Special Issue "Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine"

Alecksey Anuchin

and

Mathematics 2021, 9(22), 2859; https://doi.org/10.3390/math9222859 - 11 Nov 2021

Cited by 6 | Viewed by 1019

Abstract

The synchronous homopolar motor (SHM) with an excitation winding on the stator and a toothed rotor is a good alternative to traction induction motors for hybrid mining trucks. The main problem in the design of the SHM electric drives is that the magnetic flux forms three-dimensional loops and, as a result, the lack of high-quality optimization methods, which leads to the need to overrate the installed power of the inverter. This article discusses the procedure and results of optimization of a commercially available 370 kW traction SHM using the Nelder–Mead method. The objective function is composed to mainly improve the following characteristics of the traction SHM: total motor power loss and maximum armature winding current. In addition, terms are introduced into the objective function to make it possible to limit the voltage, the loss in the excitation winding, and the maximum magnetic flux density in the non-laminated sections of the magnetic core. As a result of the optimization, the motor losses and the maximum current required by the motor from the inverter were significantly reduced. The achieved reduction in the maximum current allows the cost of the IGBT modules of the inverter to be reduced by 1.4 times (by $ 2295), and also allows the AC component of the DC-link current to be reduced by the same amount. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Design of Constraints for Seeking Maximum Torque per Ampere Techniques in an Interior Permanent Magnet Synchronous Motor Control

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Open AccessArticle

Anton Dianov

and

Alecksey Anuchin

Mathematics 2021, 9(21), 2785; https://doi.org/10.3390/math9212785 - 03 Nov 2021

Cited by 7 | Viewed by 1571

Abstract

The efficient control of permanent magnet synchronous motors (PMSM) requires the development of a technique for loss optimization. The best approach is the implementation of power loss minimization algorithms, which are hard to model and design. Therefore, the developers typically involve maximum torque per ampere (MTPA) control, which optimizes Joule loss only. The conventional MTPA control requires knowledge of motor parameters and can only properly operate when these parameters are constant. However, motor parameters vary depending on operating conditions; thus, conventional techniques cannot be used. Furthermore, many industrial drives are designed for self-commissioning, and they do not have prior information on motor parameters. In order to solve this problem, various MTPA-seeking techniques, which track the minimum of motor current, have been developed. The dynamic performance between these seeking algorithms and maximum deviation from the true MTPA trajectory are defined by the constraints in most cases, in which proper design improves the dynamic behavior of MTPA-seeking algorithms. This paper considers a PMSM, which was designed to operate in the saturation area and whose MTPA trajectory significantly deviates from the same curve constructed for the initial unsaturated parameters. This paper considers existing approaches, explains their pros and cons, and demonstrates that these methods do not utilize full potential of the motor. A new constraint design was proposed and explained step by step. The experiment verifies the proposed technique and demonstrates improvements in efficiency and dynamic behavior of the seeking algorithm. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Comparative Study of Energy Consumption and CO₂ Emissions of Variable-Speed Electric Drives with Induction and Synchronous Reluctance Motors in Pump Units

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Open AccessArticle

Victor Goman

and

Mathematics 2021, 9(21), 2679; https://doi.org/10.3390/math9212679 - 22 Oct 2021

Cited by 12 | Viewed by 1512

Abstract

This study carried out a comparative analysis of indicators of electricity consumption and CO₂ emissions for four-pole induction motors (IMs) of efficiency classes IE3 and IE4 with a rated power of 2.2–200 kW in a variable speed pump unit. In addition, innovative IE4 converter-fed synchronous reluctance motors (SynRMs) were evaluated. The comparison was derived from the manufacturer’s specifications for the power drive systems (PDSs) at various rotational speeds and loads. The results showed that the emission indicators for IE3 class motors were significantly worse compared with IE4 class motors for low power ratings, which make up the vast majority of electric motors in service. This justifies expanding the mandatory power range for IE4 motors to at least 7.5–200 kW or even 0.75–200 kW, as it will dramatically contribute to the achievement of the new ambitious goals for reducing greenhouse gas emissions. In addition, the operational advantages of IE4 SynRMs over IE4 IMs were demonstrated, such as their simpler design and manufacturing technology at a price comparable to that of IE3 IMs. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Feasibility Study of Direct-on-Line Energy-Efficient Motors in a Pumping Unit, Considering Reactive Power Compensation

