- Equivalent Circuit Definition: An equivalent circuit of a transformer is a simplified model used to calculate impedance, resistance, and leakage reactance.
- Primary Side Equivalent Circuit: To draw the equivalent circuit referred to the primary side, use the general equivalent circuit and modify it for primary side calculations.
- Excitation Branch: The primary current splits into no-load and load components, requiring a parallel path in the equivalent circuit known as the excitation branch.
- Approximate Equivalent Circuit: The excitation circuit can be ignored for simplification, combining resistance and reactance into equivalent values referred to the primary side.
- Secondary Side Equivalent Circuit: The equivalent circuit can also be referred to the secondary side, following similar steps as for the primary side.
What is the Equivalent Circuit of a Transformer?
An equivalent circuit of a transformer is a compact model for impedance, resistance and leakage reactance.
You need the equivalent impedance of transformer. Compute it from the circuit referred to the primary or to the secondary. Percent impedance comes from that same figure.
Check percent impedance before you install a transformer. Matching percent impedance is required for parallel operation of power transformers.
Percent impedance is taken from equivalent impedance, so the equivalent circuit is also used when % impedance is calculated.
Equivalent Circuit of Transformer Referred to Primary
To draw the equivalent circuit referred to primary, start from the general equivalent circuit, then shift quantities onto the primary. Begin with the full vector diagram of the transformer, shown below.
Let the transformation ratio be
Applied voltage to the primary is V1 and the voltage across the primary winding is E1. Total current into the primary is I1. V1 drops by I1Z1 or I1R1 + j.I1X1 before it appears across the winding.
The voltage across the winding is balanced by primary induced EMF E1. The voltage equation for this part of the transformer is
The circuit for that equation is below.
From the vector diagram, primary current I1 has two parts: no-load Io and load component I2′. Two current branches mean a parallel path beside the primary winding.
That parallel path is the excitation branch of the equivalent circuit. Its resistive and reactive arms can be written as
Load component I2′ flows through the primary winding. Induced voltage across that winding is E1, as in the figure at the right.
Induced voltage E1 appears on the secondary as E2. Load component I2′ appears on the secondary as I2. Secondary current is I2.
Voltage E2 across the secondary winding then drops by I2Z2 or I2R2 + j.I2X2 before it reaches the load as V2.
The complete equivalent circuit is below.
Seen from the primary, that secondary voltage drop is K times larger: K.Z2.I2.
Again I2′.N1 = I2.N2
Therefore,
From that equation, secondary impedance referred to primary is
The complete equivalent circuit referred to primary is then:
More transformer questions sit in our MCQs on transformers.
Approximate Equivalent Circuit of Transformer
Io is small next to I1, under 5% of full-load primary current, so Io barely changes the voltage drop.
The excitation branch can therefore be left out of the approximate equivalent circuit.
Winding resistance and reactance in series then combine into equivalent resistance and reactance referred to one side. Here that side is the primary.
Equivalent Circuit of Transformer Referred to Secondary
The same steps give the approximate equivalent circuit referred to the secondary.
Equivalent impedance referred to the secondary is
