**1. Introduction**

Line-start synchronous motors have gained popularity as an alternative to asynchronous squirrel cage motors, especially in constant speed applications, due to the strict regulations that have been imposed worldwide regarding the efficiency classes of motors that can be used. The asynchronous squirrel cage motors can achieve the IE3 or IE4 efficiency class (in general, efficiency above 89%) with numerous modifications which increase the motor dimensions, material consumption or even imply usage of more expensive materials such as copper bars in the squirrel cage winding or steel laminations with low losses. From 1 July 2021, low-voltage motors up to 1000 kW must meet at least efficiency class IE3 according to a new EU Directive. In a second step, from mid-2023, efficiency class IE4 will become mandatory for the 75–200 kW performance range. Some manufacturers of the motors have answered these challenges and have offered to the market three-phase asynchronous induction motors of the IE4 class [1,2]. Researchers have also analyzed various modifications of motor slots such as adding magne<sup>t</sup> wedges in induction motors with semi-closed slots in order to reduce copper and core losses and increase motor efficiency [3]. The IE4 efficiency class can be more easily achieved with the line-start synchronous motor

**Citation:** Sarac, V.; Minovski, D.; Janiga, P. Parametric Analysis for Performance Optimization of Line-Start Synchronous Motor with Interior Asymmetric Permanent Magnet Array Rotor Topology. *Electronics* **2022**, *11*, 531. https:// doi.org/10.3390/electronics11040531

Academic Editor: Ahmed F. Zobaa

Received: 26 January 2022 Accepted: 5 February 2022 Published: 10 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(LSSM) as there is no induced current in the rotor winding due to the synchronous speed of rotation, so the rotor copper losses are nullified [4]. The high power factor at LSSM allows smaller line current and lower copper losses in the stator winding, that in turn increase the efficiency factor; therefore, this type of motor can easily achieve efficiency class IE4 (in general, efficiency above 89%). The combination of the squirrel cage winding and the magnets in the rotor allows for direct starting of the motor with voltage from the mains without the need of the voltage inverters, which are typically needed for starting synchronous motors without squirrel cage winding, as well as synchronization of the motor, provided by the magnets that pull the motor into synchronism. Yet, the proper design of cage winding and the magnets is essential, as the magnets produce the breaking torque that lowers the motor's starting torque and prolongates the motor starting; however, their improper design results in failure of motor synchronization [5–9]. Not only are the magnets responsible for motor operating regimes, starting and steady-state; the stator winding turns also affect the winding resistance, current and the power factor [10]. Another aspect of motor operation is the material of the squirrel cage winding, which is usually aluminum or copper that affects the motor starting and the temperature distribution [11]. The temperature distribution also affects the partial demagnetization of the magnets and the operation of the motor, and one such example is analyzed in [12]. Other authors propose innovative solutions regarding rotor design that include two different types of rotor slots or that focus on the optimization of the rotor slot that allows the best operating characteristics of the motor [13,14]. Various optimization techniques have been implemented in the optimization of the magne<sup>t</sup> thickness, magne<sup>t</sup> width or the rotor slots at line-start synchronous motors with hybrid magnets (combination of two types of magne<sup>t</sup> materials) or the line-start synchronous motor with a configuration of magnets with radial flux distribution [15–17]. A very small number of works can be found regarding optimization of LSSM with asymmetric permanent magne<sup>t</sup> array topology. Optimization of the flux barriers of LSSM with asymmetric permanent magne<sup>t</sup> array topology, which decreases the flux leakage, is found to be a good optimization approach in efficiency optimization, together with the optimization of the dimensions of the rotor slot in [18]. This paper presents a two-step design modification of LSSM with asymmetric permanent magne<sup>t</sup> array topology. Authors' previous research has shown that there are some differences regarding motor operating characteristics and material consumption in correlation with the specific rotor topology of LSSM [19]. The starting point of the analysis is a three-phase squirrel cage motor type 5AZ 100LA-4, which is a product of the company Rade Konˇcar. The design of the asynchronous motor was modified with a rotor with an asymmetric permanent magne<sup>t</sup> array topology, thus obtaining the starting model of LSSM (BM). The main constrain of the motor design is the new derived LSSM having the same output power as the asynchronous motor of 2.2 kW. The laminations of the stator and the rotor were obtained from Konˇcar and they remain unchanged in the process of modification of the asynchronous motor into LSSM. The BM, due to the limited space for magne<sup>t</sup> placement, imposed by the dimensions and shape of rotor slots (Konˇcar design), has a relatively low consumption of permanent magne<sup>t</sup> material, but poor overloading capability, although the efficiency and the power factor are high. Therefore, as the first step in the design modification was to modify the rotor slots in order to provide more space for magnets and flux barriers. Apart from rotor slot modification and magne<sup>t</sup> dimensions, no other modifications were made in the design of this second model (M1). The model M1 has good efficiency and an improved power factor and overloading capability but has the relatively high consumption of a permanent magne<sup>t</sup> material. Therefore, the second step in the design modification was to run the optometric analysis of the M1 model where the outer rotor diameter, magne<sup>t</sup> thickness and width, along with number of conductors per stator slot, are varied simultaneously within predefined limits and the overload capability, efficiency, power factor and magne<sup>t</sup> consumption are followed in each combination (iteration of model solving) of those four varied parameters. A total of 25,257 combinations were solved, resulting in model M2, which was found to have the highest efficiency factor, and a good power factor and overloading capability, along with low consumption of permanent

