resolution of variability that can be quantified for 1-second 

resolution dataset using the Fourier coefficient metric is 2-

seconds.

B. Average Irradiation Ramps

The average irradiation ramp metric at a temporal resolution 

is obtained in three steps. Step 1. Obtain a series of averages of 

solar irradiation using (1) with the averaging interval equal to 

the desired temporal resolution (e.g., if a dataset has the highest 

resolution of 1-minute, and the desired temporal resolution is 5-

minutes, 5-point moving average is calculated). Step 2. Obtain 

a series of magnitudes of irradiation ramps using (2), which 
2

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

calculates the absolute value of the difference between two 

consecutive average irradiation values obtained in step 1. Step 

3. Average irradiation ramp metric at the desired temporal 

resolution is obtained using (3) as the mean of the ramps

calculated in step 2

xx�ıı = �∑ xxjj TT∗ii

jj=TT∗(ii−1)+1 �

TT ; ii = 1, 2, ... , MM (1)

rrii = |�xx�ıı

�

+�1

� − xx�ıı|; ii = 1, 2, ... , MM − 1 (2)

aaaaaa aaaaaa ii iiii iiiiiiii rr rrrr mm = (∑ rrii MM−1 ii=1 )

MM − 1 (3)

Where, MM = ffff �

LL

TT

�; xxjj is the jjtth solar irradiation value; 

LL is the length of the solar irradiation data collected over a day; 

TT is the desired temporal resolution, which is always less than 

the temporal resolution of the solar irradiation data (e.g., if the 

irradiation data is collected at a resolution of 1-minute, TT

cannot be less than 1-minute).

III. APLLICATION OF VARIABILITY METRICS 

Table I lists the six MIDC solar irradiation datasets whose 

variabilities were evaluated using the two metrics.

TABLE I. SIX MIDC DATASETS

Station State Latitude/

Longitude Resolution Dataset Length Sensors

Oahu [13] HI 21.31N/

158.09W 1 second 10 months 17

SolarTAC 

[14] CO 39.76N/104.62W 1 minute 1 year 1

NREL 

Station 

[15]

CO 39.74N/

105.18W

1 minute 1 year 1

UNLV 

[16] NV 36.11N/115.14W 1 minute 1 year 1

UAT 

(OASIS) 

[17]

AZ 32.23N/

110.96W

1 minute 1 year 1

UTPASRL 

[18] TX 26.31N/98.17W 1 minute 1 year 1

A. Solar Variability Analysis Using The Oahu Dataset

The Oahu dataset had the highest temporal resolution and it 

also had 17 sensors spread over an area of 1 sq. km, which is 

why this dataset was first used to validate and compare the 

performance of the two metrics. Fourier coefficients were 

obtained at six temporal scales - 2, 10, 60, 300, 900, and 3,600 

seconds and four spatial scales using the Global Horizontal 

Irradiance (GHI) of 1 sensor (AP3), average GHI of 4 sensors 

(DH6, 8, 10 and 11), average GHI of 9 sensors (DH2-7,9,10 and 

AP1), and the average GHI of all 17 sensors. Sensor layout is 

available in [19].

Fig. 1, Fig. 2 and Fig. 3 plot the Fourier coefficients from 1, 

4, and 9 sensors against the Fourier coefficients of all 17 

sensors, respectively. Table II and Table III list the highest and 

lowest variability days identified for the four sensor 

aggregations, respectively. Fig. 4 shows the average GHI of 17 

sensors and the GHI of sensor AP3 for the maximum and 

minimum variability days listed in Table II and Table III for 2-

seconds and 5-minute resolutions.

Plots similar to those in Fig. 1, Fig. 2 and Fig. 3 for the 

average irradiation ramp metric are shown in Fig. 5, Fig. 6, and

Fig. 7, respectively. The maximum and minimum variability 

days identified using the average ramp metric are shown in

Table IV and Table V. Fig. 8 is the same plot as Fig. 4 but for 

the average ramp metric.

Key observations from these figures and tables are:

• Both metrics suggest that single sensor shows much 

larger variability at seconds-level temporal resolutions 

compared to that obtained using average of 4, 9 and 17 

sensors, while variability obtained from all the sensors

at 5-minutes and lower temporal resolutions are very 

similar. Significantly larger scale of the Y axis w.r.t to 

the X axis in Fig. 1, Fig. 2 and Fig. 3 and Fig. 5, Fig. 6,

and Fig. 7 for seconds level variabilities support this 

observation. This suggests that correlation in solar 

irradiation at various locations in a large plant at higher 

temporal resolutions is lower and it increases as the 

temporal resolution reduces. In other words, secondslevel solar PV plant variability obtained from one sensor

may significantly exaggerate its impact on the grid. 

