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Synchronous reluctance motors show nonlinear behavior in the high torque region due to core saturation, especially on the $d$ -axis. In this study, the maximum torque per ampere (MTPA) solution is sought in the mathematical frame. First, flux linkage data are obtained from finite element method, and fitted as the plane functions of currents by the least square method. Thereafter, the inductances are derived as binomials in $i_d$ and $i_q$. These analytic expressions of inductances are used in deriving a necessary condition for the MTPA, and constructing an on-line MTPA control method. The effectiveness is verified through simulation and experimental results. [ABSTRACT FROM AUTHOR]