EN 
PT_BR 
The Performance Ratio, or PR, is one of the most important variables for evaluating the efficiency of a photovoltaic plant.
Specifically, the Performance Ratio is the ratio between the actual power delivery and the theoretical power delivery of the plant. It is independent of the orientation and location of the photovoltaic plant and the incident solar irradiation. For this reason, PR can be used to compare plants in different locations around the world.
This document explains what Performance Ratio is and its function. You will also learn how to calculate the PR for your photovoltaic plant and learn about the factors that influence the calculation of this number.
What is the Performance Ratio?
The Performance Ratio is a quality measure of a photovoltaic plant that is location independent and therefore often described as a plant quality factor. PR is typically expressed as a percentage and describes the relationship between actual power delivery and theoretical generation from a PV plant. In this way, it shows the proportion of energy that is actually available to the grid after discounting losses (for example, thermal and electrical losses) and the energy consumed in the operation of the plant itself.
A number as close as possible to 100% indicates that the plant is operating efficiently. In practice, the value of 100% cannot be reached, considering that inevitable losses always occur during the operation of any photovoltaic system. However, high-performance plants can reach values of up to 80%.
What is the role of the Performance Ratio?
The Performance Ratio tells you how efficient and reliable your plant is. With PR you can compare your plant's energy delivery with that of other plants or monitor the status of your own plant over an extended period.
Determining PR at fixed intervals does not provide an absolute comparison. It provides the operator with the option to check performance and delivery: if the plant is assumed to be operating optimally when commissioning takes place, having a certain initial PR, then measuring PR values over time allows the identification of deviations , which means that appropriate measures can be adopted to prevent losses. Deviations in the PR value in the form of values below normal, therefore, indicate probable failures in the initial stages of the plant.
How is Performance Ratio calculated?
You need different variables to be able to calculate the PR of your plant. On the one hand, there are solar irradiation values for the plant location. You can determine these values using an instrument that measures incident solar irradiation. On the other hand, you need to know the peak power of the photovoltaic plant, based on the characteristics and number of photovoltaic modules.
Requirements for the calculation
If you use an instrument that measures incident solar irradiation, the orientation of the modules and the meter must be the same for the calculation to be correct. It must be ensured that the modules and the meter are exposed to the same amount of solar irradiation and temperature.
Analysis period
The ideal period for analyzing the Performance Ratio is 12 months. However, you can select shorter periods if you want to compare your plant directly with another or if you want to do an initial analysis of the plant's performance in the first few months of operation. In any case, a minimum period of 1 month must be selected to ensure that momentary environmental conditions (rainy or cloudy days), low temperatures and possible shadows do not have a major influence on the calculation.
PR calculation
The PR of a photovoltaic plant with conventional (non-bifacial) modules can be calculated according to the following formula:
PR=Energy generated [kWh] / Expected energy [kWh]
The real energy generated by the plant in kWh, which corresponds to the numerator of the PR equation, can be measured on the export meter to the grid.
The expected theoretical energy of the plant, which corresponds to the denominator of the PR equation, can be calculated by the following equation:
Expected energy [kWh] = Solar energy collected [kWh] . Module efficiency [%]
In the expression above, the solar energy collected corresponds to the irradiation incident on the surface of the photovoltaic modules multiplied by the area of the modules, as shown in the following equation. Efficiency, in turn, is the conversion efficiency in STC (standard test condition) found in the data sheet.
Solar energy collected [kWh] = Solar irradiation [kWh/m2] . Module area [m2]
Conceptually, the expected energy corresponds to the sum of solar energy collected by photovoltaic modules in a given time interval, simply multiplied by the photovoltaic conversion efficiency.
It should be noted that the calculation of expected energy disregards all existing losses in a photovoltaic system and provides a theoretical expectation of electrical energy generation from solar irradiation collected by the surface of the photovoltaic modules.
Calculating the expected energy by the product of solar irradiation, module area and efficiency from the data sheet, according to the expressions shown previously, is the most intuitive way possible to obtain the expected value.
