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Contract No. DE-AC36-08GO28308

Downscaling Solar Power 

Output to 4-Seconds for Use in 

Integration Studies

Preprint

M. Hummon, A. Weekley, K. Searight, 

and K. Clark

To be presented at the 3rd International Workshop on Integration of 

Solar Power in Power Systems

London, England

October 21–22, 2013

Conference Paper

NREL/CP-6A20-60335

October 2013
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Downscaling Solar Power Output to 4-Seconds for 

Use in Integration Studies

Marissa Hummon, Andrew Weekley, Keith Searight, Kara Clark

National Renewable Energy Laboratory

Golden, CO

Author contact: marissa.hummon@nrel.gov

Abstract— High penetration renewable integration studies 

require solar power data with high spatial and temporal 

accuracy to quantify the impact of high frequency solar 

power ramps on the operation of the system. Our previous 

work concentrated on downscaling solar power from one 

hour to one minute by simulation. This method used clearness 

classifications to categorize temporal and spatial variability, 

and iterative methods to simulate intra-hour clearness 

variability. We determined that solar power ramp 

correlations between sites decrease with distance and the 

duration of the ramp, starting at around 0.6 for 30-minute 

ramps between sites that are less than 20 km apart. The subhour irradiance algorithm we developed has a noise floor that 

causes the correlations to approach ~0.005. Below one 

minute, the majority of the correlations of solar power ramps

between sites less than 20 km apart are zero, and thus a new 

method to simulate intra-minute variability is needed. These 

intra-minute solar power ramps can be simulated using 

several methods, three of which we evaluate: a cubic spline fit 

to the one-minute solar power data; projection of the power 

spectral density toward the higher frequency domain; and 

average high frequency power spectral density from 

measured data. Each of these methods either under- or overestimates the variability of intra-minute solar power ramps. 

We show that an optimized weighted linear sum of methods, 

dependent on the classification of temporal variability of the 

segment of one-minute solar power data, yields time series 

and ramp distributions similar to measured high-resolution 

solar irradiance data.

Keywords – downscaling solar power; solar power 

integration; automatic generator control; power spectral 

density; solar power variability

I. INTRODUCTION

Integration studies of solar power range from capacity 

expansion to operations and production cost to highfrequency transient stability analysis. The impact analysis 

framework of each integration study defines the geographic 

and temporal scope, as well as the resolution of the input 

data. For instance, production cost operation studies require 

solar power data with temporal resolution less than 5-

minutes in order to accurately calculate operating reserve 

requirements [1] and 5 to 60 minutes to optimize the unit 

commitment and economic dispatch models [2,3]. The 

distance between injection busses in the transmission or 

distribution network often determines the geographic 

resolution required for the solar power data. Aggregation of 

point source solar power data to the injection busses should 

show a reduction of solar power variability with an increase 

in area “covered” by the aggregated data [4]. In addition, 

the solar data set should be coherent across geographic and 

temporal scales, such that nearby sites have a higher degree 

of correlation in the change in solar power output (ramp) 

than sites that are further apart. Likewise, ramps with a 

shorter duration have a lower correlation between two sites 

than longer duration ramps [2,5].

The power system balances generation and load on a 

second-to-second basis via several mechanisms including 

automatic generator control (AGC). The majority of 

demand is met by scheduling generation units 24 to 36 

hours in advance to come online. However, system 

operators also schedule “spare” capacity to make up any 

real time differences between the schedule generation and 

the actual demand [6]. The rules and procedures for 

balancing the system by deploying operating capacity, at 

time scales of less than 5-minutes, are based on a long 

history of operating the system. High temporal resolution 

solar data enables researchers to explore new methods of 

balancing the system [7], as the penetration of variable 

generation increases. This paper consists of four sections: 

overview of the four-second algorithm (FSA), analysis of 

four-second variability, modelling of four-second 

variability, and comparing the FSA outputs to measured 

data.

II. FOUR-SECOND ALGORITHM OUTLINE

The FSA was designed on two premises. First, the 

correlation between changes in solar power output over a 

time interval of 4-seconds at one site are uncorrelated with 

simultaneous ramps at any other site in the system. In other 

words, the cloud properties that cause high frequency 

changes in solar power are uncorrelated over the region. 

Indeed, below one minute, the majority of the correlations 

of solar power ramps between sites less than 20 km apart 

are zero. Second, the variability of the 4-second solar 

power ramps is related to the 1-minute solar power ramp

variability. Thus, if the 1-minute solar power values are 

smooth, we expect that the 4-second solar power values 

are also smooth. Fig. 1 outlines the steps in the FSA. The 

first step is converting the solar irradiance data to clearness 

index (measured solar data divided by the clear sky 

expected solar data), which removes the diurnal shape of 

the solar data. The second step segments the data into 60-

minute periods for analysis and computation. There are 

four phases for step 2: classify the variability (discussed in 

Section III), calculate the fast Fourier transform (FFT), 

model high frequency behavior (discussed in Sections IV
2 

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and V), and calculate the inverse FFT (IFFT). Step 3 

concatenates the segments of modelled 4-s data, removes 

discontinuities, and applies the appropriate spatial filter. 