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Open AccessArticle

Safarbek Oshurbekov

and

Mathematics 2021, 9(18), 2196; https://doi.org/10.3390/math9182196 - 08 Sep 2021

Viewed by 1008

Abstract

The paper compares the economic effect of using capacitors in fixed speed drives of a pumping station when using energy-efficient motors of various types. Induction motors of IE2 and IE3 energy efficiency classes, a direct-on-line synchronous motor with a permanent magnet in the rotor, and a direct-on-line synchronous reluctance motor are considered. The comparison takes into account not only the efficiency of the motors, but also their power factor, on which the losses in the cable and transformer depend. The possibility of using static capacitors to compensate for the reactive power of motors and reduce the losses is also considered. The feasibility analysis takes into account that the motors have different initial costs. The cost of capacitors is also taken into consideration. The analysis shows that the use of static capacitors can have a significant impact on the comparison between different motors in this application. Without considering capacitors, the permanent magnet motor has the shortest payback period, otherwise the synchronous reluctance motor has the shortest payback period. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Novel Single Inverter-Controlled Brushless Wound Field Synchronous Machine Topology

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Open AccessArticle

Syed Sabir Hussain Bukhari

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Mathematics 2021, 9(15), 1739; https://doi.org/10.3390/math9151739 - 23 Jul 2021

Cited by 6 | Viewed by 1298

Abstract

This paper proposes a novel brushless excitation topology for a three-phase synchronous machine based on a customary current-controlled voltage source inverter (VSI). The inverter employs a simple hysteresis-controller-based current control scheme that enables it to inject a three-phase armature current to the stator winding which contains a dc offset. This dc offset generates an additional air gap magneto-motive force (MMF). On the rotor side, an additional harmonic winding is mounted to harness the harmonic power from the air gap flux. Since a third harmonic flux is generated in this type of topology, the machine structure is also modified to accommodate the third harmonic rotor winding to have a voltage induced as the rotor rotates at synchronous speed. Specifically, four-pole armature and field winding patterns are used, whereas the harmonic winding is configured for a twelve-pole pattern. A diode rectifier is also mounted on the rotor between the harmonic and field windings. Therefore, the generated voltage on the harmonic winding feeds the current to the field winding for excitation. A 2D-finite element analysis (FEA) in JMAG-Designer was carried out for performance evaluation and verification of the topology. The simulation results are consistent with the proposed theory. The topology could reduce the cost and stator winding volume compared to a conventional brushless machine, with good potential for various applications. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Analysis and Optimization of Axial Flux Permanent Magnet Machine for Cogging Torque Reduction

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Open AccessArticle

Hina Usman

Junaid Ikram

Khurram Saleem Alimgeer

Muhammad Yousuf

Syed Sabir Hussain Bukhari

and

Jong-Suk Ro

Mathematics 2021, 9(15), 1738; https://doi.org/10.3390/math9151738 - 23 Jul 2021

Cited by 8 | Viewed by 1338

Abstract

In this paper, a hexagonal magnet shape is proposed to have an arc profile capable of reducing torque ripples resulting from cogging torque in a single-sided axial flux permanent magnet (AFPM) machine. The arc-shaped permanent magnet increases the air-gap length effectively and makes the flux of the air-gap more sinusoidal, which decreases air-gap flux density and hence causes a reduction in cogging torque. Cogging torque is the basic source of vibration, along with the noise in PM machines, since it is the main cause of torque ripples. Cogging torque is independent of the load current and is proportional to the air-gap flux and the reluctance variation. Three-dimensional finite element analysis (FEA) is used in the JMAG-Designer to analyze the performance of the conventional and proposed hexagonal-shaped PM AFPM machines. The proposed shape is designed to reduce cogging torque, and the voltage remains the same as compared to the conventional hexagonal-shaped PM machine. Further, optimization is performed by utilizing an asymmetric overhang. Latin hypercube sampling (LHS) is used to create samples, the kriging method is applied to approximate the model, and a genetic algorithm is applied to obtain the optimum parameters of the machine. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

