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Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine and Power Converters

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 17225

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Dr. Vladimir Prakht

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Guest Editor

Department of Electrical Engineering, Ural Federal University, 620002 Yekaterinburg, Russia
Interests: energy efficiency; electric machines; electric motors; electric generators; electric drives; gearless generators; gearless motors; high-speed electric machines
Special Issues, Collections and Topics in MDPI journals

Dr. Mohamed N. Ibrahim

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Guest Editor

Department of Electromechanical, Systems and Metal Engineering, Faculty of Engineering and Architecture, Ghent University, 9052 Ghent, Belgium
Interests: electrical machines and drives for industrial and sustainable energy applications; numerical models for electromagnetics; photovoltaic pumping systems
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Dr. Anton Dianov

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Guest Editor

System Lab, Daeyoung R&D Center, Yongin 16954, Republic of Korea
Interests: electrical drives for home appliances, industrial and automotive applications; sensorless and advanced control algorithms
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

With the recent tendencies towards green energy and decreased carbon emissions, electric energy is becoming more and more popular. As a result, research in the field of electric machines and power converters has intensified, aiming to increase one device characteristic without significantly worsening others. In this sense, the first and most important step is proper mathematical modelling, which can decrease the number of prototypes, reduce the development time, and save a significant amount of money. Another important step is the proper mathematical processing of test results, which reduces the duration of tests and the complexity and cost of test benches. There is no one ideal mathematical model that fits all tasks. Their methodology and accuracy vary depending on application requirements, and therefore developing the optimal modelling technique is a challenging task that depends on requirement specifications and may significantly vary from one project to another.

This Special Issue aims to collect papers reporting on mathematical approaches to the modeling, optimal design, and control of electric machines and power converters. The main topics of this Special Issue include, but are not limited to:

Analytical models (electromagnetic, thermal, etc.) of electric machines and power converters;
Numerical models (finite element method, boundary element method, equivalent circuits, etc.) of electric machines and power converters;
Multi-physics models of electric machines and power converters;
Lifetime modeling of electric machines and power converters;
Loss modeling of electric machines and power converters;
Optimal design methodologies of electric machines and power converters;
Optimization techniques for the fast and efficient optimal design of electric machines and power converters;
Advanced test methods for electric machines and power converters;
Offline and online methods for parameter identification of electric machines and power converters;
Field-oriented control and direct torque control;
Model predictive control of electric machines and power converters;
Sensorless and reduced sensor control of electric machines and power converters;
Robust control of electric machines and power converters;
Optimal control techniques for electric machines and power converters.

Dr. Vladimir Prakht
Dr. Mohamed N. Ibrahim
Dr. Anton Dianov
Guest Editors

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

electric machines
electric motors
electric generators
electric drives
power converters
mathematical modelling
optimal design
advanced test methods
optimal control techniques

Published Papers (9 papers)

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Research

14 pages, 6073 KiB

Open AccessArticle

An In-Phase Unit Slot-Opening Shift Method for Cogging Torque Reduction in Interior Permanent Magnet Machine

by Linwei Wang, Shuai Lu, Yangming Chen and Shiya Wang

Mathematics 2023, 11(7), 1735; https://doi.org/10.3390/math11071735 - 05 Apr 2023

Cited by 2 | Viewed by 1002

Abstract

The cogging torque reduction methods in permanent magnet (PM) machines are more or less FEA trial and error-based and cause undesirable side effects, such as distorted back EMF, new harmonic components, and structure asymmetry. A slot-opening grouping method can address these issues. However, it needs to model all slots in FEA design validation during practical cogging torque optimization iterations, and also leads to back-EMF reduction. In this paper, a new grouping strategy, termed in-phase unit (IPU), is introduced, together with the slot-opening angle-shift method. The slot openings with the same cogging torque distribution pattern are grouped into an IPU, and the cogging torque peaks of the slot openings within an IPU can now be interleaved. Thereby, the major harmonic components of the cogging torque are cancelled out, instead of being summed up. The IPU grouping principle, the slot-opening shift angle computation, and the selection of the harmonic order to cancel are analyzed in detail. By comparison, the proposed method not only simplifies cogging torque optimization iterations by only modeling the slots in one IPU in FEA, but also compensates for the back-EMF constant reduction. The effectiveness of the proposed methods is validated by two typical interior PM machine design cases. Full article

