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Figure 7. Distribution of genetic algorithm (GA) analysis parameters according to the number of evolutions. The torque ripples in the motor shaft torque resulted in Tripple = 19.98 (SI in the model, whereas this value was decreased to T,ippie = 7.08 (SI) in the new design. Optimization works were carried out for the optimization of this value, which was still quite high in the later stages of the study. The component generated especially in the pole transitions generates ripples in the torque, because of the interactions between the permanent magnets and the stator tooth in LS-PMSM’s [35]. It was observed that when the studies for reducing the ripples in the torque were examined, the focus was on the optimization of the stator tooth and/or permanent magnets, production of the skewed stator, or rotors [36-40].

Figure 7 Distribution of genetic algorithm (GA) analysis parameters according to the number of evolutions. The torque ripples in the motor shaft torque resulted in Tripple = 19.98 (SI in the model, whereas this value was decreased to T,ippie = 7.08 (SI) in the new design. Optimization works were carried out for the optimization of this value, which was still quite high in the later stages of the study. The component generated especially in the pole transitions generates ripples in the torque, because of the interactions between the permanent magnets and the stator tooth in LS-PMSM’s [35]. It was observed that when the studies for reducing the ripples in the torque were examined, the focus was on the optimization of the stator tooth and/or permanent magnets, production of the skewed stator, or rotors [36-40].

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Figure 1. Torque components of the line start permanent magnet synchronous motors (LS-PMSM). Figure 1 shows the torque components of the LS-PMSM. The dotted curve in the figure represents the torque generated by the start cage without a permanent magnet (T;,), and the dashed line represents the braking torque generated by the permanent magnets (Tym). The asynchronous torque (Tasyn zenerated by electromagnetic torque (Te), which is the sum of T; and Tym, is represented by a normal ine. The cage torque (T-) should overcome the braking torque (Tym) generated by the permanent magnets, the load torque (T,), and motor inertia (J;,) in order for the synchronization process in LS-PMSM to be successful.
Figure 1. Torque components of the line start permanent magnet synchronous motors (LS-PMSM). Figure 1 shows the torque components of the LS-PMSM. The dotted curve in the figure represents the torque generated by the start cage without a permanent magnet (T;,), and the dashed line represents the braking torque generated by the permanent magnets (Tym). The asynchronous torque (Tasyn zenerated by electromagnetic torque (Te), which is the sum of T; and Tym, is represented by a normal ine. The cage torque (T-) should overcome the braking torque (Tym) generated by the permanent magnets, the load torque (T,), and motor inertia (J;,) in order for the synchronization process in LS-PMSM to be successful.
Table 1. Main dimensions of the reference motor.
Table 1. Main dimensions of the reference motor.
Figure 2. Optimal LS-PMSM design algorithm. 2.1. Determining the Main Dimensions of the Machine
Figure 2. Optimal LS-PMSM design algorithm. 2.1. Determining the Main Dimensions of the Machine
Table 2. Stator design details. The label information for the standard IE2 IMs taken as reference have been given in Table 3.
Table 2. Stator design details. The label information for the standard IE2 IMs taken as reference have been given in Table 3.
Table 3. Label information for the reference motor. 2.3. Rotor Design
Table 3. Label information for the reference motor. 2.3. Rotor Design
einai © The slot structures that determine the motor torque characteristic are standardized by NEMA with class A, B, C and D [34]. According to the NEMA standard classes A and B are used in general purpose motors. Also, Class C and D are preferred in applications requiring higher starting torque. As a result a new rotor typology making use of both of the slot types is suggested in this study, to ensure that both the motor start and synchronization performances are high (Figure 3).
einai © The slot structures that determine the motor torque characteristic are standardized by NEMA with class A, B, C and D [34]. According to the NEMA standard classes A and B are used in general purpose motors. Also, Class C and D are preferred in applications requiring higher starting torque. As a result a new rotor typology making use of both of the slot types is suggested in this study, to ensure that both the motor start and synchronization performances are high (Figure 3).
Figure 4. Ty = 35 Nm; Jm = 1 p.u. Starting process of the analytical model: (a) speed characteristic and (b) torque characteristic. steady state operation as I, = 9.6 A and n = 91.14%, respectively. When this efficiency value is compared with the 85% value obtained with the standard IM rotor, it can be observed that an efficiency increase of 6.14% has been attained. IE3 efficiency levels have been reached with this efficiency value, obtained using the analytically modelled design without any optimization.
Figure 4. Ty = 35 Nm; Jm = 1 p.u. Starting process of the analytical model: (a) speed characteristic and (b) torque characteristic. steady state operation as I, = 9.6 A and n = 91.14%, respectively. When this efficiency value is compared with the 85% value obtained with the standard IM rotor, it can be observed that an efficiency increase of 6.14% has been attained. IE3 efficiency levels have been reached with this efficiency value, obtained using the analytically modelled design without any optimization.
