Phase of Current and Voltage on Primary Side of Transformer

Question

I don't really understand the workings of a transformer and how the voltage and current on the primary side can be the same phase.

As far as I understand, a transformer is two coils that are connected via a magnetic core. However, the primary and secondary sides are still coils, and therefore would obey the equation EMF = L di/dt.

If the primary side of a transformer is connected to an AC source, then the EMF generated due to changing current (and therefore flux) would be equal to the AC source voltage. (similar to how AC steady state analysis works). This would then mean that the current and voltage are out of phase by 90 degrees. I don't quite understand how then transformers are treated with the voltage and current in phase.

Answer 1

You can simplify your view of the transformer to just the load reflected to the primary via the turns ratio squared with the magnetizing inductance in parallel. At no load, the magnetizing inductance will consume current 90 degree out of phase with your supply voltage (reactive power). At max load, the magnetizing current is very low compared to your load and if the load is resistive, you'll see close to 0 degree phase shift between voltage and current.

^{simulate this circuit – Schematic created using CircuitLab}

In the top schematic, a simplified transformer model is used with separate magnetizing inductance of 10 mH but otherwise ideal. The 1 Ω load will be transformed to 100 Ω equivalent on the primary. If you have no load, only your magnetizing inductance will draw current 90 degree out of phase. The more resistive load you have, you will get closer and closer to 0 degrees.

Answer 2

I don't really understand the workings of a transformer and how the voltage and current on the primary side can be the same phase.

Secondary voltage phase angle relative to primary voltage source:

• Let's say the primary voltage has a phase angle of 0°

• The magnetization current (not the load current) lags by 90°

• It lags by 90° because magnetization current feeds the magnetization inductance

• That's a simple case of re-arranging: \$V = L\cdot\frac{di}{dt}\$ (for a sine wave): -

• Or, the integral of the applied sine wave is a negative cosine wave: -

• Image from HyperPhysics: Inductor voltage-current relationship

• The magnetic flux in an ideal core is proportional to current

• And, the induced secondary EMF is \$-N\cdot\frac{d\Phi}{dt}\$

• This puts the induced secondary EMF in phase with the applied voltage on the primary.

The above explanation deals with the situation of producing a secondary induced voltage that is in phase with the primary applied voltage.

Load currents:

If the secondary is connected to a resistive load then, there is secondary load current and, for a 1:1 transformer, that secondary current also flows in the primary IN ADDITION to the magnetization current.

And, when there is a load current (1:1 transformer), the secondary load current is 180° out of phase with the primary load current. The net effect of these two loads currents is that their individual fluxes cancel each other meaning that the only flux in the core is due to the magnetization current. In other words: -

Please don't confuse magnetization current and load current in the primary.

However, the full current entering the primary is the addition of magnetization current and load current. Given a resistive secondary load, the phase angle of actual current entering the primary is somewhere between a few degrees lagging (full load current) and 90° lagging (zero load current).