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

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21 pages, 3051 KiB

Open AccessArticle

Optimal Performance of Photovoltaic-Powered Water Pumping System

by Mohammad R. Altimania, Nadia A. Elsonbaty, Mohamed A. Enany, Mahmoud M. Gamil, Saeed Alzahrani, Musfer Hasan Alraddadi, Ruwaybih Alsulami, Mohammad Alhartomi, Moahd Alghuson, Fares Alatawi and Mohamed I. Mosaad

Mathematics 2023, 11(3), 731; https://doi.org/10.3390/math11030731 - 01 Feb 2023

Cited by 3 | Viewed by 1945

Abstract

Photovoltaic (PV) systems are one of the promising renewable energy sources that have many industrial applications; one of them is water pumping systems. This paper proposes a new application of a PV system for water pumping using a three-phase induction motor while maximizing the daily quantity of water pumped while considering maximizing both the efficiency of the three-phase induction motor and the harvested power from the PV system. This harvesting is performed through maximum power point tracking (MPPT) of the PV system. The proposed technique is applied to a PV-powered 3 phase induction motor water pumping system (PV-IMWPS) at any operating point. Firstly, an analytical approach is offered to find the optimal firing pattern of the inverter (V-F) for the motor through optimal flux control. This flux control is presented for maximizing the pump flow rate while achieving MPPT for the PV system and maximum efficiency of the motor at any irradiance and temperature. The provided analytical optimal flux control is compared to a fixed flux one to ascertain its effectiveness. The obtained feature of the suggested optimal flux control validates a significant improvement in the system performances, including the daily pumped quantity, motor power factor, and system efficiency. Then converting the data from the first analytical step into an intelligent approach using an adaptive neuro-fuzzy inference system (ANFIS). This ANFIS is trained offline with the input (irradiance and temperature) while the output is the inverter pattern to enhance the performance of the proposed pumping system, PV-IMWPS. Full article

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

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18 pages, 6414 KiB

Open AccessFeature PaperArticle

Testing of an Adaptive Algorithm for Estimating the Parameters of a Synchronous Generator Based on the Approximation of Electrical State Time Series

by Mihail Senyuk, Svetlana Beryozkina, Alexander Berdin, Alexander Moiseichenkov, Murodbek Safaraliev and Inga Zicmane

Mathematics 2022, 10(22), 4187; https://doi.org/10.3390/math10224187 - 09 Nov 2022

Cited by 15 | Viewed by 1092

Abstract

The results of testing the algorithms of the adaptive model of a synchronous generator using theoretical and real physical data are presented in this study. The adaptive model of a synchronous machine is an equations system, which describes both the static and transient operation of a generator. Parameters of the adaptive model are found using measurements of a generator’s operational parameters. The single-machine model was created in Matlab/Simulink software to test the theoretical data. This single-machine model consists of a synchronous generator, a step-up transformer, and a transmission line. The test model also includes models of the automatic voltage regulator and steam turbine governor. The real electrodynamic model was used to verify the adaptive model of a synchronous machine. It consisted of four synchronous generators, with values of power capacity of 5 kW and 15 kW. The data logger with a sampling rate of 57.8 kHz was developed and installed to measure the operating parameters of each generator. As a result of testing on both models, the following values were estimated: inertia moment, d-axis and q-axis reactance, and load angle. These values were compared with the reference values. The adaptive model of a synchronous machine can be used in systems of emergency control and assessment of generator state. Full article

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

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20 pages, 13486 KiB

Open AccessArticle

High Accuracy Modeling of Permanent Magnet Synchronous Motors Using Finite Element Analysis

by Hanaa Elsherbiny, Laszlo Szamel, Mohamed Kamal Ahmed and Mahmoud A. Elwany

Mathematics 2022, 10(20), 3880; https://doi.org/10.3390/math10203880 - 19 Oct 2022

