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Solar Power Math Problems – Part II, Calculating Wire Size
In Part 1, we discussed how to calculate solar electrical circuits to avoid potential safety issues during installation and use. Our calculated circuit current from part 1 was 10.585 A.
Now that we have determined how much current we can produce, I need to choose the correct wire size. I use USE-2 type cable from the solar panels to the combiner box where the circuit breakers are located. The USE-2 cable is UL rated, suitable for outdoor use in hot (90 C) locations and is also resistant to sunlight. USE-2 temperature drop at 141-158 F is 0.58
- USE-2 cable capacity, 10AWG: 40 amps
- 40 amps times 0.58 = 23.2 amps
- USE-2 cable, 12AWG capacity: 30 amps
- 30 A times 0.58 = 17.4 A
- USE-2 cable, 14AWG capacity: 25 amps
- 25 A times 0.58 = 14.5 A
The wire size must be able to handle 125% of the stepped down PV source 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 size meets electrical regulations.
Temperature reduction for multiple cables. There is an additional factor to be aware of when these wires are run through conduit. Based on the number of current-carrying conductors (positive conductors), the conductor is reduced as follows: [NEC 310.15(B)(2)(A)]
- 4-6 wires: 80%
- 7-9 wires: 70%
- 10-20 wires: 50%
If this circuit runs through 10 wires, the 10AWG (40A > 23.2A) rating is reduced again. 23.2 times 0.5 = 11.6 amps. I can run 9 circuits in conduit and 1 circuit free (allowable with USE-2 cable) and reduce the circuits in conduit to 70% (16.24A) or split the runs with 5 circuits per protection channel and derating to 80%. (18.56A).
Something else to consider is resistance. Thinner wires have more resistance than thicker wires, which reduces the power 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/1000ft
- DC resistance of 10AWG wire: 1.1 ohms/1000ft
I have a fairly short connection (less than 50 feet). The following table shows the calculated voltage drop (loss) of a 50′ circuit at different DC voltages with a 10 amp load. During longer runs, the voltage decreases further. At 12 V, a 500′ circuit loses so much that there is only 2.4 volts at the other 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
- 12 AWG:
- 12VDC: 10.4V
- 24VDC: 22.4V
- 48VDC: 46.4V
- 96VDC: 94.4V
Once the PV source circuits are at the breakers, they are combined in the PV combiner box to create the PV output circuits. The PV combiner box can combine 12 PV source circuits with 1 PV output circuit, or divide the same 12 PV source circuit into 2 PV output circuits. After taking into account the math (and based on the limitations of the charge controller), we combine our 10 PV source circuits into 2 PV output circuits:
- PV source circuit current times the number of circuits equals 1.25 (twice) the PV output circuit current.
- 7.3 A × 10 circuits = 73.0 A × 1.25 = 91.25 × 1.25 = 114.06 (round up to 115 A).
- 7.3 A × 5 circuits = 43.8 A × 1.25 = 54.75 × 1.25 = 57.03 A (round up to 60 A).
The charge controllers (Outback MX-60) are rated for continuous operation at 60 amps and 125 VDC. We had to take this limit into account when determining the system voltages. Again, more math:
- the 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 times 1.13 = 150 volts, which is well over the 125 volt limit.
If I need more voltage in the future, I may be able to rewire the panels and mix them with 24v panels. Assuming the 24V panels have a maximum voltage of 44.2V (as with the BP 3160 solar panels): 66.4 + 44.2 = 110.6 times 1.13 = 124.978, which is exactly the 125V charge controller is at its limit. Of course, I also have to keep in mind the circuit currents of the source.
Everything from this point (the combiner box) to the DC equipment inside the house is rated for 60 Amps.
THHN/THWN wire is rated at 70°C and is suitable for use in pipelines. The first set of solar cells consists of two circuits. There is room for more solar panels on the roof, which could mean 2 more circuits in the future, so we plan ahead and use larger wire. We know that eventually there can be 4 circuits in the wire and the wire will be hot (but not as hot as the solar panel wires). [Table 310.16]
- THWN wire is derated as follows: Rated times 0.88 (96-104°F ambient) times 80% (4 wires in wire)
- 3AWG is rated at 100A × 0.88 = 88A × 0.8 = 70.4A
- 2AWG is rated at 115 A × 0.88 = 101.2 A × 0.8 = 80.96 A
We could use 3 AWG wire, but 2 AWG provides less current loss (and is usually readily available and in stock at most DIY places).
You also need an equipment ground wire, the size of which depends on the size of the largest breaker (60A), BUT if the PV output circuit wire is oversized (like ours), then the equipment ground wire is also oversized compared to the size of the PV output circuit wires.
[NEC 690.45], [NEC 250.122]
Finally, there will be 4 PV output circuits, as well as the equipment ground wire running from the roof in one conduit. Each circuit has two wires, so the total number of wires is 9, including the ground wire. We use 2″ wire, which has room for a total of 12 wires (if they are all 2AWG).
When wires are first installed in the conduit, a 40% charge is allowed based on the diameter of all wires involved. The number of wires installed and the 40% fill ratio determine the minimum allowable pipe size, and just one extra wire may mean installing a larger diameter wire (which gets expensive pretty quickly). There is a provision in the NEC that can save you money, although it’s not very pretty: If the equipment ground wire is 6 AWG or larger, the ground wire can be connected to the outside of the conduit. [NEC 250.64]
There are many types of cords, but not all of them are allowed outdoors in rain and sun. Rigid metal conduit (RMC) and intermediate metal conduit (IMC) are approved. A liquid barrier is permitted if it is resistant to sunlight. Schedule 40 PVC conduit is also approved if it is sun resistant, but I have still seen it warp in normal summer temperatures. Electrical Metallic Conduit (EMT) is not permitted outdoors where it is exposed to the weather, and Schedule 80 PVC Conduit is not permitted outdoors where it is exposed to sunlight.
Where several wires are integrated into the conduit, the cross-section of the wires may only fill 40% of the cross-section of the protective tube. #2 AWG THWN wire has a cross section of 0.1158 square inches. Nine wires have a cross section of 1.0422 square inches. The conductor fill tables in Chapter 9 of the NEC specify that 1.5″ RMC is no more than 0.829 square inches and 2″ RMC is no more than 1.363 square inches.
If you are concerned about exceeding the conduit loading, there is a provision in the NEC that allows us to attach the equipment ground wire to the outside of the conduit IF the equipment ground wire is 6 AWG or larger. But remember, if your equipment ground wire is 6 AWG or smaller, it MUST have green insulation (marking with green tape is not allowed). Larger ground wires with green tape, etc.
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