# PMSM dynamic model

I have been working on a dynamic model of the PMSM with surface mounted magnets and sinusoidal stator winding. I am little bit confused by formulas for the $$\L_d\$$ and $$\L_q\$$ inductances. I have found several formulas for these inductances and I don't know which of them are correct.

So I have attempted to derive the equations alone and I have followed these steps

1. Formulas for magnetic fluxes for individual stator phases ($$\L\$$ stator phase self inductance, $$\M\$$ mutual inductance for stator windings, $$\\psi_m\$$ magnetic flux of permanent magnet,$$\\theta\$$ rotor position i.e. angle between axes of stator phase $$\a\$$ and permanent magnet axes $$\d\$$)

2. Clarke transform ($$\\hat{a}=e^{j\frac{2\pi}{3}}\$$)

3. Magnetic fluxes in $$\(\alpha,\beta)\$$

4. Park transform

5. Magnetic fluxes in $$\(d,q)\$$

Based on the formulas for magnetic fluxes in $$\(d,q)\$$ I have following formulas $$\L_d=\frac{2}{3}(L-M)\$$ and $$\L_q=\frac{2}{3}(L-M)\$$. Is my derivation correct? I am confused because my formulas are totally different from what I have seen so far. Thank you for any ideas.