Transformer On Load Condition

When the transformer is on the loaded condition, the secondary of the transformer is connected to load. The load can be resistive, inductive or capacitive. The current I₂ flows through the secondary winding of the transformer. The magnitude of the secondary current depends on the terminal voltage V₂ and the load impedance. The phase angle between the secondary current and voltage depends on the nature of the load.

Contents:

• Operation of the Transformer on Load Condition
• Phasor Diagram of Transformer on Inductive Load
• Steps to draw the phasor diagram
• Phasor Diagram of Transformer on Capacitive Load
• Steps to draw the phasor diagram at capacitive load

Operation of the Transformer on Load Condition

The Operation of the Transformer on Load Condition is explained below:

• When the secondary of the transformer is kept open, it draws the no-load current from the main supply. The no-load current induces the magnetomotive force N₀I₀ and this force set up the flux Φ in the core of the transformer. The circuit of the transformer at no load condition is shown in the figure below:
  • When the load is connected to the secondary of the transformer, I₂ current flows through their secondary winding. The secondary current induces the magnetomotive force N₂I₂ on the secondary winding of the transformer. This force set up the flux φ₂ in the transformer core. The flux φ₂ opposes the flux φ, according to Lenz’s law.
    
    • As the flux φ₂ opposes the flux φ, the resultant flux of the transformer decreases and this flux reduces the induced EMF E₁. Thus, the strength of the V₁ is more than E₁ and an additional primary current I’₁ drawn from the main supply.
      The additional current is used for restoring the original value of the flux in the core of the transformer so that V₁ = E₁. The primary current I’₁ is in phase opposition with the secondary current I₂. Thus, it is called the primary counter-balancing current.
    • The additional current I’₁ induces the magnetomotive force N₁I’₁. And this force set up the flux φ’₁. The direction of the flux is the same as that of the φ and it cancels the flux φ₂ which induces because of the MMF N₂I₂

    Now, N₁I₁’ = N₂I₂
    Therefore,

• The phase difference between V₁ and I₁ gives the power factor angle ϕ₁ of the primary side of the transformer.
• The power factor of the secondary side depends upon the type of load connected to the transformer.
• If the load is inductive as shown in the above phasor diagram, the power factor will be lagging, and if the load is capacitive, the power factor will be leading. The total primary current I₁ is the vector sum of the currents I₀ and I₁’. i.e

Phasor Diagram of Transformer on Inductive Load

The phasor diagram of the actual transformer when it is loaded inductively is shown below:

Steps to draw the phasor diagram

• Take flux ϕ, a reference
• Induces emf E₁ and E₂ lags the flux by 90 degrees.
• The component of the applied voltage to the primary equal and opposite to induced emf in the primary winding. E₁ is represented by V₁’.
• Current I₀ lags the voltage V₁’ by 90 degrees.
• The power factor of the load is lagging. Therefore current I₂ is drawn lagging E₂ by an angle ϕ₂.
• The resistance and the leakage reactance of the windings result in a voltage drop, and hence secondary terminal voltage V₂ is the phase difference of E₂ and voltage drop.

V₂ = E₂ – voltage drops
I₂ R₂ is in phase with I₂ and I₂X₂ is in quadrature with I₂.

• The total current flowing in the primary winding is the phasor sum of I₁’ and I₀.
• Primary applied voltage V₁ is the phasor sum of V₁’ and the voltage drop in the primary winding.
• Current I₁’ is drawn equal and opposite to the current I₂

V₁ = V₁’ + voltage drop
I₁R₁ is in phase with I₁ and I₁X_I is in quadrature with I₁.

• The phasor difference between V₁ and I₁ gives the power factor angle ϕ₁ of the primary side of the transformer.
• The power factor of the secondary side depends upon the type of load connected to the transformer.
• If the load is inductive as shown in the above phasor diagram, the power factor will be lagging, and if the load is capacitive, the power factor will be leading.       Where I₁R₁ is the resistive drop in the primary windings
  I₂X₂ is the reactive drop in the secondary winding

Similarly

Phasor Diagram of Transformer on Capacitive Load

The Transformer on the Capacitive load (leading power factor load) is shown below in the phasor diagram.

Steps to draw the phasor diagram at capacitive load

• Take flux ϕ a reference
• Induces emf E₁ and E₂ lags the flux by 90 degrees.
• The component of the applied voltage to the primary equal and opposite to induced emf in the primary winding. E₁ is represented by V₁’.
• Current I₀ lags the voltage V₁’ by 90 degrees.
• The power factor of the load is leading. Therefore current I₂ is drawn leading E₂
• The resistance and the leakage reactance of the windings result in a voltage drop, and hence secondary terminal voltage V₂ is the phasor difference of E₂ and voltage drop.

V₂ = E₂ – voltage drops
I₂ R₂ is in phase with I₂ and I₂X₂ is in quadrature with I₂.

• Current I₁’ is drawn equal and opposite to the current I₂
• The total current I₁ flowing in the primary winding is the phasor sum of I₁’ and I₀.
• Primary applied voltage V₁ is the phasor sum of V₁’ and the voltage drop in the primary winding.

V₁ = V₁’ + voltage drop
I₁R₁ is in phase with I₁ and I₁X_I is in quadrature with I₁.

• The phasor difference between V₁ and I₁ gives the power factor angle ϕ₁ of the primary side of the transformer.
• The power factor of the secondary side depends upon the type of load connected to the transformer.

This is all about the phasor diagram on various loads.