Dear , see this paper,. regards 

hi

I think you may be looking for a simple explanation . Hope following helps

1 Plot say phase  Vm vs Im ( either max or rms ie saturation curve ). (test or calculate) .

2 For desired rated voltage find Im and corresponding average XM  = Vmdesired / Im from sat curve.

3 Set Xm (from2 )= Xc  and compute cap

4 Intuitive theory  from eqvt circuit     simplified say xm  with series voltage  vserfrom rem magnetism )in parallel with rr/s  . slip s = 0 at no load so we get only  vser. With capacitor  on no load we have to match vterminal = imXc  with Im*(Xm +vser).

5 To see 4 plot vc= Ic *Xc st line on saturation curve . The intersection point will fetch you the operating point. If you have lag load this will have to be supplied with additional cap value.

Cheers

So is Xm fixed for certain voltage? If voltage is 240V then Xm for that voltage will not change? 

There are a host of  assumptions and simplifications in the model ie ignoring Hysteresis, Harmonics eddy effects etc only the fundamental is considered and saturation. Note flux linkage lambda vs i (current ) is nonlinear . We can have incremental inductance at an operating point or average (here LM as given by Vm/Im for fundamental). If you intend to simulate steady state using phase eqt cct represent the xm branch as Vm=f(Im) saturation curve. You can see then at Vm=240v we get Im and then Xm=Vm/Im,A dq transient model is a little more complicated.

Cheers

When the Lm or Xm varying, use the maximum value as a value for the minimum required capacitance.

Regards