Transient simulation of an electrical rotating machine achieved through model order reduction

Abstract

Model order reduction (MOR) methods are more and more applied on many different fields of physics in order to reduce the number of unknowns and thus the computational time of large-scale systems. However, their application is quite recent in the field of computational electromagnetics. In the case of electrical machine, the numerical model has to take into account the nonlinear behaviour of ferromagnetic materials, motion of the rotor, circuit equations and mechanical coupling. In this context, we propose to apply the proper orthogonal decomposition combined with the (Discrete) empirical interpolation method in order to reduce the computation time required to study the start-up of an electrical machine until it reaches the steady state. An empirical offline/online approach based on electrical engineering is proposed in order to build an efficient reduced model accurate on the whole operating range. Finally, a 2D example of a synchronous machine is studied with a reduced model deduced from the proposed approach.

Comparison of DEIM and BPIM to Speed Up a POD-Based Nonlinear Magnetostatic Model

“…with X(t) the vector of unknowns of size Nun=Ne+Nst and (Ij(t))1jNst =(ij(t))1jNst. To solve (7), an implicit Euler scheme combined with a fixed point approach or the Newton method can be used. In 3D, when A is not gauged, conjugate gradient methods are used to solve the matrix system.…”

“…In order to reduce the computational time required to solve the previous problem (7), the POD technique combined with an interpolation method of the nonlinear terms can be applied. The POD and the interpolation method enable to reduce the size of the matrix system and the computational cost of nonlinear terms.…”

“…Both approaches can easily be combined with the POD. In electromagnetic modeling, the POD_(D)EIM was used to study a three phase transformer and an electric machine [7][8], a magneto-quasistatic problem solved by boundary element method including a motion of a subdomain [9] or a nonlinear magnetodynamic problem with a model order reduction of an adaptive subdomain [10].…”

Reduced order modeling for transient simulation of power systems using trajectory piece-wise linear approximation

“…They employed model order reduction in parts of the system that remains unaffected by the failures. POD based model order reduction has found applications in diverse fields and is the preferred method in electrical engineering applications such as in the study by Montier et al [8]. In their study, POD is applied in combination with discrete empirical interpolation method.…”

Proper Generalized Decomposition Applied on a Rotating Electrical Machine

“…Equation (16) can be solved using an explicit scheme and by chaining electrical and mechanical equations [7]. This approach makes sense since the time constant of the mechanical equation is much larger than the one of the electrical equations for synchronous machines.…”