But the RMS values of an instant are e and i.
More nonsense.
But the RMS values of an instant are e and i.
So I guess you eventually added enough qualifiers to your OP until you got it to match the answer you had in mind all along.Agreed, but we have for the most part limited our discussion to sinusoids
yesand is this "transient impedance" vary with time?
Zo is only for a uniform transmission line and can be the same as the instantaneous impedance. However, even if it is uniform but terminates in something that does not match the characteristic impedance, the impedance will change. Think about a uniform open-ended line where the instantaneous impedance starts out the same as the characteristic impedance but eventually goes to infinity.Sounds like it is more like Zo of a xmission line??
The most important characteristics of synchronous machines when calculating short-circuit currents are the internal reactances and resistances. In practice, a single machine reactance is assumed to vary (with time) from a subtransient to a transient to a sustained or steady-state impedance; these variations control the ac component of the fault current. The resistance controls the dc rate of decay. The machine time constants that determine the rate of ac decay of the components of current are also important.
Expression of the synchronous machine variable reactance at any instant requires a complicated formula involving time as one of the variables. However, for the sake of simplicity the reactance is considered fixed over the time interval for which the fault current is calculated.
Now you are just toying with us. :grin:E and I represent RMS values, e and i represent instantaneous values.
So I guess you eventually added enough qualifiers to your OP until you got it to match the answer you had in mind all along.
Zo is only for a uniform transmission line and can be the same as the instantaneous impedance. However, even if it is uniform but terminates in something that does not match the characteristic impedance, the impedance will change. Think about a uniform open-ended line where the instantaneous impedance starts out the same as the characteristic impedance but eventually goes to infinity.
But what I had in mind was fault analysis where the impedance changes with time. From the IEEE Violet book:
Your clarification is analogous to putting blinders on a horse, or forcing someone to have tunnel vision.Not really, just adding clarification.
...which I did not think to disqualify from the discussion.
"...for the sake of simplicity the reactance is considered fixed..."
But not "constant" like in the steady-state case. In the transient case, the value is picked so the current can be approximated using a constant voltage input. One is a derivation, the other is a replacement.But even there, they make the assumption of constant reactances.
"However, for the sake of simplicity the reactance is considered fixed over the time interval for which the fault current is calculated."
But not "constant" like in the steady-state case. In the transient case, the value is picked so the current can be approximated using a constant voltage input. One is a derivation, the other is a replacement.
I'm thinking there is a difference in a value that can be derived vs one that you pick as a substitute."Fixed" or "constant" in this case mean the same thing, no?
There are certainly time-dependent impedances, although not within the walls of the city you have built.It is just that in this case, the approximations are more drastic than it is in our steady state cases. And, I would think the inductance would be a function of current rather than time.
It is not constant but does eventually reach a steady-state value.Now does "transient impedance" mean it is not constant, or does it mean a value to be used in a transient analysis?