That's going to depend on a few factors - the initial water temperature, the rate at which heat is lost from the system etc.
This seems to give some idea of the maths needed -
How to Calculate Time to Heat Water
Assuming 15L starting from a tap temperature of 10 degrees (i.e. needs to gain 90 degrees C)
Code:
Pt = (4.2 × L × T ) ÷ 3600
= (4.2 x 15 x 90) ÷ 3600
= 1.575 kWh
t = 1.575 kWh / 1.5 kW
= 1.05 hours
That's a minimum time of 63 minutes to get to boiling, although in reality it'll take longer than that as heat will be lost from the pan as you bring it to the boil.
Once it's at a boil, I
think you just need to make sure that the power you're putting into the system is equal to the amount which is being lost to the environment.
(Based on my poorly remembered physics lessons - happy to be corrected if not)