I'm a little weak on the physics, but if you could express the problem as 3 equations and 6 unknowns (or whatever it works out to be) and identify the variables of interest, I'd be happy to try to figure out the maxima and minima over the solution space. My understanding is that since the magnitudes of the load currents are known, the delta currents will be bounded in magnitude as well.You have six unknowns (three currents with three phase angles or three vector currents with two components each).
If you know phase of the load currents as well as magnitude you have six equations.
If you can approximate load currents as PF = 1, then there is a unique solution. If not, then the solution is undetermined but you can still place upper limits on the delta currents by assuming worst case or worst credible case phasing.