In a transformer, is induced voltage or current in phase with voltage source?

[gauthamtechie]

I need some clarification: If I have a voltage source connected to the transformer, voltage induced in the transformer(open circuit) primary is opposing the change in current direction.

Now My question is which of these is actually in phase with the source?

Is it the current in the circuit which is in phase with the source voltage and is it the induced voltage which is leading? Or is the voltage applied in phase with the voltage induced(opposing emf) and is it the current which actually lags by 90; making it lag the source voltage as well?

In short, I want to know what(current or voltage) follows the source and what leads or lags the other as an effect.

 

[MikeMl]

This should help: Arrows show which direction conventional current flows. Ideal 1:1 transformer with unity coupling.

V(a) and V(b) are in phase.

I(L1) Primary and I(R2) are in phase except for the effect of a bit of leakage inductance (which LTSpice models)

Notice the dots on the coupled windings.

 

[Diver300]

In any reasonably efficient transformer, the input and output voltages are in phase.

This is why:-

The magnetic flux is almost exactly the same though both windings. (Ok, it won't be exactly the same, as the windings are in different places, but the magnetic core is there to make sure that all the flux goes though both windings.

If the transformer is efficient, there will be little resistive loss, so that can be ignored until you get into more complicated analysis. Also, because the resistive loss is small, the induced voltage on the primary has to be almost exactly equal to the supply voltage at all times. A transformer with no load takes very little current, even though its input resistance is small. That is because the voltage induced by the magnetic field almost completely opposes the supply voltage.

At any instant, the induced voltage is equal to the number of turns and the rate of change of flux. As the flux is the same in both coils, the induced voltages are in phase and only differ because of the different numbers of turns. The primary induced voltage is just about equal to the supply, so the secondary voltage also only differs from the primary by the turns ratio.

 

[Diver300]

The currents are also quite simple. There is a magnetising current in the primary. That will lag the supply voltage by 90°.

Whatever current the load takes has to ultimately come from the supply. The energy stored by the transformer only depends on the supply voltage, so any current in the secondary causes exactly the same current (divided by the turns ratio) in the primary. If that current leads or lags the voltage, if it has a big DC component in it or contains funny harmonics, it doesn't change the fact that the secondary current has to come from the supply, and it is only changed by the turns ratio.

The secondary current, divided by the turns ratio, plus the magnetising current, is the current the transformer takes from the supply. Whether that leads or lags the supply, and whether it is sinusoidal or not, depends on the load current.

 

[gauthamtechie]

Mike ML,

But isn't the current in the primary supposed to be the integral of the supply voltage, thereby have a 90 degree lag? It is seen in phase in the image you posted?
what am confusing it with here?

 

[Diver300]

Mike ML,

But isn't the current in the primary supposed to be the integral of the supply voltage, thereby have a 90 degree lag? It is seen in phase in the image you posted?
what am confusing it with here?

It is the magnetising current that lags the supply by 90°. In Mike's example, there is a large load current, and that is in phase with the supply voltage because the load is a resistor. That large load current is far bigger than the magnetising current, so the total of the load current and the magnetising current only lags by a few degrees.

 

[Ratchit]

gauthamtechie,

I need some clarification: If I have a voltage source connected to the transformer, voltage induced in the transformer(open circuit) primary is opposing the change in current direction.

Now My question is which of these is actually in phase with the source?

Is it the current in the circuit which is in phase with the source voltage and is it the induced voltage which is leading? Or is the voltage applied in phase with the voltage induced(opposing emf) and is it the current which actually lags by 90; making it lag the source voltage as well?

In a power transformer, the designers usually try to make the inductive reactance high enough so that the rated voltage can be connected across the primary without any series resistance and not exceed the primary current. Now, the impedance from the secondary is reflected back to the primary, so you have to know what load you are feeding. You should study in a text book how everything relates to each each other. If you got lots of inductance the current will lag the voltage.

Ratch

 

[gauthamtechie]

Yes now it makes sense. I did not see the current as a whole; instead I just took the concept of magnetizing current but the resultant is the magnetizing plus load current even in the primary. Also when I thought about the load being resistive, I thought that it is about having a Large RESISTANCE value to achieve negligible lag. I increase the resistance to few hundreds of ohms and notice the primary current and primary voltage have a near 90 degree phase shift.

In this case it is not a large resistance value that means "Large Resistive load" instead it is the "large current drawing resistive portion", if i can put it that way, which determines the phase shift.

EDIT: Adding an inductor in series does change things a bit. I seem to understand that the effect of the inductance in comparison to that of the resistance is what decides my Secondary V and I phase shifts. So cosine inverse (R/Z) can give me the secondary phase shift. What about the Primary Phase shift? My understanding is that it is R/Z but in this case the Magnetizing current in primary also contributes to the phase shift, so the Z value differs. Thus whatever phase shift in secondary, the primary phase shift is greater could I say?