It can be demonstrated that the calculation shown above corresponds exactly to the definition of PR according to the IEC 61274-1:2021 standard, item 14.3.1, which presents the following equation:
PR = (Energy generated [kWh] / Peak power [kW]) / (Irradiance [kWh/m2] / Standard irradiance [kW/m2])
In the expression above, the standard irradiance corresponds to the value used to determine the peak power of the photovoltaic module, that is, 1000 W/m2 or 1 kW/m2.
Dividing the irradiance [kWh/m2] for a given time interval by the standard irradiance (1 kW/m2) results in the number of hours of full sun for that period. Then, multiplying the peak power of the photovoltaic array by the number of hours of full sun results in the expected energy of the system.
In a much more intuitive way, the same result is reached by simply multiplying the solar irradiation for the period considered [kWh/m2], the area of the photovoltaic modules [m2] and the conversion efficiency found in the data sheet. This calculation method can be easily used by owners of photovoltaic systems to calculate the PR as long as they have two very important pieces of information: the energy injected into the electrical grid [kWh] and the solar irradiation [kWh/m2] in the plane of the modules – This information can be found in the solar plant's monitoring system, as long as it has the necessary instrumentation.
Example: calculation of the Performance Ratio over a 1-year analysis period
This example describes the PR calculation using data extracted from the Sunny SensorBox and Sunny WebBox accessories of a solar plant employing SMA inverters.
Calculation should be seen as an alternative option. SMA Solar offers automatic PR calculation on the Sunny Portal monitoring platform.
To carry out the calculation we need the following information:
- Analysis period: in this example the period is 1 year.
- Plant generation area: is the number of modules multiplied by the frontal area of the module, which can be found in the data sheet.
- Module efficiency: is the STC efficiency found in the module data sheet.
- Actual exported energy: measured on the solar plant's exported energy meter.
- Expected energy from the plant: calculated using the formula presented previously.
- Incident solar irradiation: irradiation [kWh/m2] in the plane of the modules recorded in the period considered.
If you use inverters and accessories from SMA, you can use the irradiation values sent by the Sunny SensorBox to the Sunny WebBox to determine this value.
The Sunny WebBox regularly requests the values measured by the SensorBox. WebBox then calculates the daily average of these individual values. To determine the average solar irradiation over the analysis period, you need to extrapolate the daily average values. To do this, proceed as follows.
The Sunny WebBox stores the plant's average incident irradiance values, depending on the user interface settings, in intervals of 5, 10 or 15 minutes. Sunny WebBox stores the average values for each month together with other average values for your plant in the correct directories such as .csv or .xml.
To calculate the irradiation value in 1 year, for example, you must first calculate the monthly values. To do this, add up the average daily values for the specific month. You then divide the amount by the number of days in the month, which then gives the average monthly amount. This way you can calculate the monthly average for all 12 months of the year.
To calculate the annual average, you simply add the 12 monthly averages and divide the value by 12. You then extrapolate the average value calculated for your generation area. This way, you obtain the nominal value of the plant for the analysis period of the year, which you can include with the other values in the formula to calculate the Performance Ratio.
The following values are used in this example:
- Analysis period: 1 year
- Average solar irradiation in 1 year: 120 kWh/m²
- Plant generation area: 10 m²
- Modules efficiency: 15%
- Electric energy exported to the grid: 110 kWh
The irradiation values measured on site return an average solar irradiation value for the entire analysis period of 120 kWh/m². This irradiation value is then extrapolated by the plant area as follows, to calculate the solar energy collected:
Irradiation Value inkWhm2·Plant Area in m2=120kWhm2·10 m2=1200 kWh
To subsequently calculate the plant's expected energy, the value of the solar energy collected is multiplied by the module's efficiency:
1200 kWh ·15%=180 kWh
Therefore, an expected delivery of 180 kWh is obtained for the analysis period. This expected energy, if achieved, would correspond to a PR of 100%. However, the actual value of energy delivered to the grid was only 110 kWh.
From the values obtained we have the Performance Ratio:
PR=110 kWh180 kWh=61%
The PR value found in this example is approximately 61%. This means that approximately 39% of the solar energy that would be converted into electrical energy is no longer available due to thermal, electrical and optical losses, among others, existing in the plant.
