- Transformer Definition: A transformer is defined as an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction.
- No-Load Transformer Theory: On no-load, the transformer experiences core losses but no copper loss or leakage reactance, with current components for magnetizing and core losses.
- Magnetizing and Core Loss Currents: The no-load current consists of a magnetizing component (reactive) and a core loss component (active).
- Transformer on Load: When on load, the transformer’s secondary current depends on the load and secondary voltage, requiring additional primary current to maintain the main flux.
- Transformer on Load with Resistive and Reactive Drops: In practical transformers, voltage drops occur due to winding resistance and leakage reactance, affecting the voltage equations.
The ideal transformer page set the lossless model. This page covers a practical electrical power transformer on no load and on load, with a vector diagram at each step. A real core has losses in transformer from hysteresis and eddy current.
Theory of Transformer on No-Load
Having No Winding Resistance and No Leakage Reactance
Take a transformer that has core loss only: no copper loss and no leakage reactance of transformer. An alternating current source on the primary supplies the current that magnetizes the core of transformer.
That source current is a little larger than the magnetizing current alone. It has two parts: the magnetizing current that sets up core flux, and a second part that covers core loss.
Because of that core-loss part, no-load current lags the supply by an angle θ less than 90°, not a full 90°. Total current Io therefore has a component Iw in phase with supply voltage V1. Iw is the core-loss component.
Iw sits in phase with the source voltage because it accounts for active or working core loss. The other source-current component is Iμ.
This component produces the alternating magnetic flux in the core, so it is wattless: the reactive part of source current. Iμ therefore sits in quadrature with V1 and in phase with flux Φ. The total primary current on no-load is then:
That is the theory of transformer on no load.
Theory of Transformer on Load
Having No Winding Resistance and Leakage Reactance
Now connect a load to the secondary of the same machine. Still assume core loss only: no copper loss and no leakage reactance. Load current then flows in the load and in the secondary winding.
That current depends on the load and on the secondary voltage of the transformer. Call it secondary or load current I2. I2 in the secondary produces an MMF N2I2, where N2 is the secondary turns count.
That secondary MMF produces flux φ2. φ2 opposes the main flux, weakens it for a moment and tends to cut primary self-induced EMF E1. If E1 falls below source voltage V1, extra current flows from the source into the primary.
That extra primary current I2′ produces extra flux φ′ which cancels the secondary counter flux φ2. Main core flux Φ therefore stays the same at any load. The current drawn from the source then splits into two parts.
The first part magnetizes the core and covers core loss: Io, the no-load component of primary current. The second part cancels the secondary counter flux. That is the load component of primary current. Total primary current I1 for a machine with no winding resistance and no leakage reactance is then
where θ2 is the angle between secondary voltage and secondary current.
The next step adds winding resistance.
Theory of Transformer On Load, with Resistive Winding, but No Leakage Reactance
Now keep leakage reactance at zero and add winding resistance. Earlier windings were ideal: no resistance and no leakage. Resistive windings drop voltage along each coil.
On load the source still supplies I1. Primary resistance R1 drops R1I1. Induced EMF E1 is therefore not equal to source voltage V1. E1 is below V1 by I1R1.
On the secondary, induced E2 does not all reach the load. It falls by I2R2, where R2 is secondary winding resistance and I2 is load current.
The secondary voltage equation is then:
Theory of Transformer On Load, with Resistance as well as Leakage Reactance
Now add leakage reactance as well as winding resistance.
Let primary and secondary leakage reactances be X1 and X2. The impedance of primary and secondary winding of transformer with resistances R1 and R2 is then
The earlier transformer on load voltage equations used resistance only. Drops there were resistive drops alone.
With leakage reactance, each winding also drops voltage across the impedance of transformer windings. Replace R1 & R2 in those earlier equations with Z1 and Z2.
The voltage equations become
Resistance drops lie along the current vector. Reactive drops sit at right angles to the current, as in the vector diagram of the transformer.
