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Enhancing power electronics (PE) converter reliability is crucial for ensuring a reliable operation of current and future operating Wind Turbines (WTs). Achieving high reliability of variable speed WT PE systems requires careful consideration of their operation, and particularly their thermal cycling. This paper presents a methodology for evaluating and reconsidering operational strategies of WTs with relation to the thermal loading and lifetime consumption of the converter. The methodology is applied to compare control strategies for the WT generator and evaluate their impact on the converter reliability by observation of the thermal cycles and by calculating the resultant lifetime consumption of those stress cycles. The thermal stress on both the Machine Side Converter (MSC) and the Grid Side Converter (GSC) is examined and compared. It is shown that the least reliable of the three evaluated control strategies is the one that tracks the power curve below rated speed most closely. This paper suggests that dynamic transients associated with the WT control largely influence the IGBT module wear-out and their modelling needs to be prioritized for lifetime studies. These dynamic transients are captured by the improved model whose value is confirmed for the comparisons in the case study of the paper. [ABSTRACT FROM AUTHOR]

To research the impact of temperature-dependent characteristics of windings and magnets on the electromagnetic power loss and thermal properties of high-speed (HS) interior permanent magnet synchronous machines (PMSMs), an electromagnetic-thermal bi-directional coupling method (BDCM) is proposed for water-cooled HS PMSMs considering the assembling gaps between the motor components in this paper. The electromagnetic power loss is calculated by 3-D transient finite-element method and loaded into the 3-D temperature field according to the actual loss distribution, and the materials’ properties are in turn updated according to the temperature distributions. The loss and temperature calculation results of a 15kW HS amorphous metal PMSM are calculated by two different coupling methods in the conditions of the rated-load sinusoidal supply and converter supply, and compared with the measured results in the case of converter supply. The results obtained by the BDCM are more consistent with the experiment results, verifying the superiority of the proposed analyzing method in improving the calculation accuracy of motor loss and temperature rise. In addition, the applicable conditions of the proposed method are also summarized in the paper. [ABSTRACT FROM AUTHOR]

In this paper, the boundary discretization method is used to improve the traditional subdomain model. The improved model can be used to calculate the magnetic field distribution in the region containing non-orthogonal boundary, avoiding the influence of the simplified stator slot or permanent magnet shape on the results in calculating the motor magnetic field using the traditional subdomain model. In addition, the improved subdomain model can also be used to calculate the air-gap flux density when the rotor is eccentric, instead of segmenting the air-gap to an equivalent state without eccentricity. The calculation object of this paper is a surface-mount permanent magnet motor with a rectangular stator slot. The air-gap flux density under no-load and load conditions is calculated, respectively. Since the improved subdomain model does not need to simplify the stator slot shape, the magnetic potential in the stator slot is also calculated. Finally, the air-gap flux density under rotor eccentricity is calculated, and the influence of the calculating parameters on the results of the improved subdomain model is discussed. All the calculated results are compared with those obtained by the finite element method, which verifies the accuracy of the improved calculation model. [ABSTRACT FROM AUTHOR]

The papers in this special section brings together papers focused on the recent advancements and breakthroughs in the technology of modeling and enhanced active/reactive power control of wind power conversion systems, ranging from components of wind turbines to wind farms. [ABSTRACT FROM PUBLISHER]

This paper presents a fast analytical model for estimating the components of the PM flux density distribution in the air-gap for a number of interior permanent magnet synchronous machines (IPMSMs). Deriving the two-dimensional (2-D) analytical model for IPMSMs is more challenging compared to that of surface-mounted permanent magnet synchronous machines (SPMSMs) due to the inconsistent geometry of the rotor in polar coordinates. IPMSMs are usually modeled by using 0-D or 1-D methods such as the magnetic equivalent circuit (MEC); however, the MEC method is unable to take into account the tangential component of the magnetic flux density vector. In this paper, a 2-D analytical no-load electromagnetic model for five rotor topologies of IPMSMs is proposed. The effects of the stator slots on the radial component of the PM flux density distribution in the air-gap are then included by defining an air-gap function. The effects of the stator slots on the tangential components of the PM flux density distribution in the air-gap are also considered by injecting virtual surface currents (VSCs) or virtual permanent magnets (VPMs). For verification purposes, the analytical results are compared with those of the finite element method (FEM) and the experimental results of one of the cases. [ABSTRACT FROM AUTHOR]

Magnetic gears can perform the same function as mechanical gears with the added benefits inherent to contactless power transfer. However, quick and accurate analysis tools are required for magnetic gears to reach their full potential. As end effects can significantly impact the slip torque of a magnetic gear, 2D models often overestimate the slip torques, so 3D models are frequently required. Therefore, this paper proposes a 3D linear Magnetic Equivalent Circuit (MEC) or reluctance network model of radial flux magnetic gears with surface mounted magnets. This is an extension of a previously developed 2D MEC model, and, like the previous 2D model, it is thoroughly parametrized so that it can be directly applied to a wide range of parametric cases. This is Part I of a two-part paper and focuses on the implementation of the 3D MEC model. Part II compares the 3D MEC model against nonlinear finite element analysis (FEA) models to validate the MEC model's accuracy and to develop guidelines for discretizing the geometry. [ABSTRACT FROM AUTHOR]

This paper presents an approach for systematically modeling a class of microgrid (MG) systems. The derived model accommodates grid-connected and islanded operation of the MG simultaneously, and allows modeling of converter-based as well as directly interfaced resources. Full modeling of virtual synchronous machines and actual synchronous generators is addressed. The originally nonlinear model is then converted to a linear model whose eigenvalues determine local stability of the MG. The model is used to analyze impacts of cross-coupling droop terms on the MG stability. The conclusions of this analysis are as follows. Addition of cross-coupling droop terms reduces the losses, compromises the stability in the grid-connected mode, and improves the stability in standalone mode. Therefore, for an MG that is intended to continuously operate at grid-connected and standalone mode, only a modest amount of cross-coupling terms is recommended to increase the efficiency without compromising the grid-connected stability. Simulation and experimental results are presented to verify the derivations. [ABSTRACT FROM AUTHOR]

