Analysis of Synchronous Machines, 2nd Edition

Equation (3.123) states that the electromagnetic torque can be viewed as the instantaneous cross product of the stator flux linkage vector and the stator current vector. Because of the dot product taken with respect to the ${\widehat{u}}_{ns}$ direction, only the cross product of the flux linkage and current components in the d–q plane contributes to torque production since it is only the cross product of these components which results in a vector in the n–axis direction and therefore is non-zero when dotted with the unit vector in the direction of the n–axis.

If this equation is reduced to vector form, it can be readily shown that the scalar version for electromagnetic torque is

$T_e=\left(\frac{3}{2}\right)\left(\frac{P}{2}\right){\widehat{u}}_{ns}^t\cdot {\widehat{\lambda }}_{dqns}\times {\widehat{i}}_{dqns}$

(3.124)

This expression for torque is, in fact, ...