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Conference Paper

NREL/CP-5K00-76021

June 2020

Estimating Subhourly Inverter Clipping Loss 

From Satellite-Derived Irradiance Data

Preprint

Kevin Anderson and Kirsten Perry

National Renewable Energy Laboratory

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

June 15 - August 21, 2020
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Conference Paper

NREL/CP-5K00-76021

June 2020

Estimating Subhourly Inverter Clipping Loss 

From Satellite-Derived Irradiance Data

Preprint

Kevin Anderson and Kirsten Perry

National Renewable Energy Laboratory

Suggested Citation

Anderson, Kevin and Kirsten Perry. 2020. Estimating Subhourly Inverter Clipping Loss From SatelliteDerived Irradiance Data: Preprint. Golden, CO: National Renewable Energy Laboratory. 

NREL/CP-5K00-76021. https://www.nrel.gov/docs/fy20osti/76021.pdf
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under Solar Energy Technologies Office (SETO) Agreement Number 34348. The views expressed in the article do 

not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the 

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Estimating Subhourly Inverter Clipping Loss From

Satellite-Derived Irradiance Data

Kevin Anderson

National Renewable Energy Laboratory

Golden, USA 

kevin.anderson@nrel.gov 

Abstract—Photovoltaic system production simulations are conventionally run using hourly weather 

datasets. Hourly simulations are suÿciently accurate

to predict the majority of long-term system behavior

but cannot resolve high-frequency e ̇ects like inverter

clipping caused by short-duration irradiance variability.

Direct modeling of this subhourly clipping error is 

only possible for the few locations with high-resolution

irradiance datasets. This paper describes a method of

predicting the magnitude of this error using a machine

learning regressor ensemble model, comprised of a 

random forest and an XGBoost model, and 30-minute 

satellite irradiance data. The method predicts a correction for each 30-minute interval with the potential to

roll up into 60-minute corrections to match an hourly 

energy model. The model is trained and validated at 

locations where the error can be directly simulated 

from 1-minute ground data. The validation shows low

bias at most ground station locations. The model is

also applied to gridded satellite irradiance to produce

a heatmap of the estimated clipping error across the 

United States. Finally, the relative importance of each

predictor satellite variable is retrieved from the model

and discussed. 

Index Terms—photovoltaic, inverter, clipping, saturation, high-frequency, irradiance, variability, modeling, satellite 

I. Introduction

The energy production models driving photovoltaic 

(PV) system development and fnancing are usually based 

on hourly weather fles sourced from satellite imagery. 

Although these satellite-derived datasets are somewhat 

less accurate than measurements recorded by meteorological stations on the ground, they have the advantage 

of being available for any location in the satellite’s coverage area, enabling energy models to simulate systems 

at any location of interest without having to deploy a 

weather monitoring station ahead of time. The uncertainty 

associated with using hourly averages instead of higherfrequency measurements has been previously studied [1] 

and is usually considered acceptable for the production 

forecasts used in system fnancing deals. However, as the 

price of PV modules decline, it is becoming increasingly 

common for PV system designers to “over build” systems by increasing the size of the PV array relative to 

the system’s inverter capacity. This capacity di ̇erence 

Kirsten Perry

National Renewable Energy Laboratory

Golden, USA 

kirsten.perry@nrel.gov 

is quantifed as the “DC/AC” ratio or inverter loading 

ratio (ILR). Systems with high ILR are more likely to 

experience inverter saturation where the array’s maximum 

power point is higher than the inverter’s maximum capacity and the array is operated at a less eÿcient point on its 

IV curve to avoid overloading the inverter. This behavior 

is called “inverter clipping” because it clips the top o ̇ 

the system’s daily power production curve. In practice, 

modern PV systems with ILRs of around 1.4 can clip 

on sunny days year-round. The production loss associated 

with this clipping is o ̇set by the additional production in 

less sunny periods and made economical by the declining 

price of PV modules. 

This clipping behavior is easily captured in production 

modeling by comparing the array’s power output to the 

inverter’s maximum power limit. However, as shown in 

Figure 1, calculating the e ̇ect of clipping at hourly scale 

will overestimate total system production compared to 

a higher-resolution simulation. This is because irradiance 

can vary signifcantly over the course of an hour depending 

on the nature of the cloud cover over the array. In some 

cases, irradiance can cycle between overcast (~300 W/m2) 

and full sun (>1000W/m2) several times in a single hourly 

interval. Taking the average of these irradiance values 

might yield an hourly value below the system’s clipping 

point, making it look like the system was able to capture 

all of the hour’s insolation when in reality the peaks 

would all get clipped o ̇. For modeling purposes, this 

could be described as the di ̇erence between “total interval 

insolation” and “harvestable interval insolation”. 

