Solar String Size Calculator
Max and min modules per solar string from cold Voc, hot Vmp and the inverter voltage window.
What it does
String sizing is the step that decides how many solar modules you can wire in series to one inverter. A module is rated with an open circuit voltage at standard test conditions, but the real number changes with temperature, and it changes in the wrong direction. Cold air pushes the voltage up, so a string that looks fine on a warm afternoon can break the code limit on a cold January morning.
There are two limits and they pull in opposite directions. The upper limit is a safety and code limit: the maximum DC voltage the inverter and the wiring can handle. The lower limit is a performance limit: when the cell gets hot, the working voltage of the string drops, and if it falls below the window the inverter can track, the system loses power or stops entirely.
This calculator works the numbers the way NEC 690.7 asks. The cold case corrects the module open circuit voltage to your design low temperature using the temperature coefficient printed on the datasheet. The hot case uses the nominal operating cell temperature model to find the cell temperature on a hot, bright afternoon, then corrects the maximum power voltage to it.
You need the datasheet numbers for one module and the limits from your inverter. Almost every modern module lists Voc, Vmp, both temperature coefficients and NOCT. The inverter datasheet lists the maximum DC input voltage and the MPPT window. Put those in and the tool tells you how many modules fit.
The result is a design aid, not a permit. Every jurisdiction has its own electrical code, and the inspector may want the cold voltage calculated with the table in the code instead of the coefficient method. The NEC table and the coefficient method usually land within a module of each other, so check which one your local authority expects before you order panels.
How to use
- Open the datasheet for one module and write down Voc, Vmp, the Voc temperature coefficient, the Vmp temperature coefficient and NOCT.
- Open the inverter datasheet and find the maximum DC input voltage and the minimum MPPT voltage. These are DC numbers, not the AC power rating.
- Choose your unit system and enter the design low and high ambient temperatures for the site.
- Type the module numbers and the two inverter limits into the form, then enter how many modules are in your string today.
- Read the voltage check first. If the cold voltage is over the limit, drop the number of modules the tool suggests.
- Then read the MPPT check. If the hot voltage is under the floor, add modules until the string clears it.
Formula
- Voc
- Module open circuit voltage at standard test conditions, in volts
- beta Voc
- Voc temperature coefficient in percent per degree Celsius, a negative number
- Vmp
- Module voltage at the maximum power point, in volts
- beta Vmp
- Vmp temperature coefficient in percent per degree Celsius, a negative number
- NOCT
- Nominal operating cell temperature of the module, in degrees Celsius
- T cell min
- Lowest ambient temperature at the site, in degrees Celsius
- T cell hot
- Cell temperature on a hot bright day, in degrees Celsius
Temperatures are always handled in Celsius inside the formula, so the tool converts the Fahrenheit entries first. The cold case uses the ambient temperature as the cell temperature, which is what NEC 690.7 does when it asks for the expected lowest ambient temperature. The hot case uses the NOCT model with a plane of array irradiance of 1000 W/m2, so the cell sits (NOCT - 20) x 1000 / 800 degrees above the air. A darker roof mount runs hotter than this model assumes, and the code table method gives a slightly different answer from the coefficient method, so leave room in your design.
Worked example
Example: 10 modules on a 600 V residential inverter
A module rated 50 V Voc and 41 V Vmp with a -0.30 %/°C Voc coefficient, a -0.35 %/°C Vmp coefficient and NOCT 45 °C. The site runs from 5 °F to 95 °F. The inverter takes 600 V maximum DC input and needs 100 V to start tracking. Ten modules are wired in series.
- Coldest case: 5 °F is -15 °C. The corrected module voltage is 50 x (1 + (-0.30 / 100) x (-15 - 25)) = 50 x 1.12 = 56.0 V.
- String open circuit voltage: 10 modules x 56.0 V = 560.0 V, which is 40.0 V below the 600 V limit, so the string passes.
- Maximum modules for this inverter: 600 / 56.0 = 10.7, so 10 modules in series is the limit at this temperature.