Acoustic noise modeling, analysis, and reduction are critical in the design of switched reluctance machines for noise-sensitive applications. Although the analytical method can provide a fast simulation of the acoustic noise, it is generally less accurate compared to the numerical method. In order to improve the simulation accuracy, a novel analytical method is presented in this paper. The proposed method considers the excitation of the high-axial-order vibration modes to simulate the vibration behavior and the acoustic noise in the three-dimensional (3D) domain. Methods of obtaining the input data for the 3D analytical simulations are presented. The acoustic noise results obtained from the numerical simulations and experiments from an 8/6 switched reluctance motor drive are used to validate the analytical method presented in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a dynamic thermal model which predicts the winding temperature of electrical machines at steady-state and transient conditions where windings are used in integrated battery chargers (IBCs) for DC charging in a stationary position. Using winding in high current charging process causes rising winding temperature which affects insulation life. Switched reluctance machines are a proper choice for using in electric vehicles (EVs) because of their advantages such as simple and sturdy structures. IBCs can reduce volume and weight of EVs and total cost is diminished because of integration. The analytical thermal model proposed in this paper can calculates the winding temperature in balanced and unbalanced currents injection because of the phase inductance in each rotor angle is distinct, so current excitation in each phase should be different for obtaining zero total torque and keeping rotor in a stationary position, also a reduced-order model is proposed with minor impact on the accuracy of the model. Special attention has been paid to monitor the winding temperature with considering the motor lifetime in DC charging mode, this view has not been addressed in IBCs before. The proposed model is then validated against experimental results and 3D finite element method. [ABSTRACT FROM AUTHOR]

A hybrid analytical and lumped-parameter thermal model is proposed in this paper to estimate the transient and steady-state two- and three-dimensional (2/3-D) spatial magnet temperature distributions for an interior permanent magnet synchronous machine (IPMSM). On the basis of a lumped-parameter thermal model (LPTM), the magnet analytical thermal models (ATMs) are synergized to establish the hybrid thermal model. By utilizing the transient or steady-state boundary conditions calculated by the LPTM, the ATMs are obtained by solving the heat conduction equations to estimate the spatial magnet temperature distributions in the 2-D horizontal-vertical and axial-vertical planes, which can also be extended to the 3-D temperature distribution by utilizing the multi-slice method. Meanwhile, the non-uniform magnet eddy current loss is also considered. Finally, both electromagnetic-thermal coupled finite element analysis method and experiments are used for verification based on a totally enclosed IPMSM. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear analysis model for predicting the performance of eddy current recoil brakes (ECRB) is proposed by combining the magnetic equivalent circuit (MEC) model and the subdomain model. The subdomain model introduces the equivalent region to improve the inherent shortcomings of the equivalent current sheet (ECS) method. The outer tube is divided into a magnetic saturated region and an unsaturated region in the subdomain model to simulate the magnetic saturation of the outer tube during recoil. The MEC model is applied to calculate the air gap magnetic flux density and the relative permeability of the equivalent region. Leakage flux and magnetic saturation are considered in the MEC model. The eddy current resistance of ECRB is calculated by the subdomain model. The model is verified by the finite element model, and it is able to predict the performance of ECRB with different structural parameters. In addition, the prototype of the ECRB was manufactured. A test was carried out on a 155 mm artillery to verify the accuracy of the proposed nonlinear analysis model. [ABSTRACT FROM AUTHOR]

This paper analyzes magnet defect fault signature in the surface-mounted permanent magnet motor (SPMM) using nonlinear analytical model considering the influence of magnet shape and magnetization direction. Based on the surface current method and conformal mapping technique, the magnet defect equivalent current and equivalent nonlinearity current are proposed to represent the magnet defect. Accordingly, the performance of SPMM can be obtained. The proposed model has great potential to investigate SPMM with non-uniform magnet defect and gives theoretical basis for fault diagnosis. The extra sensing coil is added to measure the voltage waveforms, which can also be predicted using the nonlinear analytical model and shows the influence of magnet defect fault. Finally, the finite element analysis and experimental results verify the high accuracy of nonlinear analytical model. [ABSTRACT FROM AUTHOR]

The magnetic field calculation for axial flux motors (AFMs) is always intricate and time-consuming. To this end, a fast quasi-three-dimensional (3D) analytical model is proposed in this paper for magnetic field prediction in AFMs. The 3D magnetic field problem can be simplified into a two-dimensional (2D) one by dividing the AFM into several annular slices in the radial direction. Then, for the first time, the harmonic modeling method (HMM) in Cartesian coordinates is adopted to solve the magnetic field in these slices cut from the AFM. The corresponding electromagnetic parameters of the AFM can be acquired subsequently. The critical step for the field prediction of using HMM in Cartesian coordinates is to adopt a variable substitution method when solving the partial differential equations. Next, the magnetic saturation of soft-magnetic material within AFMs is considered by adopting an iterative approach. Ultimately, the effectiveness of the proposed quasi-3D analytical model is validated by the nonlinear finite element analysis (FEA). The proposed analytical model is computationally efficient, which makes it suitable for the preliminary design of AFMs. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach to determine the air-gap magnetic field and the winding inductance in the brushless doubly-fed reluctance machine (BDFRM) with flux barriers. By dividing one flux guide layer into several segments, a calculus method based on magnetic circuit analysis is developed and specific analytical expression of the air-gap flux density is rigorously derived. Then, the included angle between fundamental components with the same pole pairs is also discussed. Based on the air-gap flux density distribution, the inductance expressions between different windings are also presented. Three kinds of finite element analysis models are established and studied. As a result, the accuracy of the analytical model can be verified by simulations and experimental data from an existing BDFRM prototype. [ABSTRACT FROM AUTHOR]