Because this e ̇ect manifests during periods with highly 

variable irradiance (which as noted earlier is dependent 

on the nature of cloud cover), the modeling error of an 

hourly simulation is dependent on climate. In locations 

with highly stable irradiance like southern California, the 

error should be quite low. In locations with more variable 

irradiance, the expected error would be larger. 

A few case studies have been published on this topic. 

Analysis of a 1.23 ILR system in San Diego, California 

reported an increase in estimated clipped energy from 

less than 1% to over 2.5% when switching from hourly 

to 1-second irradiance data [2]. Analysis of a system 

in Freiburg, Germany reported a decrease in inverter 

1

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Fig. 1. Simulated system power as a function of plane-of-array

(POA) irradiance. The orange dots are from an hourly simulation

and show low scatter. The blue points are from a 1-minute simulation

and averaged to hourly for the plot. The 1-minute simulation shows

some underperformance around the clipping knee because it correctly

averages irradiance and the nonlinear power response, but the hourly

simulation misses it and overestimates production as a result. 

eÿciency (including clipping loss) from 95% to 94% by 

switching from hourly to 1-minute irradiance and a further 

0.5% decrease by using 10-second data [3]. Finally, an 

analysis of irradiance data from Oak Ridge, Tennessee 

reported using hourly irradiance instead of 1-minute irradiance underestimates clipping loss by 0.4% and 1.5% 

for ILRs of 1.25 and 1.5, respectively [4]. These studies 

were able to quantify the error by taking advantage of 

high-frequency irradiance data from a co-located weather 

station. However, as mentioned earlier, high-resolution 

irradiance datasets are rarely available for a given area of 

interest. To support the modeling of this clipping error in 

locations without high-resolution ground data, we present 

a method for predicting the theoretical clipping error from 

30-minute satellite-derived weather data from the National 

Solar Radiation Database (NSRDB) [5]. 

The method uses an ensemble regressor model, which 

is comprised of a random forest and an XGBoost model 

and trained to predict the interval clipping errors simulated from 1-minute ground station data using only lowresolution satellite weather data. Because the model uses 

only satellite data for its predictions, it can be applied to 

any location within the coverage area of the NSRDB. The 

model’s predictions are validated across the ground station 

network by retraining the model excluding each ground 

station in turn and comparing its predictions against the 

ground truth values. 

II. Methodology

The approach taken here is to use known clipping 

errors and the associated NSRDB weather data to train a 

machine learning model to predict error using only satellite 

data that is sampled at a lower frequency. In this case, 

the known clipping errors are generated by simulating the 

ground-truth clipping error at various locations around 

the United States where 1-minute ground irradiance data 

Fig. 2. A map showing the geographic spread of the ground station

locations, colored by the source station network. Note that some 

stations are members of multiple networks, only one of which is shown

here. 

is available. The 30-minute satellite data associated with 

each ground station’s location and data set time range is 

then processed and used to predict the clipping error. 

In an e ̇ort to make the model as generally-applicable 

as possible, we combine the data from several ground 

station networks [6]–[10] with good coverage across various 

climates in the United States. The geographic distribution 

of the stations is shown in Figure 2 and specifc station 

details are presented in Table I. 

To generate the ground-truth clipping error values, 

we use the detailed PV model included in the National 

Renewable Energy Laboratory’s System Advisor Model 

(SAM) [11] using the PySAM [12] wrapper to enable 

scripted model runs. SAM is capable of running detailed 

PV system simulations down to 1-minute resolution. In 

this case, we use it to predict two array output signals for 

each ground station: one using the raw 1-minute dataset, 

and another using the 30-minute average of the 1-minute 

dataset. The simulations are performed assuming a southfacing fxed-tilt system at 20 with an ILR of 1.4. We 

do not expect the specifc hardware details to be relevant 

for this calculation, but for completeness, the simulation 

modeled DC power for a JA Solar JAP6-72-305/3BB 

polycrystalline module. Other inputs not specifc to this 

simulation (such as wiring losses) were left as the default 

values. We then post-process the SAM outputs to calculate 

two 30-minute average timeseries: frst, applying a simple 

clipping model to the 1-minute simulated array power 

and then calculating the 30-minute average clipped power, 

and second, clipping the 30-minute average array power. 

