While designing an power inductance (shape of magnetic core:U ; 25KV as voltage and 22A as current) to protect  capacitor banks(used as power factor correction's) from transient switching conditions (over-current ), i realized that it is very important to have B (the magnetic flux density ) as high as possible. You can play with your airgap to store more energy but there are consequences.

In fact, at the time B=Bsat, an increasing magnetic flux density lead to the decreasing of the permeability of the magnetic core. Therefore, the inductance value will decreases too since you want it to be kept constant .

At this point, i have 03 questions:

1. Which material core can be used to solve this issue, since trying to increase B sometime leads to increase losses in magnetic core too.

2. How to solve arcing issues due to capacitors banks switching which creates harmonics.

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