Voltage drop and wire size are important considerations when
designing and installing solar PV systems. Voltage drop occurs in any
electrical circuit carrying power. A percentage of the power running through the
conductors will be lost as heat. This amount is dependent on the size of
the wire along with the voltage and current of the load, and some environmental
factors as well (circuit length, temperature, conductor material). This post will cover selecting the correct
wire size based on your maximum solar current and calculating the voltage drop
based on that. I will be heavily
referencing the NEC 2011 codebook throughout this post.

Conditions of Use

Before getting into selecting wire sizes, I want to cover conditions
of use. These are factors that need to
be applied to the maximum current we calculated earlier based on environmental
conditions. The most obvious condition
of use is ambient temperature, found in Table 310.15(B)(2)(a). Based on most sources, the average high
temperature for the location should be used.
This can be obtained from the ASHRAE handbook (the 2% value) or
determined from weather data available online.
The other conditions of use are more complicated. Conduit fill is an important consideration
for large systems and long conduit runs, it is found in Table
310.15(B)(3)(a). This is because wiring
will generate heat during operation and the hotter it gets inside the conduit
the worse the voltage drop will get.
Conduit distance above roof for roof mounted systems is very important
as well, and can make the conductors even hotter, reference Table
310.15(B)(3)(c) for more information.
For the purpose of this post, conduit fill and conduit distance factors
will both be assumed as 1 for power production.
Ambient design temperature will be fixed at 85° F, which gives a
modifier of 1 on our current calculation for simplicity.

Wire Sizing

From my previous submission, maximum DC solar current is
based on the solar panel’s Isc rating multiplied by 1.56. The maximum AC solar current is the
inverter’s maximum continuous current multiplied by 1.25. Taking these maximum calculated currents,
proper wire sizes for them can be selected using NEC 2011 wire sizing methods
and tables. These methods will assume
conductors and terminals are rated for 75° C.
The first table to reference is 310.15(B)(16), where the 75° C Copper
column will be used to select wire size based on the maximum calculated
current. For example, for a solar panel
Isc rating of 8.5A, our maximum DC current is 13.26A. Using table 310.15(B)(16), the minimum wire
size #14 AWG. For a solar inverter with
a rated current of 25A, maximum AC current will be 31.25A. This results in #8 AWG wire. Conditions of use, if we had them, would be
applied here to the overall ampacity of the wire to derate it and check against
our maximum calculated current.
Conveniently, all of our conditions of use for this example are fixed at
“1”.

Now that the wire size has been found for the maximum
calculated current, it needs to be checked against worst case voltage drop in
the conductor for the designed length of the circuit. If the voltage drop would be too high the
wire has to be upsized to the next size to correct for it. The maximum voltage drop is 1.5% for DC and
1.5% for AC circuits based on my previous post.

Calculating Voltage Drop

The heart of voltage drop calculations is Ohm’s law, which
reads V (Voltage) = I (Current) x R (Resistance). The units are Volts, Amps,
and Ohms, respectively. Voltage drop
calculations are based on values for Resistance (Ohms) per 1000 feet found in NEC
tables in Chapter 9, Table 8 or 9 (DC circuits Table 8, AC circuits Table 9). The value we need is
for stranded, uncoated copper conductors.
This changes the formula from V = I x R to Voltage Change = I x (R / 1000’)
x Total Circuit Length

Written another way, it can be expressed in terms of 1-way
circuit length and converted into a percentage value:

Equation for Voltage Drop based on NEC 2011 Chaper 9 Tables 8 & 9 |

Going back to my example in Wire Sizing, let’s consider a DC
and an AC wire run for a 100 foot distance and calculate the voltage drop for
each. For DC, we have:

#14 AWG Wire 300V
String I = 13.26A L = 100 feet R = 3.26 (NEC Chapter 9 Table 8)

VD = 2 x 100 x 13.26
x 3.14 / 1000 = 8.33V 8.33V
/ 300V = 2.78% Voltage Drop

Based on our maximum desired DC voltage drop of 1.5%, this
obviously will not do. We need to upsize
the wire to get a better voltage drop.
Rerunning the numbers for a #12 wire gives:

VD = 2 x 100 x 13.26
x 1.98 / 1000 = 5.44V 5.44V/
300V = 1.75% Voltage Drop

Close, but not quite what we wanted. Obviously a #10 AWG wire is the way to go,
but just to be sure:

VD = 2 x 100 x 13.26
x 1.24 / 1000 = 3.42V 3.42V
/ 300V = 1.10% Voltage Drop

That’s got it right there!
A #10 AWG wire will give us ~1.1% voltage drop for a 300V circuit over
100 feet (In general, I’ve found that a #10 wire is best for solar string
wiring for most roofs). Now that we’ve
figured out DC voltage drop, AC voltage drop is pretty simple. Using Table 9 of Chapter 9, we need to use
the values in the column labeled “Alternating-Current Resistance for Uncoated
Copper Wires”. Going back to our earlier
example:

#8 AWG Wire 240V AC I = 31.25A L = 100 feet R
= 0.78 (NEC Chapter 9 Table 9)

VD = 2 x 100 x 31.25
x .78 / 1000 = 4.875V 4.875V
/ 240V = 2.03% Voltage Drop

Again, we’re close but not quite where we want to be for
this AC wire run. Upsizing the wire to
#6 results in:

VD = 2 x 100 x 31.25
x .49 / 1000 = 3.06V 3.06V / 240V = 1.28%
Voltage Drop

Based on our examples, a #10 wire will give us a 1.1%
voltage drop for a 300V, 8.5A string of solar panels over 100 feet. A #6 wire will give us a 1.28% voltage drop
for a 240V, 25A solar inverter over 100 feet.

Wire sizing and voltage drop calculations are an extremely
important consideration for any solar designer or installer, and it’s essential
to understand the fundamentals behind them.
The calculations and examples in this post have been kept simple on
purpose, the subject can get complicated in a hurry when multiple conditions of
use need to be applied. In my next post,
I will share some of my favorite tools and rules of thumb for calculating wire
size and voltage drop.

References

NEC 2011

Conditions of Use: 310.15(B)(2), 310.15(B)(3)

Wire Ampacity: Table 310.15(B)(16)

Wire Resistance: Chapter 9 Tables 8 & 9

Hey,

ReplyDeleteReally Nice Information!!

Now I know very relevant information about wires their resistances with formula.

Thanks for sharing:)

Regards

Ganpati Wires