It is recognized that the rotor with shielding cylinder (SC) is one of the effective measures to restrain the rotor eddy current loss (RECL) for high-speed surface-mounted permanent magnet synchronous motors (PMSMs). At present, the RECL of PMSMs with multilayer composite rotor structure is mainly analyzed by the finite element method (FEM), which has obvious shortcomings in time-consumption and the mesh generation of thin SC. In this paper, a multi-layer subdomain analytical model for calculating the RECL of high-speed PMSMs with both non-ferromagnetic retaining sleeve and SC is proposed by taking the effects of eddy current reaction, stator slotting and current harmonics into account. Moreover, the 3-D distribution coefficient of eddy current in the SC is derived by the equivalent impedance method and the effects of temperature on the conductivity of the SC and RECL are obtained through equivalent thermal network (ETN) model. Based on the analytical model, the SC parameters are calculated to obtain the variation ranges when the RECL is minimum. Finally, the C-shape core experiment was built up to verify the correctness of the multilayer analytical model under different shielding layer conductivities and thicknesses. [ABSTRACT FROM AUTHOR]

This paper aims to disclose the noticeable effect of local tangential force on vibration performance in fractional-slot concentrated-winding permanent magnet synchronous machines (PMSMs). The mechanism to induce vibrations by tangential force is revealed at first. It is found that tangential force is able to deflect the yoke through the tooth's lever arm effect. This phenomenon is detailedly explained through finite element simulation and analytical description of the microscopic deformation in this paper. With the aid of a 10-pole/12-slot PMSM, the quantitative contribution of tangential force to the vibration is also investigated through simulation, vibration synthesis, and experiments. Results show that due to the strong lever arm effect and not so small force amplitudes as commonly expected, the contribution of tangential force to final vibration is comparable to that of radial force. Besides that, the synthesized vibrations indicate the contribution of tangential force decreases with the increase of non-zero spatial order, in a way similar to radial force. In order to underpin the findings, more situations such as with different pole-slot combinations are also analyzed at last. [ABSTRACT FROM AUTHOR]

Compared to the AC microgrids, the advantages of DC microgrids are notable. However, the development of DC microgrids is being constrained by the lack of mature protection schemes. For the foundation of designing protection schemes, the existing fault analysis focused on the fault characteristics of voltage source converters and ignored other generators. However, in DC microgrids with high permeability of photovoltaic (PV) powers, the effects of PV powers should be paid considerable attention. In this paper, the cable fault characteristics of the PV powers are analyzed in detail, and both the pole-to-ground fault and the pole-to-pole fault are considered. The fault processes are divided into several stages, and the fault circuits and main equations are described for each stage. All of the analyses are verified by the simulation model based on the PSCAD/EMTDC, and with the help of simulation results, the two main challenges the protection system confronted with are emphasized and the impacts of fault distance are analyzed. Finally, this paper proposes to employ a more reasonable converter structure and a transverse differential protection to overcome the main challenges; the effectiveness of the methods is verified by the simulation. [ABSTRACT FROM AUTHOR]

Grid converters need a synchronization which is often a phase-locked loop (PLL) to get connected to the grid. In the literature, impedance-based models using small-signal technique have been widely utilized to describe the behaviors of PLL-synchronized grid converter. However, most of them target at specific problems and are able to represent the phenomenon under certain scenarios. For the analysis during phase transient, like phase jump due to grid fault, an accurate model is still missing. To address this issue, a general impedance-based model using Maclaurin expansions for its trigonometric function approximation has been proposed in this paper, so that it can well represent the system behavior during phase transient. Moreover, different deepness of the general model can be scaled, leading to different models including phasorial model, current source model, impedance-based model with/without PLL effects. A guideline on how to choose a proper model based on the problems to be studied and grid conditions has been provided in this paper. Simulation and experimental results are given to validate the effectiveness of the model and the theoretical analysis. [ABSTRACT FROM AUTHOR]

Grid connected inverter controllers require the magnitude and phase of the point of common coupling voltage for the generation of unit vectors from a phase locked loop. However, weak grid conditions or grid voltage sensor failures might substantially increase control difficulty in the inverter due to unknown grid impedance which causes instability in the phase locked loop. In this paper, an internal model based grid voltage estimation architecture has been presented. The proposed control architecture relies on the current measurements along with nominal values of filter parameters for the point of common coupling voltage estimation and unit vector generation. Detailed stiffness and robustness analyses are presented to show that the proposed control and estimation architecture is nearly insensitive to parameter variations. In comparison to conventional current control with both voltage and current sensors, the proposed current control scheme provides better transient response during both ideal and non-ideal grid voltage conditions. Experimental results on a reduced scale laboratory prototype validate the efficacy of the proposed architecture. [ABSTRACT FROM AUTHOR]

This paper presents a new Magnetic Equivalent Circuit (MEC) to model the Variable Reluctance Resolver (VR-Resolver) and study the effect of different windings configurations on its performance. Therefore, VR-Resolver with non-overlapping (constant turn) and overlapping (variable turn) windings are modeled to investigate their effect on the accuracy of obtained results. The proposed method gives the possibility to model both healthy and faulty conditions by a unique model to analyze faults effects on the position error. For this purpose, the inter-turn fault is considered on the excitation winding, and both dynamic and static eccentric rotors (DE and SE) are studied. It is shown that the variable turn VR-Resolver has more accuracy and lower sensitivity to eccentricity fault, while the constant turn type is less sensitive to inter-turn fault. However, the latter may be preferred in some applications thanks to its simpler windings and lower manufacturing costs. Finally, the MEC results are proved by Finite Element Method (FEM) and experimental results. Generally, the model flexibility and shorter processing time can be considered as the proposed MEC advantages over FEM. [ABSTRACT FROM AUTHOR]