The Performance Ratio acts as an indicator and can indicate the need for a more detailed inspection of the plant so that, for example, dirt in the modules is removed or components are replaced.
Automatic calculation of PR by the monitoring platform
You can also calculate the Performance Ratio automatically by transmitting the corresponding data from your plant to Sunny Portal. In Sunny Portal, you can also see the Performance Ratio present in graphical format.
The following requirements must be met for calculating PR in Sunny Portal:
- Have a Sunny WebBox that transmits the requested data to Sunny Portal
- Having a Sunny SensorBox connected to the Sunny WebBox
- Have the Sunny SensorBox irradiation sensors
Factors that influence the Performance Ratio
The Performance Ratio is a variable purely based on definitions, which, under the influence of certain factors, may present incorrect results. This is because the performance characteristics of photovoltaic modules are defined based on standard parameters (1000 W/m² and 25 °C). Deviating conditions during actual operation can influence the Performance Ratio.
The following factors can influence the PR value:
- Environmental factors: module temperature, solar irradiation and energy dissipation, errors in measuring instruments, shadows, dirt
- Other Factors: recording period, electrical losses, error in the specification of photovoltaic modules, efficiency of inverters, difference in solar cell technology of the module and solar radiation meter, orientation of the measuring instrument (Sunny SensorBox)
Environmental factors
Temperature of photovoltaic modules
The performance and efficiency of a solar cell depend, among other factors, on the operating temperature. At lower temperatures, a photovoltaic module is particularly efficient. For example, the module is cold when the sky is cloudy in winter. This can briefly generate high PR values. After a certain period, the module heats up and efficiency drops again.
Solar irradiation and energy dissipation
During the morning, late afternoon and especially in winter, when the sun is low, the irradiance value (light power per square meter) approaches the dissipation value (= difference between energy input and output) more closely than at other times of the day and year. For this reason, the PR value is lower than normal.
Measuring instrument (Sunny SensorBox) in the shade or dirty
Depending on the location of the installation, plants and buildings may shade the measuring instrument (Sunny SensorBox) temporarily or permanently. Especially when the sun is low, parts of the power plant itself can shade the instrument. Shading, whether partial or complete, can lead to incorrect PR values of more than 100%. Furthermore, environmental factors such as dust or pollen can cause dirt in the plant and also generate higher values of 100%.
Shadow or contamination of photovoltaic panels
Depending on the location of the installation, plants and buildings may shade the measuring instrument (Sunny SensorBox) temporarily or permanently. In addition to dirt caused by environmental factors, there may be shading of the panels. This shading causes the panel to absorb less radiation than normal. Module efficiency and PR also drop.
Other factors
Measurement period
If the measurement period is too short (less than 1 month), there are not enough measurements for a reliable Performance Ratio calculation. Low solar elevation, low and high temperatures and shading influence the result more strongly, considering that there is not enough data.
Electrical conduction losses
With the transmission of energy from the inverter to the energy meter exported to the grid, conductivity losses may occur depending on the type of cables used. The PR value can be reduced by electrical losses.
Efficiency of photovoltaic modules
The efficiency of the modules has a decisive influence on the plant’s Performance Ratio. The higher the efficiency, the higher the PR (limited to the corresponding environmental conditions).
Inverter Efficiency
If the inverter used in the plant is highly efficient, it can result in a higher PR. SMA inverters with efficiency above 90% enable PR values above 80%)
Different photovoltaic cell technologies in modules and measuring instruments
There are different types of photovoltaic cells for modules. The following three types are the most common: monocrystalline silicon and polycrystalline silicon. If the measuring instrument installed in the plant (Sunny SensorBox) uses a different technology than that used in the modules, PR deviations may result.
Degradation of photovoltaic cells
Age-related degradation of photovoltaic cells can result in lower PR values over time.
Measuring instrument orientation (Sunny SensorBox)
If the plant has a measuring instrument (Sunny SensorBox) that is not aligned with the plant modules, PR values of more than 100% may result due to error in measuring the irradiation collected by the photovoltaic modules.
Reference
This article was freely based on the SMA technical document “Performance Ratio – Quality factor for photovoltaic system”, available in this link, with review and technical addenda by the Canal Solar engineering team.
