Ref frame transf when one of the ref frame speeds changes w/ time
Ref frame transf when one of the ref frame speeds changes w/ time
(OP)
There are some oddities which occur when we have a time-varying frequency argument f(t) of a function like cos(2*pi*f((t) *t). What happens is that the instantaneous frequency of the sinusoid is nothing like f(t). Product rule tells us the instantaneous frequency is w_instantaneous = d/dt(2*pi*f((t) t) = 2*pi*(f(t)*t)' = 2*pi*(f'(t)+f(t))'
The simplest example is ramp change in frequency as shown in attached slides 1 and 2. You can see in slide 1 that even though f(t) is changing smoothly, the time waveform instantaneous frequency changes abruptly as we enter and leave the ramp. The analytical proof of this unexpected (to me) behavior is shown in slide 2.
I have simulations results in the synchronous reference frame (ref fram speed w is w=2*pi*LF) that I want to convert to the rotor reference frame. I thought I could use the equations shown on attached slide 3 from Krause, and simply use w=wre(t) where wre = 2*pi*RotorSpeed(t)*Poles/2 = radian speed of an equivalent 2-pole motor based on my computed simulation results. Slide 4 seems to imply that it is ok for the reference frame w to be a time-varying function. But it occurs to me that this might introduce unexpected or unwanted behavior similar to slides 1 and 2..
The bottom line question: do you think it is acceptable to use a time-varying frequency in the reference frame transformation? i.e. in slide 3 one of the theta's would be represented by theta = w(t) * t where w changes over time.
The simplest example is ramp change in frequency as shown in attached slides 1 and 2. You can see in slide 1 that even though f(t) is changing smoothly, the time waveform instantaneous frequency changes abruptly as we enter and leave the ramp. The analytical proof of this unexpected (to me) behavior is shown in slide 2.
I have simulations results in the synchronous reference frame (ref fram speed w is w=2*pi*LF) that I want to convert to the rotor reference frame. I thought I could use the equations shown on attached slide 3 from Krause, and simply use w=wre(t) where wre = 2*pi*RotorSpeed(t)*Poles/2 = radian speed of an equivalent 2-pole motor based on my computed simulation results. Slide 4 seems to imply that it is ok for the reference frame w to be a time-varying function. But it occurs to me that this might introduce unexpected or unwanted behavior similar to slides 1 and 2..
The bottom line question: do you think it is acceptable to use a time-varying frequency in the reference frame transformation? i.e. in slide 3 one of the theta's would be represented by theta = w(t) * t where w changes over time.
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(2B)+(2B)' ?





RE: Ref frame transf when one of the ref frame speeds changes w/ time
w_instantaneous = d/dt(2*pi*f((t) t) = 2*pi*(f(t)*t)' = 2*pi*(f'(t)+f(t))'
should've been
w_instantaneous = d/dt(2*pi*f((t) t) = 2*pi*(f(t)*t)' = 2*pi*(f'(t)+f(t))
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
w_instantaneous = d/dt(2*pi*f((t) t) = 2*pi*(f(t)*t)' = 2*pi*(f'(t)+f(t))'
should've been
w_instantaneous = d/dt(2*pi*f((t) t) = 2*pi*(f(t)*t)' = 2*pi*(f'(t)*t+f(t))
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Ref frame transf when one of the ref frame speeds changes w/ time
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
Cut that back to two exclamation marks. grin.
Bill
--------------------
"Why not the best?"
Jimmy Carter
RE: Ref frame transf when one of the ref frame speeds changes w/ time
=======================
In case it wasn't clear, the only thing that was corrected in this thread was the very end of the first paragraph of my original post...
(f'(t)+f(t))' becomes (f'(t)*t+f(t))
Everything else stays the same. Nothing changes in the spreadsheet.
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
So if I were trying to do a simulation involving a ramp change in frequency of applied voltage, what kind of expression would be used for that?
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
Sorry... "never mind!"
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
1 - theta(t) = integral{w(t)}dt where w(t) is the specified frequency profile such as a ramp
2 - v(t) = Vmagnitude*cos(theta(t))
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(2B)+(2B)' ?
RE: Ref frame transf when one of the ref frame speeds changes w/ time
Milovan Milosevic
RE: Ref frame transf when one of the ref frame speeds changes w/ time
If distance can be desbribed by equation s= k*t then k is speed only if k is constant in time. If not than it is not speed. So lineary increasing speed (or in your case frequency) doesnt mean that k should increase lineary, and because of that graphs dont have sense.
Milovan Milosevic
RE: Ref frame transf when one of the ref frame speeds changes w/ time
To follow the linear analogy, my graph of the original post would be equivalent to saying I drove 1 hour at 30 mph and 1 hour accelerating from 30-60 mph, so I compute my distance travelled as 60mph*2hrs =120 miles
Thanks.
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(2B)+(2B)' ?