Control characteristics for quasi-optimal operation of switched reluctance motors

This paper presents the control characteristics of switched reluctance (SR) motors defined for the maximum efficiency of the motor or the motor–converter system and for the minimum ripple level of electromagnetic torque. Curves for control variables—switch-on and switch-off angles (or conduction angle) and average phase voltage—are obtained by computations from a simple mathematical model. This lumped-parameter model takes into account the magnetic saturation of the motor and the parameters of the power converter necessary to guarantee reliable results concerning power losses in the system. The investigations were carried out for two typical SRM with the number of teeth N_s/N_r=8/6 and 6/4 for a battery supply and for a 310-V rectifier supply. Time curves obtained from mathematical model and control characteristics resulting from numerous optimization computations were validated by thorough measurements performed on a special test rig.List of symbols D viscous friction damping, Nms - e_k back EMF in the kth winding, V - i_k current in the kth winding, A - J moment of inertia, kg/m² - L() phase winding's inductance in unsaturated state H - L(,i) phase winding's inductance considering saturation H - m number of phases - N_s/N_r number of teeth: stator/rotor - n rotational speed, 1/s - R phase winding's resistance, - R_i current measurement resistor value, - R_k total resistance in the kth phase circuit, - R_s resistance of a power source, - R_TDSat drain-source resistance of a transistor in the saturated state - r_D dynamic resistance of a diode, - T_e electromagnetic torque, Nm - T_l load torque, Nm - u_k voltage of the kth phase, V - U phase voltage RMS value, V - U_av phase voltage average value, V - _on switch-on angle, rad - _off switch-off angle, rad - _z=_on–_off conduction angle, rad - stroke angle of the motor, rad - _s efficiency of a motor - _u efficiency of a motor–converter system - rotor position angle, rad - (,i) saturation function of the winding's inductance - m_p level of the torque ripples, % - _r=2/N_r, rad rotor tooth pitch - _k rotor position angle reduced to the kth tooth-pitch, rad - (,i) flux linkage of a phase winding, Wb - angular velocity, rad/s - angular acceleration, rad/s²