NEC Code Calculations
Fall 2015
22.525
Prof Thomas
For these calculations, we are assuming we are located in Lowell, MA.
690.7 Maximum Voltage
Why calculate this? To make sure cables, disconnects, overcurrent devices and
other equipment are rated to handle the highest possible voltage the system could
produce. Also, to make sure voltage should remain within max power point (MPP)
range of inverter.
Variables include minimum temperature, module specifications, and string size
Note: it says to use Table 690.7 unless open-circuit voltage temperature coefficients
are supplied by the manufacturer. If they are, then use those instead of the table. Since
just about every manufacturer includes these temperature coefficients in their data
sheets, Table 690.7 is seldom necessary.
As temperature decreases, voltage increases. Hence, at ambient temperatures below
25° C, modules’ voltages will be greater than rated. Hence, it is necessary to correct
for colder temperatures when calculating max system voltage.
Example:
SunPower X21 335/345 Modules Datasheet:
Temp coefficient for open circuit voltage (TVOC) = -167.4 mV/°C
To find the appropriate cold temperature to use, consult the ASHREA Fundamentals
Handbook. Or, go on-line to this website and simply enter the city & state:
www.solarabcs.org/about/publications/reports/expedited-permit/map/index.html
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ASHRAE temp for Lowell, MA: -18 °C
Note: this is NOT the record cold temperature for Lowell. Rather, it is the “extreme
annual mean minimum design dry bulb temperature”, meaning that 99% of the
time, the temperature will be greater than this cold temperature. Hence, it is
realistic and sufficient, per the informational note in the NEC in 690.7, to use this
temperature for these calculations. (ASHRAE does not have these temperatures for
every location, so use the one closest to the PV system’s site. In this example, we are
using the temperature from Lawrence, MA.)
Temperature difference (dT) between ASHRAE cold temp and STC temp:
𝑑𝑇 = −18℃ − 25℃ = −43℃
Voltage increase because of temp below STC:
𝑑𝑇 × 𝑇VOC = −43℃ × −0.1674
𝑉
= 7.20𝑉
℃
From table above, for 335W module, open circuit voltage:
VOC = 67.9 V
Expected voltage of module at cold temp:
67.9V + 7.2V = 75.1 V
Assuming there are 7 modules per string:
𝑀𝑎𝑥 𝑆𝑦𝑠𝑡𝑒𝑚 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = # 𝑜𝑓 𝑚𝑜𝑑𝑢𝑙𝑒𝑠 𝑝𝑒𝑟 𝑠𝑡𝑟𝑖𝑛𝑔 × max 𝑚𝑜𝑑𝑢𝑙𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
= 7 × 75.1 = 536𝑉
For 1 or 2 family dwellings, max voltage shall be permitted up to 600 V. Other
installations may have a max voltage up to 1000 V.
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Second example:
Given:
12 Jinko 255P Modules per string in Sacramento, CA. Find max system
voltage corrected for temperature.
For the high temperature to use, again consult the ASHREA temp found here:
www.solarabcs.org/about/publications/reports/expedited-permit/map/index.html
Solution:
VOC = 38.0V
(TVOC) = -0.31%/°C
(Note that this is a percentage!)
ASHRAE temp for Sacramento, CA: -3 ℃
𝑑𝑇 = −3℃ − 25℃ = −28℃
Increase in VOC for each module due to temp:
𝑑𝑇 × 𝑇VOC × 𝑉𝑂𝐶 = −28℃ × (−0.0031)
1
× 38.0𝑉 = 3.30𝑉
℃
38.0V + 3.30V = 41.3V
𝑀𝑎𝑥 𝑆𝑦𝑠𝑡𝑒𝑚 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 = # 𝑜𝑓 𝑚𝑜𝑑𝑢𝑙𝑒𝑠 𝑝𝑒𝑟 𝑠𝑡𝑟𝑖𝑛𝑔 × max 𝑚𝑜𝑑𝑢𝑙𝑒 𝑣𝑜𝑙𝑡𝑎𝑔𝑒
= 12 × 41.3 = 496𝑉
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690.8 Circuit Sizing and Current
Calculation of max circuit current. Here, we determine the max current that will be
flowing from the PV array, through the combiner boxes and protection devices into
the inverter.
Start with short circuit current for PV module. In this case, using the 335 W module
in the table above, ISC = 6.23 A.
Then, per 690.8(A)(1), ISC must be multiplied by 1.25 to account for currents > ISC
that can occur around solar noon on very sunny, cold days:
𝐼𝑚𝑎𝑥1 = 𝐼𝑆𝐶 × 1.25 = 6.23𝐴 × 1.25 = 7.79 𝐴
Remember, modules in a single string are connected in series, so the current flowing
through each module is the same as the current flowing out of the string of modules.
