Estimated cable sizes using Root Sum Squared

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):

https://www.westmarine.com/WestAdvisor/Marine-Wire-Size-And-Ampacity

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