Capcitors, when switched on, act as a short-circuit momentarily. A single uncharged capacitor can draw 30 times its rated current, this being limited by the supply impedances.
When multiple capacitors are being switched, the already charged capacitors will discharge into the new one, and, impedances being very low now, the current drawn can reach 150 times the rated current ! Since it is also at 10-15 kHz, reactors are used to attenuate this high inrush.
A good explanation is available in NEMA ICS 2. It is available for free download, please download and study.
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Similarly, if you apply a voltage to an inductor, the current doesn't flow immediately.... it rises exponentially as per the time-constant of the inductor {I = Imax*(1-e-Rt/L)}
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But i don't know them ! If the OP asks, you will have to answer !
As you know, i am a switchgear guy, and i love that beautiful product, the capacitor-switching contactor ! So, will you excuse me on harping on what i know....
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Nothing worthwhile can ever be taught, it can only be learnt.
The company in which I am working now use battery charger-cum-regenerative-dischargers. There are 4000 to 6000 circuits at each of our manufacturing facilities. These equipment leads to very high harmonics generation (VTHD 6 to 8% % & up to ITHD 36%). I am able to handle these harmonics with out using any filter. Idle would be "Active Filter" but very costly. As you said correctly, reactors are used to prevent frequencies other than fundamental reach capacitor and damage them.
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