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## Solar Power Math Problems – Part II, Calculating Wire Size

In part 1, we explained how to calculate the electrical circuits of solar panels to avoid possible safety problems 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 between the solar panels and the combiner box where the circuit breakers are. The USE-2 cable is UL listed for outdoor use in hot areas (90C) and is also resistant to sunlight. Temperature derating of USE-2 in 141-158F is 0.58

[NEC 310.16]

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

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

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

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

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

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

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

I have fairly short cables (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, that there are only 2.4 volts at the opposite end!

• 2AWG
• 12 VDC: 11.84 V at 10 A
• 24 VDC: 23.84 V at 10 A
• 48 VDC: 47.84 V9 at 10 amps
• 96 VDC: 95.84 V at 10 A
• 10AWG
• 12 VDC: 10.9 V
• 24 VDC: 22.9 V
• 48 VDC: 46.9 V
• 96 VDC: 94.9 V
• 12AWG:
• 12 VDC: 10.4 V
• 24 VDC: 22.4 V
• 48 VDC: 46.4 V
• 96 VDC: 94.4 V

After the PV source circuits are at the circuit breakers, they are combined with 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 into account the calculations (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)]

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

The charge controllers (Outback MX-60) are designed for continuous operation at 60 amps and 125 volts DC. In deciding the voltages of the system, 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 climatic correction factor
• 66.4 + 66.4 = 132.8 volts, times 1.13 = 150 volts, which is well above 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 maximum voltage of 44.2 volts (like BP 3160 solar panels): 66.4 + 44.2 = 110.6, times 1.13 = 124.978, which is exactly the 125 volt charge controller limit. Of course, I should also keep the source circuit currents in mind.

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

THHN/THWN wire is rated for 70C and is suitable for passing through conduit. The first set of solar panels is composed of two circuits. There is room on the roof for even more solar panels, which could be 2 more circuits in the future, so we plan ahead and use larger ducts. We know that we will eventually have 4 circuits in the conduit and the conduit will be hot (but not as hot as the solar panel wires). [Table 310.16]

• THWN wire is derated as follows: Rating multiplied by 0.88 for (ambient temperature 96 to 104°F), multiplied by 80% (4 conductors in one conduit)
• 3AWG is rated at 100A times 0.88 = 88A times 0.8 = 70.4A
• 2AWG is rated at 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 usually readily available and in stock at most DIY places).

An equipment ground wire is also required, and its size is based on the size of the largest circuit breaker (60A), BUT if the wiring on the PV output circuits has been oversized (like ours), then the wire The equipment ground must also be oversized to 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 running in conduit from the roof. 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 2AWG).

When wires are first installed in conduit, you are entitled to a 40% infill based on the diameter of all wires involved. The number of wires you install and the 40% fill rate determines the minimum conduit size allowed, and just one more wire may require the installation of larger diameter conduit (which starts to get expensive pretty quickly ). There’s a provision in the NEC that can help save money, although it’s not very pretty: If the equipment ground wire is 6 AWG or larger, the ground wire can be attached to the outside of the duct. [NEC 250.64]

There are many types of ductwork, but not all are approved for outdoor use where rain and sun are present. Both 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 rated as sunlight resistant, but I’ve still seen it warp in normal summer temperatures. Electrical Metallic Tubing (EMT) is not approved for outdoor use when exposed to the weather, and Schedule 80 PVC Conduit is not approved for outdoor use when exposed to sunlight.

When multiple wires are installed in a conduit, the cross section of the wires 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 wires is 1.0422 square inches. The NEC Chapter 9 Conduit Fill Charts specify that 1.5″ RMC allows up to 0.829 square inches and 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 attached equipment ground wire outside of the conduit, IF the equipment ground wire is 6 AWG or greater. But remember that 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]

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