# Estimated cable sizes using Root Sum Squared

Registered Users Posts: 38 ✭✭
I'm building a system in a sprinter based motorhome. The loads at maximum potential are shown below. Rather than sizing cables using the total, a knowledgeable fellow suggested using the RSS, which I calculated as 223A. Although I did NOT include these in the table above, I estimated the total loads that could not function at the same time, as 100A. I gather that using the RSS accounts for the practical reality that not all loads are at 100% if operating, nor are they working at the same time. As I say, I didn't include the 100A in the RSS calculation, but show it for informational purposes.

All these loads attach to the load side of a 500A shunt used for a Trimetric 2030.

First, I'm curious whether this RSS method is applied appropriately to my circumstance. Secondly, I'm curious about the accuracy of my estimate. The purpose of the RSS estimate is to appropriately size various cables for the solar system.

Any thoughts?

Thanks so much.

 LOADS AT MAX POTENTIAL Inverter 167.00 DC/DC Charger 60.00 AC/DC Charger 40.00 Load Center (40A fuse) 40.00 Solar: System A 30.00 Solar: System B 20.00 Refrigerator 6.20 Generator fan 4.50 Espar heater 2.00 Reserve: Future additions 50.00 Safety factor (25%) 104.93 SUMSQ 49560.95 Root 223 Say 250 DELETIONS: NO SIMULTANEITY Charging devices 50 Misc devices 15 Load center 35 Total 100

I think you need to take a realistic look at your loads and understand how they will affect your system.

For example, you probably will not run your system at maximum current for each branch circuit. 167 amps on the inverter + A + B + C...

Also, direction of current flow matters too (for DC systems). The 167 amps inverter - (minus) 60 amp DC charger - 40 amp AC charger = 67 max amps with everything running--Not 267 Amps. So, simply adding all current is not "useful" by itself.

In the case of those three loads, 167 amps would be the maximum current flow (inverter running 100% and no charging).

And then there is looking at the load profiles themselves. I would expect that you would run the AC inverter at 25% to 50% maximum power 99% of the time... And any heavier loads will probably only be running for seconds to a few minutes at a time (surge loads).

Vs the charging sources. When you substantially discharge your battery bank (less than 80% State of Charge)--Your chargers can run for a few hours at maximum rated current (say from 50% to 80% State of Charge, then >80%, the lead acid battery bank naturally limits charging current). So--In terms of "stress", you would rate or "over rate" the branch circuits for your charging circuits vs that of the AC inverter loads.

Then there is voltage drop. Especially with 12 VDC battery bus systems, you have very little room for "acceptable" voltage drop. I suggest that you use 0.5 volt drop for your rated loads, and that gives you 1.0 volt drop for surge loads (typically 2x rated loads... I.e., battery bank at 11.5 volts - 1.0 volt drop at surge current = 10.5 volts at AC inverter input terminals aka "battery cutoff voltage" for inverter).

For DC battery bus wiring, short and heavy for solar to keep voltage drops low. For example, say you started with 167 Amp inverter branch circuit, 0.5 volts, and 5 foot "one way" wire run (some voltage drop calculators use "two way run"--Just be sure which your calculator uses). Playing around with the numbers, the wire AWG required would be:

https://www.calculator.net/voltage-drop-calculator.html?material=copper&wiresize=0.8152&voltage=12&phase=dc&noofconductor=1&distance=5&distanceunit=feet&amperes=167&x=66&y=34

5 feet of 4 AWG cable and 167 amps of current would be (based on voltage drop):

## Result

Voltage drop: 0.41
Voltage drop percentage: 3.46%
Voltage at the end: 11.59

And there is looking at wire maximum current rating... There is the "marine" rating (not conservative, uses SAE wire awg which is a little smaller vs same number in AWG NEC system):

The marine table says 4 AWG is good for 160 Amps maximum (there are different ratings between engine room vs outside engine room, etc.)

Here is a rather complex looking table that shows wire size vs current rating vs length of wire run:

https://www.bluesea.com/resources/1437

And then there in the NEC table which tends to be more conservative (simplified):

https://lugsdirect.com/WireCurrentAmpacitiesNEC-Table-301-16.htm

Where 4 AWG is rated for 70-95 amps (depending on temperature rating for insulation)--And there are other deratings (fill factor in conduit, ambient temperature, etc. in "real table"):

https://lugsdirect.com/WireCurrentAmpacitiesNEC-Table-301-16.htm

Keeping your 12 VDC wiring short and heavy is critical for a successful design (avoid a 10-20+ foot wire run for your heavy 12 volt loads/charging systems).

