
Definitions
Voltage drop is defined as the amount of voltage loss that occurs through all or part of a circuit due to conductor resistance.
Conductor resistance is determined by conductor material, size, and ambient temperature.
Voltage drop highly depends on the total length of conductors that carry the electrical current. In DC systems, the voltage drop length is the total (round-trip) distance that current travels in a circuit. So the total length used in calculations is usually twice the length of the conductor run. In AC systems, the distance equals the length of the conductor.
Reflection
Why is the conductor length different for AC and DC circuits?
ANSWER: Since the current flows constantly in DC circuits, the current will travel back and forth. In this case, the distance is twice the length of a conductor. In AC systems, the current follows a sinusoidal wave form that has a positive value on one half of the wave cycle while the other half is negative. In this case, the total distance is cut in half and that means the distance equals the conductor length.
Voltage drop from PV array to inverter
NEC doesn’t require the calculation of voltage drop because it’s not a safety issue. However, it does recommend a maximum voltage drop of 3%. It is recommended to have up to 2% voltage drop at the DC side while only 1% is accepted at the AC side of the system for a total of 3% in voltage drop for the entire system.
Wires should be sized to reduce resistive (heating) loss to less than 3%. This loss is a function of the SQUARE of the current times the resistance, which is another manifestation of Ohm’s law:
V= I x R, or,
I = V/R.
And the resistive loss is I x I x R in Watts.
Note:
Use a wire-sizing table to choose the right wire size for the current and voltage you are working with. Visit Encorewire.com for an example.
Example
Computing the voltage drop formula:
Vdrop= Iop x Rc x L
Where:
Iop is the circuit operating current, which for source circuits is usually taken as the maximum power current, Imp,
L is the total conductor length.
Vdrop is the voltage at which you want to find VD, and
Rc is the wire’s resistivity in Ohms per 1000 feet and is found from NEC Chapter 9, Table 8 conductor Properties.
Example
If we have a PV array that is located 150’ away from the inverter (L=150 ft) and we are using wire # 14 AWG since it handles the current of 8.23A and it has resistivity of 3.14 (Ω/kft).
Vdrop = 8.23(A) x 3.14(Ω/kft) x 0.3(kft)= 5.168 V
The operating Voltage is
Vmmp= 12 x 37.2= 357.6 V
The voltage drop then is calculated as:
Vdrop%=Vdrop/Vmmp= 7.75/357.6 = 2.16% , which is not within the limit of 2% but this wire is running to a combiner box and to the inverter. In this case, the voltage drop should be less and the size of conductor must go up.
Upgrading to a larger conductor size for the same length and conductor type:
L=150 ft and # 12 AWG, Rc=1.98 (Ω/kft)
Vdrop = 8.23(A) x 1.98(Ω/kft) x 0.3(kft) = 3.386 V
The voltage drop then is calculated as:
Vdrop%= Vdrop/Vmmp= 4.98 /357.6 = 1.37% , which is within the limit of 2%.
As can be seen, both conductors sizes # 12 and #14 work for ampacity but the voltage drop calculation shows that both of them still not the best option for the long term. As a result, cable # 10 AWG is more conservative design but it will cost more.
Note:
There are some freely available tools that can be used for voltage drop calculation. This is an example of an Online Calculator. If there is no DC option for the calculator, you can use single phase and choose the right length.