# Voltage Regulation of Transformer-Definition, Formula

Last Updated on February 2, 2024 by Electricalvolt

## What is the Voltage Regulation of a Transformer?

Voltage regulation of the transformer is defined as the percentage change in the transformer’s secondary voltage from no load to full load. In other words, the transformer voltage regulation describes the ability of the transformer to provide a constant voltage from no load to full load. The secondary voltage of the transformer should not vary with load when the input supply is constant. The transformer can be treated as a voltage source, and the variation in the secondary terminal voltage from no load to full load depends on the voltage drop in the transformer winding.

When current flows through the transformer, the voltage drop takes place due to the reactance and resistance of the transformer. The variation in the secondary output voltage of the transformer from its no load to full load is called the voltage regulation of the transformer.

## Transformer Voltage Regulation Formula

The voltage regulation of the transformer shows how well a transformer maintains constant secondary output voltage from no load to full load condition when the primary voltage is constant.

Where,

Vno load is the voltage at no load, and Vfull load is the voltage at full load.

The secondary output voltage decreases as the current flowing through the transformer is increased. This happens because of the voltage drop in the transformer winding. The secondary output voltage at full load is always less than the output voltage at no load. The lesser the voltage difference of no load to full load condition, the better the transformer regulation.

#### Example of Voltage Regulation :

The transformer’s secondary output voltage is 220 volts at no load. The secondary voltage decreases from 220 to 210 volts when the transformer is loaded up to its full load current capacity.

The drop in the secondary output voltage from no load to full load = 10 Volts

If the secondary voltage decreases from 220 to 215 volts when the transformer is loaded up to its full load current capacity. The regulation of the transformer, in this case, is 2.32 %. The % regulation of the transformer should be as minimum as possible to have almost constant secondary output voltage. Also, the copper loss decreases when the regulation of the transformer is improved.

## What Factors Affect the Transformer Voltage Regulation?

The following factors affect the voltage regulation of the transformer.

1. Resistance per phase – The resistance of the primary and secondary winding causes a voltage drop: the more the resistance, the more the voltage drops. Transformer with higher primary and secondary resistance has poor voltage regulation.
2. Reactance per phase – The reactance of the primary and secondary winding causes a voltage drop. The more the reactance, the more the voltage drops. Transformer with higher primary and secondary reactance has poor voltage regulation.
3. Leakage Flux – If leakage flux is higher, the leakage reactance XL increases, which increases the Ia XL voltage drop. Hence, regulation becomes poor.
4. The magnitude of secondary load current- If load current increases, IaRa and IaXL voltage drop increases. Therefore, the terminal’s voltage drops, which makes regulation poor.
5. Load Power factor: The load power factor also affects the transformer voltage regulation. The lagging power factor demands more current, and it causes more voltage drop in transformer winding. As a result, the voltage regulation of the transformer deteriorates. The leading power factor increases the transformer’s secondary voltage, and thus, the regulation of the transformer improves.

The transformer has primary and secondary winding. The winding has resistance and reactance. The primary resistance and reactance can be referred to as the secondary side or vice versa. The voltage regulation of the transformer depends on the reactance and the resistance of the transformer. The equivalent secondary circuit of the transformer is given below.

When the transformer is at no load, the secondary current I2 =0, and the transformer draws only a no-load current. The voltage drop I2Z2  across secondary impedance occurs with an increase in the secondary current. The voltage drop in the secondary winding is maximum when the transformer operates at its rated kVA capacity, delivering the rated secondary current to the load.

At no load, the secondary terminal voltage = E2
At rated secondary current, the voltage drop = I2Z2
At rated secondary current, the terminal voltage = V2

According to KCL,
E2   =  I2Z2 + V2
E2 – V2 =  I2Z2

The regulation of the transformer depends on the power factor of the load. Now, we will discuss the regulation of the transformer at lagging, leading, and unity power factor.

## Voltage Regulation of Transformer for Lagging Power Factor

Let the angle between the secondary terminal voltage Vand secondary current I2 be θ2. The phasor diagram of the no-load voltage(E2 ), full load voltage (V2), and current (I2)is shown below.

From the above diagram,

OC  = OA + AB + BC
In triangle ABE
AB = AE Cosθ2

In triangle DEF,
DC = DE Sinθ2

The angle between OC and OD is very small, and OC is equal to OD.

OC = OD
OC = OA + AB + BC
E2  = V2  + AE Cosθ2 + DE Sinθ2
E2  = V2  + I2R2 Cosθ2 + I2X2 Sinθ2
E2  – V2  =  I2R2 Cosθ2 + I2X2 Sinθ2

## Voltage Regulation of Transformer for Leading Power Factor

The phasor diagram of the transformer operating at the leading power factor is shown below.

From the above diagram,

OC  = OA + AB – BC
In triangle ABE,

AB = AE Cosθ2

In triangle DEF,
BC = DE Sinθ2

The angle between OC and OD is very small, and OC equals OD.

OC = OD
OC = OA + AB – BC

Here, OA = V2
E2  = V2  + AE Cosθ2 – DE Sinθ2
E2  = V2  + I2R2 Cosθ2 – I2X2 Sinθ2
E2  – V2  =  I2R2 Cosθ2 – I2X2 Sinθ2

### Zero Voltage Regulation of Transformer

The secondary voltage at no load can’t equal the secondary voltage at the load. The zero voltage regulation of the transformer is an ideal case, but practically, it is impossible. An ideal transformer has zero hypothetical voltage regulation.

## Solved Problem on Voltage Regulation of Transformer

The secondary terminal voltage is;