In Solar Power systems, many times it is voltage drop that sets wiring size vs current capacity (especially for 12 volt systems).

And there is simply the practicable amount of current your battery bank can reliably source or sink for a useful amount of time. Say you have 2x 6 volt @ 220 AH "golf cart'" batteries in series for a 12 volt @ 220 AH battery bank (typical for a simple/smaller RV installation). And you plan for 1 night of power usage @ 5 hours to 50% discharge (for a cable I would suggest 2 nights at 5 hours a night or 10 hours total--But for RVs, many times you do not have the space/weight capacity for a larger battery bank and solar array for a "cabin" type installation).

The maximum "cost effective" charging current usually works out to ~10-13% rate of charge (for solar) or 20-25% maximum for an AC battery charger (mains or genset powered). For a 220 AH battery bank, that would be:
• 220 AH * 0.13 solar max charging = 28.6 amps max solar "cost effective" solar charging
• 220 AH * 0.20 max AC charger rating = 44 amps
And I would use the 1.25x rating especially for chargers (tend to be many hours at full rated charger current to bring battery bank from 50% to >80% SoC).
• 220 AH * 0.13 solar max charging * 1.25 NEC derating = 35.75 amps Branch circuit and fuse/breaker rating minimum (round up to next standard size)
• 220 AH * 0.20 max AC charger rating * 1.25 NEC derating = 55 amps Branch circuit rating
Of course, the above current is suggested size--Use rated current of "your actual charge controller(s)" for calculations.

Fusing/breakers... Remember they are there to protect the wiring from overheating when overloads/shorted--Not to protect your loads/chargers themselves.

And then there is what the battery bank can output. For example, your average overnight load of 5 hours and 100% to 50% discharge current would be:
• 220 AH * 1/5 hours * 0.50 bank discharge = 22 Amp "nominal" practicable load
The practical load currents would be:
• 220 AH * C/8 (maximum continuous load = 27.5 amps (somewhat less than ~4 hours from 100% to 50% discharge)
• 220 AH * C/5 (maximum short term load of minutes to 1 hour) = 44 Amps
• 220 AH * C/2.5 (maximum surge current of a few seconds to a minute) = 88 Amps
So--There is the limitations of your battery bank too (larger battery bank = more current available for charging/discharging). Also AGM and LiFePO4 batteries can support higher discharge and charging currents (AH rating for capacity is still roughly the same as the old fashion FLA deep cycle battery).

Depending on your actual battery bank, you may have other limitations to worry about too (besides max current and voltage drop of your wiring).

Does this make sense? Questions?

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Registered Users Posts: 38 ✭✭
BB. said: Depending on your actual battery bank, you may have other limitations to worry about too (besides max current and voltage drop of your wiring).

Does this make sense? Questions?

-Bill
Bill, Thank you so much! I studied this and understand it. Before asking any questions, I'm crawling under my rig, estimating distances by tracing some cable paths with loom, and verifying some other facts. I wish you have a "paypal" box so I could make a donation.
• Solar Expert Posts: 1,526 ✭✭✭✭
You may find the NAWS store has very good pricing and no sales tax. They only sell quality merchandise. buying merchandise from them is like making a donation in that NAWS sponsors this forum.

2.1 Kw Suntech 175 mono, Classic 200, Trace SW 4024 ( 15 years old  but brand new out of sealed factory box Jan. 2015), Bogart Tri-metric, 700 ah @24 volt AGM battery bank. Plenty of Baja Sea of Cortez sunshine.

edited June 2019 #5
OWB,

Thank you--But this is all "Free". I don't work for any solar related company (or anybody at this point in life--for better or for worse).

And as LittleHarbor2 says, our forum is fully funded and admin'ed by NAWS (Northern Arizona Wind & Sun) (I am a volunteer moderator here).

At least considering them for your solar purchases (where it makes sense, for you)--Is all we ask.

http://solar-electric.com

Take care,
-Bill

PS: And I should add... Document your install and how it works for you (good and things you would have liked to done differently) so that everyone here can learn.

Much of my/our rules of thumbs and suggestions have been honed and simplified based on feedback from members. It is always a tradeoff between details and simple rules of thumbs... And I have been tending towards rules of thumbs vs detail. Once you understand the overview, then details (when needed) tend to be less confusing.

For example, the "simple" what size wire should I use--You have a lot of issues that drive the solution, and you may find out that some of your assumptions (like power usage or battery bank "abilities") make for a "too expensive" solution--And you have to go back to the beginning (loads) and rethink your needs (choosing energy efficient loads, conservation of usage, etc. are all usually cheaper than a "bigger" off grid power system. -BB
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset