Voltage Regulation of Transformer

The term voltage regulation is used to identify voltage change characteristics in the transformer as the load varies.

In most conditions, the load is connected to the secondary winding, and the supply is given to the primary winding.

As the current taken from supply changes, the load terminal voltage of the transformer changes because of the voltage drops in internal impedance.

Definition

“The arithmetic difference in the secondary terminal voltage between no-load and full-load at a given power factor with the same value of primary voltage for both rated load and no-load is defined as the voltage regulation of transformer.”

The voltage regulation is calculated in either per unit or percentage of the rated load voltage.

It is an important parameter to measure the performance of the transformer.

Conditions

The voltage regulation of a transformer is calculated under followed conditions.

  • At rated voltage, current, and frequency.
  • Rated load is understood when the regulation is calculated without specific reference to the load condition.
  • The waveform of a load voltage is assumed as a pure sine wave unless given in a specific waveform shape.
  • The power factor of load should be counted while calculating voltage regulation. If a power factor is not specified, assume unity power factor.

The voltage variation at a the load side is defined in terms of voltage regulation.

A transformer in public supply must not be adjusted that the voltage at the consumers’ terminals must not exceed ±5%.

Voltage Regulation in Terms of Primary Values

Per-unit voltage regulation;

    \[ VR (PU) = \frac{|V_{2nl}|-|V_{2fl}|}{|V_{2fl}|} \]

    \[ V_{2nl} = \frac{V_1}{a} \]

Where, ‘a’ is turns ratio or transformation ratio.

Therefore,

    \[ VR (PU) = \frac{|\frac{V_1}{a} |-|V_{2fl}|}{|V_{2fl}|} \]

Calculation of Voltage Regulation

The voltage regulation of the transformer is calculated from its circuit parameter. The approximate equivalent circuit of the transformer is as shown in the figure below.

Approximate Equivalent Circuit Referred to Secondary
Approximate Equivalent Circuit Referred to Secondary

By KVL;

    \[ \frac{V_1}{a} = V_2 + I_2 Z_{e2} \]

Since,

    \[ I_2Z_{e2} \]

depends on the power factor. Therefore, the voltage regulation depends on the power factor.

To calculate the voltage regulation, following steps are used.

Step-1 Take V2 as reference phasor,

    \[ \therefore V_2 = V_2 \angle 0^{\circ} \]

Step-2 Calculate I2 in phasor form,

For lagging power factor,

    \[ I_2 = I_2 \angle - \phi_2 = I_2 cos \phi_2 - j I_2 sin \phi_2 \]

For lading power factor,

    \[ I_2 = I_2 \angle + \phi_2 = I_2 cos \phi_2 + j I_2 sin \phi_2 \]

For unity power factor,

    \[ I_2 = I_2 \angle 0^{\circ} = I_2 + j0 \]

Step-3 Calculate Ze2,

    \[ Z_{e2} = R_{e2} + jX_{e2} \]

Step-4 Calculate V2nl,

    \[ V_{2nl} = \frac{V_1}{a} \]

    \[ \frac{V_1}{a} = V_2 \angle 0^\circ + I_2 Z_{e2} \]

Step-5 Calculate the voltage regulation,

    \[ VR (PU) = \frac{|\frac{V_1}{a}|-|V{2fl}|}{|V_{2fl}|} \]

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