# How Much Math Do You Need To Know For Electrician Solar Power Math Problems – Part II, Calculating Wire Size

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

In Part 1, we discussed 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 USE-2 type wire from the solar panels to the combiner box where the switches are located. The USE-2 cable is UL listed for outdoor use in hot areas (90ºC) and is also resistant to sunlight. USE-2 temperature reduction at 141-158F is 0.58

[NEC 310.16]

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

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

Temperature reduction for various cables. There is an additional factor to consider if these cables are routed 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 running through a conduit, the rating for 10AWG (40A > 23.2A) is reduced again. 23.2 times 0.5 = 11.6 amps. I can run 9 circuits in the conduit and run 1 free circuit (allowed with USE-2 cable) and reduce the circuits in the conduit to 70% (16.24A) or split the runs, with 5 circuits per conduit and reduced to 80% ( 18.56A).

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

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

I have fairly short wiring runs (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 further on longer runs. At 12 volts, a 500′ circuit loses so much, that it is only 2.4 volts at the opposite end!

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

Once the PV source circuits are in the circuit 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 the same 12 PV source circuits into 2 PV output circuits. After accounting for the math (and based 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 times the number of circuits by 1.25 (twice) is equal to the PV output circuit current.
• 7.3A for 10 circuits = 73.0A for 1.25 = 91.25 for 1.25 = 114.06 (we’ll round up to 115A).
• 7.3A for 5 circuits = 43.8A for 1.25 = 54.75 times 1.25 = 57.03A (we’ll round up 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, by 1.13 = 150 volts, which is well above the 125 volt limit.

If I need higher voltages in the future, maybe I can rewire the panels and mix them with 24v panels. Assuming the 24v panels have a max voltage of 44.2v (like the BP 3160 solar panels) : 66.4 + 44.2 = 110.6, by 1.13 = 124.978, which is right at the 125 volt charge controller limit. Of course, you should also consider the source circuit currents.

From that point (the combiner box) to the house DC equipment, everything is rated for 60 amps.

THHN/THWN cable is rated at 70°C and is suitable for conduit. The first set of solar panels is two circuits. 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 a larger duct. We know that eventually we may have 4 circuits in the conduit and that the conduit will be hot (but not as hot as the solar panel cables). [Table 310.16]

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

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

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 of the PV output circuits has been oversized (like ours), then the ground wire of the equipment must also be done. oversized to the size of the photovoltaic output circuit cables.

[NEC 690.45], [NEC 250.122]

Finally, there will be 4 photovoltaic output circuits plus the ground wire of the equipment passing through the conduit from the ceiling. Each circuit has two wires, so the total wires are 9 including the ground wire. We are using 2″ conduit which has room for a total of 12 wires (if they are all 2AWG).

When the cables are first installed in the conduit, you can fill 40% based on the diameter of all the cables involved. The number of wires you are running and the 40% fill ratio determine the minimum allowable conduit size, and just one extra wire could mean having to install a larger diameter conduit (which starts to be expensive quite fast). There is 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 conduit . [NEC 250.64]

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

When multiple cables are installed in the conduit, the cross section of the cables is only allowed to fill up to 40% of the cross section of the conduit. The cross section of the #2 AWG THWN wire is 0.1158 square inches. The cross section of nine wires is 1.0422 square inches. The NEC Chapter 9 duct fill tables 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 overfilling the conduit, there is a provision in the NEC that allows us to run the equipment ground wire connected to the outside of the conduit IF the equipment ground wire is 6 AWG or more But remember, if the equipment ground wire is 6 AWG or smaller, it MUST have green insulation (green tape marking is not approved). Larger ground wires can be marked with green tape, etc.

[NEC 250.64]

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