Table 4. Design parameters used for the optimization of the model.
Table 4. Design parameters used for the optimization of the model.
The objective with the optimization studies carried out was to ensure that the motor efficiency exceeds 91.9% (IE4), by determining the proper design parameters. The optimized design parameters can be seen in Figure 5. M; and My in Figure 5 stand for the magnet thickness and width, respectively; Bs0 denotes the slot gap for the rotor upper slots; H; represents the slot depth; and Bs1 denotes the slot diameter. Finally, the rotor diameter (RO) was also included in the optimization studies for determining the optimum air gap value. The parameters used in the optimization study are shown in Table 4 together with their min. and max. values.
The objective with the optimization studies carried out was to ensure that the motor efficiency exceeds 91.9% (IE4), by determining the proper design parameters. The optimized design parameters can be seen in Figure 5. M; and My in Figure 5 stand for the magnet thickness and width, respectively; Bs0 denotes the slot gap for the rotor upper slots; H; represents the slot depth; and Bs1 denotes the slot diameter. Finally, the rotor diameter (RO) was also included in the optimization studies for determining the optimum air gap value. The parameters used in the optimization study are shown in Table 4 together with their min. and max. values.
Table 5. Change in design parameters and motor efficiency after genetic algorithm (GA) optimization. A significant number of analyses were carried out during the optimization studies for reaching an optimum rotor design with a high efficiency. The motor design was evaluated as being two dimensional during the analyses carried out, as it delivers faster solutions, and the analyses were finalized with a Maxwell 2D Transient solver. A Maxwell 3D Transient solver was used during the next stages of the study for a more detailed examination of the model obtained with a high efficiency via GA.
Table 5. Change in design parameters and motor efficiency after genetic algorithm (GA) optimization. A significant number of analyses were carried out during the optimization studies for reaching an optimum rotor design with a high efficiency. The motor design was evaluated as being two dimensional during the analyses carried out, as it delivers faster solutions, and the analyses were finalized with a Maxwell 2D Transient solver. A Maxwell 3D Transient solver was used during the next stages of the study for a more detailed examination of the model obtained with a high efficiency via GA.
The cost function obtained as a result of optimization via the genetic algorithm has been presented in Figure 6 as a graph. As can be seen from the graph, the targeted efficiency (92%) was reached after 383 evolutions. Figure 7 shows the design parameters processed via GA and the distribution of the parameters. It can be understood upon examining the graph that the values of Bs1, Hs, RO, M;, and Mw do not have a homogeneous distribution, and the optimization study has focused more on certain value intervals. In addition, the graph presented indicates that the impact of the Bs0 value on motor performance is quite low. In conclusion, the targeted efficiency was reached as a result of GA optimization at around Bs1 = 8.5 mm, H,; = 1mm, Bs0 = 1.79 mm, M; = 4.48 mm, My = 40.5°, and RO = 61.30 mm. Moreover, the torque ripples generated by the motor have been decreased down to about T,jppje = 7.09 (SI), and the motor rated current was determined as I, = 9.26 A. Table 5 summarizes the change in the design parameters and motor operating characteristic as a result of the GA optimization.
The cost function obtained as a result of optimization via the genetic algorithm has been presented in Figure 6 as a graph. As can be seen from the graph, the targeted efficiency (92%) was reached after 383 evolutions. Figure 7 shows the design parameters processed via GA and the distribution of the parameters. It can be understood upon examining the graph that the values of Bs1, Hs, RO, M;, and Mw do not have a homogeneous distribution, and the optimization study has focused more on certain value intervals. In addition, the graph presented indicates that the impact of the Bs0 value on motor performance is quite low. In conclusion, the targeted efficiency was reached as a result of GA optimization at around Bs1 = 8.5 mm, H,; = 1mm, Bs0 = 1.79 mm, M; = 4.48 mm, My = 40.5°, and RO = 61.30 mm. Moreover, the torque ripples generated by the motor have been decreased down to about T,jppje = 7.09 (SI), and the motor rated current was determined as I, = 9.26 A. Table 5 summarizes the change in the design parameters and motor operating characteristic as a result of the GA optimization.
Figure 8. Ripple and efficiency obtained for different stator skew angles. that the highest efficiency values were obtained as n (skew7) = 91.33%, n(skew8) = 91.29%, and n (skew13) = 91.28%.
Figure 8. Ripple and efficiency obtained for different stator skew angles. that the highest efficiency values were obtained as n (skew7) = 91.33%, n(skew8) = 91.29%, and n (skew13) = 91.28%.
