When we study crawling effect or any such systems that deal with harmonics, we eliminate even order harmonics which cancel out. We have mathematical proofs for that. But how can we understand that physically?
f you have differences between the negative and the positive halves of a waveform, then you may have even order harmonics. A particular case of that is when you a dc component (e.g. "0" is even in this case).
From my point of view, the best way to check the harmonic cancelation is through Fourier analysis. Most of the waveforms in power system have half-wave symmetry, thus even harmonic are not present (and DC components, as mentioned by Prof. Cardenas). Obviously in real applications these components are present, but with small magnitudes compared with odd harmonics, so they are neglectable. Some real examples are: saturated transformers (producing asymmetric waveforms) or DC components generated by a system fault that flows into the generator, thus producing even harmonics. Physically, any asymmetry or DC filtration in a sinusoidal waveform can produce even harmonics.
I agree with Mr Franco Chiarella since harmonics in power systems have several sources. Ocasionally, some of them contraposes to each other and physically they look like not been present in this system. This fact is mathematically predicted by a Fourier analysis. Most of the times, the net result is negligible.
depend of my knowledge the spectral analysis of high order harmonics has ignored energy
In Half-Wave Symmetry, we have G(t ± T/2) = -G(t) ' G(t) instantaneous current or voltage', then the corresponding Fourier series has no even harmonics,
Fourier coefficients ak and bk can be found by integrating over any half-period and doubling the results, Half-wave symmetry is common in power systems.
The book Transients in Electrical Systems from J. C. Das or similar book may help you.
Everything fine but even harmonics exist cannot be neglected. EMC standards set stringent limits to their emission and specific compatibiity levels apply. Some equipment, say AC arc- furnaces inherently produce large current of even order. Other equipment produceven even harmonic disturbance in transient condition only and the major concern is related to the occurenceof resonce conditions only. Unfortunately the quantitative evaluation of the amplitude of even harmonics (and sub-harmonics) is often rather uncertain since they depends on unwanted asymmetries
Hi. Even harmonics must not be ignored because they exist and they are responsible for physical impacts specially in DC converters (i.e electrolytic process) or arc furnaces (described Mr Santagostino). From my point of view, even harmonics must be considered or neglected on a functionality basis. For induction motors (your case) normally even harmonics do not have significative effects on torque due even harmonics are not common over industrial applications. However, if your scope or environment could include even harmonics then you will have to include them into your analysis. If it is applicable, follow the previous suggestions made by participants.
Dear Raajeshwar Elangovan,
Please reefer the attachment which derives the amplitude of each harmonic component, you can see that the amplitude becomes Zero for all even order.
you can also reefer the following link to understand the math behind it.
https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series/v/ee-fourier-series-intro
Thanks and Regards
Vadhiraj
Really its represent the noise and vebration of the machine, this is physically meaning.
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