# Parameters And Equivalent Circuit Of Induction Motor

In an induction motor, the transfer of energy from the stator to the rotor takes place entirely inductively. Hence an induction motor acts like a transformer with a stator forming primary and a rotor forming the secondary. Like in a transformer, here also the primary and secondary circuits are represented by equivalent elements called parameters of the induction motor.

## STATOR CIRCUIT

When voltage "V_{1}" is applied to stator terminals, it drops partly in the stator impedance i.e. winding resistance "R_{1}" and reactance "X_{1}" and partly is opposed by stator induced e.m.f. E_{1}.

V_{1} = E_{1} + I_{1}R_{1} + JI_{1}X_{1}

Where "I_{1}" is the stator current and is the vector sum of the no-load current "I_{o}" and rotor equivalent current I_{21}. The no-load current "Io" has further two components "I_{w}" and "I_{m}". The "I_{w}” is called a working component and is in phase with "V_{1}". It is a current passing through the core resistance R. And it produces a core loss. The component "I_{m}" is called magnetizing component and it lags behind "V_{1}". It is a current passing through the reactance "X_{m}" and it produces flux in the core. The stator circuit with circuit parameters is shown in the Figure 1.

**Figure 1: Stator Equivalent Circuit of Three-Phase Induction Motor**

## ROTOR CIRCUIT

The rotor of the induction motor is like a short-circuited secondary of transformer. The resistance and reactance of the rotor circuit are represented by "R_{2} and X_{2} See Figure 2. In running condition i.e. when

**Figure 2: Rotor Equivalent Circuit of Three-Phase Induction Motor**

The rotor rotates, and the inductive reactance no longer remains equal to "X_{2}". But it equals to slip times the inductive reactance i.e.:

X_{2} = 2πfL_{2}

During running f_{r} = Sf

Inductive reactance = 2ΔfrL_{2} = 2πSf L_{2} = SX_{2}

In figure shown

I = short circuit rotor current.

ES = induced voltage in the rotor circuit.

For simplicity and an easy analysis, the rotor circuit is referred towards the stator by the transformation ratio method. Let the referred values of rotor resistance and reactance be "R_{21} and X_{21}". The complete equivalent circuit of the induction motor becomes as shown in Figure 3. Thus, the circuit parameters of induction motors are:

Stator resistance R_{1}

stator reactance X_{1}

core resistance R_{w}.

magnetizing reactance X_{m}

rotor resistance R_{2} (or R_{2})

rotor reactance SX_{2} (or SX_{21})

** Figure 3: Equivalent Circuit of Three-Phase Induction Motor**