These observations are also consistent with those made 

in [4]. 

• As the number of sensors used to estimate solar 

irradiation variability increases from 1 to 9, the 

variability estimates become closer to those obtained 

from using all 17 sensors, particularly at 1 minute and 

lower temporal resolutions. Even the 2-seconds

variability reduced significantly with 4 sensors. E.g., the 

maximum value of Y-axis of the 2-seconds variability 

plot in Fig. 6 became 25 WW/ 2 from 50 WW/ 2 in Fig.

5, which is much closer to the 15 WW/ 2 maximum 

value of the X axis in these figures (which is the 

variability obtained from the average GHI of all 17 

sensors). This observation suggests that if a dense array 

of sensors cannot be deployed at a location, a cluster of 

a few appropriately spaced sensors may give 

significantly better estimates of solar irradiation 

variabilities at high temporal resolutions than those 

obtained from a single sensor. 

• Comparison of the relative performance of the two 

metrics suggests that ramp-based metric performs better 

than the Fourier coefficient metric. This can be observed 

from Table II and Table IV, where the total number of 

unique maximum variability days identified by the

Fourier coefficient metric are 14, compared to 10 from 

the average ramp metric. The total number of unique 

minimum variability days identified by the Fourier 

coefficient metric are 7 (Table III) compared to 2 

identified by the ramp metric (Table V). This indicates 

more consistent identification of maximum and 

minimum variability days across temporal and spatial 

scales by the average ramp metric. Moreover, 

comparison of Fig. 4 and Fig. 8 provides visual 

verification of the better performance of the average 
3

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

ramp metric at higher temporal resolutions because the 

difference between maximum and minimum variability 

days is significantly clearer for the average ramp metric

(Fig. 6) than for the Fourier coefficient metric (Fig. 3), 

for 2-seconds variability. The considerably poor 

performance of the Fourier coefficient metric in 

characterizing the 2-seconds variability is likely due to 

noise in Fourier analysis that distorted the actual 0.5 Hz 

component, which is the highest frequency that can be 

obtained in the 1-second dataset. It is likely that samples 

taken at higher resolution than 1 Hz can improve the 

performance of the Fourier analysis-based metric in 

identifying the variability at such high resolutions.

Fig. 1. Variabilities at 6 temporal resolutions obtained from sensor AP3 and 

average GHI of 17 sensors using the Fourier coefficient metric.

Fig. 2. Variabilities at 6 temporal resolutions obtained from average GHI of 4

sensors and average GHI of 17 sensors using the Fourier coefficient metric.

Fig. 3. Variabilities at 6 temporal resolutions obtained from average GHI of 9 

sensors and average GHI of 17 sensors using the Fourier coefficient metric.

Fig. 4. Plots of GHIs from sensor AP3 and the average GHI of 17 sensors of 

highest and lowest variability days obtained using the Fourier coefficient 

metric calculated at 2-second and 5-minute temporal resolutions.

Fig. 5. Variabilities at 6 temporal resolutions obtained from sensor AP3 and

average GHI of 17 sensors using the average ramp metric.

Fig. 6. Variabilities at 6 temporal resolutions obtained from average GHI of 4 

sensors and average GHI of 17 sensors using the average ramp metric

Fig. 7. Variabilities at 6 temporal resolutions obtained from average GHI of 9 

sensors and average GHI of 17 sensors using the average ramp metric.
4

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

Fig. 8. Plots of GHIs from sensor AP3 and the average GHI of 17 sensors of 

highest and lowest variability days obtained using the average ramp metric

calculated at 2-second and 5-minute temporal resolutions.