Step 4 rescales the clearness index data to irradiance data.

Weekley et al. (2013) provides a thorough discussion of 

the downscaling method described in this paper, see Ref.

[8]. Other groups have pursued algorithms for downscaling 

solar power data from satellite images [9], and from 

numerical weather prediction models [10]. 

III. HIGH-FREQUENCY SOLAR DATA

To estimate the values of 4-second time interval solar 

power from 1-minute values of solar power, we used two 

datasets of ground measured solar global horizontal 

irradiance (GHI) with a temporal resolution of 1-second. 

The Oahu dataset consists of 17 irradiance sensors covering 

an area of 0.25 km2

, which represents approximately a 10 

MW photovoltaic power plant [11]. The Golden dataset 

consists of 4 irradiance sensors in close proximity 1

. A 

single day of simultaneous global horizontal irradiance 

from all sensors in the Oahu dataset is shown in Fig. 2a, the 

average of the sensors is shown in Fig. 2b. 

Figure 1. Outline of the four-second algorithm.

As stated earlier, we expect the ramps in the 4-second 

data to be related to the ramps in the 1-minute data. In order 

to classify the temporal variability, we calculate the clear

sky GHI (GHIclear) for each location/time step and then 

calculate the clearness index: GHImeas/ GHIclear. Each 60-

 1 The sensors located at the National Renewable Energy 

Laboratory are part of the Measurement and Instrumentation Data 

Center (MIDC): http://www.nrel.gov/midc/

minute segment per dataset is assigned to one of six classes 

of clearness index temporal variability (classes are shown 

in Fig. 3). These classes of temporal variability are 

described primarily by the standard deviation of the 

clearness index ramps, from smoothly varying cloud cover 

(Class I) to cumulus cloud cover (Class V). Further 

discussion of the clearness index classification can be found 

in Ref. [2]. We use the temporal classification of the 1-

minute data as an input to the algorithm because the high 

frequency characteristics of the time series are separable by 

temporal class. For instance, Fig. 4 shows the time series 

and power spectral density of a segment from the Oahu 

dataset, classified as Class V.

Figure 2. Global horizontal irradiance time series for individual sites 

(upper) in the Oahu dataset and the average of all 17 sites (lower).

Figure 3. Examples of the five classes of temporal variability are shown 

in plots (a) through (e). Classes I-III (a-c) are based on the width of the 

distribution of ramps. Classes IV-V (d,e) are characterized by a rapid 

change between two or more different cloud cover densities (e.g., clear 

sky with small, dense clouds moving at a high altitude). Panel (f) shows 

how the temporal classes are defined in terms of the mean (μci) and 

standard deviation (σci) of the clearness index for 60 consecutive minutes.
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Figure 4. Time series and power spectral density of one hour (Class V) of 

clearness index with 4-second resolution.

The power spectral density demonstrates the magnitude 

of each frequency in the time series [12]. Fig. 5

demonstrates the average power spectral density (PSD) of 

the 1-second data for each temporal variability class, 

calculated by analyzing all of the high frequency measured 

data in the Oahu dataset over a year. The classes with the 

least variability have the lowest amplitude of power 

spectral density across all frequencies. The average PSD is

one of four downscaling methods that are linearly summed

with class-specific optimal weighting to estimate the highfrequency behavior of the solar PSD (described in Section 

V).

Figure 5. Average spectral amplitude for Oahu dataset, shown as a 

function of temporal variability class.

IV. MODELLING FOUR-SECOND VARIABILITY

The average PSDs underestimate the variability 

observed in measured 4-second data. We test this by 

comparing the ramps of the modelled data resulting from 

the IFFT to the ramps of the measured 4-second. The 

average plots of the solar PSD appear to be linear in log-log 

space, which is suggestive of a power law. Regions of 

differing slope suggest that the physical processes that 

cause variability are not continuous across all times scales. 

For instance, the physics of cloud formation, movement, 

and dissipation drive variability on time scales between 1-

minute and 20-minutes. However, variability below 1-

minute might be driven by the internal movement of clouds.

Fig. 6 shows two additional methods for estimating the 

PSD in the high frequency region. Starting with the PSD of 

the 1-minute data (the input to the four-second algorithm), 

we use a linear fit to either all of the frequencies in the 1-

minute PSD (black line) or the frequencies between 

0.004167 and 0.00833 (2 to 4 minutes, pink line) which is 

the higher half of the 1-minute PSD frequencies. The fit 

over all frequencies is representative of the general trend 

during the hour, while the fit over the higher frequency 

region, which tends to have a shallower slope, suggests that 

the variability of the data on time scales near 2-minutes is 

larger than the higher frequency data.

We compare the distribution of 4-second ramps using 

the linear fits in Fig. 6, as well as a cubic spline fit to the 1-

minute data. The linear fit over a subset of frequencies 

generally overestimated the magnitude of the 4-s ramps. 