 

[MrAl]

Hi,

Try this:
Look at the primary voltage phase and the secondary voltage phase with light load. Also consider that there is very little electrostatic action in the normal power transformer. Then ask yourself how can the secondary voltage phase be as it is. When there is no electrostatic action that means it is all magnetic, and magnetic action is current driven not voltage driven. The voltage causes the current to be there in the primary but the voltage itself can not cause the voltage in the secondary. So take it from there and see what you can figure out

 

[gauthamtechie]

MrAl,

Let me try: The primary voltage causes the primary current which has a magnetic field around it. This magnetic field is also expanding and collapsing and thus cutting the secondary. Thus an EMF is setup in the secondary to counter the change in the current induced in the secondary by this primary flux. Is this right?

If that is right, the secondary induced EMF is a result of changing current, so it will lead the current. Thus the Voltage in primary and secondary are in phase.
This is what I figured out. And regarding my previous comment, there is already a phase shifted current in the primary (The magnetizing current). In the event that the secondary is loaded, the current drawn in the primary is a result of the secondary current. So if my secondary draws a huge in-phase current due to a resistive load, then that will compensate the comparatively small magnetizing current in the primary to lend a Primary current that is nearly in phase with Primary V. In the event that the secondary is also having inductive components, then the ratio of R to Z in the load decides the secondary phase shift. Is this right as well?


Now as per the analysis, the secondary current drawn will reflect in the primary. Now here is where I hope I don't muddle things up! The Primary now draws more current because the secondary current distorts the flux linked by drawing the current. Thus net flux is nearly constant. The primary current's behavior (i.e. phase shift w.r.t Primary V) is influenced by load. So the inductive load will create an induced emf that lags behind secondary V. Since primary V and Secondary V are in phase, the lag with Primary V and Primary I is increased. Thereby this is also said to be drawing more reactive power.
Has everything adding up in my understanding?

 

[tcmtech]

In the simplest form I can come up with.

At a very low resistive load the secondary phase relationship to the primary is going to be very close, maybe only a few degrees of lagging offset at most, however as the secondary load increases the phase lag will get larger.

 

[MikeMl]

This is my LTSpice example with the secondary open, i.e. I(L2)=0.

V(a) and V(b) are perfectly superimposed (no phase shift), while I(L1) lags V(a) by ~90deg.

The earlier sim showed that with the secondary loaded, there was no phase shift between V(a) and I(L1).

 

[MrAl]

MrAl,

Let me try: The primary voltage causes the primary current which has a magnetic field around it. This magnetic field is also expanding and collapsing and thus cutting the secondary. Thus an EMF is setup in the secondary to counter the change in the current induced in the secondary by this primary flux. Is this right?

If that is right, the secondary induced EMF is a result of changing current, so it will lead the current. Thus the Voltage in primary and secondary are in phase.
This is what I figured out. And regarding my previous comment, there is already a phase shifted current in the primary (The magnetizing current). In the event that the secondary is loaded, the current drawn in the primary is a result of the secondary current. So if my secondary draws a huge in-phase current due to a resistive load, then that will compensate the comparatively small magnetizing current in the primary to lend a Primary current that is nearly in phase with Primary V. In the event that the secondary is also having inductive components, then the ratio of R to Z in the load decides the secondary phase shift. Is this right as well?


Now as per the analysis, the secondary current drawn will reflect in the primary. Now here is where I hope I don't muddle things up! The Primary now draws more current because the secondary current distorts the flux linked by drawing the current. Thus net flux is nearly constant. The primary current's behavior (i.e. phase shift w.r.t Primary V) is influenced by load. So the inductive load will create an induced emf that lags behind secondary V. Since primary V and Secondary V are in phase, the lag with Primary V and Primary I is increased. Thereby this is also said to be drawing more reactive power.
Has everything adding up in my understanding?

Hello,

That sounds about right, but im not sure what you are saying about the distortion. You mean because of the non linear characteristics of the core material? I though we could ignore that for now.

The basic idea is that the current is the vector sum of the inductive current plus the load current. The inductive current is 90 degrees out of phase with the load current but the inductive current is constant while the load current increases as the load resistance is decreased. To the vector sum starts out relatively small and at 90 degrees, and as the load current increases higher and higher it not only increases the total current but it also changes the phase pulling it more and more toward 0 decrees.

I'll have to look to see if i can find the simplified model of the transformer which should illustrate this mathematically.

 

[gauthamtechie]

Hello,

That sounds about right, but im not sure what you are saying about the distortion. You mean because of the non linear characteristics of the core material? I though we could ignore that for now.

Oh sorry I didn't mean distortion in that sense. I was reiterating the concept of constant flux even though the secondary draws larger load currents, wherein the Secondary current increase causes flux which "cancels" the primary flux to the same extent - Thereby causing primary current because the induced primary emf is decreased. This is the sequence right?

 

[MrAl]

Hello again,

Oh ok i guess i've never thought about it in that respect. I'll try to find that model i was talking about as soon as possible.

 

[crutschow]

Oh sorry I didn't mean distortion in that sense. I was reiterating the concept of constant flux even though the secondary draws larger load currents, wherein the Secondary current increase causes flux which "cancels" the primary flux to the same extent - Thereby causing primary current because the induced primary emf is decreased. This is the sequence right?

Yes. It's rather a balancing act with the primary current adjusting to counter the reverse direction flux from the secondary current to maintain a constant flux in the core.