TABLE II. MAXIMUM VARIABILITY DAYS FROM FOURIER COEFFICIENT 

METRIC

Resolution 1 sensor 4 sensors 9 sensors 17 sensors

2 s 04/16/11 04/20/10 04/04/10 04/04/10

10 s 04/02/10 07/28/11 07/15/11 07/15/11

1 min 03/28/10 04/01/10 07/21/11 05/24/10

5 min 08/10/10 08/10/10 08/10/10 08/10/10

15 min 05/26/10 07/14/11 05/26/10 05/26/10

1 hour 07/29/10 07/29/10 07/29/10 07/29/10

TABLE III. MINIMUM VARIABILITY DAYS FROM FOURIER COEFFICIENT 

METRIC

Resolution 1 sensor 4 sensors 9 sensors 17 sensors

2 s 09/24/10 07/21/10 09/05/10 04/03/10

10 s 01/10/11 01/10/11 01/10/11 01/05/11

1 min 01/10/11 01/10/11 01/10/11 01/10/11

5 min 01/10/11 01/31/11 01/31/11 01/31/11

15 min 01/31/11 01/31/11 01/31/11 01/31/11

1 hour 01/31/11 01/31/11 01/31/11 01/31/11

TABLE IV. MAXIMUM VARIABILITY DAYS FROM AVERAGE RAMP METRIC

Resolution 1 sensor 4 sensors 9 sensors 17 sensors

2 s 4/21/2010 5/24/2010 5/24/2010 5/24/2010

10 s 4/21/2010 4/2/2010 5/24/2010 7/8/2011

1 min 4/28/2010 4/2/2010 4/28/2010 4/20/2010

5 min 4/24/2010 7/14/2011 4/24/2010 4/24/2010

15 min 7/18/2010 7/18/2010 7/18/2010 7/18/2010

1 hour 3/23/2010 3/23/2010 3/23/2010 3/23/2010

TABLE V. MINIMUM VARIABILITY DAYS FROM AVERAGE RAMP METRIC

Resolution 1 sensor 4 sensors 9 sensors 17 sensors

2 s 1/10/2011 1/10/2011 1/10/2011 1/31/2011

10 s 1/10/2011 1/31/2011 1/31/2011 1/31/2011

1 min 1/31/2011 1/31/2011 1/31/2011 1/31/2011

5 min 1/10/2011 1/31/2011 1/31/2011 1/31/2011

15 min 1/10/2011 1/10/2011 1/10/2011 1/10/2011

1 hour 1/10/2011 1/10/2011 1/10/2011 1/10/2011

B. Comparison Of Solar Variability Between Stations

The average ramp metric was used to calculate the solar PV 

variability for the five single sensor stations listed in Table I. 

Fourier coefficient metric can also be used, but due to space 

constraints results using only the ramp metric are presented. 

The maximum values of the average ramp metric observed 

at each of the six stations over the length of the dataset (listed 

in Table I) for the four variability intervals (1-minute is the 

highest resolution of these datasets) are listed in Table VI. A 

very interesting observation from this table is that the maximum 

ramp sizes at the four temporal resolutions are very similar 

between the six geographical locations that are very far away 

from each other. This observation suggests that a reasonable 

size of the worst solar irradiation ramp can be approximated for 

various locations from the ramps given in Table VI. After

considering other factors that can affect the power plant output 

such as fixed or tracking axis and shadowing effects, the 

maximum power ramp at a plant can be approximated and used 

for power systems studies such as frequency response analysis.

TABLE VI. MAXIMUM AVERAGE RAMPS (WW/ 2) AT 6 LOCATIONS

Station State 1-min 5-min 15-min 60-min

Oahu HI 60 120 120 240

SolarTAC CO 67 127 135 244

NREL 

Station CO 61 120 157 304

UNLV NV 62 112 132 255

UAT AZ 91 153 131 255

UTPASRL TX 103 134 136 242

C. Reduction In Solar Variability Over A Region 

While Table VI suggests that maximum average ramp sizes 

may be similar at 1-minute or lower temporal resolutions 

between plants located over a large geographical area, it does 

not provide any information on the expected ramp sizes for the 

entire region that may have multiple plants (existing or 

planned). It is well known that decorrelation between the solar 

ramps at various sites may result in significantly reduced 

variability over the entire region [4]. It will be ideal if a relation 

between the solar PV variability of one plant vs the combined 

variability of all the plants over a large region (e.g., utility 

footprint) can be obtained. This will allow planners to consider 

the impacts of variability of solar PV for future PV installations 

by knowing the variability of an existing plant or that observed 

at an existing sensor. To this end, we tried to estimate how the 
5

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

variability of a single sensor at NREL Station and solarTAC 

compared with the combined variability of the two sensors. 

These two sensors are located about 50 km apart. Ideally, solar 

PV output of multiple sensors within 50 km radius should have 

been used to get more definitive results, but good quality, highresolution data was not available.

