Solar Power Math Problems - Part I, Calculating Solar Panel Circuits
Math problems are everywhere when solar power is concerned, not only for reducing power losses, but also for safety considerations. Article 690 of the National Electrical Code (NEC) requires derating and correction factors based on the type of wiring involved and the locations the wires are installed. There's also a default "just because it's solar" calculation with a lot of good reasons related to the NEC's goal of life safety. I installed my system using the 2003 edition, which was the current edition at the time.
The first math problem deals with solar panel output. When planning your solar panel installation, technical details for stuff Pmax, Vpm, Ipm, VOC, and Isc are needed for a safe design. Here are the specs for the solar panels I used:
Sanyo HIP-180: Pmax 180 watts, Vpm 54.0 volts, Ipm 3.33 amps, Voc 66.4 volts, Isc 3.65 amps
BP Millenia MST-43MV:Pmax 43 watts, Vpm 72.0 volts, Ipm 0.6 amps, Voc 98 volts, Isc 0.8 amps
The NEC requires a 'weather correction factor' to determine the highest possible voltage. Solar panels produce less power the hotter they get; they produce more power the colder they get. The NEC has a table (Table 690.7, Voltage Correction Factors for Crystalline and Multicrystalline Silicon Modules) that gives the correction factor, based on the coldest possible operating temperatures expected.
From the 2008 version of the NEC: [NEC 690.7]
-11C to -15C (13F to 5): 1.16
-6C to -10C (22F to 14F): 1.14
-1C to -5C (31F to 23F): 1.12
My area's coldest daytime winter temperature is usually above 22F so my weather correction factor would be 1.14, but I've seen 30 mph winds on bright sunny winter days, so I'll use the higher number to allow for windchill.
Each group of panels is a 'PV Source Circuit'. My panels are wired in parallel (two per circuit); the math runs like this: [NEC 690.8(A)(1)]
the sum of all the Isc numbers in the circuit, multiplied by the weather correction factor equals the 'PV Source Circuit Current'
3.65A + 3.65A = 7.3A times 1.16 = 8.468A
The PV Source Circuit Current is then multiplied "because it's solar" by 1.25. 8.468A times 1.25 = 10.585A. This is the maximum possible current that each circuit could possibly produce. If I selected only a 10 amp fuse for this circuit, there is a strong possibility I'd have to replace fuses pretty often in the winter time, especially on bright sunny days with lots of snow reflecting even more light onto the solar panels. [NEC 690.8(B)(1)]
Now that I've determined how much current might solar cable 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%
The first math problem deals with solar panel output. When planning your solar panel installation, technical details for stuff Pmax, Vpm, Ipm, VOC, and Isc are needed for a safe design. Here are the specs for the solar panels I used:
Sanyo HIP-180: Pmax 180 watts, Vpm 54.0 volts, Ipm 3.33 amps, Voc 66.4 volts, Isc 3.65 amps
BP Millenia MST-43MV:Pmax 43 watts, Vpm 72.0 volts, Ipm 0.6 amps, Voc 98 volts, Isc 0.8 amps
The NEC requires a 'weather correction factor' to determine the highest possible voltage. Solar panels produce less power the hotter they get; they produce more power the colder they get. The NEC has a table (Table 690.7, Voltage Correction Factors for Crystalline and Multicrystalline Silicon Modules) that gives the correction factor, based on the coldest possible operating temperatures expected.
From the 2008 version of the NEC: [NEC 690.7]
-11C to -15C (13F to 5): 1.16
-6C to -10C (22F to 14F): 1.14
-1C to -5C (31F to 23F): 1.12
My area's coldest daytime winter temperature is usually above 22F so my weather correction factor would be 1.14, but I've seen 30 mph winds on bright sunny winter days, so I'll use the higher number to allow for windchill.
Each group of panels is a 'PV Source Circuit'. My panels are wired in parallel (two per circuit); the math runs like this: [NEC 690.8(A)(1)]
the sum of all the Isc numbers in the circuit, multiplied by the weather correction factor equals the 'PV Source Circuit Current'
3.65A + 3.65A = 7.3A times 1.16 = 8.468A
The PV Source Circuit Current is then multiplied "because it's solar" by 1.25. 8.468A times 1.25 = 10.585A. This is the maximum possible current that each circuit could possibly produce. If I selected only a 10 amp fuse for this circuit, there is a strong possibility I'd have to replace fuses pretty often in the winter time, especially on bright sunny days with lots of snow reflecting even more light onto the solar panels. [NEC 690.8(B)(1)]
Now that I've determined how much current might solar cable 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%
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