High-Harmonic Injection-Based Brushless Wound Field Synchronous Machine Topology

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Open AccessCommunication

Syed Sabir Hussain Bukhari

and

Mathematics 2021, 9(15), 1721; https://doi.org/10.3390/math9151721 - 22 Jul 2021

Cited by 2 | Viewed by 1233

Abstract

This paper discusses the design and analysis of a high-harmonic injection-based field excitation scheme for the brushless operation of wound field synchronous machines (WFSMs) in order to achieve a higher efficiency. The proposed scheme involves two inverters. One of these inverters provides the three-phase fundamental-harmonic current to the armature winding, whereas the second inverter injects the single-phase high-harmonic i.e., 6^th harmonic current in this case, to the neutral-point of the Y-connected armature winding. The injection of the high-harmonic current in the armature winding develops the high-harmonic magnetomotive force (MMF) in the air gap of the machine beside the fundamental. The high-harmonic MMF induces the harmonic current in the excitation winding of the rotor, whereas the fundamental MMF develops the main armature field. The harmonic current is rectified to inject the direct current (DC) into the main rotor field winding. The main armature and rotor fields, when interacting with each other, produce torque. Finite element analysis (FEA) is carried out in order to develop a 4-pole 24-slot machine and investigate it using a 6^th harmonic current injection for the rotor field excitation to both attain a brushless operation and analyze its electromagnetic performance. Later on, the performance of the proposed topology is compared with the typical brushless WFSM topology employing the 3^rd harmonic current injection-based field excitation scheme. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Design Optimization of a Traction Synchronous Homopolar Motor

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Open AccessArticle

Alecksey Anuchin

and

Mathematics 2021, 9(12), 1352; https://doi.org/10.3390/math9121352 - 11 Jun 2021

Cited by 5 | Viewed by 2133

Abstract

Synchronous homopolar motors (SHMs) have been attracting the attention of researchers for many decades. They are used in a variety of equipment such as aircraft and train generators, welding inverters, and as traction motors. Various mathematical models of SHMs have been proposed to deal with their complicated magnetic circuit. However, mathematical techniques for optimizing SHMs have not yet been proposed. This paper discusses various aspects of the optimal design of traction SHMs, applying the one-criterion unconstrained Nelder–Mead method. The considered motor is intended for use in a mining dump truck with a carrying capacity of 90 tons. The objective function for the SHM optimization was designed to reduce/improve the following main characteristics: total motor power loss, maximum winding current, and torque ripple. One of the difficulties in optimizing SHMs is the three-dimensional structure of their magnetic core, which usually requires the use of a three-dimensional finite element model. However, in this study, an original two-dimensional finite element model of a SHM was used; it allowed the drastic reduction in the computational burden, enabling objective optimization. As a result of optimization, the total losses in the motor decreased by up to 1.16 times and the torque ripple decreased by up to 1.34 times; the maximum armature winding current in the motor mode decreased by 8%. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Improving Reliability and Energy Efficiency of Three Parallel Pumps by Selecting Trade-Off Operating Points

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Open AccessArticle

Safarbek Oshurbekov

and

Mathematics 2021, 9(11), 1297; https://doi.org/10.3390/math9111297 - 05 Jun 2021

Cited by 6 | Viewed by 1674

Abstract

Reliability, along with energy efficiency, is an important characteristic of pump units in various applications. In practical pump applications, it is important to strike a balance between reliability and energy efficiency. These indicators strongly depend on the applied control method of the pump unit. This study analyzes a trade-off method for regulating a system with three parallel pumps equipped with only one frequency converter (multi-pump single-drive system). A typical operating cycle of a pumping system with variable flow rate requirements is considered. The proposed trade-off method is compared with the traditional regulation, when a change in the operating point of the pump is achieved only by changing the rotation speed, and with the method for maximum reliability. It is shown that the proposed trade-off method makes it possible to ensure sufficient reliability of the multi-pump system operation without a significant increase in energy consumption. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Multi-Objective Optimization of Switched Reluctance Machine Design Using Jaya Algorithm (MO-Jaya)

