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

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Contract No. DE-AC36-08GO28308

High Resolution PV Power 

Modeling for Distribution Circuit 

Analysis

Benjamin L. Norris and John H. Dise

Clean Power Research

Napa, California

NREL Technical Monitor: Barry Mather

Subcontract Report

NREL/SR-5D00-60476

September 2013
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.

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Contract No. DE-AC36-08GO28308

High Resolution PV Power 

Modeling for Distribution 

Circuit Analysis

Benjamin L. Norris and John H. Dise

Clean Power Research

Napa, California

NREL Technical Monitor: Barry Mather

Prepared under Subcontract No. LAT-2-11817-01

Subcontract Report

NREL/SR-5D00-60476

September 2013
This publication was reproduced from the best available copy

submitted by the subcontractor and received no editorial review at NREL.

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High Resolution PV Power Modeling for 

Distribution Circuit Analysis

Benjamin L. Norris

John H. Dise

March 2013

Prepared for:

National Renewable Energy Laboratory

Subcontract LAT-2-11817-01

“Analysis of High-Penetration Levels of PV into the Distribution Grid in California”

Prepared by:

Clean Power Research

1700 Soscol Ave., Suite 22

Napa, CA 94559
ii

Acknowledgements

The author wishes to express his appreciation to David Chalmers for implementing the 1-minute 

SolarAnywhere resolution, and to Phil Gruenhagen for creating the user interface to build systems and 

access the simulation service.
3

Executive Summary

NREL has contracted with Clean Power Research to provide 1-minute simulation datasets of PV systems 

located at three high penetration distribution feeders in the service territory of Southern California 

Edison (SCE): Porterville, Palmdale, and Fontana, California. The resulting PV simulations will be used to 

separately model the electrical circuits to determine the impacts of PV on circuit operations.

The 1-minute simulations incorporate satellite-derived irradiance data with a spatial resolution of 

nominally 1 km x 1 km and a temporal resolution of 30 minutes. The special resolution is the highest 

available through existing satellite imagery, and is shown in Figure ES- 1 for the Porterville site relative 

to the size of the modeled PV system.

To obtain the 1-minute data, inter-image interpolations are generated with a “cloud motion vector” 

method by translating the previous image over time using wind speed and direction. The resulting 

irradiance data is fed into a PV simulation model to produce power output.

Figure ES- 1. Satellite resolution at Porterville

PV System
4

An example of the 1-minute data is shown for Fontana in Figure ES- 2 for the day having the highest 

variability of 2011, May 29. Of greatest interest is the highest variability observed on the distribution 

line, so additional analysis of ramp rates was warranted.

As shown in Figure ES- 3, the number of significant ramping events is very small, but the magnitude of 

the highest events is significant. The number of ramping events higher than 50% of PV system rated 

output per minute is taken as a metric of “significant” ramping, and this is shown for the Fontana site to 

be 37 events per year. The highest such event is shown in Figure ES- 4 with an increase in PV output 

(caused by a departing cloud) of 2.20 MW per minute, or 75% of the systems rated output.

Through methods such as the one described in this report and demonstrated through the datasets 

delivered under this project, utility engineers will be able to better predict the impacts of high 

penetration PV on their distribution circuits.

Figure ES- 2. Highest variability day at Fontana, 2011 (May 29).
5

Figure ES- 3. Ramp rate duration curve (Fontana, 2011)

Figure ES- 4. Maximum ramping event at Fontana, 2011.
6

Table of Contents

Acknowledgements....................................................................................................................................... ii

Executive Summary.......................................................................................................................................3

Table of Contents..........................................................................................................................................6

List of Figures................................................................................................................................................7

Background ...................................................................................................................................................8

Introduction: Three High Penetration Study Feeders...................................................................................9

Methods......................................................................................................................................................10

Satellite Images.......................................................................................................................................10

Cloud Motion Vector Method.................................................................................................................10

PV Simulations ........................................................................................................................................10

Delivered Data Sets.....................................................................................................................................13

1-minute production data.......................................................................................................................13

Hourly irradiance and temperature data................................................................................................13

Data Validation ...........................................................................................................................................13

