A general framework for automated physics-based reduced-order modeling of electromechanical systems

ABSTRACT

Physics-based models of electromechanical systems, such as finite element-based models and/or high-fidelity magnetic equivalent circuits, accurately represent underlying magnetic devices. However, these models usually introduce hundreds to thousands of state variables and are computationally intensive. Moreover, including relative motion in the physics-based dynamic modeling of electromechanical systems is not a trivial task. In this paper, relative motion is incorporated in highly accurate full-order models that are based on geometrical and material data. Automated linear and nonlinear order-reduction techniques are introduced to mathematically extract the essential system dynamics in the desired bandwidth, thus preserving both accuracy and computational efficiency. The resulting reduced-order systems are verified using finite element-based models and magnetic equivalent circuits in both time and frequency domains.

REFERENCES

• 1: O. Bottauscio, M. Chiampi, and A. Manzin, "Advanced model for dynamic analysis of electromechanical devices," IEEE Trans. Magn., vol. 41, pp. 36--46, Jan. 2005.
• 2: J. D. Owens and P. L. Chapman, "Automated generation of accurate low-order models for magnetic devices," IEEE Trans. Power Electron., vol. 20, pp. 732--742, July 2005.
• 3: J. M. Jin, The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
• 4: S. J. Salon, Finite Element Analysis of Electrical Machines, Boston, MA: Kluwer, 1995.
• 5: T. E. McDermott, P. Zhou, J. Gilmore, Z. Cendes, "Electromechanical system simulation with models generated from finite element solutions," IEEE Trans Magn., vol. 33, pp. 1682--1685, March 1997.
• 6: E. C. Cherry, "The duality between the inter-linked electric and magnetic circuits," in Proc. Phys. Soc., vol. 62, pp. 101--111, 1949.
• 7: E. R. Laithwaite, "Magnetic equivalent models for electrical machine," in Proc. IEE, vol. 114, pp. 1805--1809, Nov. 1967.
• 8: C. J. Carpenter, "Magnetic equivalent circuits," in Proc. IEE, vol. 115, pp. 1503--511, Oct. 1968.
• 9: A. D. Brown, J. N. Ross, and K. G. Nichols, "Time-domain simulation of mixed nonlinear magnetic and electronic systems" IEEE Trans. Magn., vol. 37, pp. 522--532, Jan. 2001.
• 10: A. D. Brown, J. N. Ross, K. G. Nichols, and M. D. Penny, "Simulation of magneto-electric systems using kirchoffian networks," in Eur. Conf. Magn. Sen. Act., July 1998.
• 11: S. M. Lee, S. H. Lee, H. S. Choi, and I. H. Park, "Reduced modeling of eddy current-driven electromechanical system using conductor segmentation and circuit parameters extracted by FEA," IEEE Trans. Magn., vol. 41, pp. 1448--1451, May 2005.
• 12: M. Moallem and G. E. Dawson, "An improved magnetic equivalent circuit method for predicting the characteristics of highly saturated electromagnetic devices," IEEE Trans. Magn., vol. 34, pp. 3632--3635, Sep. 1998.
• 13: J. G. Zhu, S. Y. R. Hui, and V. S. Ramsden, "A generalized dynamic circuit model of magnetic cores for low- and high- frequency applications- Part I: Theoretical calculation of the equivalent core loss resistance," IEEE Trans. Power Electron., vol. 11, pp. 246--250, Mar. 1996.
• 14: J. G. Zhu, S. Y. R. Hui, and V. S. Ramsden, "Discrete modeling of magnetic cores including hystersis eddy current and anomalous losses," in IEE Proc., vol. 140, pp. 317--321, July 1993.
• 15: J. J. Feeley, "A simple dynamic model for eddy currents in a magnetic actuator," IEEE Trans. Magn., vol. 32, pp. 453--458, Mar. 1996.
