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Understanding the motor equation

Understanding the motor equation

Understanding the motor equation



I was going through a technical paper for understanding the PMSM modeling, in that the author has given below equation


where P is a differential operator and Wr is rotor speed in rad/sec, Eo is voltage of BEMF
My doubt is the Eo is zero in the Vd voltage equation where I think the rotor flux is hi and the winding facing will experience more BEMF. so BEMF has to be max but as per eq it is zero

Can any one pl help me..


RE: Understanding the motor equation

I suspect that equation models the standard idealised steady-state case. In that case the stator current vector is parallel to the q-axis. That is, the d-axis component of the stator current is zero. BEMF is in phase with stator current, so is produces only a q-axis voltage component and the d-axis voltage component is zero.

If you consider the transient behaviour, which I think is the scenario you're imagining, then yes, the d-axis component will be non-zero. You can find studies of this much more complex model in textbooks.

RE: Understanding the motor equation

This is not for school Home work.. I'm a hobbyist, I try to work/understand different concepts... and not for profit too....

coming to the point, yes you are right, the equations is representing the steady state operation where the stator current vector is in phase with rotor Q axis, but still my doubt is, so the q axis stator voltage vector is pointing on the magnetic neutral axis where the field is zero so df/dt is zero => I think BEMF is zero in the q axis stator eq...

can you pl help me further

One thing I'm not questing the author, I'm trying get clarity where my thought process is going wrong...


RE: Understanding the motor equation

I can't figure out where you might have gone wrong without seeing the derivation of that equation. I couldn't find a reference that is close enough to make a comparison. It's possible that you're simply confusing f = 0 and df/dt = 0. Remember in a sinusoid, the rate of change is greatest at the zero crossings. That is, if f is a sinusoid, then f = 0 => max |df/dt| and |f| = max => df/dt = 0.

RE: Understanding the motor equation

The back EMF term is definitely on the q-axis only. Try this way of looking at it:

The back EMF is the "cost" to the electrical system of producing mechanical power through generated torque. Only the q-axis current produces torque. This is necessitated to make conservation of energy work out.

Consider the torque equation T = Kt * Iq

Now consider the back EMF equation E = Ke * wr

Kt and Ke are the same thing really. In consistent units like SI, they have the same numerical value. Combining the equations, we see that mechanical power T * wr equal electrical power E * Iq.

The equation you cite is not really correct in that it has the back EMF as a constant. The last vector should be [0 Ke] and multiplied by wr.

Curt Wilson
Delta Tau Data Systems

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