Thus, the max current calculated above is the current to plan for as the “PV Source
Circuit Current”.
Let’s assume there are two strings and their respective outputs are combined in a
combiner box. The output current from this combiner box would therefore be twice
the current from each string. Hence, the max current to plan for as the “PV Output
Circuit Current” would be:
𝐼𝑚𝑎𝑥2 = 𝐼𝑚𝑎𝑥1 × 𝑛𝑜. 𝑜𝑓 𝑠𝑡𝑟𝑖𝑛𝑔𝑠 𝑖𝑛 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 7.79 𝐴 × 2 = 15.6 𝐴
Conductor Ampacity Calculations
Why do this? Ampacity refers to the ability of a conductor to carry current safely.
Higher ampacity means a higher current-carrying capability. We need to verify that
the conductors in our PV systems will function safely under the conditions in which
they will be used. Therefore, we need to compare their ampacity against the
maximum currents we expect them to carry.
The NEC says that “circuit conductors shall be sized to carry not less than the larger
of 690.8(B)(1) or (2)”, so there are two ampacity calculations you have to make
prior to selecting the right sized conductor.
First calculation: 690.8(B)(1) simply says that the ampacity of a conductor must be
equal to or greater than the max currents as calculated above (Imax1 and Imax2),
multiplied by another 1.25. For this example, that means 7.79A X 1.25 = 9.74 A for
the PV source conductors, and 15.6A X 1.25 = 19.5 A for the PV output circuit
conductors.
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NEC Code Calculations
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Second calculation: 690.8(B)(2) says to use the max currents calculated above after
the application of adjustment and correction factors. This refers to corrections due
to exposure to high temperatures (ampacity decreases as temperature increases).
First, start with ambient temperature. Unlike max voltage, here we are concerned
with high temperatures. One should use the ASHRAE temperature again, this time
selecting the 2% average high temperature (it is below this temperature 98% of the
time). You can find this temperature at the same website:
www.solarabcs.org/about/publications/reports/expedited-permit/map/index.html
For Lowell, this is 32℃.
If the PV system is on a roof, one then has to adjust this temperature higher, since
the temperature on or just above the roof surface is considerably higher than
ambient. Use table 310.15(B)(3)(c) “Ambient Temperature Adjustment for
Raceways or Cables Exposed to Sunlight on or Above Rooftops” (Article 310 covers
conductors for general wiring, into which PV system conductors fall). Let’s say our
PV source and PV output currents flow through cables 4 inches above a roof. Per the
table, we need to add 17℃ to the ambient temperature, or 32 + 17 = 49℃.
Okay, now we need to adjust a conductor’s ampacity based on this corrected
ambient temperature. First, always use conductors with insulation types rated at
least 90℃-rated —standard practice in the PV industry. Then, go to table
310.15(B)(2)(a) “Ambient Temperature Correction Factors Based on 30℃”, and
enter the table using the temperature you just calculated above. In this example,
that’s 49℃. For that temperature, under the 90℃ conductor column, find the listed
correction factor. Here, its 0.821.
Now, take the max currents from 690.8(A) and divide them by this correction factor.
In this example, that’s 7.79 A/0.82 = 9.50 A and 15.6 A/0.82 = 19.0 A. These are the
minimum ampacities of the conductors after temperature correction.
Okay, here’s a quick summary:
Circuit
PV Source
PV Output
1
Method 1
(690.8(B)(1))
ISC X 1.25 X 1.25
9.74 A
19.5 A
Method 2 (690.8(B)(2))
(ISC X 1.25)/temp correction factor
9.5 A
19.0 A
You’ll get the same correction factor if you use table 690.31(E).
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NEC Code Calculations
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Based on the results we can see that 690.8(B)(1) yields the higher currents, hence
higher ampacity requirements. This is generally true in colder climates, but you
always should check both methods to confirm this.
Bottom line: you have to select a conductor with an ampacity greater than 9.74 A
and 19.5 A for the source and output circuits, respectively.
A quick glance at tables 310.15(B)(16) and 310.15(B)(17) will show you that even
very small gauge wires meet these relatively low currents. For instance, say we are
using copper 10 AWG USE-2 conductor for the PV source current, and copper 10
AWG THWN-2 for the PV output current (both 90℃ rated). Using table 310.15
(B)(17) for the USE-2 conductor (because the source circuit conductors are not in a
raceway or cable but rather “in free air”), we find it has an ampacity of 55 A. Using
table 310.15(B)(16) for the THWN-2 conductor (because after the combiner box, we
are assuming it is now in a raceway), we find is has an ampacity of 40 A.
