Solar Power Math Problems – Part II, Wire Size Calculation

In Part 1, we discuss how to calculate the electrical circuits of solar panels to avoid potential safety issues during their installation and use. Our calculated circuit current from Part 1 was 10,585 amps.

Now that we have determined how much current can be produced, I need to select the correct wire size. I am using a USE-2 type cable from the solar panels to the combiner box where the breakers are located. USE-2 cable is UL listed for outdoor use in hot areas (90C) and is also resistant to sunlight. USE-2 temperature reduction at 141-158F is 0.58

[NEC 310.16]

• USE-2 cable ampacity, 10AWG: 40 amps
• 40 amps times 0.58 = 23.2 amps
• USE-2 cable ampacity, 12AWG: 30 amps
• 30 amps times 0.58 = 17.4 amps
• USE-2 cable ampacity, 14AWG: 25 amps
• 25 amps times 0.58 = 14.5 amps

The wire size needs to be able to handle 125% of the derated PV source circuit current (10.585 A), so 10.585 A times 1.25 = 13.23 A. Our wire needs to be thick enough to handle 13.3 amps, so any of these sizes would meet the electrical code.

Temperature reduction for various cables. There is an additional factor to consider if these cables run through conduit. Depending on the number of current-carrying conductors (positive conductors), the cable is reduced according to the following: [NEC 310.15(B)(2)(A)]

• 4-6 drivers: 80%
• 7-9 drivers: 70%
• 10-20 drivers: 50%

If these 10 circuits are run through conduit, the rating for 10 AWG (40 A > 23.2 A) is reduced again. 23.2 times 0.5 = 11.6 amps. I can run 9 circuits in conduit and run 1 free circuit (allowed with USE-2 cable) and reduce the circuits in conduit to 70% (16.24A) or split the runs, with 5 circuits per conduit and reduce to 80% ( 18.56A).

Another thing to consider is resistance. Thinner cables have more resistance than thicker cables, which reduces the amount of power available at the end. And, the lower the voltage, the greater the power loss.

• DC resistance of 14AWG cable: 2.5 ohms/1000 feet
• DC resistance of 12AWG cable: 1.6 ohms/1000ft
• 10AWG Wire DC Resistance: 1.1 ohms/1000ft

I have fairly short runs of wiring (less than 50 feet). The following table shows the calculated voltage drop (loss) for a 50′ circuit, at various DC voltages, with a 10 amp load. The voltage drops even more on longer runs. At 12 volts, a 500′ circuit loses so much, it’s only 2.4 volts at the opposite end!

• 2AWG
• 12 V DC: 11.84 V at 10 amps
• 24 V DC: 23.84 V at 10 amps
• 48 V DC: 47.84 V9 at 10 amps
• 96 V DC: 95.84 V at 10 amps

• 10AWG
• 12 VDC: 10.9V
• 24V DC: 22.9V
• 48 VDC: 46.9 V
• 96V DC: 94.9V

• 12AWG:
• 12 VDC: 10.4V
• 24 VDC: 22.4 V
• 48 VDC: 46.4 V
• 96 VDC: 94.4 V

Once the PV source circuits are at the breakers, they are combined in the PV combiner box to form the PV output circuits. The PV combiner box can combine 12 PV source circuits into 1 PV output circuit, or split those same 12 PV source circuits into 2 PV output circuits. After taking the math into account (and depending on the limitations of the charge controller), our 10 PV source circuits are combined into 2 PV output circuits:

[NEC 690.8(A)(2)]

• The PV source circuit current multiplied by the number of circuits multiplied by 1.25 (twice) equals the PV output circuit current.
• 7.3A times 10 circuits = 73.0A times 1.25 = 91.25 times 1.25 = 114.06 (we will round up to 115A).
• 7.3A times 5 circuits = 43.8A times 1.25 = 54.75 times 1.25 = 57.03A (we will round to 60A).

