Crash course: Voltage, amperage, and resistance basics for solar installers (part 5)

Ohm's law is the only formula that matters on a solar job

V = I x R. Voltage equals current times resistance. Every PV calculation you run in the field traces back to this. Get it wrong and you undersize conductors, trip OCPDs, or melt MC4 connectors on a hot roof.

Power follows: P = V x I. On the DC side of a solar array, you are usually solving for current when you know module Vmp and Pmp from the spec sheet. On the AC side, you are sizing conductors against inverter output current per NEC 690.8(A)(3).

Memorize three rearrangements and stop reaching for the calculator on small jobs:

• I = V / R (current draw across a known load)
• R = V / I (troubleshooting a string with abnormal current)
• P = I squared x R (heat dissipation in a conductor or bad lug)

Voltage on a PV array is not what the label says

Module Voc on the data sheet is rated at STC, 25 degrees C cell temp. Real rooftops in January hit cell temps well below that, and Voc climbs. NEC 690.7 requires you to correct Voc for the lowest expected ambient temperature using either the manufacturer coefficient or Table 690.7(A).

Skip this and your string Voc can exceed the inverter max input or the 600V/1000V system rating. That is a code violation and a warranty void. Run the correction every time, even on a four-module residential string.

Tip: In northern climates, a 10-module string of 40V Voc modules can climb past 480V on a cold sunny morning. Always run the temp correction before you commit to a string size.

Amperage: where conductors actually fail

PV source circuit current is Isc x 1.25 per NEC 690.8(A)(1). Then you apply another 1.25 for continuous duty per 690.8(B)(1), giving you 156 percent of Isc as your minimum conductor ampacity before temperature and conduit fill derates.

That is the number that catches new installers. A 10A Isc module does not get a 10A wire. It gets a conductor rated for at least 15.6A after derating, which on a hot rooftop in conduit usually pushes you to 12 AWG minimum, sometimes 10 AWG.

1. Start with Isc from the module spec sheet.
2. Multiply by 1.56 for the calculated circuit current.
3. Apply Table 310.15(B)(1) ambient correction for rooftop temps.
4. Apply Table 310.15(C)(1) conduit fill adjustment.
5. Compare against 75C column ampacity in Table 310.16 for terminations.

Resistance: the silent killer on long DC runs

Resistance is fixed by conductor material, length, and cross-section. On long roof-to-inverter runs, voltage drop eats production. Industry practice is to keep DC voltage drop under 2 percent, AC under 3 percent, total system under 5 percent. NEC 210.19 informational notes back this up for branch circuits.

The math: Vdrop = 2 x L x I x R per 1000 ft, where R is from Chapter 9 Table 8. Double the length because current goes out and back. On a 150 foot run at 10A with 10 AWG copper, you are looking at roughly 3.7V drop on a 400V string. That is under 1 percent and acceptable.

Push the same current through 12 AWG and the drop nearly doubles. Push 200 feet at 15A and you are upsizing to 8 AWG to stay legal and keep the homeowner from losing kWh every year.

Where electricians blow the calculation

The most common field mistake is using Imp instead of Isc when sizing source circuit conductors. Imp is the operating current at maximum power. Isc is the worst-case short circuit current and is what 690.8 requires. Use Isc, every time.

Second most common: forgetting that 690.8(A)(1) and 690.8(B) stack. The 1.25 factors are not either/or. They multiply. 156 percent of Isc is your starting ampacity, before any derate.

Tip: If you find yourself arguing with an inspector about why your 12 AWG is too small on a 9.5A Isc module, walk through the 1.25 x 1.25 math out loud. Nine times out of ten they nod and you both move on.

Quick field reference

Tape this inside your van door. These are the numbers you reach for daily on a residential or light commercial PV install.

• Conductor sizing current: Isc x 1.56 (690.8(A)(1) and (B)(1))
• Inverter output current: nameplate continuous output x 1.25 (690.8(A)(3))
• Voc cold correction: per 690.7 and Table 690.7(A)
• DC voltage drop target: under 2 percent
• AC voltage drop target: under 3 percent
• Rooftop ambient adder: see 310.15(B)(2) for raceways above roof
• OCPD sizing: not less than 125 percent of Isc, rounded up to standard size per 240.6

Run the numbers before you pull wire. A five minute spec sheet check beats a callback to swap conductors after the inspector red tags you.