Friday, February 7, 2014

Solar System Design - String Sizing

When designing a solar system, the most important calculation is determining the length of the string of solar panels.  Solar inverters and charge controllers have set voltage windows that have to be met by a string of solar panels whose voltage can vary as much as 40 – 60% throughout the year.  With low string voltages, operation is less efficient and the system can be in danger of shutting off during hot conditions.  Design a string voltage too high and cold sunny conditions could put the inverter into an overvoltage fault mode which shuts the inverter down.  Solar designers have to hit the “sweet spot” where their string voltage will always fall within their equipment’s voltage window while maximizing the string length for more efficient operation.  This is done by designing solar strings based on the upper voltage limit of the inverter or charge controller.

Effect of Temperature on String Voltage

At its basic level, higher temperatures drop voltage and lower temperatures raise voltage in electronics.  For the solar designer, this means string voltage is at its highest when the temperature is coldest, and the extreme low temperature is used to design the solar string.  There are two methods for calculating solar string voltage based on temperature, both outlined in NEC 690.7(A) Maximum Photovoltaic System Voltage:

1)      …Maximum photovoltaic system voltage for that circuit shall be calculated as the sum of the rated open-circuit voltage of the series-connected photovoltaic modules corrected for the lowest expected ambient temperature …. The rated open-circuit voltage shall be multiplied by the correction factor provided in Table 690.7…
2)      When open-circuit voltage temperature coefficients are supplied in the instructions for listed PV modules, they shall be used to calculate the maximum photovoltaic system voltage as required by 110.3(B) instead of using Table 690.7.

The first method calls for using NEC Table 690.7.  To use the table, take your solar panel’s open circuit Voltage rating (Voc), found in the data sheet, and multiply it by the temperature correction factor based on your lowest expected ambient temperature.  The lowest expected temperature can be the record low temperature which can usually be found online.  For example, in Albuquerque, NM, our record low temperature is -17o F. Converting to C puts it at -27o C, with a corresponding adjustment factor of 1.21.  This means for Albuquerque I would multiply the solar panel’s Voc by 1.21 to find the maximum design voltage for string sizing.  Assuming a typical 60-cell solar panel with a Voc of 37V, the maximum design voltage is 44.77V.

The second method requires using an equation and referencing the temperature coefficient of voltage found on the solar panel data sheet, but it gives a more exact answer than using NEC Table 690.7.  The temperature coefficient of Voc is usually between -0.3 and -0.4 % per degree C/K, but it varies from panel to panel.  The equation for temperature effect on string voltage is:

Design Voltage = Voc *(1 + TVoc * (Design Temperature - 25o C))

Using a temperature coefficient of -0.33 %/C and the Voc and low temperature used in method 1 (37 Voc, -27 C), the design voltage becomes:

                Voc * (1  + (-0.0033 * (-27 - 25)) = Voc * (1 + 0.1716) = 43.35V

Note that the voltage determined using voltage coefficient is slightly lower than that found using the NEC table.  The NEC table is the more conservative and less exact method to use, but it’s also a little easier than using the temperature coefficient, which gives an exact answer for the extreme minimum temperature and solar panel.  Per NEC 690.7 (A), the temperature coefficient method should always be used if the temperature coefficient of voltage for the solar panel is known, which it usually is from the equipment data sheet.

Record Low vs. Minimum Dry Bulb Temperature

If you continue reading 690.7(A), there is an informational note on what data can be used for the low temperature in string sizing calculations:

Informational Note: One source for statistically valid, lowest-expected, ambient temperature design data for various  locations is the Extreme Annual Mean Minimum Design Dry Bulb Temperature found in the ASHRAE Handbook — Fundamentals.  These temperature data can be used to calculate maximum voltage using the manufacturer’s temperature coefficients relative to the rating temperature of 25°C.

While it’s a mouthful, the gist of it is if you have access to the American Society of Heating, Refrigeration, and Air Conditioning Engineers (AHSRAE) handbook or to their temperature data, you can use the extreme minimum dry bulb for the low calculation instead of the record low temperature.  This temperature is always higher than the record low.  For example, in Albuquerque, NM, the record low temperature is -17o F, while the extreme minimum dry bulb temperature is 10o F.  If I run it through the voltage coefficient equation again, the design voltage becomes 41.52V.  This is the difference between a string of 13 and a string of 14 on a 600V input solar inverter, so the improvement by using this data can be significant.

Sometimes, your exact location isn’t available in the ASHRAE data tables.  In this case, either select the closest site with similar latitude and elevation, or take an average of surrounding sites to approximate the minimum dry bulb temperature at that location.  If you want to know the minimum dry bulb temperature for your location for solar design but don’t have access to an ASHRAE Handbook – Fundamentals, someone may be able to look it up for you….

Effect of Mounting Method on String Voltage

Sometimes the solar system needs to be designed with shorter strings that are close to the lower bound of the equipment voltage window, and you need to confirm that the system will work in the hottest conditions instead of the coldest.  The voltage coefficient equation and NEC Table 690.7 are both only usable for maximum voltage calculations.  This is because maximum voltage calculations are able to make the assumption that the solar equipment’s temperature is equal to the ambient air temperature, as the low design temperature typically occurs in the hour before sunrise.  For the minimum voltage, the solar array needs to be considered when it’s at its hottest, when it’s producing power and the sun is shining on it.  At this point, the equipment can be much, much hotter than ambient temperature due to the direct solar radiation it receives.

How do you figure out the design hot temperature for a minimum voltage calculation?  To start, go back to weather data for your location and find the average high temperature for the hottest month of the year.  This will become the design temperature in a new temperature coefficient calculation of voltage.  Next, based on the solar mounting method, select the temperature rise that will be added directly to this value.  These are common values for temperature rise that the solar industry uses.

Mounting Method
Temperature Rise
< 10o on a flat roof
36o C
> 10o on a flat roof
34o C
Flush mount, pitched roof
32o C
Ground mount
30o C
Pole mount
29o C

Under optimal conditions (pole mounting), the solar array is assumed to be 29o C hotter than ambient temperature, or 82o F hotter.  It only gets worse the closer you install to the roof, as air circulation decreases and the array temperature steadily climbs.
While the max voltage calculations called for using the open circuit voltage, with minimum the “max power” voltage, or Vmp, needs to be used.  Coupled with the temperature rise factor, the minimum voltage equation becomes:

Design Voltage = Vmp *(1 + TVoc * (Design Temperature + Temperature Rise - 25o C))

Using an average high temperature of 95o F (35o C) with a solar panel Vmp of 30V, here’s an example of the minimum voltage of a solar panel installed on a flush mount:

                Vmp * (1  + (-0.0033 * (35 + 32 - 25)) = Vmp * (1 - 0.1386) = 25.84V

This is much, much lower than the 41.5V calculated earlier for the maximum solar panel voltage.  It highlights the importance of temperature effects on your minimum string size.  Based on these numbers, if a solar inverter with a minimum voltage of 200V were considered, a string of 7 would fail under hot operating conditions, while a string of 8 would continue to work.


  1. Solar energy will be tomorrow's world's fuel source. So we need to best to do best design for it. It's really most renewable and trusted energy source for future. I'm with Hawaii PV. So I've interest on it.

  2. I read your post and i appreciate your efforts. The information that you share in the above article is very nice and useful .All the things that you share with people, are very nice. Thanks for this article Redlands solar