Now a days we get LSPMSM by many vendors. wondering if a Line Start PM synch Motor be used with a VSD which is used for Induction Motor for speed or load control ? theoritically it should run ..
As you correctly note this should be possible as most VSD's are programmed to operate various kinds of motors and not just IM. They normally have internal options or a card for this. So yes there is no reason why it cannot be done. Check with the VSD vendor.
For example any VSD set at 0Hz and the correct phase angle may control a DC motor; this I have already done and it works fine if you know how.