Figure 9. Motor synchronization performance for different stator skew angles. As can be seen in Figure 9, showing the impact of s stator skew angle on the motor synchronization performance, the motor has the highest synchronization performance at angles of skew0 and skew8. However, the high torque ripples of around T,jy»1¢ = 7 (SI) are generated for both skew angles, which results in an unacceptable decrease in the motor shaft torque quality. In addition, it was also observed that motor efficiency and performance decreased significantly for skew15 at which a satisfactory decrease in the torque ripple was obtained. In conclusion, skew13 was preferred as the stator skew angle, because of its satisfactory synchronization performance and lowest torque ripples.
Figure 9. Motor synchronization performance for different stator skew angles. As can be seen in Figure 9, showing the impact of s stator skew angle on the motor synchronization performance, the motor has the highest synchronization performance at angles of skew0 and skew8. However, the high torque ripples of around T,jy»1¢ = 7 (SI) are generated for both skew angles, which results in an unacceptable decrease in the motor shaft torque quality. In addition, it was also observed that motor efficiency and performance decreased significantly for skew15 at which a satisfactory decrease in the torque ripple was obtained. In conclusion, skew13 was preferred as the stator skew angle, because of its satisfactory synchronization performance and lowest torque ripples.
Figure 10. The cogging torque generated during a 30° rotation of the motor for skew0 and skew13 skew angles.
Figure 10. The cogging torque generated during a 30° rotation of the motor for skew0 and skew13 skew angles.
Figure 11. Change in electromagnetic torque subject to rotor revolution generated by the motor for skew0 and skew13 angles.
Figure 11. Change in electromagnetic torque subject to rotor revolution generated by the motor for skew0 and skew13 angles.
Figure 12. Starting performance for the suggested model with skewed stator under different motor loads. At this stage of the study, the performance characteristic will be examined for the motor design rith a stator having a skew angle of skew13, modelled using the suggested rotor topology. The most nportant problem with LS-PMSM’s is the braking torque generated during operation, because of re permanent magnets. This results in issues such as the LS-PMSM’s becoming too sensitive to ircumstances, such as the overloading of the motor. Figure 12 shows the starting performance under ifferent motor loads for the skewed stator model suggested. As can be seen from the graph, the motor an reach a synchronous speed of 1500 rpm in 0.3 s at T, = 35 Nm (Full Load). An overloading of 14% [, = 40 Nm) results in the failure of the motor synchronization process.
Figure 12. Starting performance for the suggested model with skewed stator under different motor loads. At this stage of the study, the performance characteristic will be examined for the motor design rith a stator having a skew angle of skew13, modelled using the suggested rotor topology. The most nportant problem with LS-PMSM’s is the braking torque generated during operation, because of re permanent magnets. This results in issues such as the LS-PMSM’s becoming too sensitive to ircumstances, such as the overloading of the motor. Figure 12 shows the starting performance under ifferent motor loads for the skewed stator model suggested. As can be seen from the graph, the motor an reach a synchronous speed of 1500 rpm in 0.3 s at T, = 35 Nm (Full Load). An overloading of 14% [, = 40 Nm) results in the failure of the motor synchronization process.
Figure 13. Current and efficiency values obtained from the motor subject to load torque. The graph in Figure 13 shows the current and efficiency values subject to load torque. It can clearly be seen from the graph that the current drawn when the motor is idle is around I, = 2.3 A. This value increases up to I, = 9.84 A at an overloading of 40 Nm. The current drawn at Fi of the load is 2.8 A and 4.3 A at 3 loading. Motor efficiency at + loading increased up to 86% and up to 91% at 3, whereas a maximum value of 91.28% was reached at full load.
Figure 13. Current and efficiency values obtained from the motor subject to load torque. The graph in Figure 13 shows the current and efficiency values subject to load torque. It can clearly be seen from the graph that the current drawn when the motor is idle is around I, = 2.3 A. This value increases up to I, = 9.84 A at an overloading of 40 Nm. The current drawn at Fi of the load is 2.8 A and 4.3 A at 3 loading. Motor efficiency at + loading increased up to 86% and up to 91% at 3, whereas a maximum value of 91.28% was reached at full load.
Figure 14. The meshed model of the LS-PMSM with suggested rotor design: (a) rotor and (b) stator.
Figure 14. The meshed model of the LS-PMSM with suggested rotor design: (a) rotor and (b) stator.
Figure 15. Field reports of the LS-PMSM with suggested rotor design: (a) flux distributions at the stator and rotor cores in steady state operation and (b) vector distribution.
Figure 15. Field reports of the LS-PMSM with suggested rotor design: (a) flux distributions at the stator and rotor cores in steady state operation and (b) vector distribution.
Figure 16. Starting performance under T;, = 35 Nm constant and square load of the suggested model.
Figure 16. Starting performance under T;, = 35 Nm constant and square load of the suggested model.
Figure 17. Starting performance under different square loads of the suggested model.
Figure 17. Starting performance under different square loads of the suggested model.
Related topics:
Electrical MotorsElectrical Machines, Electrical Drives, Power ElectronicsDesign of electrical machinesElectrical Power Engineering
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