Transformer Harmonics and Impedance

[111R]

I have a few questions on transformers:

1) Is there a good explanation out there on why the 2nd and 4th harmonics are common during energization? I assume this is related to saturation of the core due to the point on wave of switching, but it seems like this would only occur on the positive half cycle or negative half cycle depending on the state of flux in the core prior to energization.

2) During overexcitation, the 5th harmonic is commonly seen. Why is this?

3) Why is the actual impedance (ohms) of larger transformers lower than smaller transformers? On a per unit basis, they are sometimes higher, but the actual reactance in ohms is almost always lower. It seems like this would be the opposite since the larger windings need to be further apart and such.

Thanks

 

[waross]

Larger transformers have larger cross section conductors.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[7anoter4]

I agree with waross: the resistance is lesser for larger transformer.
The evacuated heat is outside conductor surface area [Sext] proportional and the losses are conductor cross section area inverse proportional.
Conductor losses are: I^2*ro*length/pi()/d^2*4
The evacuated power =K*Sext*[Tconductor-Tambiant]=K*pi()*d*DT
I^2*ro*length/pi()/d^2*4=K*pi()*d*DT*length
if C=PI()*SQRT(K*DT/ro) then:
I=C*d*sqrt(d) and j[current density]= I/(PI()*d^2/4)=C/sqrt(d).
For smaller d the cooling is better and the needed cross section area is smaller.
So the resistance is more for smaller transformer.
The reactance depends on leakage magnetic flux and this depends on exterior area of the core.
The inside flux increase with the core cross section area and this proportional with the transformer power. The ratio leakage per useful-inside- flux decrease with the core cross section. More power less leakage per 1hp then less reactance per 1hp.
About harmonics see-for instance:
Modeling of Harmonic Sources Magnetic Core Saturation

https://www.calvin.edu/~pribeiro/IEEE/ieee_cd/chapters/pdffiles/c4pdf.pdf

 

[HamburgerHelper]

1. Even harmonics are associated with DC offset. On transformer inrush, depending on where you close in on the waveforms, you will have DC offset as half the wave form is affected by saturation.

2. A lot of odd harmonics are produced due to overexcitation affects being symmetrical. I believe that the 5th harmonic is used for protection since it is the first odd harmonic that is not a triplen harmonic. I think you could have the third harmonic circulate in your windings.

3. It doesn't sound right that the conductor size changes the impedance much on a transformer. On anything large, the impedance of a transformer should be very reactive. I think it has more to do with having fewer turns. I believe with larger cross sectional conductors they use fewer turns to get the same ratio, which they can do with having a larger core - lower core reluctance so less mmf needed. A larger core will then too reduce the amount of stray flux.

 

[prc]

1) The 2nd and 4th harmonics are there only in inrush current and not in normal excitation current. This is only due to the initial peaking shift towards either positive or negative side during inrush. Remember harmonic resolution is only a way for us to analyze the non sinusoidal wave in to a combination of sinusoidal waves of varying frequency.
2) During normal excitation and over excitation, the waves are symmetrical on positive and negative sides, involving only odd harmonics. Maximum magnitude(apart from fundamental) on both occasions is 5th harmonic and hence used for over excitation detection.
3) pu impedance is within a narrow band (8-18 % ) for medium and large transformers.
impedance pu= (phase current x Z in ohms)/ phase voltage. You can see that when I goes up (ie MVA goes up), for the same voltage Z comes down for the same pu of impedance.
Z consists of R =jX where R (depending on winding resistance) and X on leakage reactance. R is negligibly small for large transformers and Z depends solely on X (pu) . X depends on not core area etc, but depends on the leakage flux path cross section (ie annual area between HV &LV winding) plus square of no of turns(which comes down with increase in MVA) and inversely to height of winding.
To give a feel of these values for a typical 100 MVA 220 kV 3 phase 2 winding transformer with 12 % impedance, Z = 58.09 ohms/phase R = 1.45 ohms/phase X = 58.07 Ohms/phase,all referred to 220 kV side. The magnetization R and Z will be 968 kilo ohms and 161 kilo ohms( based on no-load losses and excitation current)

 

[HamburgerHelper]

2. This paper talks about the 3rd harmonic being the most prominent during over excitation but will get filtered out for delta connections and the fifth is reliable anyways.

https://selinc.cachefly.net/assets/...armonic_KB_20061019_Web.pdf?v=20160503-160741