Cited by 6 | Viewed by 3491

Abstract

Permanent magnet synchronous machines (PMSMs) have garnered increasing interest because of their advantages such as high efficiency, high power density, wide speed range, and fast dynamics. They have been employed recently in several industrial applications including robotics and electric vehicles (EVs). However, PMSMs have highly nonlinear magnetic characteristics, especially interior PMSMs, due to the existence of reluctance torque. Nonlinearity complicates not only machine modeling but also control algorithms. An accurate machine model is the key aspect for the prediction of machine performance as well as the development of a high-performance control algorithm. Hence, this paper presents an accurate modelling method for PMSMs. The proposed model method is applicable for all PMSMs, even multiphase machines. This paper considers a fractional slot concentrated winding 12/10 interior PMSM (IPMSM) for this study to demonstrate the effect of magnetic saturation and special harmonics. The developed model considers accurately the magnetic saturation, mutual coupling, spatial harmonics, and iron loss effects. It utilizes finite element analysis (FEA) to estimate the precise magnetic characteristics of IPMSM. The finite element model is calibrated precisely using experimental measurements. The iron losses are estimated within the simulation model as d- and q-axes current components. The model accuracy is validated experimentally based on a 12/10 IPMSM prototype. Full article

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

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18 pages, 5061 KiB

Open AccessArticle

Efficiency and Core Loss Map Estimation with Machine Learning Based Multivariate Polynomial Regression Model

by Oğuz Mısır and Mehmet Akar

Mathematics 2022, 10(19), 3691; https://doi.org/10.3390/math10193691 - 09 Oct 2022

Cited by 4 | Viewed by 2129

Abstract

Efficiency mapping has an important place in examining the maximum efficiency distribution as well as the energy consumption of designed electric motors at maximum torque and speed. Performing analysis at all operating points with FEM analysis in the motor design process requires high processing costs and time. In this article, a machine learning-based multivariate polynomial regression estimation model was developed to overcome these costly processes from FEM analysis. With the proposed method, the operating points of the motors in different conditions during the design process can be predicted in advance with high accuracy. In the study, two different models are developed for efficiency map and core loss estimation of interior permanent magnet synchronous motor design. The developed models use few parameters and predict with high accuracy. Estimation models shorten the design process and offer a less complex model. Obtained results are validated by comparison with FEM analysis. Full article

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

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26 pages, 9199 KiB

Open AccessArticle

Analysis and Demonstration of Control Scheme for Multiple Operating Modes of Energy Storage Converters to Enhance Power Factor

by Khalid Javed, Lieven Vandevelde and Frederik De Belie

Mathematics 2022, 10(19), 3434; https://doi.org/10.3390/math10193434 - 21 Sep 2022

Viewed by 1337

Abstract

Rectifiers are required by the devices connected to the distribution end of the electrical power networks for AC/DC conversion. The line current becomes non-sinusoidal when a capacitor with a significant value is used to mitigate the output voltage ripple. This type of converter emulates a non-resistive impedance to the grid, due to which a bend occurs in the shape of the line current, which results in high total harmonic distortion and a low power factor. For perceiving sinusoidal current, power factor correction techniques are required. A digital controller for parallel-connected buck-boost power factor correctors is presented in this article to maintain a constant output voltage and to deal with circulating currents amongst parallel-connected converters. The proposed digital supervisory controller also regulates the input and line currents to keep them sinusoidal according to the input supply voltage to maintain the high power factor of the system. In this paper, using the differential equations of a buck-boost converter, the duty cycle calculations are performed for both Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM), which are responsible for providing a unity power factor. A supervisory controller encompasses a feed-forward control algorithm for tuning model parameters for eliminating the harmonics from the line current. The proposed scheme helps calculate duty cycles which provides a unity power factor and minimizes the circulating currents. The proposed method was simulated in MATLAB/Simulink and their digital-hardware validation testing was also performed using C2000 MCU Launchpad. Full article

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

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18 pages, 7660 KiB

Open AccessArticle

Perovskite Solar Cells and Thermoelectric Generator Hybrid Array Feeding a Synchronous Reluctance Motor for an Efficient Water Pumping System

by Alaa A. Zaky, Mohamed N. Ibrahim, Ibrahim B. M. Taha, Bedir Yousif, Peter Sergeant, Evangelos Hristoforou and Polycarpos Falaras

Mathematics 2022, 10(14), 2417; https://doi.org/10.3390/math10142417 - 11 Jul 2022

