HARMANIC EFFECT - Is it VECTORIAL ADDITION or ARITHMATHIC ADDITION.?

I guess thats mathematical play. And the phase angle for the certain harmonics just allow the normal addition.

But I am not electrical either and just work with my bottom line.

Adding vectors that are directly time related, ignoring their absolute timing, a possible phase difference between them and its consequences (i.e. partial or absolute adding or canceling) are undetected and that is an error on its own, it's just that this error doesn't always show on adding non time related vectors. S.M.

Adding vectorially will always get you the right answer. In some cases the phases of harmonically related frequencies are aligned, i.e., they "add up in the same direction at the same time". The maximum would then be the sums of the maximums.

First of all, the voltage or current [or magnetic field] contains all the harmonics in a fundamental wave of non-sinusoidal form and are differentiated mathematically [virtually].One could represent each harmonic in a rotating plane [two-dimensional] as phasor. Each plane is rotating with velocity w=2*pi()*freq. Only the harmonics of the same frequency may be represented on the same plane.

In order to facilitate a "vectorial" operation one has to freeze the plane and to state the reference phasor [vector] as angle 0.

Quit shouting. You never learn.

AS much as I admire those who wish to expand their horizon of understanding of other subjects and topics, you seem to have taken a very small bite out of an extremely large pie, and your questions tell me you cannot digest it all.

Quite understandable, even I after 40 years of doing this stuff, I STILL have to refer to text books.

So I would suggest that you go find the IEEE 519 standards, and that will have most of your questions answered. While your questions are good, it would take way to long to answer and teach.

As you are not electrically minded, may I suggest that if you wish to understand the subject matter further, you find a friendly teacher who could explain. It would be totally impossible to coach you via this or any other forum.

In fact as you visited another forum and have questions, did you try and get a clarification from them?

Vector addition facilitates harmonic resultant calculation for any waveform (considers both amplitude and phase angle of all harmonics). Being such, it may be generic but is powerful and covers all wave forms.

A choice of mathematical addition/subtraction is valid for a limited subset where the phases are 0 or 180 degrees or multiples thereof.

Is there need for considering all wave forms - YES! - during abnormal conditions when even the utility wave shape departs from sinusoidal (however small the duration). This is also true for less expensive invertors.

My thoughts are - rather than ferret out amplitudes and phase angles for reasoned shortcuts, confidently use vector calculations for all cases.

Let's start from Euler representation of a complex wave:

A[cos(wt+f)+jsin(wt+f)]=Ae^^j(wt+f)

Ae^j(wt+f)=A.e^jwt.e^jf

If we shall draw on the Cartesian plane the phasor at time t1 and then at time t2 we conclude the phasor moved by angle w.(t2-t1).If we freeze the phasor on the plane and we start instead to rotate the plane with the velocity wt we get the same angle at time t2.

Two phasors of the same frequency could be treated as phase-vectors and operate on it the permissible mathematics: adding, subtraction, multiplication.

If they are of different frequency-different harmonic order-we cannot operate

these on both since they are of different plane velocity.

In conclusion, we may simplify the phasor relation from A.e^jwt.e^jf to A.e^jf only if it is of the same e^jwt.

Following the harmonic decomposition- mathematically, according to Fourier rule-we may represent on the Cartesian plane one-by-one. See:

http://en.wikipedia.org/wiki/Fourier_transform.

Actually, it is quite easy to visualize using simple graph paper.

First draw a sine wave of some power source (50 or 60 Hz however you like).

The 3rd harmonic is 180° out of phase with the primary at the peaks. Consequently, it is working against the primary. The 5th harmonic is in phase at the peak with the primary and the pattern continues. There may or may not be some cancellation of effects due to the magnitude of certain components, but that depends on what is creating the distortion.

All even harmonic multiples are automatically in phase.

Invariably, calculations are aimed to find out something specific. Please provide further details where arithmetic sum of currents was used, so that proper explanation can be provided.
Mean while, please refer to following examples --
In case of AC circuits, RMS (root means square) currents are used in calculations. In case of circuits where all the branch currents have same phase relationship, arithmetic sum of all branch RMS currents will give total current.
However, in case of presence of different harmonics, simple arithmetic sum is not possible.
In case of presence of harmonic currents, RSS (root sum square) is commonly used to cover complete current spectrum.