# Please help me understand how to understand/calculate asymmetrical from symmetrical



## nukem2k5 (Oct 11, 2016)

All the papers and textbooks I've read show that the peak asymmetrical current (including DC offset component) is simply sqrt(2) times the RMS symmetrical fault current.  However, when you look at breaker ratings, the given asymmetrical interrupting rating is never a simple multiplier difference (like sqrt(2)) of the symmetrical fault rating value. 

Based on what I've read, the X/R ratio determines how quickly the DC offset decays, which matters for breaker selection because it determines how much the peak current has reduced over the given number of cycles for the breaker to operate (eg 5 cycles).  Still, how do you calculate that initial (momentary?) peak current value (the symmetrical AC component + the "asymmetrical" DC component)?

I've also read about Multiplying Factors to use for de rating the breaker when the circuit X/R is larger than the X/R for which the breaker was tested. 

So do you need to somehow use X/R (whether given, assumed using typical values from IEEE 242, or calculated from the various X's and R's of the components in the circuit) when doing fault calculations to find interrupting asymmetrical values?


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## TNPE (Dec 10, 2016)

Symmetrical only relates to 3-phase faults (bolted or to ground - which really isn't a fault to ground).  No other fault will be symmetrical.  Period.  Hence, Fortescue developed the technique of symmetrical components to accurately analyze asymmetrical faults (LG, 2LG, LL).  

As for your other questions pertaining to the DC component, I don't have much I can provide.  I would say most breakers/controllers don't need any info on the DC comp., nor do they measure for it.  Depending on the relay and application, MPU, instantaneous trip and other parameters are physically set by completing a coordination analysis to develop TCC curves (of course, depending on the relay, but could be using differentials, distance, etc.).


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## mudpuppy (Dec 15, 2016)

The asymmetrical DC offset is NOT sqrt(2) times RMS... that's simply the peak value of the sinusoid.  The assymetrical offset is due to the LC nature of real-life circuits.  E.g. voltage on a capacitor cannot change instantaneously and current through an inductor cannot change instantaneously.  You'd need to go into diff. eq. to get into the true solutions to these offsets.  But I do have a note in my references that:

Iasymmetric / Isymmetric = sqrt(1+2e^(-2pi/(x/r))).  I'd have to do some digging to find that in a text, but I'm sure it's out there somewhere.

When you think about it, X/R basically gives you the damping ratio of the system you're looking at, so it makes sense it plays a role in the maximum asymmetrical offset.


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