Solar Power Math Problems - Part II, Calculating Wire Size
In Part 1, we discussed how to calculate solar panel electrical circuits to avoid possible safety issues during their installation and use. Our calculated circuit current from Part 1 was 10.585 Amps.
Now that we've determined how much current might be produced, I need to select the correct wire size. I'm using type USE-2 cable from the solar panels to the combiner box where the circuit breakers are located. USE-2 cable is UL listed for outdoor use in hot areas (90C) and is also sunlight resistant. The temperature derating of USE-2 in 141-158F is 0.58
[NEC 310.16]
Ampacity of USE-2 cable, 10AWG: 40 amps
40 amps times 0.58 = 23.2 amps
Ampacity of USE-2 cable, 12AWG: 30 amps
30 amps times 0.58 = 17.4 amps
Ampacity of USE-2 cable, 14AWG: 25 amps
25 amps times 0.58 = 14.5 amps
The wire size has to be able to handle 125% of the derated PV Source Circuit Current (10.585A), so 10.585A times 1.25 = 13.23A. Our wire has to be thick enough to handle 13.3 amps, so either of these sizes would meet the electrical code.
Temperature derating for multiple cables. There is an additional factor to be aware of if these wires are running through conduit. Based 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 these circuits are running through conduit, then the rating for 10AWG (40A > 23.2A) is reduced yet again. 23.2 times 0.5 = 11.6 amps. I can either run 9 circuits in conduit and run 1 circuit free (allowed with USE-2 cable) and derate the circuits in conduit to 70% (16.24A), or divide the runs, with 5 circuits per conduit and derated to 80% (18.56A).
Something else 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.
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 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's 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
12 VDC: 10.9 V
24 VDC: 22.9 V
48 VDC: 46.9 V
96 VDC:94.9 V
12 AWG:
12 VDC: 10.4 V
24 VDC: 22.4 V
48 VDC: 46.4 V
96 VDC:94.4 V
Once the PV Source Circuits are at the circuit breakers, they are combined at 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 factoring in the math (and based on the charge controller limitations), our 10 PV source circuits are combined into 2 PV output circuits:
[NEC 690.8(A)(2)]
PV Source Circuit Current times number of circuits times 1.25 (twice) equals PV Output Circuit Current.
7.3A times 10 circuits = 73.0A times 1.25 = 91.25 times 1.25 = 114.06 (we'll round up to 115A).
7.3A times 5 circuits = 43.8A times 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 duty at 60 amps and 125 volts DC. In deciding the system voltages, we had to take this limitation in account. Again, more math:
[NEC 690.7]
sum of the maximum voltages (Voc) of panels wired in series, times the weather correction factor
66.4 + 66.4 = 132.8 volts, times 1.13 = 150 volts, which is way 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 the 24 volt panels have a maximum voltage of 44.2 volts (like the BP 3160 solar panels): 66.4 + 44.2 = 110.6, times 1.13 = 124.978, which is right at the 125 volt charge controller limit. Of course, I would also have to keep the source circuit currents in mind as well.
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 running in conduit. The first set of solar panels is two circuits. There's room on the roof for even more solar panels, which might be an additional 2 circuits in the future, so we're planning ahead and using larger conduit. We know that eventually we may have 4 circuits in the conduit, and that the conduit will be warm (but not as warm as the wires at the solar panels). [Table 310.16]
THWN wire is derated as: Rating times 0.88 for (96-104°F ambient temperature), times 80% (4 conductors in conduit)
3AWG is rated as 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 usually readily available and in stock at most do-it-yourself places).
An equipment ground wire is also required, and its size is based on the size of the largest breaker (60A), BUT if the wiring on the PV Output Circuits has been oversized (like ours), then the equipment ground wire also has to 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 total wires is 9 counting the ground wire. We're using 2" conduit which has room for a total of 12 wires (if they're all 2AWG).
When wires are first installed in conduit, you're allowed 40% fill based on the diameter solar cable of all the wires involved. The number of wires you're installing and the 40% fill ratio determines the minimum size of conduit allowed, and just one extra wire could mean having to install larger diameter conduit (which starts getting expensive pretty fast). 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 is allowed to be attached to the outside of the conduit. [NEC 250.64]
There are many types of conduit, but not all are approved for use in the outdoors where rain and sun are present. Rigid metal conduit (RMC) and Intermediate metal conduit (IMC) are approved. Liquidtight is approved if it's sunlight resistant. Schedule 40 PVC conduit is also approved if it's rated sunlight resistant, but I've still seen it deform in normal summer temperatures. Electrical metallic tubing (EMT) is not approved for outdoors where exposed to weather, and Schedule 80 PVC conduit is not approved for outdoors where exposed to sunlight.
Where multiple wires are installed in conduit, the cross section of the wires is only allowed to 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 conduit fill tables in Chapter 9 of the NEC specifies that 1.5" RMC allows up to 0.829 square inches, and 2" RMC allows up to 1.363 square inches.
