The NEC 690.7 string voltage calculation is the first check on every US solar permit. This guide explains the exact calculation method, provides reference data for major US cities, and shows worked examples for residential and commercial systems.
The NEC 690.7 Formula
Voc_corrected = Voc_STC × N × [1 + (T_min - 25) × (β_Voc / 100)]Where:
Voc_STC= Module open-circuit voltage at 25°C (from datasheet)N= Number of modules in seriesT_min= Lowest expected ambient temperature (ASHRAE value, in °C)β_Voc= Temperature coefficient of Voc (%/°C, from datasheet — negative for c-Si)
Voltage limits:
- One- and two-family dwellings: 600V maximum
- All other systems: 1000V maximum
- Listed 1500V equipment (commercial/utility): 1500V maximum
ASHRAE Minimum Temperatures: Major US Cities
| City | T_min (°C) | T_min (°F) |
|---|---|---|
| Miami, FL | 8°C | 46°F |
| Los Angeles, CA | 3°C | 37°F |
| Phoenix, AZ | 2°C | 36°F |
| Las Vegas, NV | -5°C | 23°F |
| Atlanta, GA | -9°C | 16°F |
| Seattle, WA | -9°C | 16°F |
| Dallas, TX | -7°C | 19°F |
| Houston, TX | -2°C | 28°F |
| San Diego, CA | 5°C | 41°F |
| San Francisco, CA | 2°C | 36°F |
| Sacramento, CA | -3°C | 27°F |
| Portland, OR | -10°C | 14°F |
| Denver, CO | -24°C | -11°F |
| Salt Lake City, UT | -18°C | 0°F |
| Albuquerque, NM | -16°C | 3°F |
| Chicago, IL | -22°C | -8°F |
| New York, NY | -15°C | 5°F |
| Boston, MA | -19°C | -2°F |
| Philadelphia, PA | -13°C | 9°F |
| Washington, DC | -13°C | 9°F |
| Minneapolis, MN | -31°C | -24°F |
| Charlotte, NC | -11°C | 12°F |
| Raleigh, NC | -10°C | 14°F |
| Columbus, OH | -18°C | 0°F |
| Cleveland, OH | -18°C | 0°F |
Worked Example: 400W Residential Module, Los Angeles
Module: 400W panel, Voc = 45.0V at STC, β_Voc = -0.28%/°C Location: Los Angeles, CA — T_min = 3°C System type: Residential (600V limit)
Step 1: Correction factor
Factor = 1 + (3 - 25) × (-0.28/100) = 1 + (-22) × (-0.0028) = 1 + 0.0616 = 1.0616Step 2: Maximum string length
Max modules = 600 / (45.0 × 1.0616) = 600 / 47.77 = 12.56 → 12 modules maximumVerification (12 modules):
Voc_corrected = 45.0 × 12 × 1.0616 = 573.3V ✓ (below 600V)13 modules would give: 45.0 × 13 × 1.0616 = 621.1V ✗ (exceeds 600V)
Worked Example: 400W Commercial Module, Denver
Same module: Voc = 45.0V, β_Voc = -0.28%/°C Location: Denver, CO — T_min = -24°C System type: Commercial (1000V limit)
Step 1: Correction factor
Factor = 1 + (-24 - 25) × (-0.0028) = 1 + (-49) × (-0.0028) = 1 + 0.1372 = 1.1372Step 2: Maximum string length
Max modules = 1000 / (45.0 × 1.1372) = 1000 / 51.17 = 19.54 → 19 modules maximumAt Denver’s cold temperatures, the same module that allows 12 in series for residential LA allows only 19 for commercial Denver — the cold correction factor consumes significant voltage headroom.
Common Temperature Coefficient Ranges
| Module Type | Typical β_Voc Range |
|---|---|
| Monocrystalline silicon | -0.27% to -0.35%/°C |
| Polycrystalline silicon | -0.30% to -0.40%/°C |
| PERC (mono) | -0.27% to -0.30%/°C |
| TOPCon | -0.25% to -0.29%/°C |
| HJT (heterojunction) | -0.24% to -0.26%/°C |
| Thin film (CdTe) | -0.19% to -0.25%/°C |
HJT and TOPCon modules have lower temperature coefficients than standard PERC, meaning they gain less voltage at cold temperatures. This means HJT/TOPCon modules can sometimes fit more modules per string in cold-climate markets.
Design Software Automates This
In a production solar design environment, these calculations should be automated by your design software. SurgePV calculates temperature-corrected Voc for every string in the design using ASHRAE data for the project address and module β_Voc from the equipment database. Manual calculation is valuable for verification and permit documentation, but not for every design decision.
Automate NEC 690.7 String Sizing in Your Projects
SurgePV calculates temperature-corrected Voc automatically and exports the full 690.7 calculation table in your permit package — no manual calculation required.
See Solar Design SoftwareNEC 690 calculations · AHJ-ready permit packages · US market
Frequently Asked Questions
How do I calculate maximum string length under NEC 690.7?
Max string = Voltage limit ÷ (Module Voc × temperature correction factor). Correction factor = 1 + (T_min - 25) × (β_Voc/100), using ASHRAE T_min for the site and module β_Voc from the datasheet. Always round DOWN the maximum string length.
What voltage limit applies to residential solar?
600V DC for systems on one- and two-family dwellings. 1000V DC for commercial, industrial, and all other system types. 1500V only for systems using specifically listed 1500V-rated equipment (commercial/utility scale only).
Where do I find the ASHRAE minimum temperature?
ASHRAE Fundamentals Handbook (Chapter 14, Table 1) or design software that auto-pulls ASHRAE data from the project address. The table in this guide covers major US cities.