Both result in clipped 30-minute power signals, but the 

di ̇erence is whether clipping is applied at high-frequency 

scale (as would happen in a real system) or low-frequency 

scale (as is commonly modeled). The di ̇erence between 

2

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TABLE I 

Ground Station Metadata

Station Code Years Data Source Latitude Longitude Elevation (m) UTC O ̇set 

0 

1 

ABQ 

ATI 

2017-2018 

2006-2016 

SOLRAD 

MIDC 

+35.0380 

+39.7423 

-106.6221 

-105.1785 

1617 

1828 

-7 

-7 

2 BIL 1998-2017 BSRN +36.6050 -97.5160 317 -6 

3 BIS 2016-2018 SOLRAD +46.7718 -100.7596 503 -6 

4 BON 2010-2017 SURFRAD +40.0519 -88.3731 230 -6 

5 BOS 2010-2015 SURFRAD +40.1250 -105.2368 1689 -7 

6 BUO 2012-2018 UOSRML +43.5192 -119.0216 1265 -8 

7 DIM 2012-2018 UOSRML +45.2100 -112.6400 1590 -7 

8 DRA 2011-2017 SURFRAD +36.6237 -116.0195 1007 -8 

9 GCR 2010-2017 SURFRAD +34.2547 -89.8729 98 -6 

10 HNX 2016-2018 SOLRAD +36.3136 -119.6316 73 -8 

11 HSU 2009-2017 MIDC +40.8760 -124.0800 36 -8 

12 LMU 2011-2014 MIDC +33.9667 -118.4226 27 -8 

13 LRC 2015-2018 BSRN +37.1038 -76.3872 5 -5 

14 MSN 2016-2018 SOLRAD +43.0725 -89.4113 271 -6 

15 NPC 2010-2012 MIDC +36.0858 -115.0519 523 -8 

16 ORNL 2008-2018 MIDC +35.9300 -84.3095 245 -5 

17 PSU 2010-2017 SURFRAD +40.7201 -77.9309 376 -5 

18 SLC 2016-2018 SOLRAD +40.7722 -111.9549 1288 -7 

19 SMUDA 2011 MIDC +38.5459 -121.2403 51 -8 

20 STE 2016-2018 SOLRAD +38.9720 -77.4869 85 -5 

21 STW 2016-2018 UOSRML +47.6800 -122.2500 20 -8 

22 SXF 2010-2017 SURFRAD +43.7340 -96.6233 473 -6 

23 TFI 2014-2018 UOSRML +42.5500 -114.3500 1200 -8 

24 TSESC 2012 MIDC +35.4186 -108.0883 2106 -7 

25 UAT 2014-2015 MIDC +32.2297 -110.9553 786 -7 

26 UNLV 2007-2018 MIDC +36.1070 -115.1425 615 -8 

27 USEPCC 2011-2012 MIDC +37.6960 -113.1648 1675 -7 

28 UTPASRL 2012-2018 MIDC +26.3059 -98.1716 45 -6 

these two signals is what we call “1-to-30” clipping error, 

and represents the amount that a low-frequency simulation 

overestimates production. For convenience, we normalize 

the 1-to-30 clipping error by the simulated AC capacity 

so it spans the range [−1, 0]. Note that to avoid the 

infuence of other nonlinear e ̇ects (e.g. solar position and 

cell temperature) from confounding the results, we also 

calculate the 30-minute di ̇erence in the unclipped signals 

and remove that from the clipping error. 

Once the 1-to-30 clipping error is calculated, we pair 

it with the values used as predictors. In an e ̇ort to 

keep the prediction process as simple as possible, we 

use only raw NSRDB values and derived values that are 

easily scripted using the open-source library pvlib-python 

[13]. The NSRDB data provides the estimated surface 

irradiance components global horizontal irradiance (GHI), 

di ̇use horizontal irradiance (DHI), and direct normal irradiance (DNI), the corresponding three clearsky irradiance 

components, as well as ambient temperature and wind 

speed. From the irradiance components, plane-of-array 

(POA) irradiance and clearsky POA irradiance are calculated for a south-facing array at 20 tilt using the isotropic 

di ̇use sky model as implemented in pvlib-python. Additionally, we calculate estimated cell temperature using 

pvlib-python’s Sandia Array Performance Model (SAPM) 

temperature function with the “open rack/polymer back” 

thermal parameters. 

In addition to these PV variables, two additional feature 

variables are derived to aid the model: the “velocity” of 

POA irradiance, i.e. the frst-order di ̇erence of the time 

series, and the di ̇erence between POA irradiance and 

clearsky POA irradiance at each time interval. 

