Calculating Basic Wire Sizes For Grid Tied System

LHawes

I'm pretty comfortable sizing wires for a given application but I need to CALCULATE wires sizes for a solar building permit for Tucson. Where do I start?

I've got 2 systems of 30 Sharp NE-170U1 panels each hooked to (2) Sunny Boy 4000US inverters. The first system will sit right on top of its inverter and I imagine we'll need a run of maybe 20 ft. from the panels to get there. I'm thinkin #10's should be plenty but I have no idea how to calculate that wire size.

The other system will be located about 60 ft. away and I was going to use #8 wire and feel pretty good about that decision as well but again I have no idea how to calculate that wire size. Clueless. I need to get something to the city of Tucson to justify those wire sizes.

I've seen the wire sizing spreadsheet but don't need to necessarily know losses, just a way to justify the wire sizes with some calcs. Any help?

Thanks in advance

HadesOmega

Re: Calculating Basic Wire Sizes For Grid Tied System

Sorry I don't know how to calculate wire size, I was looking up the wire sizes for my project today and found this table on NAWS's website.

http://www.windsun.com/Hardware/Wire_Table.htm

I did learn how to choose breakers for your wires also if you need that, you take your current and multiply it by 1.25 (add 25%)

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

Thanks for the response and I'll check the table. How do I calculate current? Each panel? Each string? All panels? Short circuit current? Maximum power current?

Thanks

FL SUN

Re: Calculating Basic Wire Sizes For Grid Tied System

Figure your current for each string in series to be your 'Imp' on your module cut sheet. Since they are in series, voltage is added, but ampacity remains the same as a single panel.

niel

Re: Calculating Basic Wire Sizes For Grid Tied System

lhawes,
did you see the calculator in the solar basics section?
http://forum.solar-electric.com/showthread.php?t=29
i'm not sure if that's what it is you're looking for or not, but you can calculate for dc or ac by plugging in values. nec requires ac to be 5% or less too if i'm not mistaken.

lorelec

Re: Calculating Basic Wire Sizes For Grid Tied System

LHawes,

I'm not exactly sure what you're looking for when you say you need to calculate wire sizes. What are the criteria? Temperature rise? Voltage drop? The tables in section 310 of the NEC give maximum allowable ampacities for given wire sizes and types. Base your PV ampacity on 1.25 times the short circuit rating of your array (section 690). You'll end up using much larger wires than those specified in section 310, anyhow, if you take <2% voltage drop into consideration.

Marc

Malasombra

Re: Calculating Basic Wire Sizes For Grid Tied System

A simple to use calc, for educational purposes.
If you dont mind to move mm2 to AWG:roll:....
http://www.hmsistemas.es/index.php?section=17

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

I really appreciate all the replies and advice and I'd like to post what I came up with the hopes it may help someone else.

I started with the short circuit AMPS which remain the same (I know that is some really basic stuff but the post that mentioned that really helped me - thanks) and there is a section in the NEC that requires the ampacity of all PV circuits be multiplied by 1.25 TWICE. Dividing by the 80% you see is the same as multiplying by 1.25.

I then de-rated the circuit by .58 using a really hot 63C or around 145F to end up with 14.74A for the source circuit from the panels to the first J-box.

The feeder circuit from the J-box to the Inverter uses the same figures as that will carry the same amps (lower temp but using the same figures keeps things really conservative.)

You can see the other calcs as well below.

It doesn't sound like anyone's ever had to do this or perhaps I asked the question incorrectly. Anyway we're going to the city tomorrow. I'll update you all on the progress.

