Understanding System Limitations

[spiral]

I have a 7KW inverter and understand that 7KW is the maximum load that it can handle.
I have an electric shower that draws a load of ~10KW and usually when it does this my battery discharge + solar generation = 7KW with the remainder coming from the grid.
So if I'm generating 3.5KW, the battery will supply 3.5 and the grid 3.0 to make the 10 total.
One thing I have noticed though is that my battery discharge never exceeds 5.79KW
So if I'm only generating 0.21KW, the battery will supply 5.79 (or sometimes less) and the remaining 4+ will come from the grid.
My battery's capacity is 5.76KW so is there a limitation along the lines of batteries will not discharge at a rate of > their capacity per hour or is there a setting I need to check/alter?

[MaterialBarracuda48]

Easy, Max discharge rate is 30Amps, at a nominal 192V = 5760W (5.76kW)

[spiral]

Easy, Max discharge rate is 30Amps, at a nominal 192V = 5760W (5.76kW)

Brilliant, that answers my original question too (which evolved into this one) in that why when the additional cost of larger inverters is relatively small, why wasn't I offered a bigger one.
So presumably the only real benefit of larger inverters is for much larger generating capacity.

[MaterialBarracuda48]

For your system, the battery is your limitation, my EP11 runs at a lower sustained 27Amps, but higher nominal Voltage of 384V, giving over 10kW of power on tap.

For me, my limit is my Inverter and the temperature of the battery (as Winter will affect your charge/discharge rates... heads up on that!)