3rd harmonic in generator current energizing a transformer 5

[stason]

Hello,

I am performing some simulations in PowerFactory where I energize a transformer (13 MVA, 57/10,5 kV, YNd11) on the LV side (delta side) from a 7 MVA synchronous generator (with the star point solidly grounded).

The inrush current causes 2nd and 3rd harmonics to appear in the generator's currents.

If I look at the simulated zero-seqence current of the generator, it equals zero. I figured this could not be true, since the star point of the gen is connected, which would allow the 3rd harmonic currents to flow in the gen's neutral, which they also do. Is this correct? And if it does flow in the neutral, might the ground current relay trip?

Besides, will the 2nd harmonic current in the generator make the differential relay think it could be an internal fault?

Thank you in advance!
Regards,
stason

 

[dpc]

Very few 7 MVA generators have solidly grounded neutrals.

Transformer inrush contains a lot of 2nd harmonics.

Differential relays used with transformers have harmonic restraint to prevent false operation on inrush.

I would have low expectations of any simulation software being capable of accurately modeling transformer inrush. It's a very complex event.

David Castor

http://www.cvoes.com

 

[jghrist]

Differential relays use 2nd harmonic currents to inhibit tripping during inrush. Third harmonic currents, if they are balanced, are zero-sequence and will not flow because of the delta transformer winding. During inrush, however, the third harmonic currents are not balanced. Third harmonic currents are present in the line during inrush even with a delta winding, and they sum to zero.

See the attached graphs which were developed from a Fourier analysis of inrush current in the primary feed to a 100-24.9 kV, 30 MVA delta-wye transformer. One shows Phase X raw waveform with harmonic RMS components. One shows the 3rd harmonic RMS in all phases.

 

[jghrist]

Here's the graph with Phase X.

 

[stason]

THank you for your responses.

jghrist, why do the 3rd harmonic currents sum to zero if they are unbalanced?

The question, however, was primarily: will there be a current flow in the generator's neutral due to the 3rd harmonic currents, which would cause the ground current relay at the generator to trip (when the pick-up value is reached)?

And if yes, what is the return path of this current? It can't return to the delta winding of the transformer, right? Or will it return to the HV wye-winding of the transformer, which is solidly grounded?

Concerning the differential relay, I meant the one for the gen's stator differential protection. But I guess I was thinking wrong. The 2nd harmonic currents are negative-sequence ones and they actually appear at the both sides of the stator of same amplitude and they cancel each other at the neutral, since they are 120 degrees apart. Unless they are unbalanced and then have a third harmonic content. So I guess the stator differential protection relay should not react to the negative-sequence currents.

Thanks!

 

[electricpete]

jghrist, why do the 3rd harmonic currents sum to zero if they are unbalanced?

If 3rd harmonic components are balanced they are zero sequence and do not sum to zero. Therefore only unbalanced 3rd harmonic component can sum to 0.

Balanced means there is a time shift between phases which corresponds to 120 degrees of fundamental. That same time shift corrresponds to 240 degrees of 2nd harmonic and 360 degrees of 3rd harmonic. So balanced 3rd harmonic is always zero sequence and can't flow where zero sequence can't.

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[jghrist]

The question, however, was primarily: will there be a current flow in the generator's neutral due to the 3rd harmonic currents, which would cause the ground current relay at the generator to trip (when the pick-up value is reached)?

And if yes, what is the return path of this current? It can't return to the delta winding of the transformer, right? Or will it return to the HV wye-winding of the transformer, which is solidly grounded?

There will not be current flow in the generator neutral. As you say, there is no return path because of the delta winding.

Concerning the differential relay, I meant the one for the gen's stator differential protection.

The transformer inrush current is seen by both inputs of the generator differential so it will not cause a trip.

 

[davidbeach]

There will not be current flow in the generator neutral. As you say, there is no return path because of the delta winding.

But, but, but...

There will be 3rd harmonic in the neutral. That's the whole basis of the 3rd harmonic 100% stator ground fault detection. No, it won't flow beyond the delta winding, true, but it is flowing in all the capacitance, both deliberate and parasitic, in the circuit between the neutral and the delta winding.

 

[stason]

Thanks again, guys.

What I don't understand though is that the 3rd harmonic is present in gen's phase currents during the inrush, although the transformer is energized at the delta winding. How can the 3rd harmonic current flow then?

davidbeach, the parasitic capacitance is connected in parallel to the system, which would enable the flow of the current through the neutral, yes. But this current still must return to the transformer, which caused it. Right?

Regards

 

[davidbeach]

Generators produce 3rd harmonic. Generator -> out through capacitances to ground -> up the neutral to the generator. Complete circuit.

 

[slavag]

Hi.
Please take in account. Standard generator diff protection, 87G is not include 2-nd harmonic detector/blocking.

What Dvaid saied:
Generators produce 3rd harmonic. Generator -> out through capacitances to ground -> up the neutral to the generator. Complete circuit

But isnt influence on the diff protection.

Best Regards.
Slava

 

[stason]

Hmmm, the weird thing is that the 3rd harmonic also appears in another generator, whose star point is not grounded at all.

