AE 868
Commercial Solar Electric Systems

Voltage Drop

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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 some AC systems, the distance equals the length of the conductor.

Reflection

Why is the conductor length different for AC and DC circuits?

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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. The same applies to two-wires single phase (120V in the USA or 220 in Europe), the AC Voltage Drop is calculated in the same way in which the distance is twice the length of the wire. (to account for the Phase and the Neutral wire lengths as the current travels back and forth through them). 
- In the three-wires single phase (AKA split-phase in the USA), the voltage is still 120V between the phase and the neutral but the current doesn't travel back through the Neutral wire. This is a result of the nature of the phases being split (with180 degree phase shifted) so the Neutral wire only returns the imbalanced current. In balanced load condition, the return current (through the Neutral wire) equals Zero.  
- In the four-wires three phases systems, the same situation arises as the Neutral is not supposed to return any current under balanced load conditions. 

Since most single-phase PV inverters are rated at 240V, the Voltage Drop for split-phase is calculated as follows: 
One can calculate the voltage drop using the two-way trip distance at 120V (the same equation used for DC circuit) but your voltage will be the phase-to-neutral 120V instead of the 240V phase-to-phase. Or we can use the one-way wire distance at 240V. Both methods should give the exact same results.  
 

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×R , or,

I=V/R .

And the resistive loss is I×I×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:

V drop = I op × R c ×L

Where:
I op is the circuit operating current, which for source circuits is usually taken as the maximum power current, Imp,
L is the total conductor length.
V drop is the voltage at which you want to find VD, and
R c 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).
V drop =8.23(A)×3.14(Ω/kft)×0.3(kft)=5.168V The operating Voltage is

V mmp =12×37.2=357.6V

The voltage drop then is calculated as:
V drop% = V drop / V mmp =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 AWGRc=1.98(Ω/kft)
V drop =8.23(A)×1.98(Ω/kft)×0.3(kft)=3.386V
The voltage drop then is calculated as:

V drop% = V drop / V mmp =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.