Both the linear fit over all frequencies and the cubic spline 

fit underestimated the 4-s ramps. However, some classes of 

variability seemed to be better suited to each of the four 

methods presented. For instance, Class 0 and I are best 

described by either the linear fit over all frequencies or the 

average PSD from measured data, while Class V data 

between 30s and 2 minutes is best described by a linear fit 

over higher frequencies. This suggests that a linear

combination of methods, with a different set of coefficients 

to weight the contribution of each method, for each class of 

variability, may yield the most accurate results.

Figure 6. Power spectral density for measured 1-second data, 

corresponding 1-minute data, and three methods of estimating highfrequency amplitude: linear fit to a subset of frequencies (2-4 minutes), 

average fit over all Class V data, linear fit to all frequencies in the 1-

minute data. Vertical lines are labeled in the corresponding time domain.
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V. RESULTS

The weights of the four downscaling methods listed in 

Table 1 were optimized using a constrained least-squares 

linear fit. The objective function of the optimization was to 

minimize the difference between the ramp distributions of 

the weighted sum of the four methods and the measured 

data. Table 1 shows the coefficients for calculating a 

weighted linear sum of the downscaling methods. Spline is 

the dominant method for the low variability classes (0, I, 

II, III), which is consistent with our observation that low 

variability in the 1-minute data is correlated with low 

variability in the 4-second data. Class V data, which is 

representative of cumulus cloud movement, is fit primarily 

by the linear fit to the subset of higher frequencies in the 1-

minute PSD. One possible physical explanation for this is 

that cumulus cloud edges have non-uniform cloud optical 

depth and move, relative to a point on the surface, on the 

order of 1 to 20 seconds.

Fig. 8 shows the ramp distributions of measured and 

modelled 4-second clearness index, for a single site in 

Colorado. Both datasets have been filtered to represent a 

2.4 MW PV plant, covering an area of 0.063 km2

. Each 

hour of daytime data was classified by the measured 1-

minute variability; hours with the same classification were 

binned together. Table 2 shows both the mean square error 

for the time series comparison, as well as the 4-s ramp 

distribution comparison. Clearness index ranges from 0 to 

1 for the time series and from 0 to 0.5 for the ramp 

distribution. Classes 0, I, and II perform extremely well, as 

expected since the variability of the 1-minute and 4-second 

GHI is very small. Classes III, IV, and V perform less well 

in term of mean squared error for the time series. This is 

also expected given that the modelled data is not meant to 

predict “when” the 4-second variability occurs in the hour, 

but is meant to model the frequency and magnitude of the 

4-second variability. That is apparent in the low mean 

squared error of the ramp distributions for all classes.

Table 1. Coefficients for a weighted linear combination of downscaling 

methods (in time domain), by class of temporal variability.

Downscaling 

Method

Class of Temporal Variability

0 I II III IV V

Spline 0.47 0.71 0.44 0.47 0.31 0.32

Linear fit over 

all frequencies 0.27 0.01 0.28 0.35 0.36 0.22

Linear fit over a 

subset of higher 

frequencies 

0.11 0 0.11 0.1 0.16 0.45

Spectral 

amplitude 

estimated from 

historical 

average FFT

0.15 0.15 0.16 0.08 0.17 0.01

Table 2. Mean square error of modelled 4-second clearness index data 

compared to measured data.

Measure Class of Temporal Variability

0 I II III IV V

time 

series

9.2E056.3E065.2E041.8E031.9E031.6E02

4-s 

ramp 

dist.

6.6E078.8E113.6E069.1E061.0E054.9E06

CONCLUSION

Solar power studies have moved from questions like

“can the grid operate with high penetrations of variable 

energy?” to “what are the economics to operating the grid 

with high penetrations of variable energy?” Four-second 

solar power data enables researchers to investigate new 

methods of balancing the system under high penetrations 

of solar power. We present a method of downscaling 1-

minute solar data to 4-seconds by optimizing the linear 

combination of four methods for extending the PSD from f

= 1/120 to 1/2 Hz (from 2-minutes to 2-seconds): spline, 

historic average, full linear fit to PSD, and linear fit to 

subset of higher frequencies in the PSD. The optimized 

weights vary by classification of the 1-minute temporal 

variability. We demonstrate the quality of the fit by 

observing the mean squared error of the modelled data in 

both the time series and the distribution of 4-second ramps. 

The modelled data performs very well in comparing the 

distributions of ramps, which makes this dataset ideal for 

use in integration studies concerned with the rapid change 

in solar power output effecting system balancing 

requirements.

ACKNOWLEDGMENT

This work was supported by the U. S. Department of 

Energy under Contract No. DE-AC36-08-GO28308 with 

the National Renewable Energy Laboratory. The authors 

gratefully acknowledge the support of Kevin Lynn, Venkat 

Banunarayanan, and the U.S. Department of Energy Solar 

Energy Technologies Office SunShot Initiative for funding 

this work. The authors would like to thank the 

Measurement and Instrumentation Data Center at NREL 

for collecting, calibrating, and providing quality 

control/quality assurance for the measured datasets used in 

this study.

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Figure 7. Comparison of 4-s ramp distributions (by variability class) for 

modelled and measured data.