# Induction motor magnetising current and R0, X0 calculation

#### bizuputyi

Joined Aug 3, 2014
21
The question has a 4-pole, star-connected, squirrel-cage induction motor fed from a 50Hz supply. The following table shows results as the supply voltage was reduced with the motor running on no-load.

$$\begin{array}{|l|l|l|c|c|c|} \hline \text{stator line voltage (V)} & 220 & 164 & 112 & 88 & 42\\ \hline\\ \text{stator line current (A)} & 6.8 & 5.4 & 3.9 & 3.8 & 3.7\\ \hline\\ \text{stator power (W)} & 470 & 360 & 278 & 244 & 232\\ \hline\\ \end{array}$$

I estimated the sum of windage and friction losses to be 210W by plotting a graph stator voltage squared against power and extrapolating the curve until it cuts the power axis. The question asks for the no-load magnetising current $$I_0$$ and the equivalent circuit magnetising circuit parameters $$R_0$$ and $$X_0$$. The question specifically says: assume no load current $$I_0$$ is magnetising losses.

Which I think it means that power factor cos$$\phi = 0$$. I know in practise this is impossible, but in theory if this is the case then line current must equal magnetising current and resistance is zero and reactance is line voltage divided by line current.

Is that correct? If not how do I get magnetising current?