However, there are two other factors to consider—overcurrent protection devices
and voltage drop—before making a final decision on conductor sizing.
690.9 Overcurrent Protection
Why do we need overcurrent protection? We do not want any equipment failing
(because that will cause down time and lost production) nor do we want to cause
any fires (because that will cause damage and potentially injury/death). Therefore,
the NEC calls for protecting our circuits with appropriate devices. These are
generally fuses and circuit breakers (CBs).
With the exception of small arrays with only one or two strings, all PV systems will
require overcurrent protection on both the dc and ac sides.
These calculations are straightforward. 690.9 (B) states that “overcurrent device
ratings shall be not less than 125 percent of the maximum currents calculated in
690.8 (A)”. The 125 percent is because PV conductors and overcurrent protection
devices (OCPDs) are considered “continuous duty” equipment. Therefore, OCPDs
must be rated at or above short circuit current times 1.25 times 1.25, or ISC X 1.56
for source circuits, and ISC X 1.56X # of strings for output circuits.
For our example:
Source circuit OCPDs must not be rated less than2:
𝐼𝑆𝐶 × 1.56 = 6.23 × 1.56 = 9.72 𝐴
Output circuit OCPDs must not be rated less than:
Note that rounding caused a slight difference between multiplying by 1.56 vs. multiplying
by 1.25 twice. Since we always round up to the highest integer, this is not a factor.
2
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𝐼𝑆𝐶 × 1.56 × # 𝑜𝑓 𝑠𝑡𝑟𝑖𝑛𝑔𝑠 𝑖𝑛 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 6.23 × 1.56 × 2 = 19.4 𝐴
Article 240.6(A) lists standard size fuses and circuit breakers. The minimum size
OCPD we need to use is the next standard size greater than the values calculated
above, e.g., 10 A and 20 A fuses, respectively, for the source and output circuits (or
15 A and 20 A CBs, since the smallest standard size CB is 15 A). Usually, smaller
means less expensive, so the minimum is generally what we go with. However, you
cannot arbitrarily use a fuse or CB that has a larger rating than the rating of the
conductors it is protecting. For example, if you have a conductor rated for 40 A, you
cannot protect it with a fuse rated at 50 A—the wire would melt/catch on fire prior
to the fuse failing!
There is one more NEC condition to consider. Section 240.4 (D) lists maximum
OCPD sizes for small conductors. This essentially adds a safety factor. For example,
though a copper 12 AWG USE-2 conductor is rated at 30 A (table 310.15 (B)(16)),
240.4 (D)(5) states that it will be protected by an OCPD rated no greater than 20 A.
Would this ever come into play? It could. Maybe an installer has some 25 A fuses he
wants to use up on a job. He plans on using 12 AWG USE-2 conductor after the
combiner box in a system using the panels in our example (hence max current =
19.4 A). The 25 A fuses meet the minimum requirements we calculated above, and
the conductor’s ampacity is rated at 30 A, so he thinks he is good to go. BUT, section
240.4 (D)(5) says he has to use 20 A or smaller fuses for that size wire. Hence, he
can’t use his extra 25 A fuses.
Voltage Drop Calculations
Why worry about this? Voltage drop means that the voltage at the end of a cable
(relative to ground) is smaller than at the beginning. Since power is voltage times
current, voltage drops result in lost power, which in turn means less energy
produced. Hence, designers always need to minimize voltage drop when possible.
How do you do that? Voltage drop is related to conductor cross-sectional area,
which is proportional to the resistance of the conductor3. Smaller conductors have a
greater voltage drop per linear foot than larger conductors. So, you can reduce
voltage drop by minimizing the length of the conductor and/or increasing the size of
the conductor. There will be physical constraints on the former and fiscal
constraints on the latter.
Good designers will strive to run conductors along the shortest distance between
two points, e.g., placing a combiner box so that the “homeruns” from the strings to
Voltage = current X resistance. For a given current, a lower resistance means a
lower voltage. The thicker the conductor, the lower the resistance, and hence the
lower the voltage drop across it.
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that combiner are as short as possible. Likewise, inverters should be sited so that
runs between the combiner boxes to the inverter are also minimized. This is one
reason to have an inverter sitting in the middle of a ground-mounted array, for
instance. Finally, you’ll also need to consider the distance from the inverter to the
grid interconnect. Higher voltages have lower drops per linear foot, too, so that is
another thing to think about.
Table 8 at the back of the NEC lists properties for conductors, including their
resistance per linear foot (R in the formula below).
