How to calculate how fast i can speed up a fan with remaining full load amperage 1

[AirMD]

Hello all,

I am trying to calculate how much faster I can speed up a fan without going over the nameplate amperage. It is a 20hp 3ph 575v motor with eff. and power factor of 0.8. The motor is currently drawing and average of 16.0 amps across 3 phases nameplate is 18.9. If someone could help me out with this it would be much appreciated

 

[electricpete]

After googling a little bit about vector drives, I find this

http://literature.rockwellautomation.com/idc/groups/literature/documents/td/7000-td002_-en-p.pdf

the torque producing component (Isq)

magnetizing component (Isd)

You probably already knew that piece, but I didn't. So now it makes more sense to me. There are two different rectangular coordinate systems by which we can express the stator current vector:

(Ireal, Ireactive) decomposes the total current vector into orthagonal components using the applied voltage as a reference. Ireal is in phase with applied voltage, Ireactive is the vector remainder resolved in the perpendicular direction. This coordinate system is useful for determining power flow (real and reactive).

(Itorque, Imagnetizing) decomposes the total current vector into orthagonal components using the magnetizing current as a reference. (The magnetizing current is Im = Is - Ir' where Ir' comes from an model within the drive). Imag is in the direction of Imag (same thing). I torque is the vector remainder resolved in the perpendicular direction. This coordinate system is useful for examining/controlling motor behavior.

It may be tempting to equate (Itorque, Imagnetizing) to (Ireal, Ireactive) since they are both rectangular expressions of the stator current vector, and they're very close at low load. But they are different as discussed above. While Imagnetizing is itself reactive, it is not the only contributor to Ireactive (there is also a component due to current flow in leakage reactances). The net result is that the two sets of coordinate axes (Ireal, Ireactive) and (Itorque, Imagnetizing) are rotated by some angle with respect to one another (and that rotation angle is not a constant but would vary with motor conditions, including load).

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[electricpete]

actually, you'd better ask on the motor forum. That last post may not be 100% correct.

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[electricpete]

Yes, delete this sentence "While Imagnetizing is itself reactive, it is not the only contributor to Ireactive (there is also a component due to current flow in leakage reactances)"
That sentence is wrong, all else looks good to me.
I'm done now.

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[electricpete]

The reason I deleted that sentence is the ambiguous clause "While Imagnetizing is itself reactive". It is true in one sense and not true in one sense... let us say possibly misleading. The term "Reactive" implies a voltage reference. There are two different voltage references to consider here. The voltage vector across the magnetizing branch does not have exactly the same phase as the applied voltage vector. So while the magnetizing current is 90 degrees lagging the voltage accross the magnetizing branch (purely reactive in that sense), it is not lagging 90 degrees from applied voltage (not purely reactive in that sense). We have to be careful when we say reactive about what voltage reference we are using. A better way to look at it: we know that the Im flowing in the magnetizing reactance does consume vars which must be supplied by the input power. In a similar manner the current through leakage reactance is in quadrature with the voltage accross it but not in quadrature to the applied voltage but it does consume vars that must be fed from the input power. So instead of saying that the reactive current has components from magnetizing and leakage (which is a little misleading... implies simple addition), it would be more accurate to say:
Im(V x Is*) = Im^2xXm + I1^2xX1 + I2^2xX2
The left side is reactive power that flows into the motor, the right side is reactive power dissipated in each reactance.
Notation above: x represents vector multiplication (not cross product) and * represents conjugate

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[electricpete]

The very last comment. I talked about difference in phase between voltage accross magnetizing branch and supply voltage... and that phase difference is important because it is exactly the angle by which the (Itorque, Imagnetizing) coordinate system is rotated with respect to the (Ireal, Ireactive) coordinate system.
Let Zpara be parallel impedance of magnetizing branch and rotor branch. Compute it as a product/sum of impedances:
Zpara= (R2/s+j*w*X2) j*w*Xm/ (R2/s+j*w*X2+j*w*Xm)
By voltage divider, we can find voltage accross magnetizing branch in terms of supply voltage and circuit parameters:
Vm = Vs * [Zpara / (Zpara + j*w*X1+R1)]
The phase angle of the quantity in the square brackets is the angle shift between the two coordinate systems.
I'm really done now.


