Air Core

i have used air-cored inductors for limiting the high frequency inrush currents when switching multiple capacitors... here is an image from ABB..hope it is visible...

You're correct, this might be about an air core inductor instead of the air gap of a transformer I thought it was about. Your explanation and diagram only explains the mathematics of making a particular inductance value though. You do not explain how this will effect the inrush current of the circuit. Then again, hopefully this student does know how to analyze a circuit response to a step input.

It must be the curmudgeon in me, but I'm getting much less tolerant of imprecise students and their lazy questions.

Our posts were simultaneous, otherwise, i might have held back too, since you were quite right.

Coming to the effect of the inductor, i attach an extract from AEG, which i hope will be visible :

The fully charged capacitors will discharge into the newly switched capacitor, and so a high frequency surge will result. However low the inductor value is, at 15kHZ it should do a good job

NEMA ICS 2 mentions this same solution without too much math :

Red, I think you were being kind, I would have reversed "imprecise" and "lazy". jmho

Regardless of my kindness or word order, this kid wasted their time and money. I won't waste anymore of my time on this one.

Thank you, kvsridhar! We'd like to know more about the inductors you made to limit the inrush current between capacitors.

I found (link) your drawing and its discussion on page 29 of this 39-page ABB application guide, called Contactors for Capacitor Switching (it can also be found (link) on page 11 of this 18-page two-language document). ABB says in the introduction, "In Low Voltage industrial installations, capacitors are mainly used for reactive energy correction (raising the power factor). When these capacitors are energized, overcurrents of high amplitude and high frequencies (3 to 15 kHz) occur during the transient period (1 to 2 ms)."

Special contactors should be used to switch these capacitors onto the AC line. At the moment of switching, especially if the AC-line is at its voltage peak, a very high inrush current will occur, limited primarily by the inductance and series resistance of the supplying transformer. If multiple "steps" of capacitors are used in a capacitor bank, very high peak currents from capacitors already on duty will rush into the discharged capacitor, limited primarily by the inductance and esr of the capacitor. Even small PFC capacitors have quite low esr values, for example 3.3mΩ for a 1kvar 240vac cap (3x15µF), so we can't rely on resistance to limit the current.

With inductance limiting, the peak current between charged and discharged caps is I_peak = 2 Vac (2 C/L)^½, where C and L are in µF and µH, and the extra factor of two is because the capacitor can "ring" up to twice the peak AC line voltage. For example, for a large 20 kvar correction cap and L=10uH (e.g., roughly for a 6" dia 6-turn coil mentioned in NEMA ICS 2), I get I_peak = 3750A (that's twice what ABB's formula gives, so they seem to have omitted the extra factor of two), with a ringing frequency of 2.9kHz. The resonant reactance for that is 0.18 ohms, so if the associated ac loss-resistances are say 2mΩ (proximity-effect in the 10µH air coil), it could ring down with a 30ms time constant.

By contrast, in the absence of the inductor and any other limiting element, the current peak could be sqrt 2 * 240 / 0.25mΩ = 1300kA, lasting a few µs, Whoaaa! No, that's not right, maybe there'd be say 0.25µH of cabinet wiring inductance, etc., then we'd be talking in the neighborhood of 20 to 30kA, ringing near 20kHz, lasting a few ms.

Actually, you can tell from this discussion that I'm an electronics engineer, not an electrical engineer, so even tho I'm well-enough experienced with kA and MVA pulse circuitry, etc., I really don't know about PFC cabinets, and whatever contactor you might be using to connect say a 20kvar cap to a bank of PFC caps. Some have internal equalizing resistors, etc., isn't that right?

So, anyway, kvsridhar, and others, some of us would like to hear your stories, more about your hand-made air-core inductors, etc.

"I really don't know about PFC cabinets, and whatever contactor you might be using to connect say a 20kvar cap to a bank of PFC caps. Some have internal equalizing resistors, etc., isn't that right?"

I should have mentioned ABB's suggested Dynacomp system, which switches the contactor near the AC-line zero crossing. They show the damaging effect of ordinary random switching, near the peak of the cycle (above, link), presumably even with an inductor. The voltage scale is 250V/div and the current scale is 1000A/div.

There's a 5.5kA p-p current spike causing a 250V voltage drop followed by a 150V excess-voltage surge beyond the AC-line peak. ABB also shows a Dynacomp waveform with no spikes. :-)

I suppose this is especially important in a system that senses the power factor moment-by-moment, and quickly switches in appropriate levels of PFC correction. Without ZCS there'd be frequent disturbances on the AC line.

Hello Win !

WOW ! What an awesome post ! You caught me out. i NEVER did the math !

To get the chronology right, i was asked in 1984 by a customer whether my contactors were good enough to switch on the 8th capacitor when the earlier 7 are on already ... i didn't hesitate, i said it will weld ! The customer, their chief engineer, laughed and said, i have finally met a man who values professional ethics above commercial gain. Ok, mutual backslapping apart, what is the solution ? asked the guy. i showed him NEMA ICS2. He studied it, said great, lets try it out in your lab. (He wasn't good at math either). So i welded a couple of 40A contactors on 10A duty. And demonstrated that the NEMA coil did its job, and even a 25A Contactor was ok.

25 years have passed.He says they work like a dream still !

Now we have the special cap contactors with clever little early-make auxiliaries which make sure the initial peak is attenuated. So, why bother ? No one calculates any more. They use CAPCAL software.

Sorry to disappoint you. i haven't ever needed to actually calculate.

Here are some links that give info on current-limiting reactors. The issue of air-core vs. other construction (oil-immersed iron-core, etc.) is secondary to the concept of their operation.

http://www.nokiancapacitors.ru/documents/theory/EN-TH07-11_2004-Series_Reactors_and_Voltage_Control.pdf

http://www.nwl.com/contents/view/95

Here's an example on a different forum where someone was trying to size a reactor:

http://www.eng-tips.com/viewthread.cfm?qid=227993&page=2

Hope this helps.

You didn't learnt this when you were supposed to do so, don't expect other to do your job, I would stay one more year in this situation.

OK so he's a student, if he has the basic concept of what he's asking, the question would have been more structured.

I am really thankful for all of you ..............and sorry for my bad english...... can I ask more thing........I need some book titles for superconductor (FCL)......... you were so kind to me......thank again ..... If there is no books about it pleas help me with an informations