Equivalent Circuit of Induction Motor

EQUIVALENT CIRCUIT OF INDUCTION MOTOR

The three phase induction motor is generally treated as a rotating transformer. The transformer has two winding - one is primary and another one secondary winding. Similarly in an induction motor, stator acts as primary and rotor acts as rotating secondary (or short circuited).

Hence the transfer of energy from stator to rotor in an induction motor takes place entirely inductively linking the two. How an induction motor takes place entirely inductively linking the two. How an induction motor takes can represented as a transformer.

Fig 3.11

Let

V₁ = Supply voltage per phase (it produces the flux which line with stator and rotor)

E₁ = The induced emf in stator/phase due to self induction

E₂ = The induced emf in the rotor due to mutual induction at standstill

R₁ = Stator resistance/phase

X₁ = Stator resistance/phase

R₂ = Rotor resistance/phase

X_2r = Rotor resistance/phase in running condition (sX₂)

E_2r = Rotor induced emf in running condition/phase (sE₂).

When the induction motor operates under no load condition, if draws some current from the supply. It is to produce flux is in the air gap and to supply iron losses. Normally the no load current consist of two components I_W Iµ,

Where

I_W = Working Component which supplies no load losses.

Iµ = Magnetizing Component which sets up flux.

R₀ = No-load resistance/phase (It represents no load losses) = V₁ / I_W

X₀ = No-load reactance/phase (It represents flux set up in the core) =V₁ / I_µ

Equivalent Circuit of an Induction Motor

 When the induction motor load changes, the motor speed also changes. Correspondings slip also changes. Due to this reactance X_2r changes. So it is indicated as a variable element.

Equivalent Circuit of the Rotor

The rotor current under running condition:

from this equation rotor circuit consists of a fixed reactance X₂ in series with a variable resistance R₂/S and supplied with fixed voltage E₂.

Now, the variable resistance can be written as:

Now, the variable resistance R₂/S consists of two parts R₂, R₂ (1-S)/S

(i) The part R₂ is rotor resistance itself, which represents that part when rotor copper loss takes place.

(ii) The part R₂(1-S)/S represents load resistance R_C.

So it is indicate as an electrical equivalent of the mechanical load on the motor. Equivalent of the mechanical load on the motor.

Equivalent Circuit Referred to Stator

K = transformation ratio =E₂/E₁

Rotor parameters are transferred to stator

E₂' = E₂/K.

Rotor current referred to stator:

Rotor reactance referred to stator (X₂)

X₂' = X₂/K²

Rotor resistance referred to stator (R₂')

R₂' = R₂/K²

Load resistance R_L referred to stator:

Equivalent circuit referred to stator.

Approximate Equivalent Circuit

The exciting circuit consists of R₀ and x₀ this existing circuit is transformed to the left of R₁ and X₁, the in accuracy involved due to this is negligible. Hence the calculation are very simple this is known as approximate equivalent circuit

Fig 3.15

Now the circuit is further simplified.

Combined resistance R₁ and R₂ and similarly for reactance X₁ and X₂'

R₀₁ = Equivalent resistance referred to stator = R₁ + R₂' = R₁ + (R₂/k²)

X₀₁ = Equivalent reactance referred to stator = X₁ + X₂' = X₁ + (X₂/k²)

The equivalent circuit (referred to stator).