Unbalanced Motor Voltage

[mityeltu]

My Question is based on ANSI C50.41 which read in part:

13.4.1 Effect on Performance - General
The effect of unbalanced voltages on polyphase induction motors is equivalent to the introduction of a "negative sequence voltage" having a rotation opposite to that occurring with balanced voltages. This negative-sequence voltage produces an air gap flux rotating against the rotation of the rotor, tending to produce high currents. A small negative-sequence voltage may produce current in the windings considerably in excess of those present under balanced voltage conditions.


My question is this, how can I see this mathematically? I'm drawing a complete blank on what to do to visualize what this is telling me.

 

[dkarst]

I'm sure an expert may drop by later but I'll give it a try. In the study of symmetrical components, the positive sequence voltages are the "normal" abc rotation phasors we normally think of and the negative sequence are counter rotating or acb (zero sequence are where all the phasors are rotating but rather than being displaced by 120 degrees, they are coincident). This positive sequence voltage (normal) when applied produces a rotating field and the current is very roughly proportional to slip, ie, when slip is large at standstill or under heavy load, lots of current flows; when running at light load, slip is small and current is small(er).

Now if in addition, we could hook a source with negative sequence up (which is the claim here with unbalanced voltages), it would produce a field counterrotating to the one set up with our positive (normal) sequence. Drawing on the previous analogy, the slip (or difference between the rotor going fast clockwise for example and this new rotating field (CCW for example) would give us a very high slip and hence high current. I know this explanation may be a little loose but hoping it will help.

 

[mityeltu]

In the study of symmetrical components ....

I've never managed a decent grasp of symmetrical components (not from a lack of trying), which probably isn't helping me any here.

That helped, but let me see if I can cement it into this block of a head I have.

C50.41 is dealing with induction machines. So, since this thing works on the principle of induction, and inductors work to COUNTER changes in current, then, if I see this correctly,…..

The BALANCED source in the stator hits all the poles and induces a balanced current in the rotor. Now, If I change the voltage on one phase of my stator, as it hits each of the phases, the flux has changed and hence will induce a voltage on the rotor to try to counter that change. Because the change is happening very quickly (large di/dt), the resulting induced current will be large.

Am I on the right track, or did I just make a bigger block for my head?

 

[dkarst]

... the positive sequence voltages are the "normal" abc rotation phasors we normally think of and the negative sequence are counter rotating or acb (zero sequence are where all the phasors are rotating but rather than being displaced by 120 degrees...

In my haste I was playing a little fast and loose in terminology... the negative sequence phasors are rotating CCW as all phasors do but the phase sequence is acb vs. the phase sequence of abc for positive sequence.

Am I on the right track, or did I just make a bigger block for my head?

I'm not sure I'm following your inductance argument so I'll let the next person step up.

I have not read this but when looking for a reference for sym components I ran across this article. http://helios.acomp.usf.edu/~fehr/TE-2006-000213-draft.pdf