# Optimal feedforward torque control for nonlinear induction machines considering stator & rotor copper losses and current & voltage limits

In order to analytically solve the optimal feed-

forward torque control (OFTC) problem of induction machines (IMs), the unified theory for synchronous machine introduced in [1] is extended by considering relevant IM nonlinearities and incorporating stator and rotor copper losses. Instead of the well known Maximum Torque per (stator) Current (MTPC) operation strategy, Maximum Torque per (copper) Losses (MTPL Cu ) is realized and extended by the Maximum (rotor) Current (MC r, ext ) strategy due to stator and rotor current limitations. Modeling magnetic saturation and cross-coupling effects leads to a con-

strained nonlinear optimization problem which is solved based on the idea of sequential quadratic programming (SQP). The second order Taylor approximations are formulated in implicit form as quadrics. Applying the Lagrangian formalism to the quadratic problem leads to analytical solution for the optimal rotor currents. For a doubly-fed induction machine (DFIM), a decision tree for optimal operation management is presented and the OFTC is validated in simulations for a real nonlinear IM.

forward torque control (OFTC) problem of induction machines (IMs), the unified theory for synchronous machine introduced in [1] is extended by considering relevant IM nonlinearities and incorporating stator and rotor copper losses. Instead of the well known Maximum Torque per (stator) Current (MTPC) operation strategy, Maximum Torque per (copper) Losses (MTPL Cu ) is realized and extended by the Maximum (rotor) Current (MC r, ext ) strategy due to stator and rotor current limitations. Modeling magnetic saturation and cross-coupling effects leads to a con-

strained nonlinear optimization problem which is solved based on the idea of sequential quadratic programming (SQP). The second order Taylor approximations are formulated in implicit form as quadrics. Applying the Lagrangian formalism to the quadratic problem leads to analytical solution for the optimal rotor currents. For a doubly-fed induction machine (DFIM), a decision tree for optimal operation management is presented and the OFTC is validated in simulations for a real nonlinear IM.