*4.3.2. Depictions of condition identification for flux-weakening control*

Permanent magnet synchronous motors (PMSMs) fed by PWM inverters are widely used for industrial applications, especially servo drive applications, which always work in rated condition. But in traction and spindle drives, higher speed is needed [24]. When in constantpower region, the motor is always controlled by the flux-weakening control method.

In the constant torque region, the stator voltage increase as the internal EMF of the motor rises in proportion to the motor speed. However, when the speed rises to rated speed, the voltage Electric Drives in Alternative Fuel Vehicles — Some New Definitions and Methodologies http://dx.doi.org/10.5772/61645 21

**Figure 8.** Characteristic curve of PMSM

Rotor flux comparison is also studied, given the flux reference. Unlike the rotor speed results, estimated rotor flux is not precisely approaching the reference (see Figure 7), which is however close to actual results. The "actual value" shown in Figure 7 for comparison is obtained from normal flux calculation method through measured voltages and currents and could be considered as actual flux due to proof of incomputable applications. It is clear that the estimated flux with +200% resistance, 50% load torque, or +200% stator leakage inductance is

not influenced by these disturbances dramatically.

20 New Applications of Electric Drives

strategy to make the motor work at high speeds.

*4.3.1. Classification of traction motor operation ranges*

**Figure 7.** Comparison between references and estimated rotor flux using FBLSM observer

*4.3.2. Depictions of condition identification for flux-weakening control*

**4.3. Advanced flux-weakening control at high speeds required by AFE driving**

In AFVs, the traction motor has a very wide speed range, which needs flux-weakening control

Figure 8 illustrates the characteristics of a permanent magnet synchronous motor used in AFVs. All the operation ranges can be divided into three parts: constant torque, constant power, and high-speed region. When the rated speed is not reached, the PMSM works in the constant-torque region, exerting a constant torque (rated torque). Once the speed reaches the rated motor speed, the torque begins to drop proportionally compared with speed, leading to a constant output power. The constant-power region ends when the following high-speed region starts. Then with the square of the speed, the motor torque drops proportionally [23].

Permanent magnet synchronous motors (PMSMs) fed by PWM inverters are widely used for industrial applications, especially servo drive applications, which always work in rated condition. But in traction and spindle drives, higher speed is needed [24]. When in constant-

In the constant torque region, the stator voltage increase as the internal EMF of the motor rises in proportion to the motor speed. However, when the speed rises to rated speed, the voltage

power region, the motor is always controlled by the flux-weakening control method.

limitoftheassociatedfrequencyconverteris reached.Theinternalvoltagemustnowbeadjusted to be compatible with the applied converter voltage. However, since the permanent magnets inherently provide the equivalent of a constantfield excitation,the internal EMF ofthe machine continues to increase as speed increases. So the air gap flux should be weakened by the demagnetizing effect due to the d-axis armature reaction, which is called flux weakening [25].

**Figure 9.** *i <sup>d</sup>* −*i <sup>q</sup>* plane

On the *i <sup>d</sup>* −*i <sup>q</sup>* plane (see Figure 9), there are a current-limit cycle and voltage-limit ellipse. These two limits are all decided by the inverter capacity. The maximum torque-per-ampere current vector trajectory is used in the constant torque region to generate maximum torque. The voltage-limited maximum output trajectory makes the motor increase to higher speed.

Region I (*ω* ≤*ω*1): *i <sup>d</sup>* and *i <sup>q</sup>* are constant values given by the maximum torque-per-ampere (MTPA) trajectory. The maximum output torque is usually achieved in point A in Figure 8, where stator current *Is* = *I*lim, stator voltage *Vs* <*V*lim

Region II (*ω*<sup>1</sup> <*ω* ≤*ω*2): when the speed reaches *ω*1 and stator voltage increases to maximum voltage, the current vector starts to moves from A to B along the current limit circle as the rotor speed increases. In this region, stator current *Is* = *I*lim, stator voltage *Vs*=*V*lim

Region III (*ω*<sup>2</sup> <*ω*): when at point B, *ω*=*ω*2, the current vector starts to move along the voltagelimited maximum output trajectory, where stator current *Is* < *I*lim, stator voltage *Vs*=*V*lim [26].
