Transformer Losses & Equivalent Circuits

• Types of losses in a transformer:

  • Iron or core loss

  • Copper loss

• Iron loss:

  • Due to the reversal of flux in the core

  • Practically constant at all loads (no load to full load)

  • Subdivided into two losses:

    • Hysteresis loss

    • Eddy-current loss

• Hysteresis loss:

  • Occurs due to the alternating flux in the core

  • Depends on factors such as hysteresis loop area, core volume, and frequency of flux reversal

• Eddy-current loss:

  • Occurs due to the flow of eddy currents in the core

  • Depends on factors such as lamination thickness, frequency of flux reversal, maximum flux density, core volume, and quality of magnetic material

  • Eddy-current losses can be reduced by decreasing lamination thickness and adding silicon to steel.

• Copper loss:

  • due to the resistances of primary and secondary windings

  • depends upon the load on the transformer

  • proportional to square of load current of kVA rating

\[\boxed{W_{C u}=I_{1}^{2}R_{1}+I_{2}^{2}R_{2}}\]

• For an ideal transformer:

  1. No core loss and copper loss.

  2. Winding resistance and leakage flux are zero.

• In a practical transformer:

  1. The windings have some resistance.

  2. There is always some leakage flux.

• In an ideal transformer, it is assumed that all the flux produced by the primary winding links both the primary and secondary windings. However, in practice, this condition cannot be realized.

• The flux \(\phi_{L1}\) represents the primary leakage flux, which links only to the primary winding and does not link to the secondary winding.

• Similarly, \(\phi_{L2}\) is secondary leakage flux, which links only to the secondary winding and does not link to the primary winding.

• The mutual flux, \(\phi\) , links both the primary and secondary windings.

• \(\phi_{L1}\) is in phase with \(I_1\) and produces a self-induced emf \(E_{L1}\) in the primary winding.

• \(\phi_{L2}\) is in phase with \(I_2\) and produces \(E_{L2}\) in the secondary winding.

• The induced voltages \(E_{L1}\) and \(E_{L2}\) caused by \(\phi_{L1}\) and \(\phi_{L2}\) differ from the induced voltages \(E_1\) and \(E_2\) caused by the main or mutual flux \(\phi\) .

• Leakage fluxes generate self-induced emfs in their respective windings.

• Consequently, the leakage fluxes are equivalent to inductive coils connected in series with their respective windings.

• \[E_{L_1}=I_1X_1~~\text{and}~~E_{L_2}=I_2X_2\]
  The voltage drop in each series coil is equal to the voltage produced by the leakage flux.

• No Load \(\Rightarrow\) core loss and Cu loss in primary winding

• \(I_0\) supply core loss and very small Cu loss in primary

• \(I_0\) has two components:

  • \(I_\mu~\Rightarrow\) magnetising or reactive component

  • \(I_w~\Rightarrow\) power or active component

• \(I_\mu\) sets flux ( \(\phi\) ) in the core and is in phase with \(\phi\)

• \(I_w\) responsible for power loss and phase with \(V_1\)

\[\begin{aligned} I_\mu & = I_0\sin\phi_0 \\ I_w & = I_0\cos\phi_0\\ \bar{I}_0 & = \bar{I}_\mu + \bar{I}_w\\ I_0 & = \sqrt{I^2_\mu+I^2_w} \end{aligned}\]

• \(I_0\) is very small as compared to \(I_1\)

• \[\boxed{W_0=W_i = V_1I_0\cos\phi_0}\]
  copper loss negligible and

• Load \(\Rightarrow~I_2~\Rightarrow~\phi_2~\Rightarrow~\phi \downarrow~\Rightarrow~I_1 \uparrow ~\Rightarrow~\phi \uparrow ~\Rightarrow\) constant \(\phi\)

• \(I^{\prime}_2\) ( additional \(I_1\) is anti-phase with \(I_2\) ) sets \(\phi^{\prime}_2\) cancel \(\phi_2\) due to \(I_2\)

Capacitive load