The document discusses the exact and approximate equivalent circuits of transformers. The exact equivalent circuit models the magnetizing current, core losses, primary and secondary winding resistances and leakage reactances. The approximate equivalent circuit simplifies this by connecting the magnetizing branch directly across the supply voltage. This increases no-load current and core losses slightly while reducing voltage drop and primary copper losses slightly. An example is given to calculate the equivalent resistances referred to the primary and secondary windings.

1. Transformers equivalent circuit

2. Outline
• Exact equivalent circuit
• Approximate Equivalent Circuit

3. Equivalent Circuit of a transformer
• The equivalent circuit enables us to analyze and predict the
performance of the transformer by using electric circuit theory.
Exact Equivalent Circuit
• At no-load the current is used to create the magnetic flux and to supply
the core losses.
• The magnetizing current lags the voltage E1 by 90o while the core loss
current is in phase with E1
• Thus the phasor diagram of the magnetizing branch is shown in Figure

4. Equivalent Circuit of a transformer
•

5. Exact Equivalent Circuit
• At no-load the effect of magnetizing the core is represented by a
fictitious inductive reactance called magnetizing reactance (𝑋Φ )
across the emf E1
𝐸1 = 𝑋Φ𝐼Φ
• Core losses are represented by a fictitious resistance called the core loss
resistance (𝑅𝑐)

6. Exact Equivalent Circuit
• When the transformer is on load, secondary current flows causing the
primary current to increase over the no-load current.
• In the equivalent circuit the primary and secondary winding
resistances are represented by 𝑅𝑝 and 𝑅𝑠 respectively. The
corresponding copper losses are

7. Exact Equivalent Circuit
• The effects of flux leakages are represented by leakage reactances
𝑋1 and 𝑋2 in series with the primary and secondary winding resistances
respectively.
• The exact equivalent circuit of the double wound transformer is shown
in the figure below.

8. Exact Equivalent Circuit
• It is composed of the primary winding series impedance ,the
magnetizing impedance and the secondary winding series impedance

9. Exact Equivalent Circuit
•

10. Exact Equivalent Circuit

11. Exact Equivalent Circuit
•

12. Approximate Equivalent Circuit
• The circuit of Fig 9 can be simplified by connecting the magnetizing
branch across the supply to obtain the approximate equivalent circuit
shown in Fig 11.
• This increases the value of the no-load current and core losses slightly
while reducing the voltage drop across the series impedance ( ) and the
copper power loss in the primary winding slightly.
• Why?

13. Approximate Equivalent Circuit
•

14. Approximate Equivalent Circuit
•

15. Approximate Equivalent Circuit

16. Approximate Equivalent Circuit

17. Approximate Equivalent Circuit

18. Approximate Equivalent Circuit
•

19. Approximate Equivalent Circuit
•

20. • 4 kVA, 3200/320 V, 50 Hz step-down single phase transformer has
primary winding and secondary winding resistance of 1.25 Ω and 0.0125
Ω respectively. The primary winding and secondary winding reactances
are 3.75 Ω and 0.0375 Ω respectively. Determine:
• The equivalent resistance referred to the primary winding
• The equivalent resistance referred to the secondary winding
2.5
ep
R  
0.025
es
R  