• 16: J. G. Zhu, S. Y. R. Hui, and V. S. Ramsden, "A dynamic equivalent circuit model for solid magnetic cores for high switching frequency operations," IEEE Trans. Power Electron., vol. 10, pp. 791--795, Nov. 1995.
• 17: J. G. Zhu, S. Y. R. Hui, and V. S. Ramsden, "A generalized dynamic circuit model of magnetic cores for low- and high- frequency applications- Part II: Circuit model formulation and implementation," IEEE Trans. Power Electron., vol. 11, pp. 251--259, Mar. 1996.
• 18: P. Holmberg and A. Bergqvist, "Modeling eddy currents and hystersis in a transformer laminate," IEEE Trans. Magn., vol. 33, pp. 1306--1309, Mar. 1997.
• 19: O. Bottauscio, A. Manzin, A. Canova, M Chiampi, G. Gruosso, and M. Repetto, "Field and circuit approaches for diffusion phenomena in magnetic cores," IEEE Trans. Magn., vol. 40, pp. 1322--1325, Mar. 2004.
• 20: J. Sagarduy, A. J. Moses, and F. J. Anayi, "Eddy current losses in electrical steels subjected to matrix and classical PWM excitation waveforms," IEEE Trans. Magn., vol. 42, pp. 2818--2820, Oct. 2006.
• 21: R. C. Degeneff, M. R. Gutierrez, S. J. Salon, D. W. Burrow, and R. J. Nevins, "Kron's reduction method applied to the time stepping finite element analysis of induction machines," IEEE Trans. Energy Conv., vol. 10, pp. 669--674, Dec. 1995.
• 22: A. C. Cangellaris, M. Celik, S. Pasha, and L. Zhao, "Electromagnetic model order reduction for system-level modeling," IEEE Trans. Micrwave Theory Appl., vol. 47, pp. 840--850, June 1999.
• 23: L. Fortuna, G. Nunnari, and A. Gallo, Model Order Reduction Techniques with Applications in Electrical Engineering, New York,: Springer-Verlag, 1992.
• 24: A. C. Antoulas, D. C. Sorensen, and S. Gugersin, "A survey of model reduction methods for large-scale systems," contemporary mathematics. American mathematical society publications, pp. 193--519, 2001.
• 25: E. Grimme, "Krylov Projection Methods for Model Reduction," PhD. Thesis, University of Illinois, Urbana-Champaign, Department of Electrical and Computer Engineering, 1997.
• 26: Zhaojun Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems, Applied Numerical Mathematics, v.43 n.1-2, p.9-44, October 2002 [doi>10.1016/S0168-9274(02)00116-2]
• 27: M. Rewienski and J. White, "A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuit and micromachined device," IEEE trans. Comp. Aided Design Int. Circuits Syst., vol. 22, pp. 155--170, Feb. 2003.
• 28: Ning Dong , Jaijeet Roychowdhury, Piecewise polynomial nonlinear model reduction, Proceedings of the 40th conference on Design automation, June 02-06, 2003, Anaheim, CA, USA [doi>10.1145/775832.775957]
• 29: Peter V. Kokotovic , John O'Reilly , Hassan K. Khalil, Singular Perturbation Methods in Control: Analysis and Design, Academic Press, Inc., Orlando, FL, 1986
• 30: L. Meirovitch, Computational methods in structural dynamics, Rockville, MD: Sijthoff & Noordhoff, 1980.
• 31: Moore, B., "Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction," IEEE Trans. Auto. Cont., AC-26 (1981), pp. 17--31.
• 32: Simulink: Dynamic System Simulation for Matlab, Using Simulink Version 5, The MathWorks Inc., 2003. (Simulink LTI Viewer)
• 33: Ferroxcube, Inc. (2007). Tech. Rep. {Online}. Available: http://www.ferroxcube.com
• 34: H. Mohellebi, M. E. Latréche, and M. Féliachi, "Coupled axisymmetric analytical and finite element analysis for induction devices having moving parts," IEEE Trans. Magn., vol. 34, pp. 3308--3310, Sep. 1998.

INDEX TERMS

Keywords:
electromechanical systems, finite element model, magnetic equivalent circuit, model-order reduction, power electronics