- Hottest case: 95 °F is 35 °C. Cell temperature = 35 + (45 - 20) x 1000 / 800 = 66.25 °C.
- Hot working voltage: 41 x (1 + (-0.35 / 100) x (66.25 - 25)) = 41 x 0.855625 = 35.08 V per module, so 350.8 V for the string.
- Minimum modules for the MPPT window: 100 / 35.08 = 2.85, so 3 modules in series are needed at the low end.
- The 10 module string sits between both limits: 560.0 V on the coldest night and 350.8 V on the hottest afternoon.
Reference table
| Where the array sits | Maximum DC voltage | Typical use |
|---|---|---|
| One or two family dwelling | 600 V | Residential string inverter |
| Other buildings and structures | 1000 V | Commercial or larger string inverter |
Limits
- This sizes voltage only. It does not size conductors, fuses, disconnects, grounding or the inverter itself.
- The design low temperature is your choice, so a wrong low temperature produces a string that is not code compliant.
- The NOCT model assumes 1000 W/m2 at the panel and ignores wind and mounting height, so a hot roof mount can run hotter than shown.
- Local codes, utility interconnection rules and the AHJ may set limits stricter than the ones in the table.
Common mistakes
- Sizing the string from the nameplate voltage and forgetting that cold weather raises the open circuit voltage.
- Using the inverter AC rating instead of its maximum DC input voltage from the datasheet.
- Leaving out the hot case, then finding that the string drops below the MPPT window on a summer afternoon and production falls.
- Mixing modules from different manufacturers in one string without checking that their voltage and current match.
- Assuming the rule applies when the system uses microinverters or DC optimisers, where there is no string voltage at all.
Try it yourself
Quick checks. Answers sit tucked under each question.
A 50 V module with a -0.30 %/°C Voc coefficient feeds a 600 V inverter. With a design low temperature of -15 °C, how many modules fit in one string?
10 modules. Cold Voc per module = 50 x (1 + (-0.30 / 100) x (-15 - 25)) = 56.0 V, and 600 / 56.0 = 10.7, so round down to 10.
A 41 V module with a -0.35 %/°C Vmp coefficient and NOCT 45 °C sits on an array designed for 35 °C. What is the hot working voltage per module?
35.08 V. Cell temperature = 35 + (45 - 20) x 1000 / 800 = 66.25 °C, then 41 x (1 + (-0.35 / 100) x (66.25 - 25)) = 35.08 V.
With that hot voltage of 35.08 V per module, how many modules does a 100 V MPPT floor need?
3 modules. 100 / 35.08 = 2.85, so round up to 3 modules in series.
Questions
What is the maximum DC voltage for a home solar array?
600 V for photovoltaic circuits on or in one and two family dwellings and 1000 V for circuits on or in other buildings, under NEC 690.7. Your inverter datasheet and your electrical inspector set the number that actually applies.
Why does cold weather matter more than hot weather?
Open circuit voltage rises as the cell gets colder, so the coldest night produces the highest string voltage. Hot weather lowers the working voltage, which matters for the MPPT floor instead.
What is NOCT and where do I find it?
NOCT is the nominal operating cell temperature, the cell temperature a module reaches at 800 W/m2 irradiance and 20 °C ambient with light wind. Every module datasheet lists it.
Do I need this if I have microinverters?
No. Microinverters and DC optimisers work on one module at a time, so there is no string voltage to size. This page applies to modules wired in series to a string inverter.
Why did the tool say 10 modules when my installer used 12?
The count depends on the design low temperature and the Voc coefficient. A warmer design low temperature allows more modules, and the code table method can differ slightly from the coefficient method used here.
Does the calculator pick an inverter for me?
No. It works with the two inverter limits you enter, the maximum DC voltage and the minimum MPPT voltage. Check both numbers against the datasheet before you order modules.
Sources
- Miami-Dade County PV electrical inspector checklist, quoting NEC 690.7
- PV Performance Modeling Collaborative: NOCT cell temperature model (Sandia)