Voltage regulation of transformer

The voltage regulation of transformer is used to understand the characteristics of transformer under loaded conditions. When a transformer is loaded with constant primary voltage, the secondary voltage decreases because of load current, internal resistance, and leakage reactance. The change in secondary voltage from no-load to full load at constant frequency and voltage is known as voltage regulation of transformer. It is usually expressed as a percentage of the rated terminal voltage.

If V₂ is the secondary terminal voltage at full load and E₂ is the secondary terminal voltage at no load. Then the percentage regulation of transformer is given by,

$Voltage Regulation = \frac{E_2 - V_2}{E_2} \times 100$

It is also called as ‘down-regulation’. If the change in voltage from no-load to full-load is divided by full-load secondary terminal voltage, it is known as ‘up regulation’.

$Voltage Regulation = \frac{E_2 - V_2}{V_2} \times 100$

However, unless stated otherwise, down-regulation is considered as the voltage regulation of transformer.

Voltage regulation of transformer referred to primary values

The voltage regulation of transformer can also be explained in terms of primary values. In the simplified equivalent circuit of transformer, as shown in the figure below, the secondary no-load terminal voltage as referred to primary is V₁ and the secondary full load voltage as referred to primary is V₂^‘. Then the percentage regulation of transformer is given as,

$Voltage Regulation = \frac{V_1 - {V_2}^{'}}{V_1} \times 100 --->(1)$

From its phasor diagram, as shown below for pure inductive load, the voltage relationship between V₁ and V₂^‘ can be written as below. (Refer: Equivalent resistance and reactance of transformer to understand the phasor diagram and voltage equations)

V₁ = V₂^‘ + I₁R₀₁ cos Φ + I₁X₀₁ sin Φ

V₁ – V₂^‘ = I₁R₀₁ cos Φ + I₁X₀₁ sin Φ

Phasor diagram of transformer for lagging power factor

Equation(1) becomes,

$Voltage Regulation = \frac{I_1R_{01} cos \phi +I_1X_{01} sin\phi}{V_1} \times 100 --->(2)$

The above equation is the voltage regulation of transformer with pure inductive load.

For a pure capacitive load, the phasor diagram can be drawn as below, which has a leading power factor. Hence the current I₁ leads the voltage V₂^‘. In this case, the voltage relation becomes,

V₁ – V₂^‘ = I₁R₀₁ cos Φ – I₁X₀₁ sin Φ

Phasor diagram of transformer for leading power factor

The voltage regulation of transformer for capacitive load is,

$Voltage Regulation = \frac{I_1R_{01} cos \phi - I_1X_{01} sin\phi}{V_1} \times 100$

For pure resistive load, the phasor diagram is drawn as below, which has a unity power factor. Hence the current I₁ is in phase with the voltage V₂^‘. In this case, the voltage relation becomes,

V₁ – V₂^‘ = I₁R₀₁