Table VII shows twice the maximum of the average ramp

metric (multiplication by 2 was done to reflect the assumption 

of perfect correlation between the two locations) calculated 

over the entire length of the dataset for the individual stations 

and maximum of the average ramp metric for the combined 

output of the two stations. The ramp size of the combined 

output is smaller by at least 13% over all the temporal 

resolutions compared with the case if the solar GHIs were 

completely correlated. On average, the variability reduction is 

24%, 30%, 32%, and 22% for the combined output for 1, 5, 15, 

and 60-minute time resolutions, respectively. The available 

dataset is too small and variations in reductions in variability 

between the combined output and the outputs of individual sites 

too large to come to any definitive conclusion regarding the 

percentage decrease in sizes of ramps compared to the ramps of 

individual plants when multiple solar plants over a radius of 50 

km are combined. Nonetheless, this analysis does indicate that 

significant reduction in variability of the combined output of 

multiple plants spread over a region can be expected and the 

reduction can be quantified if more high quality, high resolution 

solar irradiation measurements are available from multiple 

locations in a region.

TABLE VII. COMPARISON OF RAMPS (WW/ 2) FROM SOLARTAC, NREL

STATION, AND THE COMBINED OUTPUT OF THESE TWO STATIONS 

Station 1-min 5-min 15-min 60-min

Combined 97 173 198 423

NREL Station 122 240 314 608

SolarTAC 134 254 270 488

% reduction in 

combined w.r.t NREL 

Station

20% 28% 37% 30%

% reduction in 

combined w.r.t 

solarTAC

28% 32% 27% 13%

IV. CONCLUSION

This paper attempted to quantify solar PV plant variabilities 

at various temporal resolutions ranging from seconds to an 

hour. Considering the challenges in obtaining analytical 

expressions to quantify high temporal resolution solar PV plant 

output variabilities, a data-based approach was used to quantify 

the variability. The three key takeaways from the presented 

work for power systems studies under high solar PV 

penetration, particularly for frequency response studies that 

require seconds level temporal resolution data are:

• Use multiple sensors spread over a plant (or over the site 

of a future plant) to estimate the variability that may 

occur at seconds-level temporal resolutions. Even a 

cluster of few appropriately placed sensors may provide 

significantly better results than a point sensor.

• The largest solar irradiation ramps at an existing solar 

PV plant or at a future plant location at 1-minute and 

lower temporal resolutions may be approximated by 

the largest ramps observed at existing sensors in the 

region, which do not need to be in proximity of the 

plant.

• High quality and high spatial density solar irradiation 

datasets with seconds-level temporal resolution should 

be created because few such datasets are publicly 

available today and their value cannot be overstated for 

modeling solar PV plant variability in frequency 

response studies.

The observations and findings from this work can be used 

as the foundation for more extensive solar PV plant variability 

analysis using high quality, high resolution data. The solar PV 

irradiation data can also be converted into real power output 

data by considering the location, orientation, fixed or tracking 

axis technology, and shading effects using tools such as the 

System Advisor Model (SAM) [20]. As more high quality and 

high temporal resolution solar PV irradiation data becomes 

available, the analysis presented in the paper can be used to 

evaluate expected solar variability for grid study under very 

high solar PV penetration, which can be of significant value to 

power system operators and planners for evaluating the 

reliability of power systems.

REFERENCES

[1] P. A. Jimenez et al., “WRF-Solar: Description and Clear-Sky Assessment 

of an Augmented NWP Model for Solar Power Prediction,” Bull. Amer. 

Meteor. Soc., vol. 97, no. 7, pp. 1249–1264, Jul. 2016, doi: 

10.1175/BAMS-D-14-00279.1.

[2] J. Munkhammar and J. Widén, “An autocorrelation-based copula model 

for generating realistic clear-sky index time-series,” Solar Energy, vol. 

158, pp. 9–19, Dec. 2017, doi: 10.1016/j.solener.2017.09.028.

[3] C. A. Glasbey, R. Graham, and A. G. M. Hunter, “Spatio-temporal 

variability of solar energy across a region: a statistical modelling 

approach,” Solar Energy, vol. 70, no. 4, pp. 373–381, Jan. 2001, doi: 

10.1016/S0038-092X(00)00152-3.

[4] A. Mills et al., “Dark Shadows,” IEEE Power and Energy Magazine, vol. 

9, no. 3, pp. 33–41, May 2011, doi: 10.1109/MPE.2011.940575.