magne<sup>t</sup> material. Optometric analysis is a software module within Ansys Electronics Desktop software; more precisely, it is included in the RMxprt module of the Ansys software and allows arbitrary machine parameters to be varied within defined boundaries while the arbitrary machine characteristics such as efficiency, power factor or overloading capability, depending on the designer's point of interest, are calculated for each combination of the varied parameters. In this way, the designer can choose the best combination of the motor parameters (for example, outer rotor diameter, number of conductors per slot, magne<sup>t</sup> thickness and magne<sup>t</sup> length) that produce the best performance in the machine, for example, highest efficiency, power factor or overloading capability. All motor models are analyzed for the flux density distribution by FEM. The transient characteristics of all motor models were derived, allowing analysis of motor operation at start-up and synchronization. The redesign of the rotor of the asynchronous motor for obtaining LSSM needs careful evaluation and analysis, especially when various rotor topologies are available in order to obtain optimal results regarding motor operation and material consumption.

#### **2. Computer Models for Steady-State and Transient Characteristics**

One part of the redesign of the three-phase asynchronous squirrel cage motor into LSSM is to place the magnets inside the rotor, which along with squirrel cage winding, allow starting and synchronization of the motor. The starting point in the analysis was the three-phase squirrel cage motor, a product of Rade Konˇcar, type 5AZ100LA-4, 2.2 kW, 1410 rpm, 5 A, power factor of 0.83, efficiency of 79%. The topology with asymmetric permanent magne<sup>t</sup> array was chosen for the rotor redesign as the authors' previous research showed that this topology regarding the analyzed type of the asynchronous motor has some drawbacks, including low overloading capability and relatively low power factor [19]. Therefore, it was a challenging task to improve the overloading capability, power factor and efficiency with minimum consumption of permanent magne<sup>t</sup> material while keeping the same power output of 2.2 kW, as it is in the asynchronous motor. The LSSM with the asymmetric permanent magne<sup>t</sup> array topology is presented in Figure 1a.

**Figure 1.** Cross section of line-start synchronous motor with interior asymmetric permanent magne<sup>t</sup> array rotor topology (**a**) Model BM (**b**) Model M1.

