*voltage regulation of transformer*is defined as the change in secondary terminal voltage (V

_{2}) from no-load to full load at constant primary voltage and temperature. It is expressed as a percentage of the secondary no-load voltage.

Mathematically, % Regulation of transformer = (E

_{2}– V

_{2}) x 100 / E

_{2}

**No-load voltage**: The secondary terminal voltage of transformer when no load is connected to the transformer is known as the no-load voltage of the transformer. At no load, the secondary terminal voltage will be equal to induced EMF in the secondary winding.

So, no-load voltage = E

_{2}volts

**Full load voltage**: It is the secondary terminal voltage of transformer when a rated load is connected to the transformer. We will denote it by V

_{2}.

When a transformer is loaded a voltage drop in primary and secondary impedances of transformer takes place. As the load current increases, this voltage drop will increase. This will reduce the secondary terminal voltage V

_{2}. The ideal value of voltage regulation of transformer is 0%.

# Voltage Regulation of Transformer | Formula

The approximate expression for the total voltage drop (E_{2} – V_{2}) in a transformer as referred to secondary is given by

Where,

R_{02} = equivalent resistance of transformer referred to secondary

X_{02} = equivalent reactance of transformer referred to secondary

R_{01} = equivalent resistance of transformer referred to primary

X_{01} = equivalent resistance of transformer referred to primary

Here it has been assumed that φ_{1} = φ_{2} = φ.

The positive sign is used for a lagging power factor and the negative sign for a leading power factor.

It is clear from the above expressions, the **voltage regulation of transformer** does not depend only on the magnitude of load current. But it also depends on the type of load. **The transformer regulation is positive for the resistive and inductive loads but it can be negative for the capacitive loads.**

We can determine the values of R_{01}, X_{01}, R_{02}, X_{02} of a transformer from short circuit test and calculate percentage regulation of transformer.

## Calculate Voltage Regulation of Transformer

**Example**: A 100 kVA transformer has 400 turns on the primary and 80 turns on the secondary. The primary and secondary resistances are 0.3 Ω and 0.01 Ω respectively and the corresponding leakage reactances are 1.1 and 0.035 Ω respectively. The supply voltage is 2200 V. Calculate:

- equivalent impedance referred to primary and,
- the voltage regulation and the secondary terminal voltage for full load having a power factor of 0.8 leading.

** **

**Solution: **K = 80/400 = 1/5,

R_{1} = 0.3 Ω,

R_{01} = R_{1} + R_{2}/K^{2} = 0.3 + 0.01/(1/5)^{2} = 0.55 Ω

X_{01} = X_{1} + X_{2}/K^{2} = 1.1 + 0.035/(1/5)^{2} = 1.975 Ω

Z_{01} = 0.55 + j 1.975 = 2.05 ∠74.44^{o}

Z_{02} = K^{2}Z_{01} = (1/5)^{2} (0.55 + j 1.975) = (0.022 + j 0.079)

No-load secondary voltage = KV_{1} = (1/5) × 2200 = 440 V,

I_{2} = 10 × 103/440 = 227.3 A

Full-load voltage drop as referred to secondary

= I_{2} (R_{02} cos φ − X_{02} sin φ)

= 227.3 (0.022 × 0.8 − 0.079 × 0.6 ) = − 6.77 V

% regn. = − 6.77 × 100/440 = − 1.54

Secondary terminal voltage on load = 440 − (− 6.77) = 446.77 V

Thanks for reading about ‘voltage regulation of transformer’.

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- Short Circuit Test on Single Phase Transformer
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- Regulation of Transformer
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jagannathWhile performing back-to-back test, the amount of power consumed is equal to

iron and copper losses of two transformers at full load + iron and copper losses of voltage injection unit