Why Im_ref = 2⋅T ref /3⋅p⋅λ pm for Interior PMSM? in MTPA Control Reference
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Joel Van Sickel on 1 Nov 2022
The first equation your have underlined is the maximum current reference limit used for a specific type of control ( MTPA) while the other equation is the mathematical model of of a motor (albeit a simplified equation as this is for a lumped parameter motor model). These equations are not the same nor should they be, although the controller algorithm is derived from the mathematical model equation (elimnate the (Ld-Lq)*id*iq by setting id to zero and they are identical. Further work is required in the controller after calculating maximum current to calculate reference id and iq current values.