**4. Discussion**

Obtaining the optimal motor design is not always a straightforward solution, considering that there are many design parameters that have an impact on motor operating characteristics. Improving one operating characteristic may result in deterioration of another. Therefore, four motor parameters (CPS, ORD, MW and MT) that have an impact on motor transient and steady-state characteristics are varied within the prescribed limits, which are determined by designers' experience in order to find the best combination of these four variables to allow obtaining a high efficiency, power factor, and overloading capability along with a cost effective solution regarding material consumption. The linestart synchronous motor with interior asymmetric permanent magne<sup>t</sup> array is derived from a three-phase squirrel cage motor based on data and the steel laminations from the producer Rade Konˇcar, i.e., the BM model. The BM model is derived from the model of the

asynchronous motor (AM) by adding the permanent magnets and flux barriers inside the rotor. Since the overloading capability of the synchronous motor should have a satisfactory value, the air gap length is increased when modifying the AM into BM. In the BM model, the number of conductors per slot was decreased compared to the AM model, which resulted in a lower stator current and considerably lower copper losses in the stator winding. The decrease in the current at BM is also a result of significantly improved power factor at synchronous motor (BM) compared to the asynchronous motor AM. The rotor copper losses at the rated load operation are not present in the BM model of line-start synchronous motor due to its principle of operation. No current is induced at synchronous speed of the motor in the rotor winding; therefore, no copper losses are present in the rotor winding of the synchronous motor. The detailed breakdown of all losses of the both models of the motor, the asynchronous (AM) and the synchronous (BM) are presented in Tables 1 and 4. The above-mentioned modifications of the BM model compared to AM model resulted in a significant increase in the efficiency from 78.4% at AM to 94.3 at BM. The first modification of the motor design which involved only a redesign of the rotor slots were in model M1. The reason for redesigning the rotor slots was to provide more space for magnets in the rotor since the original BM model had a low overloading capability of 1.6 and a maximum output power of 3572 W. By modifying the rotor slots, the magne<sup>t</sup> thickness and width can be increased, which in turn provides the larger overloading capability of the model of 4326 W or 1.9. The increase in the overloading capability is due to the increased weight of magne<sup>t</sup> material; consequently, the costs of production are increased as well. No significant improvement of efficiency factor can be observed in the M1 model, compared to the BM model, although the power factor is improved, the line current is decreased and so are the copper losses (Table 4). The magne<sup>t</sup> thickness and width along with outer rotor diameter, i.e., the air gap length and the number of conductors per slot, are selected as parameters to be varied in the optometric analysis, which resulted in the models M2, M3 and M4. In terms of the overloading capability, efficiency and power factor, the M4 model has the best operating characteristics of efficiency 96.1%, power factor of 0.93 and overloading capability of 2.8, i.e., a maximum output power of 6158 W. The consumption of permanent magne<sup>t</sup> material is considerable; therefore, the M4 is not the most cost effective solution in terms of material consumption. The models M2 and M3 have similar operating characteristics (efficiency 96 and 95.9, power factor 0.9 and 0.94, and maximum output power of 4929 and 4837, respectively). In terms of permanent magne<sup>t</sup> consumption, M2 has smaller consumption, 0.69 kg versus 0.8 kg at M3. The M2 model is chosen for further analysis as it has the better efficiency, overloading capability and smaller permanent magne<sup>t</sup> consumption than the M3 model. M2 also has the smaller air gap, fewer conductors per slot than M1 and, consequently, lower copper losses and greater efficiency than M1. Lower copper losses in the M2 are also a result of the decreased air gap in the M2 model compared to the M1 model, which resulted in the improved power factor; consequently, the current is decreased and, finally, the copper losses are decreased. The fewer conductors per slot, combined with the smaller air gap length, contributed to the lower stator winding resistance, greater power factor, lower current, smaller copper losses and greater efficiency of the M2 model compared to the M1 model. The M2 model also has the modified rotor slot compared to the M1 model. This modification provides more space for magnets in the rotor, which contributes to the greater power factor, lower motor current, smaller copper losses and better efficiency of the M2 model. The modification of the rotor slot is also important for the overloading capability of the motor. The increase in the amount of the magne<sup>t</sup> material (more available space for magnets in the rotor) increases the overloading capability of this type of line-start synchronous motor. The motor optimization and modification should be evaluated in terms of complete spectrum of operating characteristics, not just in terms of the efficiency or the power factor. Therefore, the rotor slot modification is important for the overloading capability of the motor and this can be clearly observed from the presented data of the M4 model in Table 4. All motor models are calculated with the same steel laminations. The type of steel in the lamination does not have such a drastic impact on the