Interactions of identical inverters in weak grids have received wide attentions. However, in a practical wind farm, parameters of grid-side inverters and lengths of collecting lines are not completely the same. In this case, a multi-inverter system is not symmetric, and thus the interaction mechanism could be more complicated than that of identical inverters. To investigate the interaction mechanism of differently parameterized inverters, this paper proposes a clustering-based modeling method, in which inverters with identical parameters are classified as one group. The clustering-based model allows for efficient stability assessment using three low-order transfer function matrices, instead of a full-order dynamic model. The root locus analysis is applied in the clustering-based model for stability analysis. Results show that the interconnection of distinct groups of inverters deteriorates common current stability, but has no impact on interactive current stability. The simulation and rtlab-based experimental results validate the effectiveness of the proposed model and the interaction mechanism of differently parameterized inverters. [ABSTRACT FROM AUTHOR]

This paper proposes the design process of an ultra-high-speed surface-mounted permanent magnet synchronous motor for a fuel-cell electric vehicle air compressor. Proposed design process enables ultra-high-speed motor design while considering mechanical stresses of the rotor materials according to the temperature. In the rotor design stage, the worst temperature condition of the permanent magnet and retaining sleeve on mechanical stress is investigated and reflected using analytical method. Rotor dimension such as permanent magnet and retaining sleeve thickness is determined considering both electromagnetic performance and mechanical characteristics. Then, from the initially designed model, the eddy current loss according to the shape ratio (SR) and torque density (TD) is analytically derived using proportional equation and finite-element analysis result. Then, SR and TD to reduce the eddy current loss and maximize the efficiency are determined while considering the first bending critical speed. Finally, to verify the proposed design process, the prototype is fabricated and tested. Test results show good agreement with the finite-element analysis results, and it is confirmed that the rotor is operated at the highest rotational speed without mechanical failure. [ABSTRACT FROM AUTHOR]

In order to realize the grid-friendly wind turbine system (WTS), applying of the virtual synchronous generator (VSG) control strategy to WTS has become a trend of research, and it is also required to analyze the grid-connected operation characteristics of the VSG controlled WTS. In this paper, the impedance modeling and impedance-based stability analysis of the VSG controlled type-IV WTS are carried out. Different from existing impedance modeling method that the WTS is modeled by a high dimensional impedance model with complex expressions, a model to describe the shaping effects of dc-link dynamics is proposed, and combined with the space vector diagram to analyze the system impedance characteristics. It is found that the impedance of the VSG controlled type-IV can be capacitive below the fundamental frequency, which is inherited from its GSC impedance and the capacitive characteristics has been weakened by the influence of dc-link dynamics. Instable risk has also been found between the VSG controlled type-IV WTS and the connected weak grid, and the instability can be avoided if the capacitive characteristics of the VSG controlled type-IV WTS are weakened by reshaping its GSC impedance or by enhancing the dc-link dynamics. Experiments are also carried out as verifications. [ABSTRACT FROM AUTHOR]

Temperature estimation is highly significant in the design stages and analysis of permanent magnet (PM) machines. In this paper, for permanent magnet couplers (PMCs), a semi-analytical model to estimate the temperature is developed, which is able to give consideration to efficiency and applied in more complicated structure. Also, the magnetic flux path, as well as the eddy currents, are depicted through a simplified geometric topology. Moreover, the eddy current loss, taken as the heat source loss, is effectively and quickly calculated by employing magnetic equivalent circuit and Kirchhoff's law. Compared with the experimental results, this model has a good agreement with the experimental results where the deviation is within 6.67%. Finally, some constructive suggestions have been given for prediction, optimization and monitoring of PMCs. [ABSTRACT FROM AUTHOR]

Permanent magnet adjustable speed drive (PMASD) has been widely applied to regulate the speeds of large pumps and fans for energy-saving. For improving the torque density and simplifying the actuator of traditional PMASD, a novel squirrel-cage rotor (SCR-) PMASD with a non-rotary mechanical flux adjuster (MFA) is proposed in this paper. An analytical model considering the slot effect and the MFA shifting is established to analyze the magnetic field and the output torque efficiently for the initial design of the proposed drive. The air-gap flux density distributions obtained by the analytical model are verified by two-dimensional (2D-) finite element analysis (FEA). During the speed regulation process, the torque characteristics, power, loss, and efficiency of the drive under different MFA shifting distances are compared with the 2D-FEA and experimental results. The analysis and measured results show that the proposed drive can achieve a wide speed regulation range. [ABSTRACT FROM AUTHOR]

In this paper, a multiphysics model is proposed for a multi-V-shape interior permanent magnet motor with concentrated winding. This paper develops a nonlinear magnetic model that computes the flux density in the motor. The analytical model includes several novel aspects: it takes into account the local saturation near the iron bridges, it proposes a method for modeling the concentrated tooth winding, and it calculates the slot tangential leakage flux and includes it in the flux linkage calculation. The magnetic model is coupled with an electrical model that computes the power factor and the voltage at the motor terminals. A loss model is developed in order to calculate the copper and the iron losses. They are used as inputs to a nodal thermal model that introduces a thermal circuit for concentrated end-winding and computes the temperature of the motor. A mechanical model is developed. It evaluates the mechanical constraints encountered by the structure. The models are verified using finite element computations and numerical calculations performed with dedicated software. Besides, the coupled analytical model is experimentally validated using a prototype motor. Finally, two multiphysics bi-objective optimizations are carried out in order to design the motor for high-torque and low-speed application. [ABSTRACT FROM AUTHOR]