CAISO stations.........................................................................................................................................14

SMUD stations ........................................................................................................................................14

Additional comparisons to ground sensors............................................................................................15

Analysis .......................................................................................................................................................16

Missing data............................................................................................................................................16

Variability ................................................................................................................................................18

Ramp Rate Duration Curve .....................................................................................................................19
7

Appendix 1: Fontana (Study Feeder 1) .......................................................................................................23

Appendix 2: Porterville (Study Feeder 2)....................................................................................................25

Appendix 3: Palmdale (Study Feeder 3)......................................................................................................27

List of Figures

Figure 1. Study feeder locations and SCE service territory...........................................................................9

Figure 2: Average %MAE of four CAISO locations versus time interval of comparison..............................14

Figure 3: Average %MAE versus time interval of comparison for over sixty locations in SMUD territory.15

Figure 4: %MAE versus time interval of comparison for the ISIS station in Hanford, CA...........................16

Figure 5. Missing data at Fontana, February 24, 2011 from 13:29 to 13:58. .............................................17

Figure 6. GOES-west satellite image, July 24, 2011 (21:30:00 UTC), showing error streak........................18

Figure 7. Highest variability day at Fontana 2011 (May 29). ......................................................................19

Figure 8. Absolute 1-minute ramp rates at Fontana, 2011. .......................................................................20

Figure 9. Ramp rate duration curve, Fontana, 2011...................................................................................20

Figure 10. Highest 100 ramp rates at Fontana, 2011. ................................................................................21

Figure 11. Maximum ramp event at Fontana, 2011 (2.20 MW/min). ........................................................21

Figure 12. Fontana PV system.....................................................................................................................23

Figure 13. Satellite resolution at Fontana...................................................................................................23

Figure 14. Porterville PV system. ................................................................................................................25

Figure 15. Satellite resolution at Porterville. ..............................................................................................25

Figure 16. Palmdale PV system...................................................................................................................27

Figure 17. Satellite resolution at Palmdale.................................................................................................27
8

Background

SolarAnywhere is the premier solar irradiance time-series source for all locations within the continental 

US, Hawaii, Mexico, the Caribbean and parts of Canada. Irradiance estimates are generated using NOAA 

GOES visible satellite images processed using the most current algorithms developed by Dr. Richard 

Perez at the University at Albany (SUNY). These algorithms extract cloud indices from the satellite's 

visible channel using a self-calibrating feedback process that is capable of adjusting for arbitrary ground 

surfaces. The cloud indices are used to modulate physically-based radiative transfer models describing 

localized clear sky climatology. SolarAnywhere irradiance estimates have several advantages over 

ground based measurements including longer histories, lower costs, faster time to market, and the 

ability to directly produce solar power and variability forecasts. 

Clean Power Research works with Dr. Perez and SUNY to capture the latest advances in methodology 

and improvements to consistently provide the highest quality estimates across the widest variety of site 

conditions. The models have, to date, provided irradiance estimates for specific sites hourly on a 10 km 

x 10 km (“Standard Resolution”) or half-hourly on a 1 km x 1 km (“Enhanced Resolution”) basis that 

extend from 1998 to the present hour plus seven day advance forecasts. Recent research advances 

have enabled the creation of 1-minute interpolated data from the 1 km images.

This new data, with a resolution of 1 km x 1 km x 1 minute is referred to as “High Resolution,” and under 

this project is used as the key input to 1-minute PV simulations.

Dr. Perez’s model was originally verified by the National Renewable Energy Laboratory (NREL) against 31 

US locations with varying climates before being selected to create updates of the US National Solar 

Radiation Data Base (NSRDB). This independent validation1found that the average hourly mean bias 

error of the model was 0.2 W/m2for GHI and 16.5 W/m2for DNI. The latest version of the model in 

Standard Resolution continues to be used to provide updates to the NSRDB, as well as serve as the 

resource database of choice for major energy agencies, such as the California Solar Initiative (CSI) and 

New York State Research and Development Authority (NYSERDA).

