# Transformer ON Load Condition

When the transformer is on the loaded condition, that means the secondary of the transformer is attached to some load, either it can be resistive, inductive or capacitive. Current I_{2} flows through the secondary winding of the transformer. The magnitude of the current I_{2} depends upon the terminal voltage V_{2} and impedance of the load. The phase angle depends upon 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 transformer is under NO load, it draws no load current I
_{0}. This no load current produces an MMF N_{1}I_{0}which sets up the flux ϕ in the core as shown in the figure below- When the transformer is loaded, current I
_{2}flows in the secondary winding as shown in the figure below. This secondary current I_{2}produces an MMF N_{2}I_{2, }which sets up the flux ϕ_{2 }in the core. This flux ϕ_{2}opposes the flux ϕ which is set up by the current I_{0}. (According to Lenz’s law).- Since the flux ϕ
_{2}opposes the flux ϕ, the resultant flux tends to decrease and causes the reduction of self-induced emf E_{1}. Thus, V_{1}predominates over E_{1}causing additional primary current know as I_{1}’drawn from the supply.The amount of the additional current is such that the flux in the core must be restored to its original value ϕ so that V_{1}= E_{1}. The current I_{1}’ is in phase opposition with I_{2}and is called Primary Counter Balancing Current. - This additional current I
_{1}’produces an MMF, N_{I}I_{1}’ which sets up flux ϕ_{1}’. The direction of the flux ϕ_{1}’ is same as the flux ϕ and it cancels the flux ϕ_{2}sets up by the MMF N_{2}I_{2}.

- Since the flux ϕ

- When the transformer is loaded, current I

- The phasor difference between V
_{1}and I_{1}gives the power factor angle ϕ_{1}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 I
_{1}is the vector sum of the current I_{0 }and I_{1}’. 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 E
_{1}and E_{2 }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. E
_{1}is represented by V_{1}’. - Current I
_{0}lags the voltage V_{1}’ by 90 degrees. - The power factor of the load be lagging. Therefore current I
_{2}is drawn lagging E_{2}by an angle ϕ_{2}. - The resistance and the leakage reactance of the windings result in a voltage drop, and hence secondary terminal voltage V
_{2}is the phasor difference of E_{2}and voltage drop.

V_{2} = E_{2} – voltage drops

I_{2 }R_{2} is in phase with I_{2} and I_{2}X_{2} is in quadrature with I_{2}.

- The total current flowing in the primary winding is the phasor sum of I
_{1}’ and I_{0}. - Primary applied voltage V
_{1}is the phasor sum of V_{1}’ and the voltage drop in the primary winding. - Current I
_{1}’ is drawn equal and opposite to the current I_{2}

V_{1} = V_{1}’ + voltage drop

I_{1}R_{1} is in phase with I_{1} and I_{1}X_{I} is in quadrature with I_{1}.

- The phasor difference between V
_{1}and I_{1}gives the power factor angle ϕ_{1}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 I
_{1}R_{1}is the resistive drop in the primary windings

I_{2}X_{2}is the reactive drop in the secondary winding

Similarly

## Phasor Diagram of Transformer on Capacitive Load

The Transformer on 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 E
_{1}and E_{2 }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. E
_{1}is represented by V_{1}’. - Current I
_{0}lags the voltage V_{1}’ by 90 degrees. - The power factor of the load be leading. Therefore current I
_{2}is drawn leading E_{2} - The resistance and the leakage reactance of the windings result in a voltage drop, and hence secondary terminal voltage V
_{2}is the phasor difference of E_{2}and voltage drop.

V_{2} = E_{2} – voltage drops

I_{2 }R_{2} is in phase with I_{2} and I_{2}X_{2} is in quadrature with I_{2}.

- Current I
_{1}’ is drawn equal and opposite to the current I_{2} - The total current I
_{1 }flowing in the primary winding is the phasor sum of I_{1}’ and I_{0}. - Primary applied voltage V
_{1}is the phasor sum of V_{1}’ and the voltage drop in the primary winding.

V_{1} = V_{1}’ + voltage drop

I_{1}R_{1} is in phase with I_{1} and I_{1}X_{I} is in quadrature with I_{1}.

- The phasor difference between V
_{1}and I_{1}gives the power factor angle ϕ_{1}of the primary side of the transformer. - The power factor of the secondary side depends upon the type of load connected to the transformer.

## 7 Comments

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