Firstly, the computer model of the asynchronous motor for calculating motor parameters and steady-state characteristics was modeled. This model will be referred to as AM. Since all the further computer models of the line-start synchronous motor will be derived from this model (AM), it was necessary to verify its accuracy by comparing data obtained from AM with the catalogue data from the producer of the motor [20]. This comparison and the obtained results are presented in Table 1. From the results presented in Table 1, it can be concluded that the AM model is sufficiently accurate and it can be further modified into line-start synchronous motor with asymmetric permanent magne<sup>t</sup> array rotor topology. The BM model of line-start synchronous motor is derived from three-phase asynchronous

squirrel cage motor 5AZ 100LA-4, a product of Konˇcar, without any alteration of the stator dimensions or the geometry of the stator and rotor slots [20]. The BM model is derived for the same output power of 2.2 kW as it is in the asynchronous motor. The model is designed to obtain the highest possible efficiency and output power with minimum consumption of permanent magne<sup>t</sup> material. Therefore, in the asynchronous motor (AM), whose data are presented in Table 1, the rotor is modified by decreasing its diameter, i.e., the air gap length is increased from 0.3 mm to 1 mm along with adding the flux barriers and permanent magnets in asymmetric array topology. The increase in air gap was due to the modification of asynchronous motor in line-start synchronous motor in order to maintain the good overloading capability of the line-start synchronous motor. The AM has an overload capability (maximum torque versus nominal torque) of 2.6. The dimensions of the magnets, height and thickness, were calculated for obtaining the highest efficiency and power factor along with a good overloading capability of the motor. This first model in the analysis of the line-start synchronous motor derived from the asynchronous motor, without the changes of the dimensions of the stator, slots of the rotor and the stator, is referred to as the BM model. This BM model will be the starting point with which the modified and optimized models will be compared.



The analytical calculations for this model were performed in Ansys software together with the calculation of steady-state characteristics. Therefore, it was necessary to input the exact dimensions of the cross-section of the motor along with the characteristics of all materials applicable in the motor design. The results obtained from the BM regarding parameters and operating characteristics showed that although BM has low consumption of permanent magne<sup>t</sup> material, it has little overloading capability. The consumption of permanent magne<sup>t</sup> material is limited due to available space for the placement of magnets in the rotor and this affects the overloading capability of the motor. This is due to the geometry of the rotor slot (Figure 1a) which was taken over from the asynchronous motor. Therefore, the first step in improving the model of the line-start synchronous motor with asymmetric permanent magne<sup>t</sup> array rotor topology was to modify the rotor slots, keeping almost the same cross-section of the slot with a modification in its geometry that allows more space in the rotor for the magnets to be placed. This second model will be referred to as M1 model. The modification of the slot in M1 in comparison to BM is presented in Figure 1b. In addition to rotor slot modification in M1, all other dimensions of the motor, features of the both windings, and material properties remain unchanged. From the

results obtained from model M1, it was observed that this model had significantly larger consumption of permanent magne<sup>t</sup> material than B1, although the overloading capability was improved. The second step in model improvement was to run the optometric analysis of the model M1 where four parameters are chosen to be varied simultaneously within predefined ranges: the outer rotor diameter (ORD), magne<sup>t</sup> thickness (MT), magne<sup>t</sup> width (MW) and number of conductors per stator slot (CPS). The motor variables and their ranges of variation are presented in Table 2.