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Open AccessArticle

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Mathematics 2021, 9(10), 1107; https://doi.org/10.3390/math9101107 - 13 May 2021

Cited by 4 | Viewed by 1273

Abstract

The switched reluctance machine (SRM) design is different from the design of most of other machines. SRM has many design parameters that have non-linear relationships with the performance indices (i.e., average torque, efficiency, and so forth). Hence, it is difficult to design SRM using straight forward equations with iterative methods, which is common for other machines. Optimization techniques are used to overcome this challenge by searching for the best variables values within the search area. In this paper, the optimization of SRM design is achieved using multi-objective Jaya algorithm (MO-Jaya). In the Jaya algorithm, solutions are moved closer to the best solution and away from the worst solution. Hence, a good intensification of the search process is achieved. Moreover, the randomly changed parameters achieve good search diversity. In this paper, it is suggested to also randomly change best and worst solutions. Hence, better diversity is achieved, as indicated from results. The optimization with the MO-Jaya algorithm was made for 8/6 and 6/4 SRM. Objectives used are the average torque, efficiency, and iron weight. The results of MO-Jaya are compared with the results of the non-dominated sorting genetic algorithm (NSGA-II) for the same conditions and constraints. The optimization program is made in Lua programming language and executed by FEMM4.2 software. The results show the success of the approach to achieve better objective values, a broad search, and to introduce a variety of optimal solutions. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

An Enhanced DC-Link Voltage Response for Wind-Driven Doubly Fed Induction Generator Using Adaptive Fuzzy Extended State Observer and Sliding Mode Control

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Open AccessArticle

Mohammed Mazen Alhato

Mohamed N. Ibrahim

Hegazy Rezk

and

Soufiene Bouallègue

Mathematics 2021, 9(9), 963; https://doi.org/10.3390/math9090963 - 25 Apr 2021

Cited by 12 | Viewed by 1321

Abstract

This paper presents an enhancement method to improve the performance of the DC-link voltage loop regulation in a Doubly-Fed Induction Generator (DFIG)- based wind energy converter. An intelligent, combined control approach based on a metaheuristics-tuned Second-Order Sliding Mode (SOSM) controller and an adaptive fuzzy-scheduled Extended State Observer (ESO) is proposed and successfully applied. The proposed fuzzy gains-scheduling mechanism is performed to adaptively tune and update the bandwidth of the ESO while disturbances occur. Besides common time-domain performance indexes, bounded limitations on the effective parameters of the designed Super Twisting (STA)-based SOSM controllers are set thanks to the Lyapunov theory and used as nonlinear constraints for the formulated hard optimization control problem. A set of advanced metaheuristics, such as Thermal Exchange Optimization (TEO), Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Harmony Search Algorithm (HSA), Water Cycle Algorithm (WCA), and Grasshopper Optimization Algorithm (GOA), is considered to solve the constrained optimization problem. Demonstrative simulation results are carried out to show the superiority and effectiveness of the proposed control scheme in terms of grid disturbances rejection, closed-loop tracking performance, and robustness against the chattering phenomenon. Several comparisons to our related works, i.e., approaches based on TEO-tuned PI controller, TEO-tuned STA-SOSM controller, and STA-SOSM controller-based linear observer, are presented and discussed. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Comparison of Flux-Switching and Interior Permanent Magnet Synchronous Generators for Direct-Driven Wind Applications Based on Nelder–Mead Optimal Designing