The hard switching operation of the insulated gate bipolar transistor (IGBT)-based multilevel converters (MLCs) in the transformer less direct integration of renewable power plants produces a considerable amount of switching and conduction power loss. This eventually causes higher junction temperature and lower thermal stability. The symmetrically designed MLC using third harmonic sixty-degree bus-clamped pulse width modulation (BCPWM) technique demonstrates reduced switching losses and better harmonic spectra. However, the development of analytical power loss model is a complex and challenging issue due to the discontinuous switching mode of IGBTs for the BCPWM in MLC. In this regard, an analytical model for calculating the average and the rms currents for the hard switching operation of IGBTs and antiparallel diodes (APDs) with BCPWM is proposed. Furthermore, to calculate the device turn-on and turn-off losses, a discrete form of equation is presented to evaluate the transition times of switching more precisely. The numerical power loss values of IGBTs and APDs found from the derived analytical equations for MLC are compared with the simulation and experimental results. The numerical results agree well with the simulated and the experimental outcomes, which validate the proposed analytical loss model. Moreover, an advanced three dimensional thermal impedance model with chip-wise interdependent multilayer thermal coupling effect is also considered in this paper to realize the critical thermal loading condition of the switching devices. [ABSTRACT FROM AUTHOR]

In this paper, a design methodology for surface permanent magnet (PM) synchronous machines, with special application to the case of high-speed machines, will be presented. Following a discussion of the principle and assumptions inherent in the methodology, the analytical model used in the study will be presented. This model will then be implemented to solve the problem of maximizing the power-to-volume ratio from an analytical perspective. It will be shown how this formulation serves to establish design rules, in addition to setting criteria values for the selection of magnetic materials (i.e., silicon steel sheet versus a soft magnetic material). At last, the paper will present a data test bench made of two PM machines designed since the methodology presented herein. [ABSTRACT FROM PUBLISHER]

This paper proposes an analytical model for analyzing the electromagnetic performance of axial flux permanent magnet machines (AFPMMs) with the coexistence of static rotor radial deviation and angular eccentricity. Firstly, a quasi-3-D analytical model for the healthy AFPMMs is established using the scalar potential. Then, the analytical model of AFPMMs with the mixed eccentricity is derived by the coordinate transformation and air gap length function. The end effect under the mixed eccentricity is considered by an end coefficient, which improves the accuracy of back EMF by 1.3%. Based on the analytical model, the air gap flux density distribution, back EMF and cogging torque of AFPMMs with different rotor radial distances and angular eccentricities are calculated and compared with the corresponding results obtained by finite element analysis (FEA). The proposed model has higher analysis speed and less computer performance requirement than FEA with the similar accuracy. According to the results, the back EMF reduces obviously as the rotor radial deviation distance increases, and the back EMF almost unchanged as the angular eccentricity becomes serious. [ABSTRACT FROM AUTHOR]

The papers in this special section examine modeling and simulation methods for the analysis and design of advanced energy conversion systems. Energy conversion lies aEnergyveral fronts including materials, conversion methods, power electronics, and controls have created new opportunities for efficient energy conversion from both the conventional and new sources of energy. Our urgent need to solve many critical problems with regards to the sustainability and security of our energy system as well as the ever-increasing environmental challenges facing humanity have further spurred unprecedented opportunities for creation of innovative solutions to address these challenges. [ABSTRACT FROM AUTHOR]

This paper proposed a hybrid subdomain model (HSM) for calculating the magnetic field distribution of interior permanent-magnet (IPM) machine accounting for slotting effect, rotor saliency, and iron nonlinearity. In the constant permeability region, i.e., slots, slot-opening, and air-gap, three subdomains are introduced to represent their magnetic field. By applying the subdomains interface conditions and nonlinear boundary conditions, the analytical air-gap field solution can be obtained based on the governing Laplace and Poisson equation. For the iron region, the magnetic reluctance network (MRN) is proposed to account for rotor saliency iron and nonlinearity. The magnetic voltage source is introduced to represent the permanent-magnet (PM) while the air-gap flux source is used to replace the air-gap reluctance network, which is the key to guarantee the computational efficiency and high accuracy. The electromagnetic performances of both flat-shaped and V-shaped IPM machines are investigated to show the advantages of different IPM machine topologies analytically. The HSM predictions for both IPM machines are validated by finite-element (FE) analysis and experimental results. [ABSTRACT FROM AUTHOR]

Type-4 wind is claimed to be immune from subsynchronous resonances (SSRs) that have been experienced by Type-3 wind with radial connection to series compensated lines. In this paper, we examine this claim through simplified analytical model building, analysis based on linearized models, and validation against electromagnetic transient (EMT) testbeds with full details. Two analytical models of Type-4 wind farm with radial connection to a series compensated line are built in $dq$ -frames. The main difference of the two models is in grid-side converter (GSC)'s control mode, with one model assuming real power control and the other assuming dc-link voltage control. Relying on the analytical models, an efficient approach is demonstrated to obtain frequency-domain impedance models. Small-signal analysis is carried out using eigenvalue analysis and frequency-domain impedance model-based analysis. Potential stability risk is demonstrated, which is due to interaction of a mode associated to voltage source converter (VSC) in weak grid (termed as “weak grid mode”) and a mode associated to network LC resonance. The weak grid mode is influenced by grid strength and VSC control parameters, including phase-locked-loop (PLL) parameters. The small-signal analysis results are validated against two EMT testbeds with full details in MATLAB/SimPowerSystems and PSCAD/EMTDC, respectively. [ABSTRACT FROM AUTHOR]

This paper proposes a dynamic model with iron saturation to obtain better dynamic performance and more accurately steady-state performance than the dynamic model without iron saturation for the dual-stator brushless doubly-fed induction generator. Based on the proposed dynamic model, the MATLAB/SIMULINK model is established. The key to the simulation model considering iron saturation is that the magnetizing inductance can be updated for each simulation cycle. The magnetizing inductance used in the simulation is experimentally measured to guarantee the simulation accuracy. Dynamic simulations including the current, voltage, flux linkage, active power, and torque are performed, showing that the dynamic model considering iron saturation contributes to the merits of reducing the setting time and the oscillation amplitudes of the torque and the power in starting stage. Experimental assessment is carried out to verify the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