[5] L. M. Hinkelman, “Differences between along-wind and cross-wind solar 

irradiance variability on small spatial scales,” Solar Energy, vol. 88, pp. 

192–203, Feb. 2013, doi: 10.1016/j.solener.2012.11.011.

[6] J. Munkhammar, J. Widén, and L. M. Hinkelman, “A copula method for 

simulating correlated instantaneous solar irradiance in spatial networks,” 

Solar Energy, vol. 143, pp. 10–21, Feb. 2017, doi: 

10.1016/j.solener.2016.12.022.

[7] Matthew Lave, Abraham Ellis, and Joshua S. Stein, “Simulating Solar 

Power Plant Variability: A Review of Current Methods,” Sandia National 

Laboratories, SAND2013-4757, Jun. 2013.

[8] H. Moaveni, D. K. Click, R. H. Meeker, R. M. Reedy, and A. Pappalardo, 

“Quantifying solar power variability for a large central PV plant and small 

distributed PV plant,” in 2013 IEEE 39th Photovoltaic Specialists 

Conference (PVSC), Jun. 2013, pp. 0969–0972, doi: 

10.1109/PVSC.2013.6744303.

[9] A. Kumler, I. L. Carreño, M. T. Craig, B.-M. Hodge, W. Cole, and C. 

Brancucci, “Inter-annual variability of wind and solar electricity 

generation and capacity values in Texas,” Environ. Res. Lett., vol. 14, no. 

4, p. 044032, Apr. 2019, doi: 10.1088/1748-9326/aaf935.

[10] J. Tan and Y. Zhang, “Coordinated Control Strategy of a Battery Energy 

Storage System to Support a Wind Power Plant Providing MultiTimescale Frequency Ancillary Services,” IEEE Transactions on 

Sustainable Energy, vol. 8, no. 3, pp. 1140–1153, Jul. 2017, doi: 

10.1109/TSTE.2017.2663334.
6

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications.

[11] North American Reliability Corporation, Standard BAL-001-2 – Real 

Power Balancing Control Performance, vol. BAL-001-2. .

[12] “NREL: Measurement and Instrumentation Data Center (MIDC) Home 

Page.” https://midcdmz.nrel.gov/ (accessed Jun. 29, 2019).

[13] M. Sengupta and A. Andreas, “Oahu Solar Measurement Grid (1-Year 

Archive): 1-Second Solar Irradiance; Oahu, Hawaii (Data),” National 

Renewable Energy Laboratory, DA-5500-56506, 2010. [Online]. 

Available: http://dx.doi.org/10.5439/1052451.

[14] A. Andreas and S. Wilcox, “Solar Technology Acceleration Center 

(SolarTAC); Aurora, Colorado (Data),” National Renewable Energy 

Laboratory, DA-5500-56491, 2011. [Online]. Available: 

http://dx.doi.org/10.5439/1052224.

[15] A. Andreas and T. Stoffel, “NREL Solar Radiation Research Laboratory 

(SRRL): Baseline Measurement System (BMS); Golden, Colorado 

(Data),” National Renewable Energy Laboratory, DA-5500-56488, 1981. 

[Online]. Available: http://dx.doi.org/10.5439/1052221.

[16] A. Andreas and T. Stoffel, “University of Nevada (UNLV): Las Vegas, 

Nevada (Data),” National Renewable Energy Laboratory, DA-5500-

56509, 2006. [Online]. Available: http://dx.doi.org/10.5439/1052548.

[17] A. Andreas and S. Wilcox, “Observed Atmospheric and Solar 

Information System (OASIS); Tucson, Arizona (Data),” National 

Renewable Energy Laboratory, DA-5500-56494, 2010. [Online]. 

Available: http://dx.doi.org/10.5439/1052226.

[18] J. Ramos and A. Andreas, “University of Texas Panamerican (UTPA): 

Solar Radiation Lab (SRL); Edinburg, Texas (Data),” National 

Renewable Energy Laboratory, DA-5500-56514, 2011. [Online]. 

Available: http://dx.doi.org/10.5439/1052555.

[19] D. Yang, “Ultra-fast preselection in lasso-type spatio-temporal solar 

forecasting problems,” Solar Energy, vol. 176, pp. 788–796, Dec. 2018, 

doi: 10.1016/j.solener.2018.08.041.

[20] “System Advisor Model (SAM) |.” https://sam.nrel.gov/ (accessed Mar. 

14, 2019).