# Exciting Current harmonics in Transformer

Due to non-linearity of magnetic core of large transformer, Which is excited by pure sinusoidal voltage source, the exciting current isn't perfectly sinusoidal. It can be thought to be composed of pure sinusoidal plus mainly 3rd harmonic component.
But does this current flows in the primary side alone or both side ? If both side, what is its distribution (i.e. Primary / Secondary)

Also, when the transformer primary is driven by pure sinusoidal current source, The core flux don't be pure sinusoidal but will have major 3rd harmonics.
So, this will create non sinusoidal Voltage with major 3rd harmonics, both in the primary and secondary in this case. Isn't it?

berkeman
Mentor
Due to non-linearity of magnetic core of large transformer, Which is excited by pure sinusoidal voltage source, the exciting current isn't perfectly sinusoidal. It can be thought to be composed of pure sinusoidal plus mainly 3rd harmonic component.
But does this current flows in the primary side alone or both side ? If both side, what is its distribution (i.e. Primary / Secondary)

Also, when the transformer primary is driven by pure sinusoidal current source, The core flux don't be pure sinusoidal but will have major 3rd harmonics.
So, this will create non sinusoidal Voltage with major 3rd harmonics, both in the primary and secondary in this case. Isn't it?

Are you referring to AC Mains power transformers (50/60Hz)? Because you don't want to be overdriving a signal transformer into its non-linear area.

The main non-linearity that I'm aware of is the hysteresis curve for mu. Since the value of B depends on the mu as you drive (and overdrive) the core, the B field is shared around the whole core, so yes, it affects both primary and secondary. At the primary side, I think you'll see it more as a modulation of the transformed load impedance.

Are you referring to AC Mains power transformers (50/60Hz)? Because you don't want to be overdriving a signal transformer into its non-linear area.
Yes I am talking about them. No, am not talking about the non-linearity due to saturation due to overdrive, I am talking about inherent non-linearity of H Vs B due to hysteresis. So, when driven by sinusoidal current source, Voltage will have harmonics and when driven by sinusoidal voltage source current will have harmonics.

I just wanted to conform that in both case, the harmonics are present in both primary and secondary or only in primary.

If transformer does not have a load connected, then obviously the harmonic current only flows in the primary.

"So, when driven by sinusoidal current source, voltage will have harmonics" I agree. Also the transformer primary and secondary voltage will have harmonics.

"when driven by sinusoidal voltage", "source current will have harmonics" I agree. Also to a first approximation the primary and secondary voltages will not have harmonics.

"when driven by sinusoidal voltage", "source current will have harmonics" I agree. Also to a first approximation the primary and secondary voltages will not have harmonics.
Everything you said was fine, but there was sloppy wording. Actually I meant like this
"when driven by sinusoidal voltage source", "currents (both Primary and Secondary) will have harmonics"
Do you agree on this too?

(quite interesting to note that the difference is created by a missing comma "...voltage source, currents...")

"when driven by sinusoidal voltage source", "currents (both Primary and Secondary) will have harmonics"

If there is no load on secondary, obviously there will be no current in secondary and so no harmonics in secondary current.

To a first approximation, the voltage on a transformer secondary is the same as the voltage on the transformer primary. So if the voltage on a transformer primary is sinusoidal, then the voltage on the transformer secondary will be sinusoidal. If the voltage on the transformer secondary is sinusoidal, then there will not be any harmonics in the transformer secondary current.
There will be harmonic currents in the transformer primary.

Disclaimer: Transformers are imperfect devices and there will actually be a small amount of harmonics in the transformer secondary current.
The harmonics in the primary current will cause a small voltage drop in the conductors used in the primary. This small voltage drop will cause the transformer primary voltage to be distorted which will cause the secondary voltage to be distorted.

The exciting current only exists in the primary for a single phase xfmr. So the odd order harmonics in the exciting current are confined to the primary alone, regardless of whether or not the secondary is loaded.

With 3 phase units, things are different. The odd order harmonics that are not multiples of 3, i.e. 5th, 7th, 11th, etc., are present only in the primary, regardless of pri-sec winding configuration (wye-delta, delta-delta, etc.), & regardless of loading. But the 3rd harmonic, & higher multiples, i.e. 9th, 15th, etc., will exist in the delta connected secondary if a wye-connected primary does not provide a low impedance path for them.