The high-frequency magnetic linked solid-state transformer (SST) has the tremendous potential to solve the issues related to interfacing the grid with renewable energy sources and the non-linear loads as well as to provide the additional control functionalities. Several H-bridges are usually connected in series for the medium voltage grid integration of the SST. The number of the dual active bridge modules and the number of high-frequency magnetic links (HFMLs) usually increase with the increase of the number of series connected H-bridges. This increases the possibility of parameter mismatches and system instability. Therefore, the multiple-active bridge (MAB) dc-dc converter concept has been proposed for next generation SST, where multiple H-bridges share the same HFML. This configuration reduces the number of HFML and increases the cross-coupling power transfer capability. However, the design process of the MAB converter involves a multi-physics research in the field of power electronics, magnetics, switching, control, and energy management. In this paper, the detailed analytical modelling and the control technique of the silicon carbide (SiC)-based MAB converter are investigated. The small and large signal average models of the converter are developed and a voltage balance controller is designed for the better understanding of the controller characteristics. The effect of connecting several H-bridges to a single HFML is investigated in detail. Moreover, to reduce the switching loss, the converter topology adopts the SiC-based switching devices instead of the traditional silicon (Si)-based devices and the nanocrystalline magnetic material is used for the HFML design due to its low specific core loss. A scaled down laboratory prototype of the MAB converter is implemented in the laboratory and can be utilized as a basic building block for the next generation SST. [ABSTRACT FROM AUTHOR]

Flywheel energy storage system (FESS) has been widely used in many fields, benefiting from the characteristics of fast charging, high energy storage density, and clean energy. Uncontrollable discharging system can be used in some special occasions which doesn't have strict requirements on the power quality, such as electric heaters, emergency power supplies, etc. Taking a charging and discharging (C&D) system of 200 kW 15000 rpm high-speed Permanent Magnet Synchronous Motor/Generator (PMSM/G) used for FESS as an example, field-circuit coupling calculation model of PMSM/G during the process of controllable charging and uncontrollable discharging is established. And then the relationships between speed and current-voltage during charging process is calculated. A variable load calculation method based on transient electromagnetic field during the process of uncontrollable discharging is presented, and the eddy current field and transient temperature field of rotor sleeve and permanent magnets during the process of C&D under different loads are also calculated. The output characteristic curves of FESS under condition of constant loads during the process of uncontrollable discharging is drawn. The conjugate analysis method of rotor multi-physical fields is proposed to study the relationships between rotor sleeve stress and eddy current distribution, and the optimized sleeve thickness for high-speed PMSM/G is also presented. Also, a solution is presented to solve the temperature and sleeve fracture problems caused by eddy current under high-speed operation. This contents of the paper can provide references for efficient and reliable design of PMSM/G under extreme conditions used for FESS. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a converter-machine system considering a set of operating points (speed, torque) composing a routine cycle. From the 1-D analytical modelling of the Permanent Magnet Synchronous Machine (PMSM) and the power electronic converter, a design methodology minimizing the power losses-to-volume ratio is established where the flux weakening control structure is considered within the system sizing. Based on a deterministic approach developed for PMSM sizing only, we propose a methodology to include the converter losses in the machine design process. Hence, we demonstrate how the computing time of calculation can be significantly reduced limiting the calculation of the flux weakening mode to a few critical power points. This method is applied to a liquid piston mechanism as part of a Compressed Air Energy Storage (CAES) system. We then validate the converter-machine design method from a 2-D analysis applied to the most significant points. Finally, the PMSM design from both methodologies with and without considering the converter losses are compared. Results highlight how the converter affects the machine sizing and the distribution of power losses to reduce the total losses of the system. [ABSTRACT FROM AUTHOR]

Electro-mechanical-actuator (EMA) is the key component to convert electrical power into mechanical power for flight control in next-generation aircrafts. Multi-domain simulation of EMA can benefit its on-going evolution process. This paper presents the real-time multi-domain modeling and simulation of an EMA as elevator for flight control by utilization of a unified solver. Several key issues concerning the computational efficiency and successful implementation of this solver are provided and its relationship with state-variable model is also elaborated. Analysis shows that this solver could be a competitive candidate for multi-domain simulation because of its high computational efficiency and relatively less modeling effort. Electrical, mechanical, and thermal parts of the EMA are modeled and simulated interactively based on the proposed solver. The multi-domain model is implemented on FPGA board and executes in real time. Simulation results from FPGA board and commercial softwares under several test scenarios coincide with each other in very high degree, which showcases the efficacy of the proposed solver with respect to computational efficiency and ability to accommodate multi-domain models. The proposed model and solver are useful for hardware-in-the-loop design and testing of EMA. [ABSTRACT FROM AUTHOR]

The magnetic potential drop in nonlinear iron can be replaced by equivalent current sheets on linear iron edges. Based on this principle, this paper proposes a nonlinear subdomain and magnet circuit hybrid model (SMCHM) for open-circuit field prediction in surface-mounted permanent-magnet machines. The values of current sheets are calculated from a magnetic circuit and used as boundary conditions in the subdomain model. The finite element (FE) validation is performed, which shows the SMCHM can accurately predict the magnetic field distribution and electromagnetic performance as nonlinear FE method does. The accuracy of SMCHM is significantly higher than the conventional subdomain model neglecting a nonlinearity effect, and the computation speed of SMCHM is dramatically faster than the FE model. [ABSTRACT FROM AUTHOR]