**Table 2.** Motor parameters and their ranges of variation at M1.


The ranges of variation of magne<sup>t</sup> geometry were defined on the base of the available space in the rotor. The computer program calculates the slot fill factor for the stator slots. The program is set to the maximum slot fill factor of 75%. When the limit is reached, the program adjusts the wire diameter in order not to succeed the limit of the slot fill factor. The rotor's outer diameter is varied, taking into consideration the inner stator diameter and the air gap length of the asynchronous motor. The length of the air gap of the asynchronous motor is 0.3 mm. The overloading capability was one of the issues that needed to be improved in the optimized model of line start synchronous motor. The larger air gap contributes to the increased overloading capability while simultaneously worsening the efficiency factor and power factor. Another design aspect is the dimension of the magnets. The increased magne<sup>t</sup> thickness has a positive effect on the increase in the efficiency, power factor and the overloading capability of the motor; however, it decreases the starting torque. The increase in the magne<sup>t</sup> width decreases the efficiency but increases the overloading capability and the power of the motor. From the above, it is obvious that various selected parameters have a contradictory effect on motor operating characteristics and there is no straightforward solution which combines the four above-mentioned varied parameters and produces the best operating characteristics of the motor at steady-state operation as well as at transient regimes. Therefore, by optometric analysis, each combination of motor variables (25,257 combinations) is implemented in motor analytical model, modeled in Ansys software and, by following the output results with respect to motor operating characteristics, the most favorable analytical motor model can be selected for further analysis by the aid of numerical and dynamic models. A total of 25,257 model combinations with the varied parameters were solved. Among all 25,257 models, the three most favorable solutions were chosen in terms of the efficiency, the power factor, the overloading capability and the consumption of permanent magne<sup>t</sup> material. These models will be referred to as models M2, M3 and M4. In terms of the highest efficiency factor and the smallest permanent magne<sup>t</sup> material consumption, model M2 has the best results; therefore, this model is further analyzed with numerical methods and applied into the simulation circuits of the dynamic models. The basic criteria for choosing the models M2 to M4 (obtained by optometric analysis) was to have an overloading capability above 2.2, efficiency above 95.9 and power factor above 0.9. Model M1 is derived from model BM without any optometric analysis, only by redesigning the rotor slots, in order for more magne<sup>t</sup> material to be placed, so as to obtain a larger overloading capability than the BM model. This was achieved, either because the M1 model has a maximum output power of 4326 W compared to 3572 W of the BM model, or because the M1 model has an increased overloading capability of 1.9 compared to the BM model which has 1.6. Another aspect of motor design is the permanent demagnetization of magnets due to reverse fields exceeding the value of Hd, a point at which the magnetic

vector polarization vector M collapses. The corresponding value of flux density is Bd. The demagnetization of magnets has been checked according to [21]:

$$I\_{\rm dgrmr} = \frac{p\pi}{6\mu\_0(K\_{\rm w1}N\_{\rm c})} (B\_r h\_m - B\_d(\mathcal{g} + h\_m)) \tag{1}$$

where *Idgmrm* is the maximum permitted value of steady-state stator current for normal steady-state operation before demagnetization (A). *p* is the number of stator poles, *Kw1* is the winding factor, *Nc* number of turns per phase of stator winding, *hm* is the magne<sup>t</sup> thickness in radial direction in meters, *g* is the air gap length in meters and *Br* is the residual flux density in Tesla at the operating temperature of the magnet. In all motor models, the SmCo28 magnets are used with remanent flux density of 1.07 T and coercitivity of 820,000 A/m. The analysis of demagnetization of the magnets is especially important during transient regimes, i.e., at motor starting and synchronization. At asynchronous starting, currents with a maximum value up to several times greater than the amplitude of the rated motor current can flow in the stator winding. Supply voltage, the magnetic flux generated by magnets, the moment of inertia of rotating masses and load torque affect the start-up course and the amplitude of the inrush current. The impact of the magnetomotive force caused by the armature interaction related to the amplitude of the stator currents may cause partial demagnetization of the permanent magnets located in the motor [12]. Due to irreversible demagnetization of the magnets, the main magnetic flux is irreversibly reduced and consequently so is the motor torque. The demagnetization of the magnets at motor starting and in the vicinity of synchronization speed is analyzed by FEM. The flux density at magnets at various speeds during acceleration of model M2 is presented in Figure 2 for a load torque of 14 Nm and a moment of inertia of 0.37 kgm2. The magnitude of the magnetic field for the same operating regimes from Figure 2 is presented in Figure 3. From the presented results in Figures 2 and 3 and for the type of magnets used, the partial demagnetization could occur in tiny areas of magne<sup>t</sup> edges in the vicinity of synchronous speed. In other analyzed operating points during motor acceleration, the demagnetization of magnets should not occur.

