*6.1. Fixed Limits*

In this method the constraints for the stator current phase were selected to consider the case where motor parameters are unknown and self-commissioning is not performed. The fixed predefined numbers equal to the theoretical minimum and maximum values where selected. As can be observed from Figure 11, the minimum value of the MTPA angle *γ* is 0◦, whereas the maximum angle is defined by curve "F" (about 32◦). For a pure reluctance motor the maximum angle cannot exceed 45◦ if it is desired to cover 100% of all motor designs. These angles were selected as the limits for the variation of the seeking algorithm disturbance factor. These limits are depicted in Figure 14 together with the MTPA trajectories and curves used for the design.

**Figure 14.** Constraints design for MTPA angle γ using fixed limits.

#### *6.2. Rated MTPA Curve with Gaps*

According to this method, the constraints are designed using the MTPA curve for rated motor parameters, which is shifted to higher and lower directions at the fixed gap. In this experiment, the gap was selected as the seeking algorithm disturbance angle Δ *γ*, which is equal to 4◦. At the same time, the MTPA angle for the test motor may not be negative; therefore, the lower limit is set to zero in this area, where parallel shift of the rated MTPA curve resulted in negative values. These limits are depicted in Figure 15 together with the MTPA trajectories and curves used for design.

**Figure 15.** Constraints design for MTPA angle γ using rated MTPA curve with gaps.

#### *6.3. Operation at Low Load*

In this experiment, the performance of the proposed technique was evaluated and compared with existing algorithms at low loads, where the motor was not saturated (zone "U"). Two cycles of the load torque used in this experiment are depicted in Figure 16a. The performance of seeking the algorithm operation with "Fixed limits", "Rated MTPA curve with gaps" and proposed constraints are demonstrated in Figure 16b–d, respectively. The measured efficiency for these constraint sets was: 47.4%, 51.9% and 52.1%, respectively.

#### *6.4. Operation at Medium Load*

In this experiment, the performance of the proposed technique was evaluated and compared with existing algorithms at low loads, where the motor was partly saturated (zone "P"). Two cycles of the load torque used in this experiment are depicted in Figure 17a. The performance of the seeking algorithm operation with "Fixed limits", "Rated MTPA curve with gaps" and proposed constraints are demonstrated in Figure 17b–d, respectively. The measured efficiency for these constraint sets was: 85.2%, 87.1% and 88.4%, respectively.

#### *6.5. Operation at High Load*

In this experiment, the performance of the proposed technique was evaluated and compared with existing algorithms at low loads, where the motor was highly saturated (zone "S"). Two cycles of the load torque used in this experiment are depicted in Figure 18a. The performance of the seeking algorithm operation with "Fixed limits", "Rated MTPA curve with gaps" and proposed constraints are demonstrated in Figure 18b–d, respectively. The measured efficiency for these constraint sets was: 85.6%, 86.1% and 86.3%, respectively.

**Figure 16.** Operation of seeking algorithm with different constraints at low load: (**a**) Torque profile; (**b**) Fixed limits; (**c**) Rated MTPA curve with gaps; and (**d**) Proposed technique.

**Figure 17.** Operation of the seeking algorithm with different constraints at medium load. (**a**) Torque profile; (**b**) Fixed limits; (**c**) Rated MTPA curve with gaps; and (**d**) Proposed technique.

**Figure 18.** Operation of the seeking algorithm with different constraints at high load. (**a**) Torque profile; (**b**) Fixed limits; (**c**) Rated MTPA curve with gaps; and (**d**) Proposed technique.
