I have a capacitor bank with 4 units in parallel and I'm trying to figure out the worst case scenario of current sharing at turn initial turn on. If 3 of the capacitors have the maximum ESR and one is say half the maximum ESR, how do I calculate the maximum current of the low ESR unit?
For any voltage step, the capacitance doesn't matter and the instantaneous impedance is just the resistance, or ESR.
In any case, when you're applying a fixed voltage to multiple things in parallel, you calculate the current draw of each thing independently, then add them for the total current.
The amount of current flowing through the capacitance is depend on the load current. If the ESR is high in any one of the capacitor, the heat generated by the capacitor is also high. How ever the current through each capacitor remains same.