Magnetic flux in tap changing transformers

[Darius Troy]

Hi guys,

Non engineer here trying to understand an engineering principle. I think I must be going wrong somewhere in my thought process.

1. Faraday tells us that the EMF generated in the secondary of a transformer is equal to the change in magnetic flux divided by the change in time.

2. The magnetic flux in the transformer core is equal to the MMF divided by the Reluctance of the core. The MMF is proportional to the current flowing through the primary winding, and the number of turns of the primary.

3. The ratio of the number of turns in the primary compared to that of the secondary determines the secondary voltage with a given applied voltage at the primary.

The example of a Step Up Generator Transformer:

This Transformer is humming along happily, when it's called on for a tap change. This particular Transformer has the tap changer on the Primary side. This particular tap operation alters the turns ratio by reducing the number of turns in the primary winding. The result of this is an increase in the voltage developed in the secondary winding as predicted by the turns ratio/voltage ratio relationship.

This is where my paradox begins, as by altering the turns ratio in this fashion one has reduced the MMF developed by the primary winding: there are less turns now. This means less peak magnetic flux in the core and so less voltage able to be developed in the secondary according to Faraday... The only way the MMF and therefore flux remains stable is if the current increases through the primary windings. This isn't implausible as the overall impedance of the primary winding would be less due to less turns, but this seems perhaps too simplistic?

It seems that it's taken for granted that the turns ratio is the only factor which governs the voltage generated at the secondary. How can this be the case when by altering the amount of turns in the primary side, one is directly altering the strength of the magnetic field?

Also, adding to my confusion (not that difficult a task) is the fact that there are formulas which show that magnetic flux is inversely proportional to the number of turns in a coil (Φ = V × T / N). This seems counter-intuitive, but also seems to contradict Rowland's law of Φ = Fm / Rm.

Any comments would be greatly appreciated.

 

[cnh1995]

Suppose you have a transformer with 100 turns on primary and 50 turns on secondary.
You apply a voltage of 100V across the primary. Hence, induced emf in primary=1V/turn. So, induced emf in the secondary is also equal 1V/turn and you get 50V across the secondary.
(Emf/turn is same for both the sides).

Now, if you change the number of turns on the primary to 50 (by tap changer) and still apply 100V across it, you'll have 2V/turn induced emf in the primary, which means you have 2V/turn in secondary. So your secondary voltage becomes 100V.

Applied voltage=Emf induced in the coil= N*dΦ/dt.
If you change the number of turns, dΦ/dt will also change such that N*dΦ/dt remains constant (since applied voltage is constant).

 

[jim hardy]

(Emf/turn is same for both the sides).

There's the key point.
When dealing with sine waves , 'Volts per Turn' is a direct measure of the magnetic flux in the core.

This is where my paradox begins, as by altering the turns ratio in this fashion one has reduced the MMF <<(there's your mistake) developed by the primary winding: there are less turns now.

In your thought experiment you must change only one thing at a time.
So hold primary voltage constant and just change the number of primary turns.
When you decreased N_turns with same applied voltage, you increased volts per turn so flux went up a little. Magnetizing current went up a little bit as well, to push that flux around the core, but in power transformers magnetizing current is usually small enough compared to load current that we ignore it.So you did NOT decrease primary mmf you actually raised it a little bit.

http://www.butlerwinding.com/power-transformers-operating-theory/

 

[Darius Troy]

Hi guys,
Thank you both so much for your interesting responses. I have done a little more reading, and now understand the 'EMF equation of a transformer', and so can indeed see that by reducing the number of primary turns we have increased the maximum flux. I find this quite interesting, as there it seems as though the magnitude of current flowing through the primary winding has no effect at all on the magnetic flux or induced voltage. Indeed, an ideal TX on no load will still induce a voltage on the secondary winding...
Amperes law tells us that the strength of the magnetic field, and therefore the flux density, depends on the current flowing through the conductor, and the number of turns. I know we can mess around with formulas to remove current from the equation, however I thought it was the physical movement of electrons which gave rise to the magnetic effect.

I've got so much more reading to do before i fully understand what is such an important and basic phenomenon. Thank you both for helping me down the path!

 

[jim hardy]

Indeed, an ideal TX on no load will still induce a voltage on the secondary winding...

An ideal transformer has infinite inductance so draws zero magnetizing current.

I find this quite interesting, as there it seems as though the magnitude of current flowing through the primary winding has no effect at all on the magnetic flux or induced voltage.

Separate in your mind magnetizing current and load current.

This oversimplified word picture might help you

Magnetomotive Force is what pushes magnetic flux around the core. Units of mmf is Amp-Turns .
In a good transformer the amp-turns required to push flux around the core is a small number compared to the transformer's design load current .
So we tend to ignore it thereby confusing beginners.
It's called "Magnetizing Current". Numerically it's very close to V_primary / L_primary .
Since an ideal transformer has infinite L_primary , its magnetizing current is zero.

You'll never meet a truly ideal transformer but real ones can be within slide rule accuracy of ideal.

In that picture, note that any secondary current allowed to flow creates a second mmf that affects magnetic flux. Primary current will rise to re-establish flux to V_primary / L_primary. So, ignoring magnetizing current , primary amp-turns will be equal to secondary amp-turns . That's the heart of those equations relating ratios of turns voltage and current .When you're ready to tackle ideal vs non ideal transformer the Wikipedia article has a pretty decent model. Tim9000 and i went into it at length a couple years ago.
https://en.wikipedia.org/wiki/Transformer

It has an ideal transformer a:1 surrounded by components representing the real world deviations from ideal.
Observe its magnetizing I_M current flows down through X_M .

old jim

 

[CWatters]

The way I was taught to think about transformers...

When calculating voltages start with the primary voltage and go forwards through the transformer to work out the secondary voltage.

When thinking about current start with the load aka secondary current and work backwards through the transformer to calculate the primary current.

Sorry if you know that already.