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

Abstract

The unified theory (introduced in [1]), which allows<br>to analytically solve the optimal feedforward torque control<br>(OFTC) problem of anisotropic synchronous machines (SM),<br>is extended by considering all relevant machine nonlinearities<br>and copper and iron losses and, thus, minimizing the overall<br>(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.

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

“…To solve the constrained nonlinear optimization problem (4), the general idea of sequential quadratic programming (SQP) [13] and, in particular, the sequence used in [1] & [11] is adopted which consists of three main stages per sequence: (i) quadratic approximation of the loss function and all constraints at the current operating point, (ii) applying the Lagrangian formalism to solve the quadratic (sub-)problems (QPs), (iii) selection of the optimal solution and the operating point for the next iteration. The sequence terminates if the solutions of the QP converged to an operating point which is equal to the local or global minimizer for a convex differentiable objective function [13].…”

“…Thus, this paper provides an advanced nonlinear IM model for OFTC which allows for analytical ORCC taking into account (i) nonlinear magnetic saturation, (ii) cross-coupling effects (i. e. the dependencies between orthogonal current and magnetic flux vectors are not neglected), and (iii) stator and rotor copper losses. In addition, the proposed OFTC approach is generic as it allows further (online) parameter adaption, such as the temperature dependent stator and rotor resistances or even iron losses [11]. The nonlinear IM model is based on magnetic flux linkage maps obtained by measurements [10] or finite element analysis (FEA) [12].…”

“…The focus of this paper is on minimizing the total IM copper losses assuming that the iron losses are negligible or constant for a given torque as in [5]. Contributions of this paper are: The unified theory for synchronous machines presented in [1] & [11] is extended and applied to IMs: Section II introduces the nonlinear IM model and problem statement; Section III-A integrates the measured magnetic flux linkage maps into the quadratic IM model approximation; Section III-B discusses quadratic programming with analytical solution; Section III-C proposes a novel operation management for OFTC in the full operating range (i. e. even at the operating limits); Section IV discusses implementation and simulation results.…”