PV SOURCE CIRCUIT

SINGLE STRING SHORT CIRCUIT = 5.47A
CONTINUOUS CURRENT: 1.25 X 5.47 = 6.84A
80% OPERATION: 6.84A/.80 (80%) = 8.55A

OPERATING TEMPERATURE 63°C
DERATING FACTOR FOR 90°C THHN CONDUCTOR OPERATING AT 63°C = .58 TABLE 310.16 NEC

8.55 A/.58 = 14.74A

USE #16 THHN WIRE OR LARGER ACCORDING TO NEC TABLE 310.16

FROM TABLE 310.16

WIRE SIZE AMPACITY THHN 90°C CONDUCTOR
- 16 18
- 14 25
- 12 30
- 10 40
- 8 55


PV FEEDER CIRCUIT

USE SAME FIGURES AS ABOVE

ARRAY OUTPUT CIRCUIT

SHORT CIRCUIT AMPS = 5.47
3 STRINGS PER ARRAY: 3 X 5.47 = 16.41A
CONTINUOUS CURRENT = 1.25 X 16.41A = 20.5A
80% OPERATION = 1.25 X 20.5A = 25.6A
DERATE AT 40°C = 25.6A/.91 = 28.13A
PROVIDE 30 A OCPD AT INVERTER DC INPUT

INVERTER OUTPUT CIRCUIT

5000W MAX/240V = 20.83A
80% OPERATION: 20.83/.80 = 26A
OPERATING TEMPERATURE = 41°C
TEMP DERATNG FROM TABLE 310.16 NEC = .87
26A/.87 = 30A
USE # 10 THHN WIRE OR LARGER FROM TABLE 310.16 NEC - SEE ABOVE

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

LHawes wrote: »

I really appreciate all the replies and advice and I'd like to post what I cam
PV SOURCE CIRCUIT

SINGLE STRING SHORT CIRCUIT = 5.47A
CONTINUOUS CURRENT: 1.25 X 5.47 = 6.84A
80% OPERATION: 6.84A/.80 (80%) = 8.55A

OPERATING TEMPERATURE 63°C
DERATING FACTOR FOR 90°C THHN CONDUCTOR OPERATING AT 63°C = .58 TABLE 310.16 NEC

8.55 A/.58 = 14.74A

USE #16 THHN WIRE OR LARGER ACCORDING TO NEC TABLE 310.16

FROM TABLE 310.16

WIRE SIZE AMPACITY THHN 90°C CONDUCTOR
- 16 18
- 14 25
- 12 30
- 10 40
- 8 55

There are some issues with your calculations. I'll start with your PV source calculation. Isc for your Sharp Panel is 5.47 A. According to NEC 2008 690.8(A)(1) you need to multiply by 1.25 to get maximum Isc for PV source circuits.

5.47 A x 1.25 = 6.84 A

NEC 690.8(B)(1) specifies how to size the actual wire (conductor) and overcurrent protection. It basically says that the conductor and overcurrent protection must handle 125% of the Isc calculated under NEC 690.8(A).

6.84 A x 1.25 = 8.55 A.

This is the current that your PV source circuit wire must handle.

NEC 310.16 is the correct table to get the maximum ampacity for various wire gauges. But you then have to correct (reduce) that value for expected temperature and conduit fill. So for your example:

#16AWG THHN 90C 14 A (Max)
Temperature Derate (61C-70C): 0.58
No conduit fill Derate (3 conductors or less)

14 A x 0.58 = 8.12 A

This is less than 8.55A so you can NOT use #16AWG wire for your PV source circuit.

You have similar issues with your other calculations. By the way, I wouldn't use less than what the panels are wired with. For your panels that is probably at least #12AWG wire.

Hope this helps,

Scott.

Solar Guppy

Re: Calculating Basic Wire Sizes For Grid Tied System

And now that the math is done, I would suggest one never uses a wire smaller than 10 AWG for any PV run, that's to keep the power losses in check, PV is expensive and losing 100 watts to smaller wires is not a good design.

500 foot rolls are 80 bucks at Home Depot

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

Solar Guppy wrote: »

And now that the math is done, I would suggest one never uses a wire smaller than 10 AWG for any PV run, that's to keep the power losses in check, PV is expensive and losing 100 watts to smaller wires is not a good design.

500 foot rolls are 80 bucks at Home Depot

Agreed.

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

solartek wrote: »

There are some issues with your calculations. I'll start with your PV source calculation. Isc for your Sharp Panel is 5.47 A. According to NEC 2008 690.8(A)(1) you need to multiply by 1.25 to get maximum Isc for PV source circuits.