An example would be a 3 wire wye (open neutral) primary with a delta secondary. The 5th, 7th, 11th, etc. harmonics of the exciting current can & do exist in the primary w/o a neutral connection regardless of secondary loading, since they cancel in phase at the Y neutral point of the xfmr primary. But the 3rd, 9th, etc. harmonics cannot exist on the primary side w/o the neutral of the xfmr connected to the neutral of the generator. These harmonics exist in the delta connected secondary windings, regardless of loading.

One can examine many combinations of primary & secondary winding configurations, as well as tertiaries & multiple secondary configurations. Utility companies have big manuels which detail these harmonic currents per each configuration. Hopefully what I've given you can get you started. Did I help?

Claude

The exciting current only exists in the primary for a single phase xfmr. So the odd order harmonics in the exciting current are confined to the primary alone, regardless of whether or not the secondary is loaded.

With 3 phase units, things are different. The odd order harmonics that are not multiples of 3, i.e. 5th, 7th, 11th, etc., are present only in the primary, regardless of pri-sec winding configuration (wye-delta, delta-delta, etc.), & regardless of loading. But the 3rd harmonic, & higher multiples, i.e. 9th, 15th, etc., will exist in the delta connected secondary if a wye-connected primary does not provide a low impedance path for them.

An example would be a 3 wire wye (open neutral) primary with a delta secondary. The 5th, 7th, 11th, etc. harmonics of the exciting current can & do exist in the primary w/o a neutral connection regardless of secondary loading, since they cancel in phase at the Y neutral point of the xfmr primary. But the 3rd, 9th, etc. harmonics cannot exist on the primary side w/o the neutral of the xfmr connected to the neutral of the generator. These harmonics exist in the delta connected secondary windings, regardless of loading.

One can examine many combinations of primary & secondary winding configurations, as well as tertiaries & multiple secondary configurations. Utility companies have big manuels which detail these harmonic currents per each configuration. Hopefully what I've given you can get you started. Did I help?

Claude
YEAH, you have helped and got me started.
I think in open neutral, Yd connection, since the Y connection doesn't allow for 3rd harmonic current to flow, so we get third harmonic voltage in the primary instead! this voltage will be induced in the secondary winding and will create 3rd harmonic current.

Is this how it works?

YEAH, you have helped and got me started.
I think in open neutral, Yd connection, since the Y connection doesn't allow for 3rd harmonic current to flow, so we get third harmonic voltage in the primary instead! this voltage will be induced in the secondary winding and will create 3rd harmonic current.

Is this how it works?

No, with a 3 wire Y connection (neutral open) on the primary, & a delta connected secondary, the 3rd harmonic of the exciting current is in the delta secondary windings, circulating within the closed path of the delta, without appearing on the line currents or load.

Since the 3rd harmonic current is in the delta secondary, there is no 3rd harmonic voltage on the primary nor the secondary. The core magnetic flux is reasonably free from harmonic distortion, 3rd, 5th, etc. As long as the 3rd harmonic (as well as 9th, 15th, etc.) current flows in either the primary or secondary windings, the core flux as well the the voltages on the primary & secondary will be harmonic-free.

The exception is that of "core type xfmrs", wound on a single 3-legged "E" core. This type can retain harmonic free flux/voltage w/o a neutral connection and w/o a delta. Again, power systems manuals should detail this. Make sense?

CLaude

The exciting current only exists in the primary for a single phase xfmr. So the odd order harmonics in the exciting current are confined to the primary alone, regardless of whether or not the secondary is loaded.

The current transformer is one of single phase transformer types, and effects of magnetizing current in secondary side (protective relays) is one of important terms in electrical protection systems. For similar discussion you can refer to http://electrical-riddles.com/topic.php?lang=en&cat=23&topic=620"

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The current transformer is one of single phase transformer types, and effects of magnetizing current in secondary side (protective relays) is one of important terms in electrical protection systems. For similar discussion you can refer to http://electrical-riddles.com/topic.php?lang=en&cat=23&topic=620"

Sorry, I beg to differ. In a single phase current xfmr, the magnetizing current cannot be in the secondary, & must be in the primary. The following illustrates the reasoning.

If the secondary is open circuited, a dangerous condition which should never be allowed in practice, the secondary voltage rises to a dangerously high value. The flux in the core as well as the primary & secondary voltages cannot exist w/o magnetizing current. The secondary is open, but the primary carries current.

When the secondary is loaded w/ a low resistance value, secondary current results in a magnetic flux which opposes the existing core flux. This is a counter-mmf which reduces the net flux in the core. The amp-turns in the secondary almost cancel that in the primary. The slight unbalance is the magnetizing current needed to provide the core flux.