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Open AccessArticle

and

Ekaterina Andriushchenko

Mathematics 2021, 9(7), 732; https://doi.org/10.3390/math9070732 - 29 Mar 2021

Cited by 2 | Viewed by 1405

Abstract

The permanent magnet flux-switching machine (PMFSM) is one of the most promising machines with magnets inserted into the stator. To determine in which applications the use of PMFSM is promising, it is essential to compare the PMFSM with machines of other types. This study provides a theoretical comparison of the PMFSM with a conventional interior permanent magnet synchronous machine (IPMSM) in the gearless generator of a low-power wind turbine (332 rpm, 51.4 Nm). To provide a fair comparison, both machines are optimized using the Nelder–Mead algorithm. The minimized optimization objectives are the required power of frequency converter, cost of active materials, torque ripple and losses of a generator averaged over the working profile of the wind turbine. In order to reduce the computational time, the substituting profile method is applied. Based on the results of the calculations, the advantages and disadvantages of the considered machines were revealed: the IPMSM has significantly lower losses and higher efficiency than the PMFSM, and the PMFSM requires much less rare-earth magnets and copper and is, therefore, cheaper in mass production. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Finite Element Based Overall Optimization of Switched Reluctance Motor Using Multi-Objective Genetic Algorithm (NSGA-II)

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Open AccessArticle

and

Mathematics 2021, 9(5), 576; https://doi.org/10.3390/math9050576 - 08 Mar 2021

Cited by 15 | Viewed by 1700

Abstract

The design of switched reluctance motor (SRM) is considered a complex problem to be solved using conventional design techniques. This is due to the large number of design parameters that should be considered during the design process. Therefore, optimization techniques are necessary to obtain an optimal design of SRM. This paper presents an optimal design methodology for SRM using the non-dominated sorting genetic algorithm (NSGA-II) optimization technique. Several dimensions of SRM are considered in the proposed design procedure including stator diameter, bore diameter, axial length, pole arcs and pole lengths, back iron length, shaft diameter as well as the air gap length. The multi-objective design scheme includes three objective functions to be achieved, that is, maximum average torque, maximum efficiency and minimum iron weight of the machine. Meanwhile, finite element analysis (FEA) is used during the optimization process to calculate the values of the objective functions. In this paper, two designs for SRMs with 8/6 and 6/4 configurations are presented. Simulation results show that the obtained SRM design parameters allow better average torque and efficiency with lower iron weight. Eventually, the integration of NSGA-II and FEA provides an effective approach to obtain the optimal design of SRM. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Robust Sensorless Model-Predictive Torque Flux Control for High-Performance Induction Motor Drives

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Open AccessArticle

Ahmed G. Mahmoud A. Aziz

Hegazy Rez

and

Ahmed A. Zaki Diab

Mathematics 2021, 9(4), 403; https://doi.org/10.3390/math9040403 - 18 Feb 2021

Cited by 8 | Viewed by 1699

Abstract

This paper introduces a novel sensorless model-predictive torque-flux control (MPTFC) for two-level inverter-fed induction motor (IM) drives to overcome the high torque ripples issue, which is evidently presented in model-predictive torque control (MPTC). The suggested control approach will be based on a novel modification for the adaptive full-order-observer (AFOO). Moreover, the motor is modeled considering core losses and a compensation term of core loss applied to the suggested observer. In order to mitigate the machine losses, particularly at low speed and light load operations, the loss minimization criterion (LMC) is suggested. A comprehensive comparative analysis between the performance of IM drive under conventional MPTC, and those of the proposed MPTFC approaches (without and with consideration of the LMC) has been carried out to confirm the efficiency of the proposed MPTFC drive. Based on MATLAB^® and Simulink^® from MathWorks^® (2018a, Natick, MA 01760-2098 USA) simulation results, the suggested sensorless system can operate at very low speeds and has the better dynamic and steady-state performance. Moreover, a comparison in detail of MPTC and the proposed MPTFC techniques regarding torque, current, and fluxes ripples is performed. The stability of the modified adaptive closed-loop observer for speed, flux and parameters estimation methodology is proven for a wide range of speeds via Lyapunov’s theorem. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Optimal Rotor Design of Synchronous Reluctance Machines Considering the Effect of Current Angle

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Open AccessArticle

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Mathematics 2021, 9(4), 344; https://doi.org/10.3390/math9040344 - 09 Feb 2021

