## 3rd harmonic in generator current energizing a transformer

## 3rd harmonic in generator current energizing a transformer

(OP)

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

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

## RE: 3rd harmonic in generator current energizing a transformer

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

www.cvoes.com

## RE: 3rd harmonic in generator current energizing a transformer

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.

## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

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!

## RE: 3rd harmonic in generator current energizing a transformer

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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## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

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.

## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

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.

## RE: 3rd harmonic in generator current energizing a transformer

notbe zero-sequence.## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

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

## RE: 3rd harmonic in generator current energizing a transformer

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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## RE: 3rd harmonic in generator current energizing a transformer

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## RE: 3rd harmonic in generator current energizing a transformer

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## RE: 3rd harmonic in generator current energizing a transformer

The offset I talk about is the negative part that appears in the current waveform, which it supose to be zero.

electicpete, could you, please, explain that offset?

Regards,

Herivelto

## RE: 3rd harmonic in generator current energizing a transformer

The answer to that question has to do with angle of voltage at time of closing as was demonstrated for simple inductive circuit.

I would be glad to elaborate on that, but I'm not sure I'm answering the question you asked....

Which current waveform (posted what date)?

I didn't see any where the negative is larger than the positive. (where?)

Why would part of the waveform be zero?

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## RE: 3rd harmonic in generator current energizing a transformer

Thank you very much for your interest. I think this phenomenon is not so trivial.

I am not talk about "components" but about the Phase X current waveform itself posted on 19 April 10 12:52 by jghrist. In that waveform, a typical transformer inrush current, we can see a negative part which does not appear normally in computer simulations.

Best regards,

Herivelto Bronzeado

## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

My question to you is why would you expect it to look differently? It is not a hard matter to construct the curve yourself by mentally integrating (assuming you start with simple model... my preference is to start with simple models... do you think something is missing from simple R/L model that would affect the results?).

My suspicion is that you may be used to viewing transients where the positive part goes much higher so the plot scale gets compressed and the negative portion of the cycle is hard to see.

By the way, you can tweak the parameters in the spreadhseet and re-run the simulation if you'd like.... I think the instructions are self-explanatory.

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## RE: 3rd harmonic in generator current energizing a transformer

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## RE: 3rd harmonic in generator current energizing a transformer

Here is a plot that closes at voltage zero crossing which gives max offset. I also extended the plot range to steady state.

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## RE: 3rd harmonic in generator current energizing a transformer

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## RE: 3rd harmonic in generator current energizing a transformer

1. Draw 3 separate horizontal lines, then 3 waveforms 120deg apart.

2. Now draw in a 3rd harminic for each one, starting a 0 degress for each one.

3. Now compare all of your 3rd harmonics. See how they are all in phase? They can't all flow into the neutral without current flowing in the neutral.

## RE: 3rd harmonic in generator current energizing a transformer

electricpete, your your simulation looks good. However, the jghrist's current waveform has a flat "zero" offset. I am sending attached another inrush current waveform that shows the same behaviour. The question is why this offset occurs? Please, explain physically, if possible.

Regards,

Herivelto Bronzeado

## RE: 3rd harmonic in generator current energizing a transformer

As I said, my guess is that this offset may be caused by the an offset magnetizing of the core during the transformer inrush.

In a three-phase transformer with three limbed core, this phenomenon can beseen in the neutral current, indicating that this should be caused by zero sequence magnetic flux (induction), which path goes outside the core.

Regards,

H. Bronzeado

## RE: 3rd harmonic in generator current energizing a transformer

In your simulation, the transformer seems to be over-excited in the steady-state.

Regards,

H. Bronzeado

## RE: 3rd harmonic in generator current energizing a transformer

As load increases the current would look more sinusoidal due to:

1 - exciting branch voltage decreases due to voltage drop across leakage reactance. Therefore not as much saturation effects

2 - In addition to magnetizing current we now have load component which is shifted in phase relative to magnetizing component and will have less distortion.

At least that's my thought. It's been 10 years since I've looked at transformer waveforms.

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## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

## RE: 3rd harmonic in generator current energizing a transformer

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