These values are collected to form a 30-minute predictor 

dataset containing: 

• GHI and clearsky GHI 

• POA irradiance and clearsky POA irradiance 

• Cell temperature 

• POA velocity 

• Di ̇erence between POA and Clearsky POA 

Finally, each of the predictor variables is max-min normalized by location so that each series spans the range 

[0, 1]. This predictor dataset and the associated 1-to30 clipping error values were generated for each of the 

ground stations at thirty minute intervals. Datasets of 

this form were used for both model training and model 

validation. Total dataset size, including all 29 locations, is 

approximately 1.31 million rows, with the size of the data 

by location varying. 

The prediction model used in this study is an ensemble model implemented with the open-source scikit-learn 

package in Python [14], comprising a random forest (RF) 

regressor model and an extreme gradient boosting (XGBoost, [15]) regressor model. In the model, each 30-minute 

interval acts independently; consequently, the model will 

treat each timestamp separately when predicting 1-to-30 

clipping error, where the only dependence on additional 

3

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time readings is the previously calculated POA velocity 

parameter. Model hyper-parameters include: 

• RF model instantiated with 100 trees. 

• Equal ffty-percent weighting for the XGBoost model 

and the RF model in the fnalized ensemble model. 

To test the model’s predictive ability at locations it was 

not trained on, we use a cross-validation technique. By 

omitting the data associated with one station from the 

training dataset, it can be used as a validation set to test 

the model’s accuracy at a novel location. This method was 

applied to each ground station to quantify the model’s 

error across di ̇erent geographies. In all, the model was regenerated 29 times, for each of the 29 locations. Root mean 

squared error (RMSE) and mean bias error (MBE) were 

calculated for each location’s predictions using the crossvalidation technique, ensuring unbiased model results. 

Additionally, we trained an “all-in” model using data 

from the entire ground station network and used it to 

predict the clipping error across a grid of points covering 

the United States. Ensemble model hyper-parameters, 

including individual model weighting, remained consistent 

while regenerating models using cross-validation, as well as 

when generating the “all-in” model. 

III. Results

Figure ?? compares clipping error predicted by the ensemble model to the simulated clipping error from ground 

station data. Each point represents clipping error as a 

percentage of monthly production, with one point per 

station per month. The results show low overall bias, 

although the scatter for individual station-months can 

be signifcant. Figure 4 shows the di ̇erence between 

predicted and actual monthly clipping errors by station 

and the associated error statistics are listed in Table III. 

The model performs well at most stations (the model’s 

predictions have |MBE| < 0.1 for over half the stations) 

and it seems much of the scatter in Figure ?? is from only 

a few stations. It is not clear why the model performs 

poorly on these stations. However, the overall results from 

the cross-validated models show that the model typically 

performs well on novel data sets, although there is room 

for improvement. We expect the prediction error would 

be reduced by refning the ensemble model structure and 

training method. 

Table II provides a list of the feature importances for 

both the XGBoost and Random Forest models which 

comprise the ensemble model. Feature importance is a 

value ranging between [0, 1], providing a fractional representation of how much each model variable a ̇ects overall 

model outcome. For both models, normalized clearsky 

POA has the highest feature importance score, indicating 

that this variable has the greatest e ̇ect on overall model 

outcome. However, the XGBoost model assigned a feature 

importance score of 0.495 to the normalized clearsky POA 

variable, which is signifcantly higher than the random 

forest model score of 0.196 for the same variable. With 

Fig. 3. Comparison of clipping error predicted by the ensemble model

and expected loss from ground station data. Units are in percent of

monthly production. A least-squares ft is shown. Results are for each

location, using cross-validated predictions. 

Fig. 4. The distribution of monthly clipping error di ̇erences (predicted - actual) by station, ranked from least to greatest overall MBE.

Units are percent of monthly production. The model shows minimal

prediction bias at most stations, although it does show signifcant

bias and scatter at some stations. 

the exception of normalized clearsky POA, feature variable 

rankings varied based on the model. 

