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 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.

F_{2}
= sF

E_{2}” = sE_{2}

X_{2}” = sX_{2}

Where,

F_{2}
= rotor frequency

F =
stator frequency

E_{2}
= induced voltage in stand still rotor

E_{2}” =
induced voltage in rotor under running condition

X_{2}
= rotor reactance in stand still rotor

X_{2}” =
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.

R_{2}’
= k^{2}.R_{2}

X_{2}’ =
k^{2}.X_{2}

E_{2}’ =
k.E_{2}

I_{2}’ =
I_{2} / k

Where R_{2}’, X_{2}’,
E_{2}’, and I_{2}’ 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 Rc and reactance Xê’.

Actually, the resistance Rc and
reactance Xu 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.

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 R_{2}’
is separated from R_{2}’/s to represent the rotor copper loss as a
separate entity the equivalent circuit can be drawn in the figure in which R_{2}’(1/s
- 1) represents the mechanical load in electrical form.

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

- R
_{1}and R_{2}’ show the resistance of stator winding and rotor winding respectively in which copper losses occur.

- X
_{1}and X_{2}’ show the reactance of stator winding and rotor winding respectively.

- Rc is the fictitious resistance which is considered as the core loss resistance.

- Xê’ is the fictitious reactance which is considered as the magnetizing reactance.

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