The numerical model allows magnetic flux density distribution to be calculated in the motor cross-section by the aid of Finite Elements Method (FEM) thus allowing parts of the magnetic core with high flux density to be detected [22–24]. Another aspect of analysis of the models is the transient characteristics where the motor behavior in transient regimes such as start-up can be analyzed [25,26]. The M2 model is implemented in the dynamic model in order to obtain transient characteristics of speed, current and torque at motor acceleration and at steady-state operation (operation with synchronous speed). The last part of the analysis is necessary due to the specific construction of line-start synchronous motor. Namely, the squirrel cage winding contributes to the motor starting directly with the voltage from the three phase supply, while permanent magnets pull the motor into synchronism. The magnets generate the breaking torque that can worsen the motor starting conditions. On the other hand, their improper design may result in the failure of motor synchronization. The dynamic models are designed for BM and M2 when the motor is accelerated with various loads and load inertia. The motor acceleration and synchronization is analyzed and adequate conclusions are derived. The motor dynamic model is presented in Figure 4. The dynamic model of the motor that allows calculation of transient characteristics is derived in Ansys Simplorer. The software has blocks that allow for modeling the symmetrical three-phase power supply. Additionally, it allows the model of the motor derived in RMxprt module of Ansys Electronic Desktop to be imported via a dynamic link. The motor output is linked to the load torque and inertia. The more detailed explanation how to derive drive design can be found in [27]. The computational time of the drive system with various loads and moments of inertia takes no more than couple of minutes depending of the set time for simulation and the set maximum and minimum time steps.

**Figure 2.** Flux density distribution at magnets of M2 at Mload = 14 Nm, J = 0.37 kgm<sup>2</sup> (**a**) 236 rpm (**b**) 510 rpm (**c**) 1409 rpm (**d**) 1498 rpm.

**Figure 3.** Magnetic field distribution at magnets of M2 at Mload = 14 Nm, J = 0.37 kgm<sup>2</sup> (**a**) 236 rpm (**b**) 510 rpm (**c**) 1409 rpm (**d**) 1498 rpm.

**Figure 4.** Dynamic model of line-start synchronous motor.

The basic equation behind the dynamic model of the motor in *d-q* reference frame is [28]:

$$
\mu\_{ds} = R\_s i\_{ds} + \frac{d\Psi\_{ds}}{dt} - (1 - s)\omega\_s \psi\_{qs} \tag{2}
$$

$$
\mu\_{qs} = R\_s i\_{qs} + \frac{d\Psi\_{qs}}{dt} + (1 - s)\omega\_s \psi\_{ds} \tag{3}
$$

where *s* is the slip defined as:

$$s = \frac{\omega\_s - \omega\_r}{\omega\_s} \tag{4}$$

$$
\mu\_{dr} = R\_{dr} i\_{rd} + \frac{d\Psi\_{dr}}{dt} = 0 \tag{5}
$$

$$
\mu\_{qr} = \mathcal{R}\_{qr} i\_{qd} + \frac{d\Psi\_{qr}}{dt} = 0 \tag{6}
$$

$$
\Psi\_{ds} = L\_{ds}i\_{ds} + L\_{md}i\_{dr} + \Psi\_{m} \tag{7}
$$

$$
\Psi\_{q^g} = L\_{q^g} i\_{q^g} + L\_{nq} i\_{q^r} \tag{8}
$$

$$\Psi\_{dr} = L\_{dr}i\_{dr} + L\_{md}i\_{ds} + \Psi\_{m} \tag{9}$$

$$
\Psi\_{qr} = L\_{qr}i\_{dr} + L\_{mq}i\_{qs} \tag{10}
$$

The coupling between the electrical system and the mechanical system is represented by the torque equation and the mechanical equation. The electromagnetic torque *Tel* developed by the motor can be expressed as:

$$T\_{cl} = \frac{p}{2} \frac{3}{2} \left( \Psi\_{ds} i\_{qs} - \Psi\_{qs} i\_{ds} \right) \tag{11}$$

The motor torque is balanced by the mechanical shaft torque *Tload* and the dynamic torque caused by the total inertia *J* [29].

$$T = T\_{load} + f\left(\frac{2}{p}\right)\frac{d\omega\_m}{dt} \tag{12}$$

Motor parameters are calculated in RMxprt module of Ansys Electronics Desktop software. This model of the motor from RMxprt module with all data and calculated parameters is linked, i.e., imported in the dynamic model which is modeled in the software module Ansys Simplorer. The motor parameters for the model M2 are presented in Table 3.


**Table 3.** Motor parameters of model M2.

The description of methodology for obtaining the numerous parameters of line-start synchronous motor can be found in [30]. Due to extent of the mathematical model, it is not presented here. Further details can be found in [30,31].
