Copper losses dissipated in the windings of electric machines are the sum of classical ohmic DC losses and additional AC eddy current losses. In fact, the level of eddy current losses is strongly correlated to the manner of disposition of coil conductors in machine slots. Then, to improve the efficiency in electric machines, the selection of an optimal winding configuration becomes substantial. Since eddy current losses derive from the strong electromagnetic coupling between current density and time-dependent magnetic field which cannot be solved easily, numerical analyses such as particularly the one using the finite element method are often used. As for the finite element modeling, it can employ moving band technique to perform the rotor motion and Newton-Raphson iterations to deal with the nonlinear behavior of magnetic circuits. It leads then to a substantial computational time that hinders any process of conception or optimization of winding geometries. To overcome this issue, a 2D finite element model reduction based on the perturbation method is proposed. It starts from one approximate finite element solution of a simplified complete machine modeling to find fast but accurate solutions in slots subdomains when any variation of geometrical or physical data occurs. It allows adapting nonconforming meshes and provides clear advantages in repetitive analyses when we search the optimized winding configuration for a given number of turns.
The simulation of electric machines in order to calculate the copper losses is about a time‐dependent electromagnetic problem. When the finite element method associated with a time stepping scheme is used to solve the problem, the solution is strongly linked to initial conditions, among which the most important is the solution at the initial time. Because it is practically chosen as an arbitrary solution, several time‐consuming electrical excitation periods must be simulated therefore to reach finally the steady‐state conditions. The copper losses can be calculated now without any transient components that can affect the credibility of the copper losses amount. This article suggests a model‐order reduction method that benefits from the complete model finite element solution of the first transient electrical period, to calculate the reduced model solution in the subsequent periods using the proper orthogonal decomposition approach combined with the discrete empirical interpolation method. Nevertheless, in case of relatively high frequency excitation, the full reduction of the problem leads to significant imprecision in the amount of copper losses. To improve the accuracy, therefore, a nonlinear subspace model‐order reduction is adopted. It ensures concurrently higher precision and a reduced computational time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.