Power Factor as a design variable 3

[Clyde38]

I’m looking for literature relating to the design of AC induction motors (or actually any motor). Specifically, I’m looking for things that affect power factor from a “design” perspective. There is a lot of information available about the effects of power factor, but I’m finding it difficult to find information relating strictly to the design of the motor. I’m interested in what the trade offs in the design choices are that make the power factor (from the design of the motor standpoint) improved or adversely effected. I’m making an assumption that someone has studied this and published their findings. It would also be of great interest to find literature relating to the design of motors that are inverter fed as opposed to line fed and the differences in design choices with respect to power factor. I hope my request is clear; sometimes I don’t put on paper what is in my head.

I am learning all the time. The tombstone will be my diploma. ~Eartha Kitt

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[electricpete]

I don't have any references specifically addressing that. But the underlying principles are well established.

The power factor can be determined from the equivalent circuit parameters and the operating conditions (load and voltage). (inductive elements consume vars, resistance elements including R2/s) consume watts. Power factor is related to the relationship among these (pf = watts / sqrt(watts^2+vars^s). Alternatively, you can view power factor as the impedance angle of the equivalent circuit, collapsed to a single element by Thevinin or equivalent transformations.

The vars consumed by magnetizing reactance have a big affect on vars, accounting typically for one half of the vars consumed at full load (the other half would be leakage reactance vars).

The fact that vars from magnetizing reactance are roughly constant with load begins to explain why power factor tends to increase with load.

Making airgap smaller would increase magnetizing reactance (increase vars). But that can have two adverse effects: 1- increase losses from high-frequency tooth-top flux; 2 - less robust against experiencing a rotor/stator rub under non-ideal conditions.

We all know slow-speed motors tend to have have lower full-load power factor. Compare a slow speed motor and fast speed motor of same horsepower rating. Assuming similar current density (amps per meter of circfumerence) and flux density (B), each unit of the stator bore surface area (pi*R^2*Length) contributes the same amount of torque in the slow speed motor as the fast speed motor. So it is evident we need to larger surface area to accomplish the same power on a slow speed motor (which has higher rated torque than a fast speed motor). Thus (for same horsepower), the slow speed motor has higher stator bore surface area => lower magnetizing reactance => more magnetizing vars for same horsepower => lower power factor at rated condtitions.

There are plenty of references that will explain behavior of the equivalent circuit parameters vs physical configuration of the motor. Some simpler ones are the book by Chapman and the book by Fitzgerald. Some more advanced books that I like for this subject are:
1 - Design of Rotating Electric Machines
2 - The Induction Machine Handbook by Boldea

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[electricpete]

I would add that the design of a motor (like anything) is an batch of tradeoffs (among various performance parameters and cost). You can't change one thing without affecting somethign else. So the best answer to your question imo would be to sit down with a book on motor design.

(no, I'm not claiming to be a motor design engineer... just my thoughts fwiw).

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[waross]

Nice explanation Pete. lps
May I add that designing for power factor may be a confused way of proceeding.
As Pete mentioned, motor design is a trade off. One of the trade offs will be magnetizing VARs, which influence power factor. But at the end of the design process the power factor is whet it is,- the ratio of to Watts VARs.


Bill
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"Why not the best?"
Jimmy Carter

 

[davidbeach]

Um, Bill, not really. Power factor is the ratio of Watts to VA. Not sure what a ratio of watts to VArs would be.

 

[electricpete]

One of those got-in-a-hurry and made an obvious typographical error things. Speaking of which, here's a correction in bold to my first post:

Making airgap smaller would increase magnetizing reactance (increase vars). But that can have two adverse effects:...

should've ?obviously? been:

Making airgap smaller would increase magnetizing reactance (decrease vars). But that can have two adverse effects:...

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[Clyde38]

Pete,
Thanks for the response. Of course as usual you have provided a very detailed and accurate response. I do have Fitzgerald’s book and Design of Rotating Electric Machines. I do not have Boldea’s induction book, just his reluctance synchronous book. I was hoping that someone had published work on the tradeoffs you speak of. With motors that are driven with electronics (VFD’s, Flux Vector, etc.) isn’t the magnetizing current controllable? I’m not so interested in design of motors that operate from the grid. I know the basics are still required, but what I mean by that is that with so many motors being controlled with other than a fixed 50 or 60 Hz it seems that attention should be given to design decisions that reflect machines operated with advanced electronics.
Thanks to all for participating. As always, very useful.

The ability to simplify means to eliminate the unnecessary so that the necessary may speak. ~Hans Hofmann, Introduction to the Bootstrap, 1993


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[electricpete]

I guess it's worth mentioning, there are various kinds of power factor. The one I talked about was "displacement power factor" (cosin of angle between fundamental voltage and fundamental current). The true power factor also includes effects from distortion (distortion power factor).

I've heard vector control offers quite a bit more flexibility. I think you may be right that the displacement power factor can be controlled with a vector control drive. I don't work with drives much, maybe someone else can comment on that.

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[waross]

I stand corrected David. Apologies. I may have been more correct to state:
"But at the end of the design process the power factor is what it is,- the relationship of to Watts VARs."
But the point I wanted to make was that VARs are a design consideration, influenced in part by the shape and characteristics of the iron and the length of the air gap. Squirrel cage design may also play a part.
Watts are also a design consideration, as far as no load losses and load losses are concerned. Also, the load losses which are dependent on the square of the mechanical load.
So we have VARs which are fairly constant with load, and load and load loss Watts which vary.
Reducing VARs at the design stage will reduce current and so reduce no load losses.
Reducing winding resistance will reduce load losses and no load losses.
But you must consider the possibility of negative interaction as an improvement to one parameter has a negative effect on another parameter.
The law of diminishing returns is also a design consideration. Will you double the cost of a motor to save 1/2% on operating cost? If you will, will you then double the size again to save an additional 1/10%?
Power factor?
A good power factor at full load may be an indication of low VAR consumption.
A poor power factor at no load may be an indication of low no load losses. (Or not, it depends.)
Let's start a new thread on power factor and VFDs.

Bill
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"Why not the best?"
Jimmy Carter

 

[dpc]

Power factor versus efficiency is a clear tradeoff, at least based on my discussions with motor engineers. The newer very high efficiency motors tend to have rather poor power factors.

Most motor designers think this is a worthwhile tradeoff, with efficiency trumping power factor. Power factor can be corrected external to the motor, but efficiency cannot.

As to the physical reasons behind this, I don't recall the specifics, or maybe never knew or cared. I suspect it related to the winding configuration and slot depth.

 

[electricpete]

Good comments.

Airgap depth is one parameter that illustrates a tradeoff between power factor and efficiency. Bigger airgap depth gives lower power factor but generally higher efficiency (due to reduced high-frequency zig-zag flux and associated core losses).

Flux density (below saturation) could be another. If we start below saturation and increase total series turns of a single-circuit winding, we decrease magnetizing flux (improve power factor) but increase full-load I^2*R at a rate that likely overwhelms any improvement in core loss (net effect decrease efficiency). Although a realistic scenario may also include change in slot size to accomodate longer wire.

Since we're talking drives, active front end drives can help improve displacement and distortion power factor on the drive input side, if that's the aspect that you're interested in.


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[LionelHutz]

Is there a reason you're interested in power factor on VFD driven motors? You might get better answers if you give a reason for your search.

You do know that the motor VAR's flow between the VFD and the motor on a VFD driven motor?