Optimal current waveforms for switched-reluctance motors

In this paper, we address the problem of finding current waveforms for a switched reluctance motor that minimize a user-defined combination of torque ripple and RMS current. The motor model we use is fairly general, and includes magnetic saturation, voltage and current limits, and highly coupled magnetics (and therefore, unconventional geometries and winding patterns). We solve this problem by approximating it as a mixed-integer convex program, which we solve globally using branch and bound. We demonstrate our approach on an experimentally verified model of a fully pitched switched reluctance motor, for which we find the globally optimal waveforms, even for high rotor speeds.

[1]  Charles A. Desoer,et al.  Basic Circuit Theory , 1969 .

[2]  Editors , 1986, Brain Research Bulletin.

[3]  Barrie Mecrow.  Fully pitched-winding switched-reluctance and stepping-motor arrangements , 1993 .

[4]  Bernard Multon,et al.  Current Feeding of Switched Reluctance Motor. Optimization of the Current Waveform to Minimize the Torque Ripple , 1993 .

[5]  Howard C. Lovatt,et al.  Computer-optimised current waveforms for switched-reluctance motors , 1994 .

[6]  J. M. Stephenson,et al.  Optimum excitation of switched reluctance motors , 1997 .

[7]  Howard C. Lovatt,et al.  Computer-optimised smooth-torque current waveforms for switched-reluctance motors , 1997 .

[8]  Sebastián Ceria,et al.  Convex programming for disjunctive convex optimization , 1999, Math. Program..

[9]  Barrie Mecrow,et al.  The modelling of switched reluctance machines with magnetically coupled windings , 2000, Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129).

[10]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[11]  S. D. Sudhoff,et al.  Design and precise realization of optimized current waveforms for an 8/6 switched reluctance drive , 2002 .

[12]  Changhwan Choi,et al.  A new torque control method of a switched reluctance motor using a torque-sharing function , 2002 .

[13]  Wolfgang Amrhein,et al.  Current shapes leading to positive effects on acoustic noise of switched reluctance drives , 2003 .

[14]  Christos Mademlis,et al.  Performance optimization in switched reluctance motor drives with online commutation angle control , 2003 .

[15]  Hamid A. Toliyat,et al.  Handbook of Electric Motors , 2004 .

[16]  Éva Tardos,et al.  Algorithm design , 2005 .

[17]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[18]  Claudio Gentile,et al.  SDP diagonalizations and perspective cuts for a class of nonseparable MIQP , 2007, Oper. Res. Lett..

[19]  Mario Vasak,et al.  Bounding the torque ripple in switched reluctance motors using polyhedral invariant set theory , 2007, 2007 46th IEEE Conference on Decision and Control.

[20]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[21]  Hanif D. Sherali,et al.  Disjunctive Programming , 2009, Encyclopedia of Optimization.

[22]  Oktay Günlük,et al.  Perspective Reformulation and Applications , 2012 .

[23]  I. Grossmann,et al.  Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming , 2013 .

[24]  Stephen P. Boyd,et al.  A perspective-based convex relaxation for switched-affine optimal control , 2015, Syst. Control. Lett..

[25]  Stephen P. Boyd,et al.  Optimal current waveforms for brushless permanent magnet motors , 2015, Int. J. Control.

[26]  Stephen P. Boyd,et al.  A simple effective heuristic for embedded mixed-integer quadratic programming , 2015, 2016 American Control Conference (ACC).