Recently, emerging oscillation issues have been caused by subsynchronous interaction (SSI) between voltage source converters (VSCs) based renewable generators and ac/dc grids. To investigate the dynamics of SSI, several impedance models (IMs) of VSC have been developed in previous studies. They are established in different reference frames and consider the entire or just parts of the control systems. However, it is still an unanswered question whether or not the existing IMs are suitable for SSI analysis and to what extent the IMs with different modeling details affect subsynchronous dynamics. To fill in this gap, this paper, first, reviews the existing IMs of VSC and clarifies their relationship. Then, their frequency characteristics are examined so as to select the proper models for the studies of sub-/supersynchronous and high-frequency dynamics. Next, both zero-pole and IM-based SSI analyses are carried out on a simplified system and a real-world wind-farm system that suffered actual SSI incidents. The results indicate that the outer-loop control has a significant impact on the subsynchronous dynamics, and only those IMs taking full-scale controls and frequency-coupling effects into account can reflect SSI accurately. Finally, both modal analysis and electromagnetic transient simulations have been conducted to verify the theoretical results. [ABSTRACT FROM AUTHOR]

For the comparative investigation on direct-drive permanent magnet (PM) wind power generators, this paper presents the analytical approach based on transfer relations. Considering various generator types, this paper provides analytical solutions for those generators’ characteristic prediction, and the analyzed results are verified. In addition, since our analysis models are designed to be connected to a grid, the power loss characteristics according to grid output power variation are presented considering harmonics in generator current caused by the grid-connected power converter. [ABSTRACT FROM PUBLISHER]

As the wind power generation develops, the doubly fed induction generator (DFIG) based wind power system is more and more likely to operate in the emerging weak network rather than in the conventional stiff network. Due to the comparatively large impedance of the weak network than the stiff grid, the DFIG system may be subject to the resonances due to the impedance interaction between the DFIG system and the weak network. Especially, when connected to a series π sections weak network, the multiple high-frequency resonances (MHFR) may occur and require careful studies. The impedance modeling of the DFIG system and the series π sections weak network is first demonstrated in this paper. Then, due to the multiple magnitude peaks of the series π sections of the weak network, the MHFR will be produced and can be theoretically explained based on the impedance modeling results. For the purpose of mitigating the MHFR, an active damping strategy which introduces a virtual impedance, including a phase leading compensation unit and a virtual positive resistance, is proposed and demonstrated. Simulations are conducted to validate the DFIG system MHFR as well as the proposed active damping strategy. [ABSTRACT FROM AUTHOR]

This paper introduces an improved conformal mapping (ICM) method for the calculation and analysis of unbalanced magnetic force (UMF) in eccentric surface-mounted permanent-magnet (SMPM) motors considering the static, dynamic, and mixed rotor eccentricities. Having the on-load air gap field components obtained through ICM, and by using the Maxwell Stress Tensor method, the ICM method accurately predicts the on-load components of magnetic local traction and UMF due to PMs, the armature reaction, and the mutual interaction between both fields under the rotor eccentricity. The other purpose of this paper is to illustrate the difference between the influences of static, dynamic, and mixed rotor eccentricities on the UMF using the ICM method. The influence of initial eccentricity angle and the magnitude of eccentricity on the UMF are also investigated under the static, dynamic, and mixed rotor eccentricities. The predicted results obtained through ICM are verified by comparing with the corresponding results obtained through finite element method and the frozen permeability method. The ICM method is also validated by the experiment. [ABSTRACT FROM AUTHOR]

In this paper, a complete sensitivity analysis of the optimal parameters for the axial flux permanent magnet synchronous machines working in the field weakening region is implemented. Thanks to the presence of a parameterized accurate analytical model, it is possible to obtain all the required parameters of the machine. The two goals of the ideal design are to maximize the power density: P\text{density} and the ratio of maximal to rated speed: n\max/n_r, which is an inductance related parameter keeping the efficiency at the target speed above 90$\%$. Different slots/poles/phases combinations are studied to reveal the optimum combination for each phase. This paper has studied the effect of the ratio of number of stator slots to number of rotor poles on the P\text{density} and n\max/n_r. It is shown that a low value of this parameter results in a better P\text{density} and n\max/n_r. The effect of the outer diameter, and the inner to outer diameter ratio are studied with respect to the two design goals. In addition, a comparison between the finite and the theoretical infinite speed designs is implemented. A complete 3D finite element validation has proven the robustness of the analytical model. [ABSTRACT FROM AUTHOR]

A reduced-order model of a converter-dominated microgrid system may not resemble its full-order system associated with uncertainties. This paper aims to provide a singular perturbation-based contraction framework for model order reduction in converter-dominated uncertain microgrid systems. For this purpose, the concerned microgrid system is modeled as a generalized multi-timescale system, and certain sufficient conditions are derived such that convergence between the trajectories of the uncertain full-order and the corresponding reduced-order model can be guaranteed. The contraction theory-based strategy also provides explicit parameter-dependent expressions for quantifying discrepancies. The derived results are utilized to analyze the inverter-based microgrid system’s convergence behavior and obtain uncertainty bounds on its parameters. Further, the effects of modeling uncertainties and different loading conditions on the reduced-order model’s validity are also discussed. It is observed that for any uncertainty associated with the microgrid parameters that are within the bounds of checkable conditions, the states of the reduced-order microgrid model converge to that of the uncertain full-order system. Further, it is also shown that the obtained discrepancy expressions are more precise than state of the art. [ABSTRACT FROM AUTHOR]

This paper focuses on the transient modelling of a specific type of permanent magnet linear synchronous machine designed for line-start operation. The machine uses conductive ladders embedded in the mover to realise a permanent-magnet machine capable of line-start operation. Transient modelling of this type of machine under line-start conditions is critical to optimising machine design, and electrical and mechanical performance prediction, which leads us to devise a novel set of matrices of electrical parameters first. These matrices are developed considering both the impact of the conductive ladders and the longitudinal end effect based on electromagnetic field analysis. The model is then suitable for numerical computation in typical simulation environments. This yields a sufficiently accurate transient model that is verified by experimental results. Hence our novel model, that includes the longitudinal end effects and the effects of conductive ladders, is proven effective in predicting the line-start transients and associated electrical and mechanical performance. The novel model assists in the design optimisation stage where a compromise between synchronised performance and line-start operation is required. The novel machine type can then be investigated as a competitive candidate topology in various applications including electromagnetic launch. [ABSTRACT FROM AUTHOR]