5.47 A x 1.25 = 6.84 A

NEC 690.8(B)(1) specifies how to size the actual wire (conductor) and overcurrent protection. It basically says that the conductor and overcurrent protection must handle 125% of the Isc calculated under NEC 690.8(A).

6.84 A x 1.25 = 8.55 A.

This is the current that your PV source circuit wire must handle.

NEC 310.16 is the correct table to get the maximum ampacity for various wire gauges. But you then have to correct (reduce) that value for expected temperature and conduit fill. So for your example:

#16AWG THHN 90C 14 A (Max)
Temperature Derate (61C-70C): 0.58
No conduit fill Derate (3 conductors or less)

14 A x 0.58 = 8.12 A

This is less than 8.55A so you can NOT use #16AWG wire for your PV source circuit.

You have similar issues with your other calculations. By the way, I wouldn't use less than what the panels are wired with. For your panels that is probably at least #12AWG wire.

Hope this helps,

Scott.

Thanks Scott,

In the example I was following the derating factor of .58, which is designed to UP the wire size if needed, was used as a divisor, NOT a multiplier. Used as a divisor this RAISES the Amps and hence (if needed) increases the wire size - which makes sense as the heat increases. If you use it as multiplier (your example) it decreases the Amps, therefore (if needed) decreasing the size of the wire which goes counter to the purpose of the heat de-rating factor.

I can't say for certain that that is the proper methodology but it made sense at the time.

Sometimes these posts are necessarily brief and leave out some details. The panels are pre-wired with #10 or #12 wire which I will not change for obvious reasons. The calcs were there simply to justify the wire sizes spec'd in the 3-line drawing.

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3 Line Link

I also spec'd #10 wire for the short run (15 ft.) and #8 wire for the longer run (45 ft.) because, as I stated in the original post, I am comfortable with those wire sizes - for all the reasons stated.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

Solar Guppy wrote: »

And now that the math is done, I would suggest one never uses a wire smaller than 10 AWG for any PV run, that's to keep the power losses in check, PV is expensive and losing 100 watts to smaller wires is not a good design.

500 foot rolls are 80 bucks at Home Depot

LHawes wrote: »

I've got 2 systems of 30 Sharp NE-170U1 panels each hooked to (2) Sunny Boy 4000US inverters. The first system will sit right on top of its inverter and I imagine we'll need a run of maybe 20 ft. from the panels to get there. I'm thinkin #10's should be plenty but I have no idea how to calculate that wire size.

The other system will be located about 60 ft. away and I was going to use #8 wire and feel pretty good about that decision as well but again I have no idea how to calculate that wire size. Clueless. I need to get something to the city of Tucson to justify those wire sizes.

I've seen the wire sizing spreadsheet but don't need to necessarily know losses, just a way to justify the wire sizes with some calcs. Any help?

Thanks in advance

Thanks Guppy but I had always planned to use #10 and # 8 wire. Just needed to find a way to show that those chosen wire sizes would have no problem carrying the amperage, just for permitting purposes. When we do the job we'll make sure we use a large enough wire size.

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

LHawes wrote: »

Thanks Scott,

In the example I was following the derating factor of .58, which is designed to UP the wire size if needed, was used as a divisor, NOT a multiplier. Used as a divisor this RAISES the Amps and hence (if needed) increases the wire size - which makes sense as the heat increases. If you use it as multiplier (your example) it decreases the Amps, therefore (if needed) decreasing the size of the wire which goes counter to the purpose of the heat de-rating factor.

I'm sorry but that is an incorrect use of the temperature derating factor. You start with the maximum amperage that a wire can carry at 25C. You then reduce that maximum due to temperature, and possibly conduit fill factors. This gives you the actual amperage the wire can safely handle according to the NEC. You do NOT apply that derate factor as a divisor to your panel's amperage calculation. As I showed, the NEC specifies how to determine what the maximum current due to the solar panels will be. This current is not derated for temperature or conduit fill.

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

solartek wrote: »

I'm sorry but that is an incorrect use of the temperature derating factor. You start with the maximum amperage that a wire can carry at 25C. You then reduce that maximum due to temperature, and possibly conduit fill factors. This gives you the actual amperage the wire can safely handle according to the NEC. You do NOT apply that derate factor as a divisor to your panel's amperage calculation. As I showed, the NEC specifies how to determine what the maximum current due to the solar panels will be. This current is not derated for temperature or conduit fill.

