AC MACHINES-1 (66761) Theory

Let us understand the voltage regulation by taking an example explained below:

If the secondary terminals of the transformer are open-circuited or no load is connected to the secondary terminals,  the no-load current flows through it.

If the no current flows through the secondary terminals of the transformer, the voltage drops across their resistive and reactive load become zero. The voltage drop across the primary side of the transformer is negligible.

If the transformer is fully loaded, i.e., the load is connected to their secondary terminal,  the voltage drops appear across it. The value of the voltage regulation should always be less for the better performance of the transformer.

From the circuit diagram shown above, the following conclusions are made

• The primary voltage of the transformer is always greater than the induced emf on the primary side. V₁>E₁

• The secondary terminal voltage at no load is always greater than the voltage at full load condition. E₂>V₂

By considering the above circuit diagram, the following equations are drawn
The approximate expression for the no-load secondary voltage for the different types of the load is

1. For inductive loadWhere,
   
   • For Capacitive load

In this way, we define the voltage regulation of the transformer.

Voltage Regulation of Transformer at Unity, Lagging, and Leading Power Factor

Voltage Regulation of Transformer

The voltage regulation of a transformer can be described as the change in the secondary voltage as the current varies from full load to no load while keeping the primary voltage constant.

It is clear from the transformer equivalent circuit in figure 1 that the secondary current I_s produces voltage drop I_sR_s and Is X_s across the resistive and reactive components respectively. Also, the primary current Ip causes primary circuit voltage drops I_pR_p and I_pX_p. Consequently, the effective primary voltage E_p is less than the input voltage V_i, and the output voltage V_o is less than the calculated value of E_s.

Fig.1: Complete Equivalent Circuit of Transformer

Voltage Regulation of Transformer Formula

The percentage change in output voltage from no-load to full-load is termed the voltage regulation of the transformer. Ideally, there should be no change in V_o from no-load to full-load (i.e., regulation = 100%). For the best possible performance, the transformer should have the lowest possible regulation. Mathematically, voltage regulation can be expressed as

Voltage Regulation=Vo(NL)−Vo(FL)Vo(FL)(1)$$\begin{array}{ccc}VoltageRegulation=\frac{V_{o(NL)}-V_{o(FL)}}{V_{o(FL)}}& & \left(1\right)\end{array}$$

Where V_o(NL) is the transformer no-load output voltage, and V_o(FL) is the full load output voltage. Voltage regulation for a transformer is illustrated in figure 2.

Fig.2: Transformer Voltage Regulation

The equation for the voltage regulation of transformer, represented in percentage, is

Voltage Regulation of Transformer for Lagging Power Factor

Now we will derive the expression of voltage regulation in detail. Say lagging power factor of the load is cosθ₂, that means angle between secondary current and voltage is θ₂.

Here, from the above diagram,

Angle between OC and OD may be very small, so it can be neglected and OD is considered nearly equal to OC i.e.

Voltage regulation of transformer at lagging power factor,

 Transformer for Leading Power Factor

Let’s derive the expression of voltage regulation with leading current, say leading power factor of the load is cosθ₂, that means angle between secondary current and voltage is θ₂.

Here, from the above diagram,

Angle between OC and OD may be very small, so it can be neglected and OD is considered nearly equal to OC i.e.

Voltage regulation of transformer at leading power factor,