Short Note on transformer basics

Short Note on Transformer | Definition of Transformer | Important topics of Transformer

Definition of Transformer:

A transformer is a static device which consists of two or more stationary electric circuits interlinked by a common magnetic circuit for the purpose of transferring electrical energy between them while keeping the frequency of operation constant. 

Important Note:

• The Basic principle behind the transformer action is Faraday's law of electromagnetic induction and Lenz's law.
• The Transformer is a constant frequency and constant power device.

Induced EMF: 

The Direction of induced emf can be found by "Lenz's law" and the magnitude of induced emf can be given by "Faraday's law of electromagnetic induction".

RMS value of induced EMF :

In Primary winding,

`E_1=\sqrt{2}\Pi N_1f\phi _m` Volts

In secondary winding,

`E_2=\sqrt{2}\Pi N_2f\phi _m` Volts

Where,

N₁ = number of turns in primary winding ; 

N₂ = Number of turns in secondary winding ; 

фₘ = Maximum value of the magnetic flux, in webers ;

f = Supply frequency in Hz

Important Note:

• EMF per turn in primary = Emf per turn in secondary
• Compensating primary mmf = secondary mmf 

I₁ٰ N₁ = I₂ N₂ (Where, I₁ٰ = Load component of primary current I₁)

• Primary volt-amperes = Secondary volt-amperes
• Instantaneous power input into primary is equal to the instantaneous power output from the secondary.
• Step-up transformer : N₁＜N₂
• Step-down transformer : N₁＞N₂

Ideal Transformer | Values of ideal transformer :

• The primary and secondary windings have zero resistance. So there is no ohmic power loss and no resistive voltage drop.
• There is no magnetic leakage flux.
• The core loss considered to be zero.

Equivalent circuit diagram of Transformer: 

Equivalent circuit of transformer

Equivalent circuit referred to primary side

Where, 

`\barV_1` = Applied voltage to primary side

`\barVٰ_2` = Secondary terminal voltage referred to primary side

`\barE_1, \barE_2` = induced emf in primary and secondary side.

`\bar Eٰ_2` = Secondary induced emf referred to primary side

`\barI_0` = No load current

`\barI_m, \barI_i` = Magnetizing and core loss component of exciting current

`\R_1, \R_2` = Primary and secondary winding resistances.

`\X_1, \X_2` = Primary and secondary winding leakage reactances.

`\Rٰ_2, \Xٰ_2` =  Secondary resistances and leakage reactance referred to primary side.

`\R_0` = Core loss equivalent resistance.

`X_m` = Magnetising reactance

Note: 

At no load, current drawn from the supply is `I_0`

`\barI_0` = `\barI_m` + `\barI_i` = (2 to 5 % of  `I_fl`)

`\barI_m` = `I_0  sinphi_0` = Magnetising current and is responsible for the production of flux.

`\barI_i` = `I_0  cosphi_0` = Core loss current responsible for the active power being drawn from the source to provide hysteresis and eddy current losses.

`phi_0` = No load phase angle (80 to 85⁰)

Secondary side parameters referred to primary side:

• If  ` \frac{N_1}{N_2} ` = a
• Secondary resistance referred to primary side, `Rٰ_2` = `a^2` `R_2`
• Secondary leakage reactance referred to primary side, `X_2` = `a^2` `X_2`
• Secondary current referred to primary side, `\barIٰ_2` = `\frac{\barI_2}{a}`
• Secondary induced emf referred to primary side, `\barEٰ_2` = a `E_2`
• Secondary terminal voltage referred to primary side, `\barVٰ_2` = a `\barV_2`

Basic Equations for transformer:

 `\barE_1` = a `\barE_2`

`\barI_0` = `\barI_m` + `\barI_i`

`\barE_2` = `\barV_2` + `\barI_2  R_2` + `j\barI_2` `X_2`

`\barV_1` = `\barE_1` + `\barI_1  R_1` + `j\barI_1  X_1`

`\barI_1` = `\frac{\barI_2}{a}` + `\barI_0`

Phasor Diagram: 

Step down transformer at lagging power factor

Note:

• `R_01` = `R_1 + Rٰ_2` = Equivalent resistances referred to primary side.
• `X_01` = `X_1 + Xٰ_2` = Equivalent reactance referred to primary side.
• `Z_01` = `\sqrt{R²_01+X²_01}` = Equivalent impedance referred to primary side.
• Core is transformer should have low reluctance and high permeability.
• Transformer core is made from CRGO (cold rolled grain oriented) material with 4 % of silicon.
• The transformer core is laminated to reduce the eddy current losses

Types of Transformer construction :

1. Core type

2. Shell type

Sr. No.	Core type transformer	Shell type transformer
1	Series magnetic circuit	Parallel Magnetic circuit
2.	2 limb and 2 yoke	3 limb and 2 yoke
3.	Suitable for low flux density application.	Suitable for high flux density application.
4.	Required more amount of copper.	Required less amount of copper.
5.	Required less amount of insulation so suitable for high voltage and high power application.	Suitable for low voltage and lower power applications.

Important Note:

• Transformer winding are made up of stranded conductors instead of solid conductors.
• Low voltage windings are placed nearer to the core, for reducing insulation requirement.