Arcing power 1

[mykh]

Going through old posts related to arc flash, I came across thread238-161138 a statement that If fault arcs are assumed to be resistive then the maximum power occurs when the arc resistance matches the source resistance. How about purely inductive source? Here, arcing resistance would have to be equal zero to produce maximum power, which does not make any sense. I think purely inductive circuit is in fact capable to produce more active power dissipated in arc than purely resistive circuit, assuming total impedance, system voltage and bolted fault current is same for both. My reasoning is that in the case with purely reactive source arcing resistance would be the only resistance present to dissipate active power.

Any comments?

 

[davidbeach]

Since you'll never find a real circuit that is purely inductive, how much does a theoretical problem really matter?

 

[mykh]

I've done power flow analysis and the results show that this statement is just not true. Did you try to do the analysis?

 

[Skogsgurra]

A linguistic problem rather than electrical. Substitute "impedance" for "resistance".

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[dpc]

This is discussed in Ralph Lee's original paper, I believe.

 

[mykh]

Skogsgurra, I think I agree with you. My observations are that maximum active power dissipation in arc occurs when arc resistance matches the source impedance

 

[davidbeach]

What statement is "just not true"? That there is no such thing as a purely inductive circuit? That is an absolutely true statement even if you can do an analysis of one. Real components, including real inductors, have resistance; real transformers have resistance, real generators have resistance, real lines have resistance.

For many purposes it is an adequate approximation to assume a purely inductive circuit, but for other purposes it is not. Back when computations were difficult it made a great deal of sense to assume the power system to be purely inductive for the purposes of fault studies; that way all of the calculations could be made with real numbers. But certain aspects of power system performance have never been able to be modeled without accurately accounting for resistance.

 

[ijl]

Take a source with some internal voltage behind some internal impedance. Connect it to a purely resistive load. Find the resistance of the load that gives the maximum power in the load (take the derivative of the power wrt the resistance). The result is that the maximum power is achieved when the resistance is equal to the magnitude of the internal impedance of the source, as stated above. This is a general result, not limited to arcs.

Purely theoretical problems are interesting. Sometimes they can even be useful. Like in this case, when considering a purely theoretical problem revealed an error, linguistic or otherwise.

 

[mykh]

thanks,ijl for making the calculations and confirming my findings. As amazing as it is, theory reveals things that are not very obvious from common sense point of view.

 

[DrDrreeeaaa]

And what are you going to do with these findings?

 

[mykh]

123MB, take it one step further and analyse arcing power and arcing current as a function of source x/r. Your finding might shatter common sence stand point again.

 

[mykh]

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