# Generic loss minimization for nonlinear synchronous machines by analytical computation of optimal reference currents considering copper and iron losses

The unified theory (introduced in [1]), which allows

to analytically solve the optimal feedforward torque control

(OFTC) problem of anisotropic synchronous machines (SM),

is extended by considering all relevant machine nonlinearities

and copper and iron losses and, thus, minimizing the overall

(steady-state) losses in the machine. Instead of the well known maximum torque per current (MTPC) operation strategy, maximum torque per losses (MTPL) is realized. The unified theory for the derivation of the analytical solution is briefly recapitulated. Moreover, current and speed dependent iron losses, as well as, magnetic saturation and cross-coupling effects are considered. The resulting nonlinear optimization problem is solved via online linearization of the relevant expressions. The linearization is exemplified for flux linkages and machine torque. The presented decision tree guarantees an optimal operation management and smooth transitions between all operation strategies such as MTPL, field weakening (FW), maximum current (MC) and maximum torque per voltage (MTPV). Finally, the extended unified theory is validated for a real, highly nonlinear SM.

to analytically solve the optimal feedforward torque control

(OFTC) problem of anisotropic synchronous machines (SM),

is extended by considering all relevant machine nonlinearities

and copper and iron losses and, thus, minimizing the overall

(steady-state) losses in the machine. Instead of the well known maximum torque per current (MTPC) operation strategy, maximum torque per losses (MTPL) is realized. The unified theory for the derivation of the analytical solution is briefly recapitulated. Moreover, current and speed dependent iron losses, as well as, magnetic saturation and cross-coupling effects are considered. The resulting nonlinear optimization problem is solved via online linearization of the relevant expressions. The linearization is exemplified for flux linkages and machine torque. The presented decision tree guarantees an optimal operation management and smooth transitions between all operation strategies such as MTPL, field weakening (FW), maximum current (MC) and maximum torque per voltage (MTPV). Finally, the extended unified theory is validated for a real, highly nonlinear SM.