Of Course the inverter causes harmonics (waveform distortion), but even the distortion is balanced, am I right. Is there any unbalance cause ?
it will cause little bit but use LC filter. it should be less than 5% according ti IEEE standard. Attached Link
Dear SALAH ELDEEN,
if the resulting waveforms from the inverter is pure sinusoidal, then the resulting three phase source will be balanced provided that the conditions mentioned by you is satisfied. From the principle point of view, inclusion of waveform distortion leading to formation of equal harmonics in the three phases will cause imbalance since the harmonics having the same frequency mayl not phase shifted from each other by 120 degrees. therefore the harmonic must be limited as Syed hinted. Complete analysis is given below in my second post.
Wish you success.
Here i assume that the distorted waveforms has the same delay as the undistorted sine waves of the three phase which is really experimentally observed. IT is also assumed that the phase sequence will be rst. Perhaps a more exact proof is that for any exiting waveform is to translate the phase shift phi into time delay of phi/w where w is the fundamental frequency of the distorted waveform. then one analyse the waveform by Fourier series. Therefore the nth harmonics can be expressed by cos (nw(t- phi/w)) = cos(nwt- n phi) for certain specific phase phi.
Then for the r phase where phi=0, then s phase harmonics will also have zero phase.
THE 2pi/3 s phase will be 2n pi/3
The 4pi/3 t phase will be 4n pi/3
Case studies:
second harmonics n=2
The s phase will be 4pi/3=240 degrees,
The t phase will be 480 degrees= 1 20,
which is balanced
n=3
The s phase will be 6 pi/3 =2 pi which will be aligned on the r phase.
The t phase will be 4 pi which is aligned also on the r phase
which is unbalanced
n=4
the s phase will be the phase will be 120 degree,
the t phase will be 240 degrees.
which is balanced
We can see that the odd harmonics will not be balanced while the even harmonics will be balanced.
i would like to thank shady for motivating me to try a rigorous answer.
Please review my answer and comment.
Thank you
Great Great Great thanks Prof. Abdelhalim and Dr. Shady. Your contributions are highly appreciated. The derivations are absolutely fantastic and the calculations you have drawn have touched the point and practically answered the question Prof. Abdelhalim.
In a PV connected to a grid, the PV is feeding a distribution system through a 2.6/6.6 kV transformer. If all of the symmetrical and unsymmetrical faults are created (one by one) at the output of the inverter (2.6 kV), is it possible to (bearing in mind all possible assumptions such as a PV with less or no controls) read voltages at the 6.6 kV side that are higher or even equal to the rated 6.6 kV? I think that the faulted phase voltage is supposed to be less. Can the amount of harmonics reach a degree that can cause faulted and the other phase(s) voltage be more than the rated.
dear Salah Eldeen,
To solve a problem one has to define it precisely. Your question if i understood it is two folds, namely, the effect of faults on the output voltage of the inverter and the effect of the harmonic content on the the output voltage of the transformer.
The effect of faults needs detailed circuit analysis. However, the effect of harmonics can be determined if the frequency response of the transformer is known. Power transformers are made such that they have a narrow band pass frequency response. since the harmonics have frequencies of multiple the fundamental frequency, then they will be normally attenuated by passing through transformer especially the higher order harmonics. This behavior of the transformer is due to the iron losses.
So, it is expected that the harmonic content in the output of the transformer will be less compared to input and consequently the the output voltage will be less than the r ated value amusing totally harmonics free input.
hope this shed some light on the answer of your question.
Eid Saeed.
Great thanks dears all. Your contributions are truly helpful.
Eid Saeed to you all.
If the harmonics are effectively removed from the output of the inverter by any method, the output voltages will be balance but still there will be small unbalance in the the input side due to high frequency harmonic reflection.
1. control voltage PV side, boost or buck, then the DC / AC.
2 transformer turns ratio adjustment.
Hi dear;
The on grid inverter is grid imposed so cannot unbalance grid.
The important issue is dc injection to grid because saturated transformer.
best regard
salehi
Hi, Dear Gasim
I agree with Professor Abdelhalim Zekry .
kind regards