 

1 Wilcox, S., R. Perez, R. George, W. Marion, D. Meyers, D. Renné, A. DeGaetano, and C. Gueymard, (2005): 

Progress on an Updated National Solar Radiation Data Base for the United States. Proc. ISES World Congress, 

Orlando, FL
9

One-minute irradiance data such as SolarAnywhere High Resolution and the associated PV simulation 

model could enable utility engineers to model PV resources on the electric distribution system. With the 

temporal resolution corresponding to the approximate timeframe of distribution voltage regulators, the 

data could be used to determine impacts of PV on distribution operations.

Introduction: Three High Penetration Study Feeders

Under the current project, NREL has contracted with Clean Power Research to provide PV simulation 

support for three high penetration distribution feeders under study in the service territory of Southern 

California Edison (SCE). The three study feeders, located in Porterville, Palmdale, and Fontana, 

California, and are mapped in Figure 1. 

Figure 1. Study feeder locations and SCE service territory2.

At each location a large PV system is interconnected to the SCE feeder. Using the High Resolution 

irradiance data, ambient temperature data, PV plant specifications, and PV simulation methods, 

 

2

Google Earth.
10

minutely PV power generation data can be calculated. The datasets can in turn be used, along with 

physical component and load data, as inputs into electrical circuit modeling tools. The datasets provide 

PV output, in MW, for each minute of 2011. This report documents the creation of these datasets and 

characterizes the systems in terms of ramp rates.

Methods

SolarAnywhere High Resolution data is derived from the same satellite image processing algorithm that 

generates both the SolarAnywhere Standard and Enhanced Resolutions. However, the High Resolution 

data uses an added method of temporal interpolation between half-hourly satellite images to create 

minute-by-minute solar irradiance estimates in SolarAnywhere’s current geographic coverage area.

Satellite Images

SolarAnywhere satellite image processing occurs using the most recent version of the Perez model. In 

general, satellite images are obtained for coverage area in the western and eastern halves of the 

continental US and Hawaii on half-hourly increments from the Space Science and Engineering Center 

(SSEC) at University of Wisconsin – Madison. Following image transfer, irradiance measurements are 

made using the Perez model by ranking pixel brightness on clear sky conditions. Half-hourly 

measurements of global horizontal irradiance (GHI) and direct normal irradiance (DNI) are derived from 

the model which is then used to calculate residual diffuse irradiance (DHI).

Cloud Motion Vector Method

To generate the 1-minute irradiance measurements, SolarAnywhere first calculates a wind vector for 

every Standard Resolution tile using consecutive satellite images. The wind vectors are then applied to 

the Enhanced Resolution irradiance map to predict movement on a minute-by-minute basis. For 

forecasting purposes, the prediction is calculated forward up to 60 minutes. For historical generation, 

the prediction occurs between half-hour segments of retrieved satellite images.

PV Simulations

SolarAnywhere High Resolution data can further be used to simulate PV system generation through 

Clean Power Research’s PV Simulator engine. PV Simulator uses a version of the PVForm model to 
11

simulate production from a series of parameters, including irradiance, wind, temperature, installation 

and equipment specifications.

The simulation process starts by passing in the location and time series weather data to the Perez 

irradiance model found in SolarAnywhere. The selected weather data source provides time series GHI, 

DNI, wind and temperature data, while the location is used to define the latitude and longitude of the 

PV system. Using the Perez irradiance model, PVSimulator then calculates the circumsolar diffuse 

irradiance, isotropic diffuse, and horizon band diffuse irradiance components. These calculations start 

with determining the declination of the sun and equation of time. Then the solar zenith angle is 

calculated based on the declination of the sun, equation of time, and latitude. The airmass is then 

estimated as a function of the solar zenith angle. Based on these values the Perez model then produces 

the circumsolar diffuse irradiance, isotropic diffuse, and horizon band diffuse irradiance components.