Scott.

Scott,

I'm obviously not an expert but I wonder if you would take the time to have a look at an example I found in a publication from Brooksolar.com. It's called Photovoltaic Power Systems And the 2005 National Electrical Code:Suggested Practices and on page E19 and 20 he shows an example of some calcs where the de-rating factor is used to divide not multiply (it's on page E20). Again, I'm not pretending to know but would really like to understand things a bit better. Why do you think he would use it this way?

By the way the publication has a WEALTH of information. So much so i printed all 149 pages.

Here's a sample bit of text from that document.

"The ampacity of conductors and the sizing of overcurrent devices is an area that demands careful attention by the PV system designer/installer. Temperatures and wiring methods must be addressed for each site [310.15]. Calculations start with the 125% of Isc value to comply with the UL 1703 requirements [also in Section 690.8(A)], and additional 125% must then be used for code compliance [690.8. 690.9]. Finally, the cable ampacity is adjusted for temperature. See Appendix E for additional examples."

When I read this it looks like the temp de-rating is applied AFTER the two previous calcs are done to determine the final ampacity. If one were to simply use the NEC tables one could apply the temp de-rating as a multiplier at any time and always get the same figure, no matter what the other numbers come out to be. So my questions is why does he recommend that the temp de-rate come after the other calcs?

He then follows that with examples - here's one:

"Calculations
The string short-circuit current is 5.6 amps.
CONTINUOUS CURRENT: 1.25 x 5.6 = 7 amps
80% OPERATION: 1.25 x 7 = 8.75 amps
The array short-circuit current is 33.6 amps (6 x 5.6).
CONTINUOUS CURRENT: 1.25 x 33.6 = 42 amps
80% OPERATION: 1.25 x 42 = 52.5 amps

The modules in each string are connected in series. The modules and attached conductors operate at 63°C. The temperature-derating factor for RHW-2 at this temperature is 0.58. The required 30°C ampacity for this cable is 15 amps (8.75 /0.58 ) RHW-2 14 AWG cable has an ampacity of 25 amps with 90°C insulation and 20 amps with 75°C insulation so there is no problem with the end of the cable connected to the fuse (with 75°C terminals) since the 7 amps is below either ampacity. Even with 30°C fuse terminals, the ampacity of a 14 AWG conductor would be 20 amps at 30°C. If the PV combiner were operating at 63°C, the fuse would have to be temperature corrected according to the manufacturer’s instruction and the use of 14 AWG conductors would still be acceptable when evaluated at 7 amps."

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

LHawes wrote: »

Scott,

I'm obviously not an expert but I wonder if you would take the time to have a look at an example I found in a publication from Brooksolar.com. It's called Photovoltaic Power Systems And the 2005 National Electrical Code:Suggested Practices and on page E19 and 20 he shows an example of some calcs where the de-rating factor is used to divide not multiply (it's on page E20). Again, I'm not pretending to know but would really like to understand things a bit better. Why do you think he would use it this way?

By the way the publication has a WEALTH of information. So much so i printed all 149 pages.

The latest version (1.9) can be downloaded from here.

What's interesting and I never noticed is that he uses the derating factor both the way you are describing and the way I showed it depending on the example in Appendix E. See pages E-13 - E-14 and E-16 - E-17 for examples of doing the calculation the way I described. I guess it comes down to an interpretation. The issue is that you could come to a different conclusion on what wire size is OK based on how the calculation is performed. My way (derating the wire's maximum ampacity due to ambient temperature and conduit fill) makes more intuitive sense to me.

Edit: And if you read the instructions on Tables 310.16 and 310.17 it's the proper way to determine the wire's maximum amperage.

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

solartek wrote: »

The latest version (1.9) can be downloaded from here.