 

[AMBMI]

Stason, please could you attach your PF .dz file with your project? I hope that your company policy could allow that.
I have some experience with Power Factory and I would like to take a look. Moreover please consider that the PF differential relay models can include 2nd harmonic measurement and differential blocking (obviously if it's present in the "real" relay we are mocking up). It could be very nice to simulate such generator behavior and see if the relay is blocked or not.

 

[jghrist]

What I don't understand though is that the 3rd harmonic is present in gen's phase currents during the inrush, although the transformer is energized at the delta winding. How can the 3rd harmonic current flow then?

The inrush 3rd harmonic is not balanced, so it is not necessarily zero-sequence. Because of the delta winding, no zero-sequence current can flow; this necessitates that the 3rd harmonic current not be zero-sequence.

 

[stason]

AMBMI, I'd like that too, but unfortunately I am not allowed to post it. One can easily build one though with some transformer that has saturation and maybe even a standard generator out of the library.

jghrist, that makes sense. I think I will go with that. Thanks.

 

[Bronzeado]

Hi folks,

jghrist is correct when says that 3rd harmonic is not a zero seguence component.
By definition, zero sequence components in a three-phase system must have the same magnitude, phase and, of course, frequence.
Any harmonic components (in a thre-phase system) that have equal magnitude, phase and frequence are, by definition, zero sequence. The 3rd harmonic (in three-phase system), in general, are, particularly, of sequence zero.
For example, a 3rd harmonic generated in just one phase of a three-phase circuit IS NOT A ZERO SEQUENCE COMPONENT and can flow with or without delta conections.

Now, I wonder if somebody could explain why there is a negative offset appears in the current waveform sent by jghrist.

Regrads,

H. Bronzeado

 

[stason]

Bronzeado,

I think the current goes below zero once every cycle as the voltage driving the transformer goes negative.

 

[Bronzeado]

stason,

My guess (only gues!) is that something happens in the magnetic core during inrush, magnetizing it "homopolarly" (sorry for the word I think does not exist in English). It may occur due to the zero sequence magnetic flux, which path leaks from the yokes (say superior yokes), goes into the transformer tank and back to the yokes (in this case, inferior ones).

I wonder if the experts on transformer in this forun could give us a good reason for that phenomena which is not generally seen in simulations.

Regards,

Herivelto Bronzeado

 

[electricpete]

Here's my explanation why there is a dc offset in transformer inrush:

Look at one phase fed by voltage v(t) = cos(w*t + theta0)

simplify it to a linear model and neglect resistance
v = L di/dt (where L is magnetizing inducatance)
i = 1/L * int(v(t) dtau from tau=0 to t

i = 1/L * int( cos(w*tau + theta0) dtau + i(0) where i(0) = 0

i = [(1/L) * (cos(w*tau + theta0) ] evaluated at tau =t minus same thing at tau = 0.

i = [(1/L) * (cos(w*tau + theta0) ] evaluated at tau =t minus same thing at tau = 0.

i = [(1/L) * (cos(w*t + theta0) ] - [(1/L) * (cos(0*t + theta0) ]

i = [(1/L) * (cos(w*t + theta0) ] - [(1/L) * (cos(0*0 + theta0) ]

i = [(1/L) * (cos(w*t + theta0) ] - [(1/L) * (cos(theta0) ]

i = [(1/L) * (cos(w*t + theta0) ] + Idc
where Idc = - [(1/L) * (cos(theta0) ] is a dc component.

You can see there is a dc component which varies depending on theta0... if theta0=+/- 90 degree (close at max or min of voltage which is the “natural current zero”, then there is no dc offset, otherwise there is a dc offset).

If you added back in the effects of resistance the dc component decays away.

If you add the iron non-linearity, the current is highly non-sinusoidal... the dc component causes much higher saturation current peak on one side of zero than the other.

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[electricpete]

Small correction in bold

v = L di/dt (where L is magnetizing inducatance)
i = 1/L * int(v(t) dtau from tau=0 to t

i = 1/L * int( cos(w*tau + theta0) dtau + i(0) where i(0) = 0

i = [(1/L) * (SIN(w*tau + theta0) ] evaluated at tau =t minus same thing at tau = 0.

i = [(1/L) * (SIN(w*tau + theta0) ] evaluated at tau =t minus same thing at tau = 0.

i = [(1/L) * (SIN(w*t + theta0) ] - [(1/L) * (SIN(0*t + theta0) ]

i = [(1/L) * (SIN(w*t + theta0) ] - [(1/L) * (SIN(0*0 + theta0) ]

i = [(1/L) * (SIN(w*t + theta0) ] - [(1/L) * (SIN(theta0) ]

i = [(1/L) * (SIN(w*t + theta0) ] + Idc
where Idc = - [(1/L) * (SIN(theta0) ] is a dc component.

You can see there is a dc component which varies depending on theta0... if theta0= 0 degree (close at max or min of voltage which is the "natural current zero", then there is no dc offset, otherwise there is a dc offset).

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