Circle Diagram of a 3 Phase Induction Motor

Circle Diagram of a 3 Phase Induction Motor

The equivalent circuit of a 3 phase induction motor is shown in the Fig. 6.3.1.

All the values shown are per phase values. The circuit is similar to a series R-L circuit. The reactance X_le is fixed while the total resistance R_le + (R₂ (1 - s) / s) is variable. This is because the slip s varies as load varies. The voltage across the parallel exciting branch is V₁. Hence we can write the expression for the rotor current referred to stator as,

The I_2r will be at its maximum when R_ie + R_L = 0 i-e., there exists an ideal short circuit. Hence current Imax is called ideal short circuit current of an induction motor.

The equation (6.3.1) represents equation of a circle with I_max as its diameter. Thus locus of extremity of I2r is a circle, as shown in the Fig. 6.3.2.

But the total stator current Ix per phase is a vector addition of current I_o and I_2r.

I₁ = I_o + I_2r   … vector addition

For any induction motor, I_o has a fixed value and phase angle 0 which is decided by its active component I_c and magnetising component I_m.

As I_o has fixed magnitude and phase, the locus of extremities of I₁ which is I_o + I_2r is also a circle with a diameter still as V₁/X_le. The only change will be that the diameter V₁/X_le will no longer be along X-axis i.e. current axis but will get shifted at the tip of the I_o phasor. All the I_2r phasors are to be drawn from I_o phasor to get I₁ as I_o has fixed magnitude and phase angle ϕ₀.

Thus the current locus for a stator current I₁ is also a semicircle which is true called circle diagram of a three phase induction motor. This diagram once obtained can be used to predict the performance of an induction motor under variable load is shown in the Fig. 6.3.3.

Let us see, how to obtain the data for plotting the circle diagram.

Review Question

1. Prove that the locus of extremity of current drawn by a three phase induction motor under variable load conditions is a circle.