What's interesting and I never noticed is that he uses the derating factor both the way you are describing and the way I showed it depending on the example in Appendix E. See pages E-13 - E-14 and E-16 - E-17 for examples of doing the calculation the way I described. I guess it comes down to an interpretation. The issue is that you could come to a different conclusion on what wire size is OK based on how the calculation is performed. My way (derating the wire's maximum ampacity due to ambient temperature and conduit fill) makes more intuitive sense to me.

Edit: And if you read the instructions on Tables 310.16 and 310.17 it's the proper way to determine the wire's maximum amperage.

Scott.

Thanks for the follow up Scott. I've read Table 310.16 and .17 and it's pretty clear how to figure the temp de-rating but it doesn't seem, nor does it seem able, to take into account the other calculation factors. I don't think there's two 'proper' ways to do the calcs because the ampacity is very different using one method over the other.

I read those pages and I'll be darned if he doesn't use a different method just as you described. Two different methods for 2 different results - don't seem right. I'll keep reading and learning and thanks again for the follow up.

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

LHawes wrote: »

Thanks for the follow up Scott. I've read Table 310.16 and .17 and it's pretty clear how to figure the temp de-rating but it doesn't seem, nor does it seem able, to take into account the other calculation factors. I don't think there's two 'proper' ways to do the calcs because the ampacity is very different using one method over the other.

I read those pages and I'll be darned if he doesn't use a different method just as you described. Two different methods for 2 different results - don't seem right. I'll keep reading and learning and thanks again for the follow up.

If by other factors you mean what that document is calling the continuous current and 80% operation factors, these come from NEC 690.8(A) and (B) and are independent of the wire maximum ampacity calculation.

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

solartek wrote: »

If by other factors you mean what that document is calling the continuous current and 80% operation factors, these come from NEC 690.8(A) and (B) and are independent of the wire maximum ampacity calculation.

Scott.

No Scott, I guess what I mean is, you and I will see this thing differently, only I won't pretend to know what the correct method is. I'll keep asking questions till I understand it better and can make an educated and informed decision.

lorelec

Re: Calculating Basic Wire Sizes For Grid Tied System

Scott's post #9 is the correct way to calculate the maximum array current and conductor derating, according to the NEC. The temperature derating is applied to the conductor's listed maximum ampacity in Table 310-X if your ambient temperature is expected to be other than 30degC. It is independent of your other calculations. Find the size of wire which, when properly derated, will accomodate the output current of your array as calculated in Section 690-8. Note that Table 310-5 limits your minimum conductor size to 14AWG. Once you've settled on a code-compliant wire size, calculate your voltage drop and resize accordingly for minimal power loss.

solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

After a good night's sleep, I realized what is going on and can now reconcile the two "methods" of calculation. What the code is asking us to do is make sure that the following relationship is valid:

PV Source Current < 80% of the maximum ampacity of the chosen wire and conditions.

Using LHawes example of his Sharp panels and referring to NEC 690.8(A) and (B) we get the following

1.25 x 5.47 A < 0.8 x (Wire maximum ampacity derated for temperature and conduit fill if in conduit)

We can easily divide both sides by 0.8 which is the same as multiplying both sides by 1.25.

1.25 x 1.25 x 5.47 < Wire maximum ampacity derated for temperature and conduit fill if in conduit.

Now for LHawes example, he chose THHN wire with a 90C insulation and a 63C ambient temperature. He chose to look at NEC Table 310.16 which means the wire will be in a raceway or conduit rather than free air. Because he does not use a conduit fill derating we can assume less than 4 conductors in conduit or raceway. Looking at the NEC Table 310.16 we see that for 90C THHN wire at 63C we need a temperature derating factor of 0.58. So now our relationship becomes

8.55 A < 0.58 x Wire maximum ampacity at 30C

It's at this point that our calculation methods diverged. I would now pick a wire size, get the maximum ampacity value at 30C, multiply it by 0.58 and then check to see if the relationship holds. It is perfectly valid, however to rearrange the relationship as so

8.55 A / 0.58 < Wire maximum ampacity at 30C

And then look at what wire size makes this relationship valid. This is the method used in the example that LHawes was following. It is perfectly valid thing to do mathematically. But any statements about "derating" the PV source current don't really have any physical meaning. And this is what was confusing me.