Droop control has been well adopted for multi-source multi-load DC microgrids (MGs) due to its inherent modularity and reliability by only using local measurements, especially with the most commonly-used voltage-current droop (V-I) mode. While another implementation named current-voltage droop (I-V) mode also can be adopted. With the same value of droop gain in these two modes, a DC MG will have the same steady-state feature, but its dynamic performance of DC voltage control may be different. Our primary motivation is to investigate this phenomenon from the perspective of equivalent RLC circuits. This paper proposes a generic reduced-order modeling method suitable for exploring the dynamic stability of DC voltage control with these two modes. By ignoring fast inner current control dynamic, each droop based DC voltage control unit can be modeled as a RLC parallel circuit in these two modes, which is convenient for modular modeling and extension. With these models, the essential cause of system dynamic stability difference and the physical meaning of key control parameters in these two modes can be revealed in an intuitive way. In addition, if the inner current control with slow dynamic cannot be ignored in some specific scenarios, a modified RLC model can be still obtained to analyze its influence. Moreover, based on reduced-order models, analytical solutions of dynamic performance indexes have been obtained, through which the impact of control parameters on dynamic performance of DC bus voltage can be characterized. Finally, the effectiveness of the proposed reduced-order modeling method has been verified by detailed simulation and experiment results. [ABSTRACT FROM AUTHOR]

This paper presents a modified Mayergoyz-based vector hysteresis model to describe the anisotropic material behavior of nonoriented (NO) steels over a wide range of rotational excitations. The proposed model adopts a new representation of a vector Everett function, which is actually an elliptical interpolation motivated by the real anisotropic behavior of NO steel, to deal with the uniaxial anisotropy characteristic, which is especially pronounced at low induction levels. The biaxial anisotropy occurring at high densities is described by a nonlinear coefficient, which is actually a function of the magnitude of magnetic flux density. A systematic identification algorithm is given in detail. The validity of this model is verified through comparison with experimental data under both alternating and rotational excitations. The 2-D finite element analysis (FEA) of incorporating this model into TEAM problem 32 simulation is also illustrated. [ABSTRACT FROM AUTHOR]

This paper proposes a monolayer Halbach array based permanent magnet spherical motor (PMSpM) using cubic permanent magnets (PM). The research aims to provide a fast computing model to calculate the magnetic field for this PMSpM, which helps for future PMSpM optimization and control study. Three thickness equivalence principles are provided and compared for cubic PMs. The magnetic scalar potential is introduced, and the spherical harmonics expansion is implemented for rotor magnetic field analysis. Engineering revision is used to reduce the Legendre function deviation in polar angle direction. Torques and forces are deduced using the Lorentz force law, and relatively simple models of this PMSpM for both magnetic fields and torques are acquired. In addition, a prototype motor has been developed, and the analytic results of air-gap flux density and torque are compared with their finite element simulation and experimental results, which are proved consistent. It is concluded that the fundamental component of the spherical harmonics can be used to present the magnetic field model, which uses fewer integrals than the Biot-Savart law based solution, and the modeling results of the magnetic field flux density, forces and torques are in line with the expectations. The analytic models are proved correct. [ABSTRACT FROM AUTHOR]

This is Part II of a two-part paper on the extension of a previously developed parameterized linear 2D magnetic equivalent circuit (MEC) for radial flux magnetic gears with surface permanent magnets to a 3D model. Part I explains the implementation of the 3D MEC. This section, Part II, evaluates the 3D MEC model's accuracy relative to 2D and 3D nonlinear finite element analysis (FEA) models. First, analysis of three base designs illustrates the impacts of the axial discretization parameters and stack length. This leads to the development of guidelines for selecting the axial discretization parameters. Additionally, the MEC is shown to accurately match 3D FEA in predicting the axial variation of flux densities. Finally, 3D MEC, 2D FEA, and 3D FEA models are deployed for a 144,000 case parametric study. The 2D FEA model significantly overpredicts the torques of designs with short stack lengths. However, the 3D MEC provides a much better agreement with 3D FEA, with less than 1% average absolute discrepancy. Additionally, the 3D MEC model is much faster than the 3D FEA model, with average 3D MEC model evaluation speeds ranging from about 100 times to 300 times faster than the 3D FEA for the base designs. [ABSTRACT FROM AUTHOR]

Doubly fed induction machine (DFIM) has been widely used in variable speed constant frequency electricity generation systems due to its small power converter capacity. Then another machine—brushless doubly fed machine (BDFM)—is widely concerned because of its similar characteristics but better reliability than DFIM. In fact, according to common features of DFIM and BDFM, these two machines can be collectively called doubly fed machine (DFM). Theoretical study on characteristics of these two machines has not formed concise, practical, and all-sided theoretical analysis system. Proceeding from basic theory of DFIM, this paper derived the physical model and established a novel synchronous–asynchronous series equivalent circuit model of DFIM at first. Based on the analysis method of DFIM, a novel equivalent circuit model of BDFM was established. These two models illustrated that the characteristic of DFM is the superposition of synchronous characteristic and asynchronous characteristic. Based on these circuit models, the characteristic under different operation mode was analyzed and corresponding analytical curves were drawn, which revealed the operation mechanism of DFM clearly. To verify the theoretical analysis of two novel equivalent circuit models, simulation models of DFIM and BDFM were established in Simulink and finite element analysis (FEA) software. Corresponding characteristic curves were drawn to compare with that obtained by circuit models. At last, combined with these characteristic curves, practical significance that circuit models and theoretical analysis bring to machine design and control theory was analyzed. [ABSTRACT FROM AUTHOR]