Those math symbols and equations really hurt my head. It would take me eons to figure out how to calculate it myself. All i really wanna know is the 400ft of 12 awg wire to pv bus 36v 8a how much watt loss to heat?
This is an interesting question, though most people simply ensure that there is no more than a 3% voltage drop across any one cable run, this ensures minimum power loss across the system as a whole. But for shits and giggles, let's do this!
Firstly some assumptions:
- A PV cell/module/panel can be thought of as an ideal constant current source in parallel with an ideal diode under normal conditions. There are both shunt and series resistances for cell/module interconnections, but this is overly complicated for our purposes.
- Kirchoff's Voltage Law tells us that all voltages in a circuit must sum to zero, therefore power loss need only be represented by P = I²R, where R is the sum total resistance of the circuit.
- A high capacity battery can be thought of as an ideal constant voltage source with a series resistance. There is an RC component but again this is overly complicated for our purposes. Because of point (2.) we can ignore the voltage aspect and to a large extent the series resistance during the Bulk charging stage i.e. during Bulk, the battery presents a very low resistance to any charging supply. In short, we can ignore the battery.
- A PWM SCC during Bulk charge can be thought of as a ideal switch i.e. an ideal short circuit
Therefore, the whole circuit can be simplified down to a constant current source in series with a load resistance, which in this case, is the resistance of all cables and connectors:
...where:
I
TOT = I
sc array 1 + I
sc array 2
I
TOT = 8.85A + 8.85A
I
TOT = 17.7A
and...
R
TOT = 2R
1 + 2R
2 + 2R
3 + 2R
4 + 2R
5 +2R
6
.. where:
R
1 = Resistance of PV panel-to-busbar1 cable
R
2 = Resistance of busbar + connections
R
3 = Resistance of busbar-to-SCC cable
R
4 = Resistance of SCC-to-busbar2 cable
R
5 = Resistance of busbar2 + connections
R
6 = Resistance of busbar2-to-batteries
..........
Future me.... I was going to work this out for you but I'm struggling with time at the moment.
To work out the resistance of any cable, refer to
here. If you want to work in feet, click the 'ohm/1000ft' at the top. Then just take the number, divide by 1000 to get resistance per foot, then multiple by the total run length i.e. there and back. Resistances of large gauge cable will be in mΩ (thousandth's of an Ohm).
To work out the final power loss, the formula is just
P(loss) = I²R, for example, if your total resistance turned out to be 10mΩ, total power loss would be: P
(loss) = 17.7A² x 10mΩ = 100W
Good luck with your calculations!