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

Scott,

Interesting - I came up with a very similar conclusion - after a night's sleep. I somehow knew that both methods were getting to the same place from different directions but the one thing that had me confused was, in your initial response, your method had concluded that #16 wire would NOT work with these figures, and the method I chose showed that it would. I therefore assumed that our methods were too different to be interchanged.

Then I re-read your post and noticed you had used 14 as the maximum ampacity for #16 wires instead of the 18A shown in NEC table 310.xx. Using 18A and the method you illustrated both methods get to (according to the tables and ignoring real world wire sizes) the same place. #18 is too small and #16 is OK, again ignoring the 14 gauge minimum etc.

This also explains the conundrum of the reference material using BOTH methods in different examples. They both work.

I personally prefer the method you presented as it leaves out the one function of dividing by the temp derating coefficient which gets unnecessarily complicated IMO and anyhting that will simplify these things is a big help.

One last thank you (to everyone) for taking the time and energy to follow up on this and I hope our discussion helps someone else in the future.

lorelec

Re: Calculating Basic Wire Sizes For Grid Tied System

One other caveat if you're planning on using 10AWG or smaller: Section 240-3(d) restricts the ampacity of smaller gauge wires by placing a limit on the circuit's overcurrent protection. For example, while Table 310-16 allows 40A capacity for 10AWG THHN at 30degC, 240-3 will limit you to 30A. If you're oversizing wires (I would personally never use 10AWG for anything over a few feet at lower voltages and higher currents because of the excessive voltage drop) this won't be an issue for you, but if you're spec'ing the minimum for your permit application based on Table 310-16, it might be.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

lorelec wrote: »

One other caveat if you're planning on using 10AWG or smaller: Section 240-3(d) restricts the ampacity of smaller gauge wires by placing a limit on the circuit's overcurrent protection. For example, while Table 310-16 allows 40A capacity for 10AWG THHN at 30degC, 240-3 will limit you to 30A. If you're oversizing wires (I would personally never use 10AWG for anything over a few feet at lower voltages and higher currents because of the excessive voltage drop) this won't be an issue for you, but if you're spec'ing the minimum for your permit application based on Table 310-16, it might be.

Thanks, Will keep that in mind.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

We got our plans approved through the city of Tucson yesterday. Thanks so much for all your help. I hope i can follow up with this install and post any problems and solutions we might come across.

Thanks again

dwh

Re: Calculating Basic Wire Sizes For Grid Tied System

Okay, I'm a journeyman electrician (24k hours high-voltage exp., and 20k hours VDV exp.) and I just have this to say...

I LOVE THIS THREAD!

No really. This thread rocks.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

I thought I'd follow up on this install. Everything went very well with the install and we're seeing about 4200 Watts max from each inverter and it's been HOT (100+) over the last few days. I have a question about heat loss I might post in a separate thread but was wondering if there's a chart or formula to figure heat losses from ambient heat?

Thanks to everyone here for the help on this project.

I'll cross post this in the other forum where I asked a different question re: this system.

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solartek

Re: Calculating Basic Wire Sizes For Grid Tied System

Larry,

Looks good. I do have one question. It looks like you didn't use any specialized hardware for doing the tilt mounting. Is it really just L-brackets on the front rail and straight standoffs on the back rail? What degree tilt do you have? (OK two questions )

Thanks,

Scott.

LHawes

Re: Calculating Basic Wire Sizes For Grid Tied System

solartek wrote: »

Larry,

Looks good. I do have one question. It looks like you didn't use any specialized hardware for doing the tilt mounting. Is it really just L-brackets on the front rail and straight standoffs on the back rail? What degree tilt do you have? (OK two questions )

Thanks,

Scott.

Scott,

In Tucson (AZ?) you need to meet a minimum tilt angle to maximize the system rebate so we decided, instead of engineering a full on tilt system, to use the L brackets and the highest stand-offs (7") available as you see. The original roof had a 2.5:12 pitch and the angle we ended up with is around 20 degrees.

dwh

Re: Calculating Basic Wire Sizes For Grid Tied System

Neat and tidy, just the way I like it. Nice job!