Permanent magnet synchronous motor (PMSM) equivalent circuit
This might give you an idea of how to do the derivative, you can use laplace transforms in LT spice. 



The model will be difficult to run if the model needs to run on more than one frequency

\$\omega_r\psi_d\$ will be a difficult parameter if it needs to vary over the course of the simulation, if it doesn't , just hard code in the parameter with a b-source.

For \$\phi_q=L_q i_q\$a bv source with 
the parameter of the be source being:  

V=omega*((inductorvalue*I(inductor))

Inductorvalue is the value of the inductor I(inductor) is the current through the inductor. Omega could be a .param statement



If omega needs to vary then you will have to find some way to turn it into a voltage signal or current signal (I suppose you could use a circuit of some type) and then turn that into a V(omega) statement.