Equivalent Circuit of Three Phase Induction Motor

Equivalent circuit of any Electrical Machine is the theoretical representation of that Electrical Machine by using standard active and passive electrical elements. An equivalent circuit of an Electrical Machine retains all the electrical characteristics of the given machine and it may be used to analyze and predict the performance of the given device.

Similarly, equivalent circuit of the 3-phase induction motor is the circuit model that contains all the electrical elements (active and passive elements) and retains all the electrical characteristics of three phase induction motor. The equivalent circuit of a three-phase induction motor can be drawn on per phase basis.

Since an equivalent circuit retains all the electrical characteristics of the given machine then it is necessitate, that we have the understanding of all the concepts about that given machine in detail.

So, before moving forward to study the equivalent circuit of the three-phase induction motor one should know about the given concepts about the three-phase induction motor in detail.

Equivalent Circuit of Induction Motor

In the working principle of three phase induction motor, we studied that an induction motor works on the Faraday Law of mutual induction which is similar to the working principle of transformer and an induction motor is also called a rotating transformer. So, on the basis of working principle, it is assumed that the equivalent circuit of an induction motor is similar to the equivalent circuit transformer.

However, there are certain dissimilarities between the induction motor and transformer which we have to keep in mind while modifying the equivalent circuit of the transformer into the induction motor.

Above figure shows the equivalent circuit of the transformer in which part 1 shows the equivalent circuit of primary winding and part 2 shows the equivalent circuit of secondary winding which are linked via transformation ratio a.

In the similar context the equivalent circuit of an induction motor at standstill rotor can be drawn as the same as that of the transformer. And also, the parameters of the standstill rotor are linked to the stator parameter via the transformation ratio of induction motor windings i.e. K.

Equivalent Circuit of Induction Motor Under Running Condition

Under the running condition the motor parameters such as frequency, reactance, induced voltage and current changes with a mechanical parameter called slip. So, the equivalent circuit of the rotor side of the transformer is not valid for the induction motor because in transformer frequency remains constant for both primary as well as secondary side but in case of running induction motor frequency changes.

The effect of the slip on rotor parameters under running condition and stand still condition is shown by the given equation.

F₂ = sF
E₂” = sE₂
X₂” = sX₂

where,

F₂ = rotor frequency
F = stator frequency
E₂ = induced voltage in stand still rotor
E₂” = induced voltage in rotor under running condition
X₂ = rotor reactance in stand still rotor
X₂” = rotor reactance under running condition

So, keeping these parameters in mind the equivalent circuit of the induction motor can be redrawn as shown in the given figure.

While analyzing the above circuit we face a difficulty that is the transformer action between the stator side and the rotor side. To remove this transformer action, we have to make the transformation ratio unity and this can be done by referring the rotor circuit to the stator side. By doing this, it is assured that the stator circuit and the rotor circuit have the same frequency.

To refer the rotor circuit to the stator side, refer all the quantities of the rotor circuit to the stator side.

R₂’ = k².R₂
X₂’ = k².X₂
E₂’ = k.E₂
I₂’ = I₂ / k

Where R₂’, X₂’, E₂’, and I₂’ are quantities of the rotor circuit referred to the stator side.

From above circuit,

Applying the above equation on the rotor side of the equivalent circuit.

In the last step of equivalent circuit development, the unit ratio transformer can now be replaced by its equivalent branch that contains a resistance R_c and reactance X_ꭒ.

Actually, the resistance R_c and reactance X_u are the fictitious quantities they do not exist physically but for analyzing the core loss and magnetizing current of the unit ratio transformer they are considered and represented as in the given figure.

Equivalent circuit of three phase induction motor

In the above circuit we see that rotor resistance is not present, actually the rotor resistance is the representation of rotor copper losses. So, if rotor resistance R₂’ is separated from R₂’/s to represent the rotor copper loss as a separate entity the equivalent circuit can be drawn in the figure in which R₂’(1/s - 1) represents the mechanical load in electrical form.

Induction Motor Equivalent Circuit Diagram

Above figure shows the equivalent circuit of three phase induction motor in which

R₁ and R₂’ show the resistance of stator winding and rotor winding respectively in which copper losses occur.
X₁ and X₂’ show the reactance of stator winding and rotor winding respectively.
R_c is the fictitious resistance which is considered as the core loss resistance.
X_ꭒ is the fictitious reactance which is considered as the magnetzing reactance.