motor harmonic current

[2dye4]

I have a motor to evaluate that draws significant
third harmonic current. It is a low cost universal motor
that is placed in a appliance. Does harmonic current
make the windings heat as fast as regular current?
I don't think so because the frequency is different.
Am I right or left

2dye4

 

[CJFlatters]

Electripete

Whilst both of my previous submissions refer to third harmonics (which are zero sequence) there is no reference or implication of three phase. As the original entry referred to a "cheap and nasty" motor I had rather assumed it to be single phase.

The 3H (or any other triplen harmonic for that matter) will have an I2R heating effect on the winding but will not produce any torque effects as it is zero sequence.

The phase sequence of harmonics basically follow on as follows.

f 2 3 4 5 6 7 8 9 10 11 12
+ - 0 + - 0 + - 0 + - 0



_______________________________________
Regards -

Colin J Flatters
Consulting Engineer & Project Manager

 

[electricpete]

<Apr 4, 2004>...A zero phase sequence (third harmonic) current cannot produce a torque - It will only cause I2R losses in the windings and eddy current losses in the frame.

Positive sequence harmonics will produce accelerating torques, negative sequence harmonics will produce deccelerating torques (contra-rotating),

I think it is clear the use of the use of the terms "positive sequence", "negative sequence" and "zero sequence" implies three phase. Do you disagree?

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[electricpete]

You wrote:
f 2 3 4 5 6 7 8 9 10 11 12
+ - 0 + - 0 + - 0 + - 0

This is for 3-phase system.
Let the fundamental be I1(t) = cos(w*t + k*delta) where
delta = (2/3)*Pi/w (120 degrees of fundamental)
k = 0, 1, 2 for phase A, B, C (assuming A,B,C rotation)

The hth harmonic has frequency h*w but still has the same time shift k*delta independent of h. That time shift corresponds to a bigger phase shift for higher harmonics. ie a time interval of 120 degrees fundamental corresponds to 240 degrees 2nd harmonic, 360 degrees 3rd harmonic, etc.

Ih(t) = cos(h*w*t + k*delta)
Ih(t) = cos(h*w*t + k*(2/3)*Pi/w)
Ih(t) = cos(h*w*t + h*k*(2/3)*Pi/(w*h))

Phase relationship between the three fundamental currents is (0,120, 240) (positive sequence)

Phase relationship between the three 2nd harmonic currents is (0,240, 480) = (0,-120,-240) (negative sequence)

Phase relationship between the three 3nd harmonic currents is (0,360, 720) = (0,0,0) (zero sequence)

Phase relationship between the three 4th harmonic currents is (0,480, 960) = (0,120,240) (positive sequence)

Phase relationship between the three 5th harmonic currents is (0,600, 1200) = (0,-120,-240)= (negative sequence)

I fail to see how we could ever hope to derive any comparable relationship for single phase.

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[electricpete]

I made an error in the symbols my proof. Please let me try it again.

Let the fundamental be
I1(t) = cos(w*(t+k*delta)) = cos(w*t+w*k*delta)
where
delta = (2/3)*Pi/w
delta represents a time shift equivalent to 120 degrees of fundamental
k = 0, 1, 2 for phase A, B, C (assuming A,B,C rotation)

The hth harmonic has frequency h*w but still has the same time shift k*delta independent of h. That time shift corresponds to a bigger phase shift for higher harmonics. ie a time interval of 120 degrees fundamental corresponds to 240 degrees 2nd harmonic, 360 degrees 3rd harmonic, etc.

Ih(t) = cos(h*w*(t+k*delta))
Ih(t) = cos(h*w*(t + k*(2/3)*Pi/w))
Ih(t) = cos(h*w*t + h*w*k*(2/3)*Pi/(w*h))

Ih(t) has a phase shift of h*k*(2/3)*Pi i.e. h * 120 degrees separation between hth haromic of phases A, B, C.

Phase relationship between the three fundamental currents is (0,120, 240) (positive sequence)

Phase relationship between the three 2nd harmonic currents is (0,240, 480) = (0,-120,-240) (negative sequence)

Phase relationship between the three 3nd harmonic currents is (0,360, 720) = (0,0,0) (zero sequence)

Phase relationship between the three 4th harmonic currents is (0,480, 960) = (0,120,240) (positive sequence)

Phase relationship between the three 5th harmonic currents is (0,600, 1200) = (0,-120,-240)= (negative sequence)

Sorry - I didn't mean to belabor the point. Just wanted to correct my slipup. btw welcome to the forum cjflatters. I enjoy your posts. Look forward to hearing more.

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[CJFlatters]

Oops - thanks electricpete

Its a fair cop - so used to thinking three phase heavy power that i missed the obvious (the preceding comments would of course apply to 3 phase machines).

_______________________________________
Regards -

Colin J Flatters
Consulting Engineer & Project Manager

 

[electricpete]

I wrote:
"Ih(t) = cos(h*w*(t+k*delta))
Ih(t) = cos(h*w*(t + k*(2/3)*Pi/w))
Ih(t) = cos(h*w*t + h*w*k*(2/3)*Pi/(w*h))"

The last equation is incorrect: It should not have any "h" in the denominator as was pointed out by jbartos.

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[jbartos]

Suggestion: The above posted equations might have shown current magnitudes and the k index to be correct and practically applicable, namely:
Ih(t) = cos(h*(w*t + k*(2/3)*Pi))
Ih(t) = cos(h*w*t + h*k*(2/3)*Pi)"
might be:
Ihk(t) = Ihk,max x cos(h*(w*t + k*(2/3)*Pi))
Ihk(t) = Ihk,max x cos(h*w*t + h*k*(2/3)*Pi)

 

[peebee]

Don't most universal motors have brushes? I'd think you'd get noise on every harmonic, including the third. They sure make enough audible noise, and they sure screw up radio transmission, they seem to be rather "broadband" transmitters.

2dye4 -- back to your original question -- yes, harmonic currents will cause the windings to heat above and beyond what you'd get from the fundemental current alone. As mentioned above, the heating will be based on I-squared R losses, where I is the rms current of the fundemental plus all harmonics.

 

[peebee]

Oh yeah -- regarding zero sequence --

Single-phase systems have no directionality. They're more like "up-down" rather than "clockwise vs. counterclockwise" (which leads to things like shaded-pole motors, etc). So "sequence" is meaningless.

That said, this motor could certainly be fed from a 3-phase supply. And if it was, its 3rd-harmonic currents would contribute to the zero-sequence currents on that system.

So, you're both right! It's win-win.

 

[jbartos]

Suggestion to peebee (Electrical) May 14, 2004 marked ///\\Oh yeah -- regarding zero sequence --

That said, this motor could certainly be fed from a 3-phase supply. And if it was, its 3rd-harmonic currents would contribute to the zero-sequence currents on that system.
///Not only third harmonics, the fundamental and other harmonics too, since the single phase motor creates an unbalanced load which in turn creates the zero-sequence current(s).\\