Cited by 3 | Viewed by 1703

Abstract

Nowadays, water pumping systems based on photovoltaics as a source of electricity have widely increased. System cost and efficiency still require enhancement in order to spread their application. Perovskite solar cells (PSCs) are the most hopeful third-generation photovoltaic for replacing the silicon-based photovoltaic thanks to their high power conversion efficiency, reaching 25.8%; tunable band-gap; long diffusion length; low fabrication temperature; and low cost. In this work, for the first time, we proposed a high-power-density hybrid perovskite solar cell thermoelectric generator (TEG) array for feeding a synchronous reluctance motor (SynRM) driving a water pump for use in an irrigation system. A control technique was used to achieve two functions. The first function was driving the motor to obtain the maximum torque/ampere. The second was harvesting the maximum perovskite solar cell array output power on the basis of the maximum power point tracking (MPPT) algorithm using the perturbation and observation approach. Thus, the proposed hybrid perovskite solar cell–thermoelectric generator feeds the motor via an inverter without DC–DC converters or batteries. Accordingly, the short life problems and the high replacement cost are avoided. The proposed complete system was simulated via the MATLAB package. Moreover, a complete laboratory infrastructure was constructed for testing the proposed high-power-density hybrid perovskite solar cell–TEG array for the water pumping system. The results revealed that using the high-power-density hybrid perovskite solar cell–TEG array, both the motor’s output power and the pump’s flow rate were improved by 11% and 14%, respectively, compared to only using the perovskite solar cell array. Finally, both the simulation and experimental results proved the high-performance efficiency of the system in addition to showing its system complexity and cost reduction. Full article

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

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16 pages, 11308 KiB

Open AccessArticle

Minimization of Torque Ripples in Multi-Stack Slotted Stator Axial-Flux Synchronous Machine by Modifying Magnet Shape

by Zia Mahmood, Junaid Ikram, Rabiah Badar, Syed Sabir Hussain Bukhari, Madad Ali Shah, Ali Asghar Memon and Mikulas Huba

Mathematics 2022, 10(10), 1653; https://doi.org/10.3390/math10101653 - 12 May 2022

Cited by 3 | Viewed by 1313

Abstract

This paper presents a proposed model of a multi-stack slotted stator axial-flux type permanent magnet synchronous machine (AFPMSM) specifically for reducing torque ripple. The proposed AFPMSM model uses pentagon-shaped permanent magnets (PMs). It has a low value of cogging torque and torque ripples compared to the conventional model with a trapezoidal magnet shape. Additionally, it has increased internal generated voltage (Ef) as compared to the conventional model. To further enhance Ef phases and minimize cogging torque of the proposed model, the proposed AFPMSM model was optimized by varying different sides of PMs using a genetic algorithm (GA). A time-stepped three-dimensional (3D) finite element analysis (FEA) was performed for the comparative analysis of conventional, proposed, and optimized AFPMSM models. From this comparative performance analysis, it is observed that torque ripples and cogging torque of the optimized AFPMSM are significantly decreased, while output average torque is appreciably increased. Ef and output power are also enhanced. Full article

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

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14 pages, 1956 KiB

Open AccessArticle

Indirect Efficiency Measurement Method for Line-Start Permanent Magnet Synchronous Motors

by Vadim Kazakbaev, Aleksey Paramonov, Vladimir Dmitrievskii, Vladimir Prakht and Victor Goman

Mathematics 2022, 10(7), 1056; https://doi.org/10.3390/math10071056 - 25 Mar 2022

Cited by 8 | Viewed by 1958

Abstract

Despite the great potential and the high performance of energy-efficient line-start permanent magnet synchronous motors (LSPMSMs), their developers face a great deal of difficulties, one of which is the lack of reliable and accurate testing methods for such electrical machines. In this paper, we propose a new method for indirectly determining the efficiency of LSPMSM through the summation of individual loss components. The standard input-output method usually used for these machines is based on torque measurement, requires expensive measuring equipment, and, as a rule, has great uncertainty. Contrarily, the proposed method does not require direct measurement of torque and mechanical power on the shaft and is less sensitive to measurement uncertainties. The theoretical substantiation of the proposed method and its experimental verification using a commercially available four-pole LSPMSM with a rated power of 0.55 kW are presented. Satisfactory convergence of the experimental results obtained using the standard input-output method and using the proposed indirect method is shown. Full article

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

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