Now that we've determined how much current might be produced, I need to select the correct wire size. I'm using type USE-2 cable from the solar panels to the combiner box where the circuit breakers are located. USE-2 cable is UL listed for outdoor use in hot areas (90C) and is also sunlight resistant. The temperature derating of USE-2 in 141-158F is 0.58
[NEC 310.16]
Ampacity of USE-2 cable, 10AWG: 40 amps
40 amps times 0.58 = 23.2 amps
Ampacity of USE-2 cable, 12AWG: 30 amps
30 amps times 0.58 = 17.4 amps
Ampacity of USE-2 cable, 14AWG: 25 amps
25 amps times 0.58 = 14.5 amps
The wire size has to be able to handle 125% of the derated PV Source Circuit Current (10.585A), so 10.585A times 1.25 = 13.23A. Our wire has to be thick enough to handle 13.3 amps, so either of these sizes would meet the electrical code.
Temperature derating for multiple cables. There is an additional factor to be aware of if these wires are running through conduit. Based 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 these circuits are running through conduit, then the rating for 10AWG (40A > 23.2A) is reduced yet again. 23.2 times 0.5 = 11.6 amps. I can either run 9 circuits in conduit and run 1 circuit free (allowed with USE-2 cable) and derate the circuits in conduit to 70% (16.24A), or divide the runs, with 5 circuits per conduit and derated to 80% (18.56A).
Something else 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.
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 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's 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
12 VDC: 10.9 V
24 VDC: 22.9 V
48 VDC: 46.9 V
96 VDC:94.9 V
12 AWG:
12 VDC: 10.4 V
24 VDC: 22.4 V
48 VDC: 46.4 V
96 VDC:94.4 V
Once the PV Source Circuits are at the circuit breakers, they are combined at 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 factoring in the math (and based on the charge controller limitations), our 10 PV source circuits are combined into 2 PV output circuits:
[NEC 690.8(A)(2)]
PV Source Circuit Current times number of circuits times 1.25 (twice) equals PV Output Circuit Current.
7.3A times 10 circuits = 73.0A times 1.25 = 91.25 times 1.25 = 114.06 (we'll round up to 115A).
7.3A times 5 circuits = 43.8A times 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 duty at 60 amps and 125 volts DC. In deciding the system voltages, we had to take this limitation in account. Again, more math:
[NEC 690.7]
sum of the maximum voltages (Voc) of panels wired in series, times the weather correction factor
66.4 + 66.4 = 132.8 volts, times 1.13 = 150 volts, which is way 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 the 24 volt panels have a maximum voltage of 44.2 volts (like the BP 3160 solar panels): 66.4 + 44.2 = 110.6, times 1.13 = 124.978, which is right at the 125 volt charge controller limit. Of course, I would also have to keep the source circuit currents in mind as well.
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 running in conduit. The first set of solar panels is two circuits. There's room on the roof for even more solar panels, which might be an additional 2 circuits in the future, so we're planning ahead and using larger conduit. We know that eventually we may have 4 circuits in the conduit, and that the conduit will be warm (but not as warm as the wires at the solar panels). [Table 310.16]
THWN wire is derated as: Rating times 0.88 for (96-104°F ambient temperature), times 80% (4 conductors in conduit)
3AWG is rated as 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 usually readily available and in stock at most do-it-yourself places).
An equipment ground wire is also required, and its size is based on the size of the largest breaker (60A), BUT if the wiring on the PV Output Circuits has been oversized (like ours), then the equipment ground wire also has to 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 total wires is 9 counting the ground wire. We're using 2" conduit which has room for a total of 12 wires (if they're all 2AWG).
When wires are first installed in conduit, you're allowed 40% fill based on the diameter solar cable of all the wires involved. The number of wires you're installing and the 40% fill ratio determines the minimum size of conduit allowed, and just one extra wire could mean having to install larger diameter conduit (which starts getting expensive pretty fast). 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 is allowed to be attached to the outside of the conduit. [NEC 250.64]
There are many types of conduit, but not all are approved for use in the outdoors where rain and sun are present. Rigid metal conduit (RMC) and Intermediate metal conduit (IMC) are approved. Liquidtight is approved if it's sunlight resistant. Schedule 40 PVC conduit is also approved if it's rated sunlight resistant, but I've still seen it deform in normal summer temperatures. Electrical metallic tubing (EMT) is not approved for outdoors where exposed to weather, and Schedule 80 PVC conduit is not approved for outdoors where exposed to sunlight.
Where multiple wires are installed in conduit, the cross section of the wires is only allowed to 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 conduit fill tables in Chapter 9 of the NEC specifies that 1.5" RMC allows up to 0.829 square inches, and 2" RMC allows up to 1.363 square inches.
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