If the secondary is opened (a dangerous condition), there is no secondary current. Hence the counter-mmf is zero, & all the primary current is unbalanced & becomes magnetizing current. This results in a drastic increase in core flux as well as primary & secondary voltages reaching much higher values, & shock hazard is present.

The magnetizing current in a current xfmr is in the primary winding, never in the secondary winding. Any energy conversion text will affirm the same. The "electrical riddles" site provides some interesting discussions & generally good info. However, every single answer is not subject to peer review. You cannot rely 100% on every answer. Even peer-reviewed textbooks used in the best unis around the world have errors which prompt errata sheets being published. No web site is above reproach.

I would advise you to carefully examine a contrarian viewpoint before rebuking a well established principle. If the magnetizing current in a CT was really in the secondary, every peer-reviewed text would say so. The fact they don't should give you reason to have doubts about a web site that states otherwise. It's just an honest mistake, I'm not dissing the web site. I've posted there, & for the most part it is a pretty good site.

Claude

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If the magnetizing current in a CT was really in the secondary, every peer-reviewed text would say so

Thank you very much my dear friend.

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I am no expert in transformer by any stretch. Claude is the man for that. I just want to put in my 2 cents in the eye of a guitarist. The output transformer is very important. It definitely change the characteristic of the sound by adding harmonics. I notice a very famous brand amplifiers.....Mesa Boogie that made famous by Carlos Santanna which he is still using it. I looked at a few of their amps, the output transformer is very small compare to other brands. I bet they are pushing the core into saturation to generate the desired harmonics.

The output transformer in an electron tube audio amplifier is rather a special case. Here the impedance driving the transformer primary will be relatively high, compared to that nomally seen by a voltage transformer of similar rating used for AC mains distribution. As a result, harmonic content in the audio transformer magnetizing current can have a more appreciable effect on the primary voltage waveform, because of the relatively large voltage which can be developed in the driving impedance. One of the factors adding to the size, weight and cost of tube amplifiers is the need for a large enough output transformers to handle the required power levels, particularly at bass frequencies.

In addition, relatively small levels of harmonics will be significant for audio, because of the way in which they can affect the musical result. That said, the distortion products normally account for only a small percentage of the total power in a good design, when run within its limits. The distortion will naturally increase if the transformer core becomes saturated, possibly contributing to the sound of an amplifier when it is driven hard, as mentioned by the last contributor.

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m.s.j Vs Cabraham, with whom do I go with?

sophiecentaur
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@cabraham
"If the secondary is opened (a dangerous condition), there is no secondary current. Hence the counter-mmf is zero, & all the primary current is unbalanced & becomes magnetizing current. This results in a drastic increase in core flux as well as primary & secondary voltages reaching much higher values, & shock hazard is present."

That's because the transformer is being driven from a valve anode (pretty much a Current Source and not a Voltage Source). This it not what the OP is discussing.

If you think of the secondary induced voltage as being proportional to the rate of change of flux in the core (related to rate of change of Primary Current) then this will consequently include harmonic content (boosted by the fact that the harmonics change at a higher rate. For small loads (i.e. high resistance), the secondary current will also contain harmonics, I reckon.

@cabraham
"If the secondary is opened (a dangerous condition), there is no secondary current. Hence the counter-mmf is zero, & all the primary current is unbalanced & becomes magnetizing current. This results in a drastic increase in core flux as well as primary & secondary voltages reaching much higher values, & shock hazard is present."

That's because the transformer is being driven from a valve anode (pretty much a Current Source and not a Voltage Source). This it not what the OP is discussing.

If you think of the secondary induced voltage as being proportional to the rate of change of flux in the core (related to rate of change of Primary Current) then this will consequently include harmonic content (boosted by the fact that the harmonics change at a higher rate. For small loads (i.e. high resistance), the secondary current will also contain harmonics, I reckon.

Yes I know that is not what the OP is discussing. But "m.s.j." in post #10, brought up the CT as a counter-example to my assertion that in single phase xfmrs the exciting current, fundamental plus all harmonics, is present in the primary exclusively. Member "m.s.j." states that in a CT, single phase, that harmonics exist in the secondary.

This topic does stray a bit from the OP, since the OP specified constant voltage source excitation, with a low source impedance. This OP stipulation excludes CTs from the discussion. But the CT was brought into the thread, with the argument presented that the secondary of a CT carries exciting current, even though it is single phase, rebuking my statement that single phase xfmrs have all exciting current in the primary.

I stand by what I already stated. The text reference provided by m.s.j. states that the primary amp-turns of a CT must equal the secondary amp-turns including exciting current, which said reference details as "Ie", which gets multiplied by "N2", the secondary number of turns.