efficiency. The authors' preliminary analysis showed that various types of steel affect the efficiency by no more than two to three percent (depending of the type of the steel and its specific losses). Further research can be extended with the detailed analysis of the impact of the type of the steel laminations and their specific losses on the motor efficiency. The impact of CPS on motor efficiency is presented in Figure 9. The program adjusts the wire diameter according to the CPS in order not to exceed the limit of slot fill factor of 75%. The wire diameter has an impact on the stator winding resistance and, consequently, on the line current, the copper losses and the efficiency. The impact of CPS on the stator winding resistance, line current, copper losses and total losses is presented in Figure 20.

**Figure 20.** Impact of CPS on (**a**) stator winding resistance (**b**) line current (**c**) stator winding copper losses (**d**) total losses.

The impact of CPS on the stator winding phase resistance is significant and it contributes greatly to the copper losses and, consequently, to the total losses and the efficiency factor (Figure 20c). The impact of CPS on line current is not as pronounced as it is on the winding resistance (Figure 20b). The cooper losses which are significant part of the motor total losses are determined by the impact of CPS on stator winding resistance. The decrease of the number of CPS has a positive impact on the decrease of winding resistance and has a negative impact on the stator current since the current increases and consequently the copper losses as well. Yet, the decrease in the winding resistance and its contribution to the copper losses and consequently to the total losses is more pronounced than the impact of the increase of the line current on the copper losses and consequently to the total losses. Therefore, the decrease in the number of CPS has a positive impact on the improvement of total losses and results in an increase in the efficiency factor. This statement is verified by the data presented in Table 4 (model M2). Figure 20 should support presented result of impact of CPS on the efficiency (Figure 9a). The smaller number of CPS has a positive impact on the increase of efficiency but simultaneously decreases the power factor. Additionally, the smaller number of CPS contributes to the larger starting torque and the overloading capability of the motor. The CPS has a significant impact on all evaluated motor operating characteristics (efficiency, power factor, stating torque and maximum output power). The impact of ORD is more pronounced on the efficiency and the power factor, while it is not the case with the starting torque and the overloading capability (Figure 10). The larger air gap or the smaller ORD decreases the efficiency and the power factor. MW has no significant impact on the efficiency, the power factor, the starting torque and the overloading capability (Figure 11). On the other hand, MT has the greatest impact on motor overloading capability and power factor. The thicker the

magnets are, the greater the power factor and the overloading capability are (Figure 12). From all four varied parameters, CPS has the biggest impact on all four analyzed operating characteristics, efficiency, power factor, starting torque and overloading capability. ORD, i.e., air gap length, has a significant impact only on efficiency and the power factor. MW is not a critical parameter regarding analyzed operating characteristics but MT has crucial impact on the overloading capability and the power factor. The impact of varied parameter CPS, ORD, MT and MW on motor efficiency can be observed from Figures 9a, 10a, 11a and 12a). From the data presented in the above-mentioned figures, it can be concluded that variation of CPS had the biggest impact on the percentage of motor efficiency, i.e., the variation of CPS from 65 to 108 impacts the change of efficiency from 93.5 to 96.2%. The change of air gap length has also a significant impact on efficiency, which varies from 94.9% to 96.1% with the increase in the ORD, or with the decrease in the air gap length from 1 mm to 0.5 mm. The impact of magne<sup>t</sup> width on motor efficiency is not so pronounced. The efficiency percentage varies very little with the variation of magne<sup>t</sup> width, i.e., from 96.04 % to 96.07 %. The impact of magne<sup>t</sup> thickness on efficiency is more significant, i.e., it increases from 96.04% to 96.14% with the increase in the magne<sup>t</sup> thickness. From the above, it is evident that various parameters have different impacts on various motor operating characteristics; therefore, it is necessary to employ computational techniques, such is the case with optometric analysis, which involve fast and accurate calculation of various motor models that allow for the determination of optimum values of analyzed motor parameters which produce the best operating characteristics in terms of complete specter of them, combined with the most cost effective solutions regarding material consumption.