Voltage drop in 2-wire dc or ac circuit, or a 3-wire single phase ac circuit, can be
calculated using this formula:
𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 =
2×𝐿×𝑅×𝐼
1000
where:
L = length of circuit (ft)
R = resistance in Ohms per 1000 ft (see Chapter 9, Table 8 in NEC)
I = load current (amps)
We are always concerned with the maximum voltage drop, so we use the maximum
current calculated above in this formula. Let’s say we are sticking with 10 AWG
copper, coated conductor. Per Table 8, its R = 1.26 ohm/kft. The max current for the
source circuit was found to be 7.79 A. Finally, let’s say we had to put the combiner
box 50 feet away from the end of the strings, so L = 50 ft.
𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 =
2 × 50 × 1.26 × 7.79
= 0.98 𝑉
1000
Thus, the voltage at the combiner box is about 1 V lower than when it left the string
of modules. Since the maximum voltage calculated for a string was 535.7 V, a drop of
0.98 V is less than 0.2%, which is very small. So, we are not losing much power
between the strings and the combiner boxes.
Let’s say the inverter is 100 ft from the combiner box:
𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 =
2 × 100 × 1.26 × 15.6
= 3.93 𝑉
1000
The voltage drop between the combiner box and the inverter is now 0.73% (i.e.,
3.93V/535.7V = 0.0073). Add this to the drop between string and combiner box, and
we have a voltage drop 0.93% or about 1%, which is acceptable. Not exceeding a
2% voltage drop on the dc side is the rule of thumb in the industry.
Let’s look at an example of a poor design. Say a larger system—using the same
modules and string size—has a PV output current of 195 A. Basically, there are 10 78
NEC Code Calculations
Fall 2015
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module strings combined into a single combiner box (this is not uncommon—there
are combiner boxes that have terminals for 16 strings…). Max system voltage is still
535.7 V. The inverter is 500 ft away from the combiner box. Also, let’s say that the
conductor is coated 2/0 AWG copper THWN-2. It has an ampacity of 195 A (per
Table 310.15(B)(16)) and a resistance of 0.101 ohm/kft (per Table 8). Using the
voltage drop equation above:
𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑑𝑟𝑜𝑝 =
2 × 500 × 0.101 × 195
= 19.7 𝑉
1000
19.7 V drop equates to a 3.7% voltage drop, which is generally considered too high
(especially since we have not included the voltage drop in the PV source current).
Power is voltage times current. So, leaving the combiner box, the power would be
535.7 V X 195 A = 104.5 kW. By the time it reaches the inverter, the power is now
(535.7 – 19.7 V) X 195 A = 100.6 kW. This is of course a loss of 3.7%. To reduce this
loss, the distance between the combiner box and inverter should be reduced, and/or
a larger conductor with a lower resistance should be used. If moving the inverter is
feasible, that is the first choice, since there is no cost to that whereas a larger
conductor will cost more.
One must also perform voltage drop calculations on the ac side, though these are
usually lower, mainly because the distance between the inverter and load center is
often only a few feet (installers like to place inverters right next to load centers if
possible). Or, for larger systems, the inverters’ output tends to be at a higher voltage
and/or 3-phase, so the output current in each conductor is proportionately lower.
Based on the equation for voltage drop above, these lower inverter output currents
translate into a lower AC voltage drop. (Incidentally, this is why power is
transferred over long distances at such high voltages: hi-voltage means lower
current, which then means lower power loss.)
A Reality check on voltage drop. Let’s say that as a designer, you try to keep dc
voltage drop to less than 2%. In your latest design, using the smallest conductor that
meets the ampacity requirements discussed above, you find that you have a 2.3%
voltage drop. Do you automatically select the next highest conductor to reduce this?
Do you scrap your whole layout and start from scratch to try and reduce the
conductor distances? Not necessarily. Remember, larger conductors cost more, so
any savings from shaving 0.3% off the voltage drop may be offset by a higher
installation cost. Also, how often will the system really be operating at such high
power? In reality, very rarely, maybe only one or two hours per year, especially in a
climate like Lowell’s. Therefore, the extra 0.3% voltage drop usually affects the
system operating at lower power levels, and hence makes less of an impact.
So, think twice about voltage drops and what to do about them. Your firm may well
have a policy on what is acceptable. Also keep in mind that your firm may be
contractually required to keep losses (including voltage drops) built into the design
below a certain level.
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Conduit Sizing Calculations
What’s this all about? Usually, conductors are collected and run inside of conduits
(or raceways). This helps to protect them from the elements (including sunlight),
and animals, and also keeps the arrays neat in appearance. However, due to the
proximity of the conductors inside a conduit, their ampacities are also affected.
Hence, we have to be aware of this when sizing conductors. Also, we can’t simply
cram in as many conductors as possible into a conduit—there are limits to the
number of individual conductors that can be installed in to a given diameter conduit.
To be continued…
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