Nonlinear Model Order Reduction of Induction Motors Using Parameterized Cauer Ladder Network Method

In this study, we established the nonlinear model order reduction (MOR) of induction motors by parameterizing a multi-port Cauer ladder network (CLN). Appropriate parameters were selected to incorporate nonlinear magnetic characteristics. The parameterized multi-port CLN was applied to the transient analysis of a rotating induction motor. The proposed method reproduced the finite-element analysis results with various driving frequencies and slips. The parameterized multi-port CLN can effectively reduce the computation time for analyses requiring a large number of time steps

Geometrical Formulation of 3-D Space-Time Finite Integration Method

A geometrical formulation of a space-time finite-integration (FI) method is studied for application in electromagnetic-wave propagation calculations. Based on the Hodge duality and Lorentzian metric, a modified relation is derived between the incidence matrices of space-time primal and dual grids. A systematic method to construct the Maxwell grid equations on the space-time primal and dual grids is developed. The geometrical formulation is implemented on a simple space-time grid, which is proven equivalent to an explicit time-marching scheme of the space-time FI method

Pinning field representation using play hysterons for stress-dependent domain-structure model

© 2019 To predict the stress-dependent magnetization properties of silicon steel using a multiscale magnetization model called assembled domain structure model, pinning field models are developed using the play model. The hysteretic property of pinning field is identified from measured BH loops under stress-free condition. From the unidirectional hysteretic property, the distribution of the play hysterons is determined via an identification method that uses scalar and vector play models under the assumption of 2D or 3D distribution of crystal orientations. The loss properties of non-oriented silicon steel under compressive and tensile stresses are predicted successfully using an energy minimization process without parameter fitting to the stress-dependent measurement results

Anisotropic Vector Play Model and its Application in Magnetization Analysis

An anisotropic vector play model was developed by the superposition of scalar play models. An analytical identification method was derived for a uniaxially anisotropic term. Computed BH loops accurately reconstructed the measured anisotropic hysteretic characteristics of non-oriented (NO) silicon steel sheet. Its application to magnetization analysis by a physical magnetization model using multi-domain particles enhanced the prediction accuracy of the stress-dependent loss property

Model order reduction of nonlinear eddy-current field using parameterized CLN

[Purpose] The authors derive a nonlinear MOR based on the Cauer ladder network (CLN) representation, which serves as an application of the parameterized MOR. Two parametrized CLN representations were developed to handle the nonlinear magnetic field. Simulations using the parameterized CLN were also conducted using an iron-cored inductor model under the first-order approximation. [Design/methodology/approach] This work studies the effect of parameter variations on reduced systems and aims at developing a general formulation for parametrized model order reduction (MOR) methods with the dynamical transition of parameterized state. [Findings] Terms including time derivatives of basis vectors appear in nonlinear state equations, in addition to the linear network equations of the CLN method. The terms are newly derived by an exact formulation of the parameterized CLN and are named parameter variation terms in this study. According to the simulation results, the parameter variation terms play a significant role in the nonlinear state equations when reluctivity is used, while they can be neglected when differential reluctivity is used. [Practical implications] The computational time of nonlinear transient analyses can be greatly reduced by applying the parameterized CLN when the number of time steps is large. [Originality/value] The authors introduced a general representation for the dynamical behavior of the reduced system with time-varying parameters, which has not been theoretically discussed in previous studies. The effect of the parameter variations is numerically given as a form of parameter variation terms by the exact derivation of the nonlinear state equations. The influence of parameter variation terms was confirmed by simulation

Frequency-Domain Model Order Reduction of Electromagnetic Field in Induction Motor

A model order reduction (MOR) method for an induction motor using a Cauer ladder network (CLN) is developed in the frequency domain. A multiport frequency transformation between the stator and mover domains is derived by neglecting the spatial harmonic interactions. Even after neglecting the harmonic interactions, the reduced model provides a reasonably accurate frequency response, which is more accurate than that of the conventional approximated equivalent circuit

Nonlinear Multi-Scale Model Order Reduction of Eddy-Current Problems

This article presents a nonlinear multi-scale model order reduction (MOR) method based on a piecewise linearization technique. On the material scale, the eddy-current (EC) field in laminated cores is expressed through Legendre polynomials. The Cauer ladder network (CLN) method is applied to the homogenized nonlinear EC problem to generate the equivalent electric circuit. The accuracy and efficiency of the proposed method are verified by the mean of a test case with saturated stacked core and pulse width modulation (PWM) excitation

Numerical Stability Analysis of Space-Time Finite Integration Method Based on the Dependent Domain Concept

A method for estimating the stability criterion in the space-time finite integration (FI) method using the subgrid technique was developed. Numerical- and analytical-dependent domains were compared to estimate the stability limit. Space-time subgrids locally refined with two, three, and four divisions were examined. The stability limit based on the proposed method almost agrees with that of the numerical experiment

Reduced Order Modeling Based on Multiport Cauer Ladder Network for Space Harmonics of Air-gap Flux Density in Cage Induction Motor

This study investigated an efficient procedure for developing an accurate behavioral model of a cage induction motor (IM) based on the multiport Cauer ladder network (CLN). The CLN method was applied to a cage IM with semi-closed rotor slots as a model order reduction technique and a method for selecting the appropriate space harmonics included in the air-gap flux density, which is necessary for a multiport CLN method for induction machines, was discussed. Then, the developed approach was applied to the transient analysis of the cage IM coupled with a control system, and its effectiveness in terms of computational accuracy and cost was investigated

Model Order Reduction of Cage Induction Motor With Skewed Rotor Slots Using Multiport Cauer Ladder Network Method

A method for efficiently deriving a reduced-order model of a cage induction motor (IM) with skewed rotor slots is proposed based on the multiport Cauer ladder network (CLN) method. This article presents several formulations of the multiport CLN method for the skewed rotor, in which the continuity of the bar currents and the space harmonics included in the air-gap flux density waveform are treated differently. The effectiveness of the developed methods was verified from the viewpoints of computational accuracy and cost through application to a practical cage IM with skewed rotor slots