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[mikekilroy]

Since you stepped into my field now with magnetizing and torque producing components, I can tell you that most of what you say is accurate. You can see the issue you are having with defining angle with respect to voltage is just that - the power factor changes with load so it is not constant and rotates if you will as you say.

A real vector drive controls current and current only; voltage is basically ignored: ie., we don't control voltage at all - it does whatever the heck it needs to do to make the correct two currents - which are always and forever 90 degrees apart.

So if you leave voltage totally out of your descriptions then they are correct. We almost totally ignore voltage - it simply gets jerked where it needs to in order to make the two PID controlled currents. With that blinder on, what I ignored all these years was the voltage changing with load. I know can look back upon many many systems and see WHY the voltage mysteriously increased 10-20% WITH load at a given speed. Never paid attention to that leakage current before; to the point of ignoring its term in the motor model that IS there but I never had a use for it. Guess I still don't have any use for it since I control my vector motor with Isq & Isd and to hell with the leakage current. But it is there. If my motor model is not close then it does screw things up and I have to go back and tweak my model.

 

[electricpete]

Ihave assumed that under steady state load and speed conditions, the fundamental component of drive output voltage will approach a steady state value, which I called Vs (which was not intended to imply it is a constant for different loads and speeds... I simply needed a variable name). It may not be of interest because it is a hidden intermediate variable not required to compute the important motor operating parameters such as torque and output power, but I assume it exists. If it did not exist, then traditional (displacement) power factor and reactive current would have no meaning.

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[electricpete]

However, good point you bring up that varying vfd output voltage would be another important effect to consider (along with everything else discussed) in order to draw any conclusions from your data about the original discussion (motor power factor variation vs load at fixed voltage and frequency) since motor power factor also varies with voltage at a fixed real load. Another complicating factor.
Merry Xmas.

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[mikekilroy]

"Vs....If it did not exist, then traditional (displacement) power factor and reactive current would have no meaning."

since real torque producing current is 100% in phase with motor voltage, I have always just ignored the voltage as it is not required for any calcs like PF since PF is given with Isq & Isd's vector sum.

I'll tell you next systems we do I will be sneaking scope pixs as before both unloaded and in heavy metal cut loads, but also include vectored output current too, since it will show total VARS!

Agreed, tho this thread moved from how much faster can I go to this discussion, I think the bottom line for the OP question is still valid to separate both currents and calculate based on them since the motor will be almost fully loaded to fully loaded and in any case the PF given was for full load motor so this separation of currents should still be valid since it would include the full reactive currents anyway & much more accurate than just messing with composite vector current and its inherent error. My confusion remains whether torque producing current in fan app goes up by square as one post and some google searching shows or by cube like power. both seem to make sense and I have not been able to determine yet which is right. obviously only one. since speed also goes up, seems like it needs to be sq function so that the increasing speed can add the cube to it....

Merry Christmas to all.

 

[electricpete]

My confusion remains whether torque producing current in fan app goes up by square as one post and some google searching shows or by cube like power. both seem to make sense and I have not been able to determine yet which is right. obviously only one. since speed also goes up, seems like it needs to be sq function so that the increasing speed can add the cube to it....

I think the two different answers depend on whether we consider that motor speed varies with fan (direct coupled fed from vfd), or that motor speed is constant as fan speed varies (for example changing sheave ratio with fixed-frequency motor supply).

Either way, motor output power goes up as cube of fan speed (under assumptions mentioned: density constant, system does not change resistance)

If motor speed varies together with fan speed N, then
MotorTorque ~ MotorPower/MotorSpeed ~ N^3/N ~ N^2

If motor speed is constant as fan speed N varies, then
MotorTorque ~ MotorPower/MotorSpeed ~ N^3/Constant ~ N^3

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