After the irradiance model has broken down GHI and DNI into componentized irradiance values,

PVSimulator then uses the PV array geometry in order to calculate the Plane of Array Irradiance 

(POAI). The POAI calculations begin by calculating the solar time taking into account the local time, time 

zone, longitude and the previously calculated equation of time value. The solar azimuth angle is then 

calculated based on the zenith angle, latitude, and declination of the sun. The Plain of Array (POA) 

Angle of Incidence (AOI) is then calculated based on previously calculated values taking into account the 

tracking capabilities of the PV System. The components of the POAI (POA beam, circumsolar diffuse, 

isotropic diffuse, horizon band diffuse, and reflected irradiance components) are then calculated based 

on the output of the Perez model in conjunction with the tilt of the PV modules, the calculated AOI, and 

the specified albedo of the surrounding area. The shading model then adjusts the previously calculated 

POAI to account for shading as a consequence of obstructions as well as row on row shading.

The POAI values are then passed into the selected power output model in order to estimate the energy 

production of the PV system. Before calculating estimated energy production the temperature of the PV 

modules are estimated based on the POAI as well the time series wind speed, ambient temperature 

data provided by the weather data source. Then the 1-minute power output of the PV system is 

calculated based on the estimated PV module temperature and POAI along with model parameters 

defining the behavioral characteristics of the PV system as provided in the PV system specification. The 

model parameters depend on the selected power output model but for example in the case of PVForm 
12

the model parameters will consist of quantities such as the module PTC rating and efficiency reduction 

per degree C as well as inverter average efficiency and kW AC rating.

Once all this processing has been completed the primary output of the simulation is then the estimated 

1-minute power of the PV system. In addition to this each stage or processing may also output 1-minute

intermediate calculated results (such as POA and AOI).
13

Delivered Data Sets

1-minute production data

Using the methods described in the foregoing, four data sets of 1-minute PV system power generation 

were prepared and delivered3to NREL. Data files included four columns:

 Time stamp, start of interval

 Time stamp, end of interval

 Power (MW)

 Observation Type

Observation Type4includes keys (A) “Archived,” (D) “Day,” (N) “Night,” and (M) “Missing.”

Hourly irradiance and temperature data

SolarAnywhere Standard Resolution (version 2.2) data was also provided for Fontana and Porterville, 

including hourly measurements of GHI, DNI, DHI, wind speed and temperature. This data was used for 

related circuit modeling work.

Data for these two locations was provided between the dates of January 1 2002 through December 31 

2011. The 10-km gridded tile centered at 34.05 north, 117.55 west and 36.05 north, 119.05 west was 

selected for the Fontana and Porterville sites, respectively.

Data Validation

Following the implementation of 1-minute data in SolarAnywhere, studies to validate the model 

accuracy were conducted. In collaboration with organizations in California, California ISO (CAISO) and 

Sacramento Municipal Utility District (SMUD), 1-minute data accuracy was validated against highaccuracy, well-maintained ground mounted irradiance sensors throughout the state of California. This 

validation work falls outside of the current project, but is provided here for completeness. 

 

3

Results were prepared on 3/5/2013 and made available on an FTP server.

4

All data was marked as (A) archived because 2011 contains only historical data older than one month. A complete 

list of observation types is available at www.solaranywhere.com. 
14

CAISO stations

Using ground data from four CAISO ground stations, the relative mean absolute error (%MAE) was 

calculated comparing the SolarAnywhere 1-minute High Resolution GHI data. When comparing the four 

locations on an individual basis, as seen in Figure 2, the %MAE decreases from roughly 10% at a 1-

minute interval of comparison to a range of 2-2.5% when compared annually. Additionally, the black 

baseline, marked “Ground (Station 2)”, represents the relative error between the second, redundant 

ground sensor at the same location. This reflects ground measurement error at each location. Having 

two co-located ground measurement devices also accounts for the shaded green region reflecting the 

%MAE, as SolarAnywhere 1-minute data was compared to each of the two ground sensors thus creating 

the high and low accuracy boundaries.

Figure 2: Average %MAE of four CAISO locations versus time interval of comparison

SMUD stations

Additional validation of the SolarAnywhere High Resolution model was conducted using a network of 

over sixty pole-mounted pyranometers maintained by the Sacramento Municipal Utility District (SMUD)

throughout their service territory. Similarly, GHI measurements from the ground stations were 

compared individually with the corresponding SolarAnywhere High Resolution location. Figure 3
15

represents the %MAE average for all stations included, as compared by time interval of comparison. 

The red curve represents the accuracy of the High Resolution data. The blue and green lines represent 

accuracy measurements of Enhanced and Standard Resolution, respectively. The result comparing 

SolarAnywhere High Resolution to the SMUD ground sensor GHI measurements resulted in a similar 

accuracy assessment, with 1-minute SolarAnywhere data falling within roughly 7% of %MAE of the 

corresponding ground measurement and with an overall bias of either plus or minus 1-2%.

Figure 3: Average %MAE versus time interval of comparison for over sixty locations in SMUD 

territory

Additional comparisons to ground sensors

An accuracy summary of SolarAnywhere High Resolution compared to the ground collected GHI data 

from the Hanford ISIS station for the year of 2011 is presented in Figure 4.
16

Figure 4: %MAE versus time interval of comparison for the ISIS station in Hanford, CA

Analysis

The description of the analysis that follows uses only the Fontana data for simplicity in describing the 

process. Results for each of the locations are shown in the Appendices.

Missing data

Ramp rates (defined as the absolute change of power output5per unit time) were calculated for every 

minute of the year. By inspection, and it was discovered that some of the highest ramp rates were based 

on data that appeared to be invalid. This required further investigation.

Figure 5 shows the Fontana 1-minute data for the day having the highest ramp rate (the “drop in power” 

from near full power output to zero). While this behavior is possible in practice—for example due to an 

inverter malfunction resulting in complete power loss—it is not possible to see a zero output in the 

middle of the day due only to the presence of clouds. There is always some diffuse radiant energy 

 

5

For example, if the power output for one interval were 2.5 MW, and the power output for the next interval were 

2.3 MW, then the change in power is -0.2 MW and the absolute change in power is 0.2 MW. Finally, since the 

intervals are 1 minute in duration, the ramp rate is 0.2 MW per minute.
17

available, even in the darkest of overcast days. Therefore, this data is clearly missing and should not be 

included in the analysis6.

Upon further investigation, the cause of this error was found to be an aberration in the raw satellite 

image. As shown in Figure 6, the image associated with the missing data includes a streak across the 

image, and Fontana happens to lie directly along the aberrant line. Therefore, in the 30-minute period 

following this image, the calculated 1-minute data is missing. The images taken in the half hour before 

and the half hour after this image were not distorted, and the missing data is confined to only this 30-

minute period.

Figure 5. Missing data at Fontana, February 24, 2011 from 13:29 to 13:58.

 

6

The dataset includes an “M” flag in the observation type if the data is missing. The problem described here was 

not flagged as missing because the underlying satellite images do exist. The issues identified here resulted in 

removal of selected images, hence the “M” flag would show up were the datasets to be re-generated. However, 

the search for such anomalies was limited to only those resulting in the highest ramp rates. 
18

Figure 6. GOES-west satellite image, July 24, 2011 (21:30:00 UTC), showing error streak.

Analysis of data from each location showed similar cases of zeroed data. The search for such data was 

not exhaustive and satellite images were not consulted each time. Rather, only the data affecting the 

highest ramp rates were identified. In each case, two or three of the highest ramp rates were identified 

as being caused by this problem, and this data was manually excluded from the analysis. The highest 

ramp rates that that follow for each location reflect data that appears to be correct and unrelated to 

missing data.

Variability

Daily variability is defined as the standard deviation of the population of one-minute ramp rates during 

the day, and is calculated as:

 √

∑ ̅ 

 

 

 

Where N is the number of minutes in each day, riis the ramp rate for the i

th minute, and ̅is the average 

ramp rate over the day.

Fontana
19

Daily variability was calculated for every day, and the day with the highest variability, May 29, is shown 

in Figure 7.

Figure 7. Highest variability day at Fontana 2011 (May 29).

Ramp Rate Duration Curve

Figure 8 shows the ramp rates at Fontana for each of the 525,600 minutes of 2011. From this we can get 

a sense of the magnitude of the highest ramping events. The “normal” periods of ramping are difficult to 

discern, however, so this data is sorted by magnitude and presented as a “ramp rate duration curve7” in 

Figure 9.

 

7

This term is used to parallel a similar ranking of loads in electric utility planning, the “load duration curve.”
20

Figure 8. Absolute 1-minute ramp rates at Fontana, 2011.

Figure 9. Ramp rate duration curve, Fontana, 2011

This sorting illustrates that the number of significant ramping events is quite small. To further examine 

and quantify the ramping, we magnify only the top 100 minutes of the year (the top 1% of the year) and 

normalize ramping as a percent of rated PV system output. Figure 10 shows these minutes, and further 

defines a “high ramping region” of the curve, arbitrarily selected as covering those ramping events that 

correspond to an excess of 50 percent of PV system rating. There are 32 such high ramping events, and 

the largest of these is 2.20 MW per minute, or 75% of the PV System’s 2.95 MW-AC rating per minute. 

This event is shown in Figure 11.
21

Figure 10. Highest 100 ramp rates at Fontana, 2011.

Figure 11. Maximum ramp event at Fontana, 2011 (2.20 MW/min).

An inspection of Figure 11 also reveals an artifact of the high resolution irradiance data generation 

process. With the raw image data available in half-hour intervals, the “interpolation” between two 

images is actually based on a given set of wind vectors and the first image corresponding to a specific 

time. The second image at the end of the half hour period is not used. Hence the computations can 

result in a disjoint between the last minute of one period and the first minute of the next. A future 

improvement to the 1-minute data creation might be to use both images to ensure a smooth transition.

Finally, the ramping statistics for Fontana are summarized in Table 1. Similar ramping statistics are 

presented for each location in the Appendix.
22

Table 1. Fontana ramping statistics, 2011.

System rating (MW) 2.95

Max. power ramp (MW per min) 2.20

Max. power ramp (% per min) 75%

High ramping events (no. per year) 32
23

Appendix 1: Fontana (Study Feeder 1)

Figure 12. Fontana PV system.

Figure 13. Satellite resolution at Fontana.

PV System
24

Table 2. Specifications for Fontana

Coordinates 34.080, -117.517

Inverters Quantity: 4

Manufacturer: SatCon Technology

Model: 500.0 kW (Model AE-500-60-PV-A)

EfficiencyRating 95%

Modules Quantity: 33,700

Manufacturer: First Solar

Model: 72.5W (Model FS-272)

Nominal Rating (kW DC): 0.07250

PTC Rating (kW DC): 0.06980

Array Configuration Quantity: 33,700

Manufacturer: First Solar

Model: 72.5W (Model FS-272)

Nominal Rating (kW DC): 0.07250

PTC Rating (kW DC): 0.06980

Solar Obstructions 

(shading)

None

Table 3. Fontana ramping statistics, 2011.
25

Appendix 2: Porterville (Study Feeder 2)

Figure 14. Porterville PV system.

Figure 15. Satellite resolution at Porterville.

PV System
26

Specifications for Porterville

Coordinates 36.028738, -119.075886

Inverters Quantity: 7

Manufacturer: SatCon Technology

Model: 1000.0 kW (Model EPP-1000-0600-32060-200X-U-x)

Efficiency Rating 96.5%

Modules Quantity: 29,428

Manufacturer: Trina Solar

Model: 230W (Model TSM-230PA05.10)

Nominal Rating (kW DC): 0.230

PTC Rating (kW DC): 0.2089

Array Configuration Azimuth Angle: 0.000 (south)

Tilt Angle: 25.000

Tracking: Fixed Array

Solar Obstructions 

(shading)

None

Table 4. Porterville ramping statistics, 2011

System rating (MW) 4.783

Max. power ramp (MW per min) 4.31

Max. power ramp (% per min) 90%

High ramping events (no. per year) 53
27

Appendix 3: Palmdale (Study Feeder 3)

Figure 16. Palmdale PV system.

Figure 17. Satellite resolution at Palmdale.

PV System (approx. dimensions)
28

Table 5. Palmdale ramping statistics, 2011

System rating (MW) 1.437

Max. power ramp (MW per min) 1.33

Max. power ramp (% per min) 93%

High ramping events (no. per year) 186