Voltage Regulation of Transformer

Voltage regulation of a transformer is defined as the change in magnitude of the secondary (terminal) voltage, when full-load (rated load) of specified power factor supplied at rated voltage is removed i.e reduced to no-load with primary voltage (and frequency) kept constant, as a percentage of the rated load terminal voltage.

Thus, voltage regulation formula is given by

Where, V_2fl = rated secondary terminal voltage while supplying full-load at specified power factor.

V₂₀ = secondary voltage with secondary open (no-load)

Voltage regulation (V.R) derivation

The transformer equivalent circuit, shown below, is used to derive the expression for voltage regulation.

Its phasor diagram is shown below. Φ is the load impedance angle.

Transformer Voltage Regulation phasor diagram

From phasor diagram, by voltage regulation definition

Ө_eq is the equivalent impedance angle of transformer. AB can be projected horizontally as AD.

The voltage drops IR_eq and IX_eq are very small in a well designed transformer , therefore, δ is negligible. Hence, OC≃OD.

Because ( IZ_eq/V ) = Z_pu , therefore

approx V.R = Z_pu cos(Ө_eq- Φ)

As per our sign convention, Φ is positive for lagging power factor loads and negative for leading power factor.

The above V.R formula shows that Voltage regulation depends on

(1) load power factor (or load impedance angle Φ )

(2) equivalent impedance of transformer Z_eq

(3) equivalent impedance angle of transformer Ө_eq

Improvement of V.R

Regulation can be reduced by reducing Z_eq . But Z_eq consists of R_eq and X_eq . Therefore, R_eq and X_eq must be reduced.

R_eq is reduced by taking windings of low resistance value.

X_eq is nothing but circuit representation of leakage flux. Therefore, leakage flux must be reduced to reduce X_eq . This is done by placing windings as close as possible, by increasing transformer window height to width ratio etc.

Zero Voltage Regulation

V.R = 0

Ө_eq– Φ = 90⁰

Φ = Ө_eq–90⁰ ... for lagging power factor loads

Φ = 90⁰ - Ө_eq ... for leading power factor loads

So, load power factor (lagging/leading) must satisfy above conditions for zero voltage regulation.

Maximum Regulation

V.R = maximum ,when cos(Ө_eq- Φ) = 1 or Ө_eq- Φ = 0⁰

or Ө_eq= Φ (lagging)

Thus, for maximum voltage regulation of transformer , the impedance angle Φ of a lagging load, must be equal to the equivalent impedace angle Ө_eq of transformer.

Minimum Regulation

Minimum regulation is the maximum value of negative regulation.

V.R = Z_pu cos(Ө_eq- Φ)

Therefore, minimum regulation = Z_pu cos[Ө_eq– (-90⁰)]

= Z_pu cos(Ө_eq+90⁰)

= - Z_pu sinӨ_eq

= -X_pu

V.R variation with load power factor