One thing to keep in mind is that boiling water self-regulates its temperature via the boil off rate. Since the latent heat of water is so high - it takes about seven times the energy to boil off a quantity of water that it took to heat it from room temperature to boiling -, you have a lot of time to dial down your heating power once you reach the boiling point, without losing too much liquid.
Let's say you dimensioned your heaters such that you get to boiling in half an hour. If you keep going at the same power setting, you will boil off one seventh of the water (or wort) in the next half hour.
Additionally, the specific heat of water, even though small compared to the latent heat, is pretty large compared to all the other stuff around, so heat losses are not all that important in boiling (as opposed to cooling, where ambient heat gain can dominate).
I guess what I'm saying is you could use a simple linear equation to have your controller set the heating power only based on the volume your are boiling (with a fixed offset for the heat loss of your boiling vessel), and then another linear equation for the reduced steady boil power to use after a fixed delay. If you are off a bit, you are just changing your boil-off rate by a small amount.
Example: 15 kW takes about 26 minutes to heat 20 gallon of water from 25C to 100C (77F to 212F). If you left the power at 15 kW, you'd boil off 3 gallon in the next half hour. If you reduce to 5 kW, you'll boil off 2 gallon in the next hour, which is probably where you want to be at.
Adding 500 W heat loss for your kettle (assuming about 1 square meter surface area and 5 W per square meter per Kelvin heat loss, which is a good number for still air) changes time to boiling by almost nothing, and reduces the boil off rate by 10%, which is also nothing.
So, I don't think you need a PID or anything, nor could you really use it: it would be difficult to give it a good input, since you can't use temperature - the boil kettle temperature will be constant until almost the last drop of wort is boiled away.
You are simply starting with one power setting for a fixed amount of time to reach boil, and then turn some of the heaters off and run with that second power level for the rest of the boiling time.