Sometimes, even a good text has errors. Most of my uni texts included errata sheets. The trouble with the referenced text page is as follows. If the secondary is opened, then the secondary amp-turns is zero. The ref text sums the secondary load amp-turns with the (secondary) exciting amp-turns to equal the primary amp-turns. But in the open secondary case, the secondary amp-turns is zero. Hence the primary amp-turns are zero as well.

This is not correct. Anyone can set up a CT, & measure & observe. The primary amp-turns is non-zero. The exciting current is on the primary. In addition, the load current is reflected back to the primary & adds phasorially with the exciting current.

When the secondary is open, the secondary amp-turns is zero, since load current is zero. The load component of the primary current is likewise zero. But the exciting component of the primary amp-turns is non-zero. The entire primary current is magnetizing current. Since the secondary current is zero, there is no counter-mmf from the secondary. Hence the core flux & both voltages, pri & sec, reach their maximum value.

This happens because the exciting current is in the primary. When the secondary is terminated in a low impedance, the magnetic flux due to the secondary current opposes the original core flux, reducing its value. As a result the pri & sec voltages are quite small.

Anyone intimately familiar with xfmr theory & e/m fields can affirm this. BR.

Claude

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sophiecentaur
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2020 Award
I often think that some of these threads need a 'chairperson' to maintain the direction of flow. This isn't because I'm some kind of puritan, it's because I can see the danger of people getting the wrong end of the stick as they skim through a thread, picking bits at random. We've all done it, I'm sure.
That's why I pointed out the problem and apparent inconsistency.

Dear Cabraham,

What is primary or secondary side in a transformer? How can you specify the primary and secondary side of a power transformer in one transmission system which the direction flow of energy can be variable in it? Whether active power direction can determine the primary/secondary of transformers or reactive power flow direction?
I think the magnetizing current exist in all windings and metallic path which can be involved to magnetic flux of transformer generally. In transformer with open circuit in secondary, the exciting current exist in primary winding and metallic body of transformer.

For similar discussion you can refer to http://electrical-riddles.com/topic.php?lang=en&cat=23&topic=620"

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sophiecentaur
Gold Member
2020 Award
??? Isn't the primary side regarded as being the one that energy flows in from? In most circs, it's pretty easy to determine which is which.
OK, when you are talking about a transformer bridge circuit, that may be a bit hard to define but that's not what the thread is about, is it?

At a deeper level, of course, you don't even need to introduce magnetism into any problem if you really don't want to. That can involve standing up in a hammock, though.

Dear Cabraham,

What is primary or secondary side in a transformer? How can you specify the primary and secondary side of a power transformer in one transmission system which the direction flow of energy can be variable in it? Whether active power direction can determine the primary/secondary of transformers or reactive power flow direction?
I think the magnetizing current exist in all windings and metallic path which can be involved to magnetic flux of transformer generally. In transformer with open circuit in secondary, the exciting current exist in primary winding and metallic body of transformer.

For similar discussion you can refer to http://electrical-riddles.com/topic.php?lang=en&cat=23&topic=620"

The magnetizing current in a single phase xfmr can only exist in the primary, as far as I know. If the power source energizing the primary is constant voltage, then in order to maintain pure fundamental flux waveforms (single freq sinusoid), all necessary harmonic currents must have a low impedance path. If the power source connected to the primary is constant current, then the flux cannot be sinusoidal, as it will contain harmonics.

But in a current xfmr, we are not concerned w/ flux & voltage waveforms being harmonic free. We use the CT to measure large currents using a small ammeter, & obtain isolation from the power line to assure safety. If the CT primary carries 100 amp @ 50/60 Hz freq, the CT secondary will carry a scaled down current @ 50/60 Hz. The currents in both the primary & secondary of the CT will be low in harmonic content, but the flux & voltages will carry harmonics.

This is ok because we use the CT to read current not voltage. The voltage across the primary is extremely small, as well as the secondary.

With voltage xfmrs, exciting current must carry all harmonics to keep the flux pure, single freq sinusoid. This is needed so that the secondary voltage is harmonic free. In a single phase xfmr, the primary has 2 leads, providing a low impedance path for all harmonics. With 3 phase, however, this is not the case.

To keep pure flux, the exciting current must contain the fundamental, herein called the 1st, plus the harmonics 3rd, 5th, 7th, 9th, 11th, etc. If the primary is delta connected, all harmonics are present in the exciting current, which is carried by the primary. The 3 lines leading into the delta primary carry the 1st, 5th, 7th, 11th, etc. These are the harmonics not divisible by 3, aka the "non-triplen" harmonics.