Figure 5 shows the model’s prediction at a grid of locations across the United States using the NSRDB dataset 

for the year 2018. The geographic variation in the map 

is roughly consistent with an irradiance variability map 

previously published by researchers at Sandia National 

Laboratory as it relates to power ramp rates in the context 

of grid integration [16]. It shows a nation-wide average 

annual clipping error of roughly 1%, but as shown by the 

range of monthly error in Figure ??, individual months 

can be signifcantly higher or lower. We emphasize that 

the model used to generate Figure 5 was trained on a 

certain system confguration and thus its predictions are 

4

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TABLE II 

Ensemble Model Fractional Feature Importances

Feature Variable XGBoost Random Forest 

Normalized Clearsky POA 

Di ̇erence between Clearsky

POA and POA, Normalized 

0.495 

0.172 

0.196 

0.105 

Normalized POA 0.112 0.151 

Normalized POA Velocity 

Normalized Cell Temperature 

Normalized Clearsky GHI 

Normalized GHI 

0.096 

0.050 

0.039 

0.036 

0.170 

0.140 

0.128 

0.110 

TABLE III 

Cross-Validation Results by Station:

Monthly model prediction error

Station Code MBE RMSE 

0 ORNL -0.41 0.50 

1 HSU -0.26 0.42 

2 LMU -0.25 0.32 

3 BIL -0.16 0.23 

4 HNX -0.08 0.15 

5 SLC -0.07 0.18 

6 ATI -0.07 0.20 

7 UNLV -0.07 0.12 

8 DRA -0.06 0.18 

9 STW -0.05 0.16 

10 SMUDA -0.05 0.15 

11 LRC -0.05 0.19 

12 TFI -0.02 0.16 

13 BIS -0.02 0.17 

14 NPC -0.02 0.13 

15 ABQ -0.01 0.15 

16 DIM -0.00 0.17 

17 MSN 0.03 0.29 

18 BOS 0.03 0.24 

19 SXF 0.04 0.23 

20 USEPCC 0.05 0.18 

21 UAT 0.10 0.19 

22 STE 0.17 0.27 

23 BON 0.17 0.34 

24 UTPASRL 0.19 0.45 

25 GCR 0.19 0.38 

26 BUO 0.26 0.40 

27 TSESC 0.29 0.39 

28 PSU 0.29 0.46 

specifc to that system confguration. Additionally, there is 

some evidence in the literature that 1-minute data may be 

insuÿcient to fully resolve this e ̇ect (e.g. [2], [3]) and the 

true clipping error may be higher. We include the map here 

not to provide guidance for adjusting energy models to 

account for the e ̇ect, but rather to illustrate the model’s 

geographic behavior. 

A notable feature is the distinct low error region starting 

in California’s central valley and extending down into 

Arizona. Because these areas are dominated by clearsky 

conditions, the low predicted clipping error is consistent 

with expectation. An additional note is that the outlier 

pixels in Figure 5 predicting large error appear to be 

associated with bodies of water: Great Salt Lake (Utah), 

Salton Sea (California), and Mobile Bay (Alabama). 

Fig. 5. A map showing the model’s estimated 1-to-30 clipping error 

on a 0.5 × 0.5 grid across the United States for the year 2018. 

IV. Conclusions

This paper presents a method of using widely-available 

weather data derived from satellite imagery to predict 

the e ̇ect of local high-frequency irradiance variability 

on PV system production. The method can be applied 

to any location within the NSRDB’s coverage area, but 

is validated only within the United States. The method 

is trained and validated using data from an extensive 

network of ground weather stations, showing low bias 

when considering the validation as a whole. The results of 

a cross-validation analysis showed that the model generally 

performs well at novel locations (|MBE| < 0.1 at monthly 

scale for over half of the stations) but its predictions do 

have high bias and scatter at some locations. Because 

the method predicts clipping error at 30-minute intervals, 

this method has the potential to be used to be used to 

correct conventional hourly energy estimates. The model’s 

predictions across a grid of locations covering the United 

States are qualitatively consistent with existing results in 

the literature. Outlier results for pixels near large bodies 

of water suggest that predicted clipping error should be 

treated with caution in NSRDB pixels containing bodies 

of water. Overall, these results demonstrate the viability of 

using satellite data to predict the e ̇ects of high-frequency 

irradiance variability. 

V. Acknowledgement

This work was authored by Alliance for Sustainable 

Energy, LLC, the manager and operator of the National 

Renewable Energy Laboratory for the U.S. Department of 

Energy (DOE) under Contract No. DE-AC36-08GO28308. 

Funding provided by the U.S. Department of Energy’s 

Oÿce of Energy Eÿciency and Renewable Energy (EERE) 

under Solar Energy Technologies Oÿce (SETO) Agreement Numbers 34348. The views expressed in the article 

do not necessarily represent the views of the DOE or 

the U.S. Government. The U.S. Government retains and 

the publisher, by accepting the article for publication, 

acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish 

5

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.
or reproduce the published form of this work, or allow 

others to do so, for U.S. Government purposes. 

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