Then you have to figure out what alpha=beta=1 corresponds to. You say it is "constant load", but I don't know precisely what that means. Does that mean constant current? or constant power? or constant voltage etc?
So the formulae seem to be okay but one thing surprises me that why they are not mentioned anywhere. I tried to search them everywhere but couldn't find. They were just made up...?
I think the R^2-X^2 should be R^2+X^2.I proved it for Z=R+jX although my head started spinning after seeing all that math and formulas again! Please see here.
That seems reasonable. There can be many purposes, both intended and unintended. Personally, what I find interesting about the formula is that it is generalized with alpha and beta, thus allowing it to express different load types.I believe that the purpose of the formulae, at least the case α=β=2, is to be able to find the power for any other voltage_rms value other than nominal or rated voltage_rms value in a rather straightforward manner.
It would seem so.Does α=β=0 signify the case of constant power?
I'm not following your work, but it appears you took a very complicated method for what should be simple. In your previous work, the second line shows power as a function of voltage current and phase. If you look at that formula and assume current and phase is constant with only voltage varying, then it is obvious that power is proportional to voltage, which means alpha=beta=1.This is an addition to my previous post.
I tried to solve for alpha=beta=1 case without any success. I'm attaching the so-called solution which doesn't make any sense to me. Please have a look and guide me how to proceed in logical manner. Thank you for your help.
I think the R^2-X^2 should be R^2+X^2.
That seems reasonable. There can be many purposes, both intended and unintended. Personally, what I find interesting about the formula is that it is generalized with alpha and beta, thus allowing it to express different load types.
I'm not following your work, but it appears you took a very complicated method for what should be simple. In your previous work, the second line shows power as a function of voltage current and phase. If you look at that formula and assume current and phase is constant with only voltage varying, then it is obvious that power is proportional to voltage, which means alpha=beta=1.
but if you mean the amplitude of the current has to stay constant by varying the load
For example, the constant current case, we would say that the phase angle and the current are constant, to get to the desired formula.
You have to ask yourself, what assumption did you make when you did the derivation. When I did the derivation (keep in mind I spent about 1 minute thinking about it) I felt I needed to assume that the angle was constant - not just the current magnitude.Thank you.
Are you saying that power factor angle doesn't change in the context of the formulae we were discussing? It'd also imply that only the magnitude of the impedance changes.
Hi
It was written that P=Po(V/Vo)^alpha and Q=Qo(V/Vo)^beta. Later, it was said that if alpha=beta=2 then you get a constant impedance, and also if alpha=beta=1 then you get a constant load. I believe that 'Q' stands for reactive power and 'P' for real power.
I couldn't make any sense that how the two formulas above were reached at and how and why alpha=beta=2 results into a constant impedance and so on. Could you please help? Thank you.
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