The M2 model has been chosen as an optimal solution regarding operating characteristics and the permanent magne<sup>t</sup> material consumption. Both models BM and M2 are modeled with FEM for the flux density distributions. According to Figure 13, models BM and M2 have higher flux density in the stator yoke. This can be improved by redesigning the stator, i.e., increasing the stator outer diameter. In this paper, modifications of the motor are performed on the basis of a three-phase squirrel cage motor, a product of Konˇcar, without any changes in the motor outer dimensions.

The line-start synchronous motor should successfully start and accelerate up to the synchronous speed when it is plugged in the three-phase voltage. The successful starting, acceleration and synchronization are determined by the rotor cage winding and the permanent magnets. Their proper design is vital for the successful operation of the motor. The transient characteristics of speed, current and torque, presented in Figures 14–16, allow analysis of the acceleration and synchronous operation of both models BM and M2. Both models are accelerated with the rated load of 14 Nm coupled to the motor shaft. The M2 model has higher starting torque and lower acceleration time than the BM model. Both motors reach the synchronous speed and maintain the synchronous operation. After the acceleration has finished, the motor torque reaches the value of 14 Nm for both models. This can be expected as they are loaded with the rated torque of 14 Nm. Similar observations can be made for the motor current which reaches the rated load current after the motor has accelerated. The analysis is extended by loading the M2 model with different loads and load inertia, i.e., 10 Nm and load inertia of 0.24 kgm<sup>2</sup> and 14 Nm and load inertia of 0.37 kgm2. In both cases, the motor synchronizes and maintains the synchronism. Table 7 presents the comparison between results obtained in Table 4 from computer models for calculation of motor parameters and characteristics and the results of speed, torque and current from the transient characteristics (Figures 14–16). The average values of speed and torque are calculated by the dynamical model for the last time interval of characteristics and presented in Figures 14 and 15. The rms value of current for the last time interval of current characteristic is presented in Figure 16.


**Table 7.** Comparison of results from analytical and dynamic models at rated load.

From the results presented in Figure 16, it can be concluded that there is a significant distortion of current waveform due to the presence of harmonics. Harmonics are often present in the current of line-start synchronous motor as a result of permanent magnets inside the rotor. The current higher harmonics cause absorption of distortion power and increase in stray load losses [32]. The rms value of current of the dynamic model has higher value than the analytically calculated current (Table 3) due to presence of harmonics. These harmonics cause the heating effects in the conductors, as the eddy losses are proportional to the square of the frequency. Moreover, harmonics can cause interference in the protection systems, communication systems, and signaling circuits due to electromagnetic induction [33]. The harmonics contribute also to the increased noise and vibrations during motor operation. To mitigate the problem with harmonics some authors propose the usage of filters or modification of rotor teeth width [33,34].

From the results presented in Table 7, it can be concluded that computer model for analytical calculation of parameters and characteristics and the dynamic model have satisfactory similarity of results of speed, current and torque. In addition to the verification of the motor dynamic regimes, the presented results in Table 6 should verify the accuracy of both models, the computer model for calculating parameters, the steady-state characteristics and the dynamic model.

The M2 model achieves high efficiency and a very good power factor combined with good overloading capabilities, considerably higher than the efficiency of motor for the same power rating found in [4]. Yet, the derived model is theoretical, based on computer simulations. The proposed model should be verified by the prototype and experimental measurements. It can be expected that the manufactured model will have lower efficiency and power factor. The model is subject to manufacturing limitations such as achieving a good slot fill factor, manufacturing tolerances regarding length of the air gap, built-in material in the motor construction and accurate measurement of frictional and windage losses.
