# Phasor diagram of transformer

May 18, 2017 ## Phasor diagram of transformer

Lets start our lecture with phasor diagram of transformer at no load condition.

## Phasor Diagram of transformer at no load condition :

We have already known that the theory of transformer and its operation depends on mutual  induction that ” when the transformer  is connected to the AC source,  an electrical current passes  in the primary winding and this current called No load current ( Io ) “ . This current causes  a production of variable magnetic flux . This magnetic flux cuts both the primary and the secondary winding and generates in each of them an opposite Electro Motive Force (E.M.F) proportional to the number of turns and the rate of change in the flux of time. And the No load current is divided into two compounds Ia, Im Ia:  is the cause of iron loss

Im:  is the cause of magnetizing circuit

Such that :

Ia = Io * cosφo

Im = Io * sinφo

Φo:  the angle between current Io and voltage for primary side

### power of transformer at no load condition :

Because the primary winding has physical resistance (R1) and inductive reactance (X1), the current of the load causes a voltage drop at the terminals of the primary winding shown in the following relationship At no load condition, the output power of transformer is equal to “Zero” and therefore the power withdrawn from the source (input power) is consumed in the loss of iron and copper So, we can neglect the losses of copper because of the small primary current and the absence of current in the secondary.

• The input power of the transformer is almost equal to the iron loss and calculated from the following relationship :

Po = V1 * Io * cosφo

This iron loss is consumed in the resistance of the magnetic circuit Ro and shown at the following relationship :

Ro = (V1/ Ia) = (V1/ Io * cosφo)

Also we can calculate reactance Xo from following relationship :

Xo = (V1/ Im) = (V1/ Io * sinφo)

So, We notice that the current (Io) is passed in the case of  “on load ” or “without load” and also the iron loss is fixed as long as the transformer is connected to the rated operating voltage.

### How to draw phasor diagram of transformer at no load condition:

If we assume that the voltage wave V1 is a sine wave, the current (Im) causing the magnetic flux is 90 degrees lagging and therefore the flux is also lagging at the same angle due to the flow of current in the inductive reactance

So, • Angle between Im and Ia  is 90 (as Im lagging) • Induced EMF at the same angle of Ia •  #### Phasor diagram of transformer on load condition: When a load is connected to the terminals of the secondary winding (Z2) , an electrical current passes in secondary side called the secondary winding current (I2) due to the impedance of the load. This current causes a magnetic flux in the iron core. this value of magnetic flux depends on the current of I2 So,This flux must be opposite by another counter flux in the primary winding. So, at loading condition the total current of the load (I2), I2 = (V2/Z2) is the total current which drawn by the load from the source so we can represent the phasor diagram of transformer as follows : 