Analytical solution for the MTPV hyperbola including the stator resistance

In this paper a method is presented which allows to analytically calculate the Maximum-Torque-Per-Voltage (MTPV) hyperbola including the stator resistance. The method relies on a transformation of the voltage ellipse (voltage constraint) to its principle axis system. Re-formulating the optimization problem in this new coordinates of the principle axis system simplifies the derivation of the analytical solution. A backwards transformation finally gives the analytical solution of the MTPV hyperbola in the classical direct and quadrature (d, q)-reference frame. All theoretical derivations are illustrated by respective figures. The derived MTPV hyperbola "moves" in the plane according to variations of the machine parameters and the machine speed.