the electromagnetic developed torque in terms of mechanical parameters is given by, (2.4) where, and are the voltages, and are the inductances, vd vq d,q-axis Ld Lq d,q-axis id and are the stator currents, respectively; is the stator resistance per phase, iq d,q-axis Rs is the constant flux linkage due to rotor permanent magnet, is the angular rotor m r speed, is the number of pole pairs of the motor, is the differential operator (d/dt), P p and is the developed electromagnetic torque, is the load torque, is the viscous Te TL Bm coefficient and is the inertia constant. The first term of (2.3) represents the magnet Jm torque due to the rotor permanent magnet flux and the second term represents the m reluctance torque due to the complex interaction of currents and inductances of d,q-axis the IPMSM. The complexity of the control arises due to the nonlinear nature of the torque equation (2.3) because, and are not constants. All these quantities Ld, Lq, id iq vary during dynamic operating conditions [9]. To make the torque equation linear and the control task easier, usually is set to zero [32]. However, in an actual IPMSM id drive, it is inappropriate, the assumption of = 0 leads to erroneous results. If 0, id id = the reluctance torque will be zero and hence, the motor operates at below optimum torque condition. In this thesis is not considered zero. The value of is calculated id id from maintaining the armature voltage and current within the capacity of the motor iq and the inverter. This improves the performance of the drive system as compared to the 0 technique as it can utilize the reluctance torque below rated speed and operate the id = motor above rated speed by flux weakening. The motor parameters used in the simulation are given in Appendix-A. According to (2.1) and (2.2) the equivalent circuit models are shown in Fig. 2.1 d,q-axis (a) and (b), respectively.
the electromagnetic developed torque in terms of mechanical parameters is given by, (2.4) where, vd and vq are the d,q-axis voltages, Ld and Lq are the d,q-axis inductances, id and iq are the d,q-axis stator currents, respectively; Rs is the stator resistance per phase, m is the constant flux linkage due to rotor permanent magnet, r is the angular rotor speed, P is the number of pole pairs of the motor, p is the differential operator (d/dt), and Te is the developed electromagnetic torque, TL is the load torque, Bm is the viscous coefficient and Jm is the inertia constant. The first term of (2.3) represents the magnet torque due to the rotor permanent magnet flux m and the second term represents the reluctance torque due to the complex interaction of d,q-axis currents and inductances of the IPMSM. The complexity of the control arises due to the nonlinear nature of the torque equation (2.3) because, Ld, Lq, id and iq are not constants. All these quantities vary during dynamic operating conditions [9]. To make the torque equation linear and the control task easier, usually id is set to zero [32]. However, in an actual IPMSM drive, it is inappropriate, the assumption of id = 0 leads to erroneous results. If id = 0, the reluctance torque will be zero and hence, the motor operates at below optimum torque condition. In this thesis id is not considered zero. The value of id is calculated from iq maintaining the armature voltage and current within the capacity of the motor and the inverter. This improves the performance of the drive system as compared to the id = 0 technique as it can utilize the reluctance torque below rated speed and operate the motor above rated speed by flux weakening. The motor parameters used in the simulation are given in Appendix-A. According to (2.1) and (2.2) the d,q-axis equivalent circuit models are shown in Fig. 2.1 (a) and (b), respectively.
Thesis-Shahida-SGP_110002.docx