The charge controllers (Outback MX-60) are rated for continuous service at 60 amps and 125 volts DC. When deciding on system voltages, we had to take this limitation into account. Again, more math:

[NEC 690.7]

• sum of the maximum voltages (Voc) of the panels wired in series, multiplied by the weather correction factor
• 66.4 + 66.4 = 132.8 volts multiplied by 1.13 = 150 volts, which is well over the 125 volt limit.

If I need higher voltages in the future I may be able to rewire the panels and mix them with 24V panels. Assuming 24 volt panels have a max voltage of 44.2 volts (like BP 3160 solar panels) : 66.4 + 44.2 = 110.6, multiplied by 1.13 = 124.978, which is right at the limit of the 125 volt charge controller. Of course, you would also have to take into account the source circuit currents.

From this point (the combiner box) to the DC equipment inside the house, everything is rated for 60 Amps.

THHN/THWN cable is rated at 70C and is suitable for running in conduit. The first set of solar panels is two-circuit. There is room on the roof for even more solar panels, which could be 2 additional circuits in the future, so we are planning ahead and using larger ducting. We know that we may eventually have 4 circuits in the conduit, and that the conduit will be hot (but not as hot as the solar panel wires). [Table 310.16]

• THWN cable is derated as: Nominal value multiplied by 0.88 for (ambient temperature 96 to 104°F), multiplied by 80% (4 conductors in conduit)
• 3AWG is rated 100A times 0.88 = 88A times 0.8 = 70.4A
• 2AWG is rated as 115A times 0.88 = 101.2A times 0.8 = 80.96A

We can use 3 AWG wire, but 2 AWG provides less power loss (and is generally available and in stock at most DIY places).

An equipment ground wire is also required and is sized based on the size of the largest breaker (60A), BUT if the wiring of the PV output circuits has been oversized (like ours), then the equipment ground wire is Equipment ground also has to be oversized for the size of the PV output circuit wires.

[NEC 690.45], [NEC 250.122]

Eventually there will be 4 PV output circuits plus the equipment ground wire that runs in conduit from the ceiling. Each circuit has two wires, so the total number of wires is 9 including the ground wire. We use 2″ conduit which has room for a total of 12 wires (if they are all 2 AWG).

When cables are first installed in conduit, you are allowed 40% infill based on the diameter of all cables involved. The number of cables you’re running and the 40% fill ratio determines the minimum conduit size allowed, and just one extra cable could mean having to start installing larger diameter conduit (which gets expensive pretty quickly). There is a provision in the NEC that can help save money, though it’s not very nice: If the equipment ground wire is 6 AWG or larger, the ground wire is allowed to be attached to the outside of the conduit. . [NEC 250.64]

There are many types of ducts, but not all are approved for outdoor use where there is rain and shine. Rigid Metal Conduit (RMC) and Intermediate Metal Conduit (IMC) are approved. Liquidtight is approved if it is resistant to sunlight. Schedule 40 PVC conduit is also approved if it is rated as resistant to sunlight, but I have still seen it warp in normal summer temperatures. Electrical Metallic Tubing (EMT) is not approved for exteriors exposed to the weather, and Schedule 80 PVC conduit is not approved for exteriors exposed to sunlight.

When multiple cables are installed in a conduit, the cross section of the cables can only fill up to 40% of the cross section of the conduit. The cross section of #2 AWG THWN wire is 0.1158 square inches. The cross section of nine cables is 1.0422 square inches. The NEC Chapter 9 conduit fill tables specify that the 1.5″ RMC allows up to 0.829 square inches and the 2″ RMC allows up to 1.363 square inches.

If we were concerned about exceeding the conduit fill, there is a provision in the NEC that allows us to run the connected equipment ground wire to the outside of the conduit, IF the equipment ground wire is 6 AWG or larger. But remember, if the equipment ground wire is 6 AWG or less, it MUST have green insulation (marking with green tape is not approved). Larger ground wires can be marked with green tape, etc.

[NEC 250.64]