Cited by 9 | Viewed by 1599

Abstract

The torque density and efficiency of synchronous reluctance machines (SynRMs) are greatly affected by the geometry of the rotor. Hence, an optimal design of the SynRM rotor geometry is highly recommended to achieve optimal performance (i.e., torque density, efficiency, and power factor). This paper studies the impact of considering the current angle as a variable during the optimization process on the resulting optimal geometry of the SynRM rotor. Various cases are analyzed and compared for different ranges of current angles during the optimization process. The analysis is carried out using finite element magnetic simulation. The obtained optimal geometry is prototyped for validation purposes. It is observed that when considering the effect of the current angle during the optimization process, the output power of the optimal geometry is about 3.32% higher than that of a fixed current angle case. In addition, during the optimization process, the case which considers the current angle as a variable has reached the optimal rotor geometry faster than that of a fixed current angle case. Moreover, it is observed that for a fixed current angle case, the torque ripple is affected by the selected value of the current angle. The torque ripple is greatly decreased by about 34.20% with a current angle of 45° compared to a current angle of 56.50°, which was introduced in previous literature. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Comparative Evaluation for an Improved Direct Instantaneous Torque Control Strategy of Switched Reluctance Motor Drives for Electric Vehicles

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Open AccessArticle

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Mathematics 2021, 9(4), 302; https://doi.org/10.3390/math9040302 - 04 Feb 2021

Cited by 11 | Viewed by 1777

Abstract

Due to the expected increase in the electric vehicles (EVs) sales and hence the increase of the price of rare-earth permanent magnets, the switched reluctance motors (SRMs) are gaining increasing research interest currently and in the future. The SRMs offer numerous advantages regarding their structure and converter topologies. However, they suffer from the high torque ripple and complex control algorithms. This paper presents an improved direct instantaneous torque control (DITC) strategy of SRMs for EVs. The improved DITC can fulfill the vehicle requirements. It involves a simple online torque estimator and a torque error compensator. The turn-on angle is defined analytically to achieve wide speed operation and maximum torque per ampere (MTPA) production. Moreover, the turn-off angles are optimized for minimum torque ripples and the highest efficiency. In addition, this paper provides a detailed comparison between the proposed DITC and the most applicable torque control techniques of SRMs for EVs, including indirect instantaneous torque control (IITC), using torque sharing function (TSF) strategy and average torque control (ATC). The results show the superior performance of the proposed DITC because it has the lowest torque ripples, the highest torque tor current ratio, and the best efficiency over the low and medium speed ranges. Moreover, the comparison shows the advantages of each control technique over the range of speed control. It provides a very clear overview to develop a universal control technique of SRM for EVs by merging two or more control techniques. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)

Optimal Design of a High-Speed Flux Reversal Motor with Bonded Rare-Earth Permanent Magnets

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Open AccessArticle

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Mathematics 2021, 9(3), 256; https://doi.org/10.3390/math9030256 - 28 Jan 2021

Cited by 2 | Viewed by 1092

Abstract

Single-phase flux reversal motors (FRMs) with sintered rare-earth permanent magnets on the stator for low-cost high-speed applications have a reliable rotor and a good specific power. However, to reduce eddy current loss, the sintered rare-earth magnets on the stator have to be segmented into several pieces and their cost increases with the number of magnet segments. An alternative to the sintered magnets can be bonded magnets, in which eddy current loss is almost absent. The remanence of bonded magnets is lower than that of sintered magnets, and they are prone to demagnetization. However, the cost of low-power motors with bonded magnets can be lower because of the simpler manufacturing technology and the lower material cost. This paper discusses various aspects of the optimal design of FRM with bonded magnets, applying the Nelder–Mead method. An objective function for optimizing an FRM with bonded magnets is designed to ensure the required efficiency, reduce torque oscillations, and prevent the bonded magnets from demagnetizing. As a result, it is shown that the FRM with bonded magnets has approximately the same efficiency as the FRM with sintered magnets. In addition, the peak-to-peak torque ripple is minimized and the minimal instantaneous torque is maximized. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine)