Calculating PV Degradation Rates Using Open-Source Software: Page 4 of 4

Imperfect sensor data. Based on their experience analyzing numerous fielded PV systems, the team of developers responsible for RdTools observed that irradiance sensors are not always well maintained in the real world. It was important, therefore, to develop an analysis method that could tolerate imperfect sensor data. The data presented in the IEEE Journal of Photovoltaics article demonstrate RdTools’ usefulness in this regard.

The data in Figure 1a, for example, aggregate measured plane-of-array irradiance (Gpoa) values for a variety of sensors. The blue diamonds represent a regularly maintained reference cell; the red circles represent the median of 10 regularly maintained pyranometers; and the green triangles, black squares and purple triangles represent unmaintained sensors. The data for photodiodes 1 and 2 and reference cell 2 illustrate the sensor drift that can occur when technicians do not regularly clean and calibrate irradiance sensors in the field. Compared to the reference cell, data from the unmaintained sensors drift by as much as 1.5% per year. 

The data in Figure 1b illustrate the extent to which the clear-sky method in RdTools tolerates imperfect sensor data. The red circles in this figure represent YOY degradation rates according to RdTools’ sensor-based calculation method; the blue diamonds represent YOY degradation rates according to the clear-sky methodology. The dashed line shows the median of 10 different conventional methods of Rd calculation, including time-series analysis and quarterly I-V measurements, and the green lines show the range of one confidence interval for these values. These data illustrate that while sensor-based Rd calculations are sensitive to the quality of ground-based measurements, the clear-sky method is considerably more robust.

As shown in Figure 2, analysts can also use RdTools to compare clear-sky–based (2a, top) versus sensor-based (2b, bottom) results. For the graphs on the left, RdTools normalizes performance ratio data to 1 and charts these values by year. The graphs on the right aggregate these YOY data into a histogram and report the median value as the Rd. The confidence interval represents one standard deviation of a bootstrap distribution. In this example, which assumes a clear-sky index filter of ±20%, the drop-off at the end of the sensor-based data in 2016–17 indicates a recent sensor problem. In this case, the clear-sky–based results are likely to be more accurate than the sensor-based results.

When the clear-sky and sensor-based results disagree, analysts should suspect a sensor problem and if possible arrange for sensor testing, calibration, cleaning or replacement. Sensor maintenance is a best practice as there is likely an upper limit to the degree sensors can be erroneous for either analysis method. It is important to note that the mathematical uncertainty represented by a confidence interval reflects the degree of variation within the given data set, but does not account for a problem such as a defective or unmaintained sensor. Confidence intervals are susceptible to the garbage-in, garbage-out challenge of all data analysis. However, YOY analysis with clear-sky normalization enables analysts to utilize, rather than discard, some poorly maintained sensor data.

If a system has well-maintained irradiance and temperature sensors, the clear-sky and sensor methods are likely to produce similar results and graphs. In a system with well-maintained sensors, the best option is probably to use the sensor-based degradation rate calculation since the uncertainty represented by the confidence interval can be lower compared to the clear-sky method, as is the case in Figures 2 and 3b.

Seasonality and seasonal soiling. Many PV systems experience predictable seasonal performance variations based on annual weather patterns, haze, spectral sensitivity, partial shading, snow or soiling. Whereas linear regression analyses are vulnerable to seasonal effects, the YOY methods that RdTools uses to calculate Rd values are more robust.

As an example, the repetitive data patterns in Figure 3a (top) are the result of variations in power production for a PV system in California due to seasonal soiling. As shown in the inset detail, soil builds up on the array throughout the dry season, resulting in a steadily decreasing performance ratio; cleaning or rain events produce a noticeable upward data shift. The data in Figure 3b (bottom) show that a standard least square (SLS) linear regression analysis overestimates the rate of degradation compared to degradation rates obtained using clear-sky– and sensor-based YOY methods. These results suggest that the two YOY methods are robust in relation to seasonal soiling events, a characteristic that likely extends to other seasonal effects such as haze or partial shading.

While the YOY and clear-sky methods are less sensitive to a number of common data quality issues, analysts still require quality input data and good analysis decisions to achieve high-quality results. Prior to proceeding with any calculations, data analysts should assess data quality, check the PV system’s maintenance log and look for issues that can mimic module degradation. Is there evidence that overgrown weeds or trees may be shading the system? Has the site experienced tracker outages? If so, analysts can determine an appropriate response, such as applying data filters or removing certain time periods from the analysis. While it is still essential that input data are reasonably accurate, the RdTools software package provides system owners and data analysts with consistent and validated methods for calculating PV degradation rates.


Katherine Jordan / Complex Review / Denver /

Michael Deceglie / NREL / Golden, CO /

Chris Deline / NREL / Golden, CO /

Dirk Jordan / NREL / Golden, CO /


Jordan, Dirk, et al., “Compendium of Photovoltaic Degradation Rates,” Progress in Photovoltaics, February 2016

Jordan, Dirk, et al., “PV Degradation Curves: Non-Linearities and Failure Modes,” Progress in Photovoltaics, July 2017

Jordan, Dirk, et al., “Robust PV Degradation Methodology and Application,” IEEE Journal of Photovoltaics, December 2017

Stein, J.S., et al., “PVLIB: Open-Source Photovoltaic Performance Modeling Functions for Matlab and Python,” IEEE 43rd Photovoltaic Specialists Conference, 2016

Article Discussion

Related Articles