# Help me understand zero sequence currents

Hey,

I have some questions regarding zero sequence current flow in a multi phase system I was hoping some kind soul could help me with.

Imagine the following scenario illustrated in my bad paint drawing below:
A delta-wye(n) transformer are supplying a non linear load producing 3rd harmonics. These harmonics are being added and flow back in the neutral due to being in phase with each other.

Ok, fine so far.

Then the currents on the secondary side are being reflected on the primary delta side of the transformer, and from what I've read in this forum and literature they circulate inside the delta triangle.

Why do they circulate inside the delta, ok, lets see. Lets say a zero sequence current is flowing from a-c, how does it get back to a? Well, it could go a -> c -> b and back to a, and it could go a -> c -> C -> A and back to a. 1. So could one confirm if my way of thinking is correct, so I know if I fully understand this or not.
The reason the current goes a-c-b-a, is because it offers much lower impedance then a-c-C-A-a. The path a-c-b-a is essentially just the winding resistance of the transformer, while the path a-c-C-A-a is several miles of power lines + the internal impedance of the generator or supply transformer.

This is basically just based on threads posted here on the forum, and I made this post to see if someone could point to me if I understand this or not.

2. Also one final thing, is my way of drawing the schematic above correct? I mean, I've not added any voltage source in the wye connection to the left, the reason is that I assumed that there is no supply of zero sequence voltage.

-Kraake

anorlunda
Staff Emeritus
You are making it very hard on yourself trying to do harmonics and unbalanced at the same time. Why not take one at a time?

Remember that positive/negative/zero sequence symmetrical components aren't really meant to be considered separately. They are an alternative way to describe unbalanced three-phase states. When trying to visualize what happens physically, remember that it is still a three phase system, primarily positive sequence, that has some unbalance.

• berkeman
Ok, so I think I might have misunderstood something. If we think of a balanced system with 3rd harmonics, dont we have zero sequence components?

anorlunda
Staff Emeritus
Ok, so I think I might have misunderstood something. If we think of a balanced system with 3rd harmonics, dont we have zero sequence components?

Is this what you have in mind? Why do 3rd harmonic currents overload neutral conductors?

I may have misjudged your question. I thought that you were studying power systems, and that harmonics were a topic, and unbalanced 3-phase was a topic. Now is sounds like you have something more specific in mind.

I understand why 3rd harmonics are causing problems for the neutral conductor, because they are all in phase (i.e. zero sequence currents?).

My main questions, I suppose, was (based on the paint drawing):
The reason the current goes a-c-b-a, is because it offers much lower impedance then a-c-C-A-a. The path a-c-b-a is essentially just the winding resistance of the transformer, while the path a-c-C-A-a is several miles of power lines + the internal impedance of the generator or supply transformer.

Essentially, the zero sequence currents have more then one path to form a closed loop (if you're looking at my drawing). But the reason they circulate inside the delta connection is that this path offers way less impedance, correct?

Bump

jim hardy
Gold Member
Dearly Missed
If there's no sequence, are they in phase ? Question not assertion.

In my opinion, if we are talking alternative current about, the "sense of circulation" it could not be actual since in a half of the cycle the current circulates in one sense and in the next half inversely.

The "sense of circulation" it is symbolic only in order to facilitate the calculation.

Second, if it is not unbalance then sum of phase currents is zero and no zero component exist.

The current will circulate always in the closed loops as you already said.

I agree with anorlunda, the actual current break down into symmetrical components is only in order to facilitate the calculation.

Let's take-for instance- the case of single-phase to neutral [or ground] short-circuit. The short-circuit current will flow through faulted phase and grounding conductor and no current in the other phase.

If we calculate the symmetrical components and use only Io each phase gets 1/3 of this current.

It will be wrong to use only one type of symmetrical component.

Id=(IR+a^2*IY+a*IB)/3=IR/3 [short-circuit between R and N; IY=0;IB=0.] a=exp(j2*pi()/3)

Ii=(IR+a*IY+a^2*IB)/3=IR/3

Io=(IR+IY+IB)/3=IR/3

Recalculating the actual current I1=3*IR/3=IR and IY=IB=0 [1+a+a^2]=0

So in this case only phase R -low voltage-gets actually the current and by induction phenomenon high-voltage corresponding winding [R-Y] will get the current and this will run through all available closed loops.

If you look at my drawing, the wye side of the transformer is connected to 3 balanced loads each injecting 3rd harmonic current. When this current (3rd harmonics)
reaches the transformer, it gets magnetically coupled over to the primary delta side.

If we think that the supply is wye connected, now the 3rd harmonic have many closed loop to circulate, right? For example inside the delta loop, or in the lines and back

But the reason it "circulates" inside the delta is because this closed loop offer way less impedance than the path back to the source and back to the delta connection?

I have problem formulating me in a good way I feel.

But basically my question is: Why the 3rd harmonics circulate inside the delta winding, and do not flow further upstream the power system?

anorlunda
Staff Emeritus
My consulting engineer friend always replies to such questions with, "send me a photo of the transformer nameplate." He does not trust clients to accurately describe what they actually have.

• cnh1995
jim hardy
Gold Member
Dearly Missed
But the reason it "circulates" inside the delta is because this closed loop offer way less impedance than the path back to the source and back to the delta connection?

Draw them as sinewaves on a piece of paper. You'll see 3rd are in phase with one another.
So the delta winding connects three in phase voltages in series aiding
What then limits 3rd harmonic current ?

• cnh1995 and KraakeCrest
The fundamental frequency balanced three-phase currents you can draw them on a phasor diagram at 60 Hz but the third harmonic component you have to draw on a 180 Hz diagram. The third harmonic component is not a symmetric component resulting from breaking down the phase currents at fundamental frequency. That means it is not any connection between third harmonics and
homopolar component [zero component, Io].
In my opinion, if the lv windings are delta connection then the winding reactance is small and most of third harmonic current will flow around.Of course, the source have to be the low voltage supplied premise.
At high voltage the most of harmonics will run through high voltage supply side since the transformer reactance at this side is more elevated than the source side.

• KraakeCrest