The "triplen harmonics", which are divisible by 3, i.e. 3rd, 9th, 15th, etc. are carried by the delta primary windings. They circulate inside the closed loop of the delta primary. The flux & voltages are harmonic free.

If the pri & sec are both Y connected, & the primary Y has a 4th wire, i.e. the neutral of the source is connected to the neutral of the xfmr Y primary w/ low impedance, than the following occurs.

The non-triplens are carried in the 3 lines, & the triplens are carried in the 3 lines & the neutral. The neutral carries the sum of all 3 line triplen currents. The flux & voltages are harmonic free.

With a Y-Y with no neutral connection, or very high impedance connection, the non-triplens flow in the 3 lines, & the triplens do not flow at all, since there is no neutral path. The flux is missing these triplen components & waveform distortion exists. The distortion consists of the missing triplen frequencies from the exciting current. The exception to this behavior is the 3-legged "E core" type of 3 phase xfmr. It behaves like a Y-delta.

In a Y-delta w/o a neutral connection, the non-triplens are carried in the 3 lines, & the triplens circulate inside the delta secondary closed loop. The flux is harmonic free.

This is detailed in any utility power reference book. I've just given you what the power companies have known for almost a century or more. It's no secret. If any further explanation is needed, I can help. But I've given everyone here plenty. I ask people seeking answers to try to get them on their own. I can't just write a book here. BR.

Claude

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I can't just write a book here.

Fact is simple, but finding it is difficult. Please go back to basic and try to answer my questions, I think you don't like to leave your traditional belief.

sophiecentaur
Gold Member
2020 Award
Fact is simple, but finding it is difficult. Please go back to basic and try to answer my questions, I think you don't like to leave your traditional belief.

Are you telling us or asking us? Is this some sort of exam question, with you as the examiner?

Fact is simple, but finding it is difficult. Please go back to basic and try to answer my questions, I think you don't like to leave your traditional belief.

Of course I don't like to leave my traditional belief, when every utility power company, machine producer, xfmr producer, etc. has already researched this topic & published the results for all to see.

Your questions were answered over 100 years ago by people better than me. The amount of money & man-hours spent on researching xfmrs is staggering. When you say "traditional beliefs", you seem to be suggesting that there is something wrong with them.

Please enlighten me where my traditional beliefs are wrong. Take a specific question & put it up for discussion. If an answer I've already given is wrong, tell me why it's wrong. The best way to attack these questions is with Maxwell's equations.

Ampere's law, one of Maxwell's, states that:

integral H*dl = Ni

The "Ni" represents magnetomotive force, or "mmf". Thus to obtain an H field, amp-turns are required. If a load is placed across a secondary winding, the current in the sec produces an mmf/emf/flux whose polarity is opposite to the original. This is stated in the law of Lenz.

The primary voltage begins to drop, but since a voltage xfmr is excited from a constant voltage source, said source outputs more current to the primary to counter the flux of the secondary current. The secondary amp-turns is balanced by that of the primary, plus the exciting current is in the primary, & is not balanced. This exciting current is needed to keep the core flux.

In a CT, with the secondary open, the flux, pri & sec voltages are all at maximum value. Without exciting current there can be no flux. The secondary is open, so where is the exciting current?

Amperes law says that for a given integral of H*dl, the line integral of the H field around the closed magnetic path, there has to be a non-zero amp-turns. Only the primary can & does provide said amp-turns. The secondary has no current so there is no flux cancellation. All of the primary amp-turns is unbalanced making all amp-turns exciting current. Maximum flux/voltage are the result.

Every experiment has affirmed the same. I was a graduate teaching asst in the late 70's in charge of electric machines lab. I personally conducted said experiments as a senior student in EE, & as a grad asst. In the 70's this stuff was very old, established, archaic, been there done that, so what else is new. No mysteries exist here.

Again, using Ampere's law, how can the secondary of a CT provide exciting current? Please use AL and/or other Maxwell eqns like Faraday's law. I presume that the CT is the point you are disputing. If you disagree with my 3 phase explanation, let me know what needs to be clarified. BR.

Claude

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If you are seriously interested in transformers, three of the best books are:

Transformer Engineering; Blume, Boyajian, Camilli, Lennox, Minneci, Montsinger, (General Electric)

Transformers for the Electric Power Industry; Richard L. Bean, Nicholas Chackan Jr., Harold R. Moore, Edward C. Wentz (Westinghouse Electric Corporation)

Electric Transformers and Circuits; Reuben Lee, Leo Wilson, Charles E. Carter