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Subdomain modeling is among the most reliable and accurate analytical tools for designing and analyzing permanent magnet machines. However, the application of the two-dimensional (2-D) subdomain model is mainly limited to permanent magnet machines with homogeneous rotor structures (with uniform permeability), such as surface-mounted or surface-inset permanent magnet machines. Solving Maxwell's equations and applying 2-D boundary conditions on structures with permanent magnets embedded in the rotor core, such as interior permanent magnet machines, are quite complex. Given the importance of enabling the tangential field component to capture accurate results, a 2-D hybrid analytical solution is proposed and applied to a multilayer interior permanent magnet machine. For this purpose, the radial components of the permanent magnet flux and the armature flux are first calculated using the magnetic circuit and the magnetic islands methods, respectively. Next, their respective tangential flux components are computed by solving Poisson's equation and applying a 1-D boundary condition along the tangential direction. Meanwhile, the stator slotting effect is included via the theory of virtual surface current. Finally, the steady-state performance metrics of the motor are calculated and verified via finite-element and experimental measurement. [ABSTRACT FROM AUTHOR]

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]

An analytical model is proposed for the prediction of electromagnetic quantities of slotted flux-reversal permanent magnet (FRPM) machines. Equivalent current theory is used to model the effects of permanent magnets (PMs), stator slots and rotor grooves. First, the stator slots and rotor grooves are nullified and the Poisson equation is solved in a slotless stator and cylindrical rotor machine. The effects of the stator slots and rotor grooves are then considered by injecting equivalent magnetization currents (EMCs) respectively on the stator slots wall and on the rotor groove edges. The PMs are also replaced by EMCs. Finally, the results of the proposed analytical model are verified by means of the finite element analysis. [ABSTRACT FROM AUTHOR]

The improvement of synchronous generators (SGs) stability is one of the most important issues in power systems. To this aim, doubly fed induction generator (DFIG) can be helpful. The main purpose of this paper is to improve both transient and dynamic performance of SG by using local DFIG-based wind turbines. Firstly, a transient controller (TC) is designed in controlling block of DFIG which changes its operating mode from generator to motor regime. Secondly, two damping controllers which are named electromagnetic torque band damping controller (ETBDC) and reactive power band damping controller (RPBDC) are suggested to improve dynamic stability of SG. Each damping controller includes three feedbacks namely, SG speed changes, SG electromagnetic torque and DFIG electromagnetic torque. Moreover, genetic algorithm (GA) is used to adjust these controlling parameters. The performance of TC is examined by comparison of system transient indexes such as critical clearing time (CCT), SG accelerating energy and DFIG inertia energy with and without using the proposed TC in a two-area test network. Similarly, system dynamic performance indexes such as overshoot, settling time, eigenvalue and damping torque of SG are compared with and without using two dynamic controllers. The obtained results show the effectiveness of proposed controllers. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive analytical analysis of line start permanent magnet (LSPM) synchronous motors in both steady‐state and transient domains. The PM flux, the back‐EMF and the winding inductances are first calculated in the steady‐state based on the hybrid solution of magnetic circuit and the magnetic islands. Next, the motor voltage relations are mapped into an arbitrary d‐q reference frame to dynamically assess the transient speed response as well as the individual motor torque components. Based on the presented analytical modelling, the parameters of the motor are optimised via genetic algorithm to maximise the back‐EMF voltage and the overall steady‐state performance. Given the parabolic relation between the back‐EMF and the braking torque, the starting capability of the motor is defined as the optimisation constraint. Finally, the analytical results are verified by using a finite element analysis software package. [ABSTRACT FROM AUTHOR]

In this paper, by solving the Maxwell's equations, an analytical model is developed for the prediction of the air gap flux density in the eccentric permanent magnet (PM)-inset machines at no-load and on-load conditions. Since in this model neither Schwartz–Christoffel transformation nor perturbation analysis is used, it is fast and accurate. In the modeling process, the stator of the eccentric machine is replaced with an equivalent surface current (ESC), which is injected at the stator bore. Distribution of the ESC is unknown and must be selected, such that the resultant tangential field satisfies the boundary condition at the stator bore contour. To apply this condition, the flux density of the PMs, armature current, and the ESC are obtained by applying the subdomain analysis and using a conformal transformation. The armature current and ESC are considered as a surface current sheet at the stator bore. The back electromotive force and inductances of the eccentric machine are obtained in the proposed model. In addition, using the Maxwell stress tensor, the unbalanced magnetic force, and the electromagnetic torque are computed. Finally, the model is verified by means of finite element analysis. [ABSTRACT FROM AUTHOR]

In this paper, existing feasible slot/pole combinations of the fractional slot permanent magnet (FSPM) machines are extended. In comparison with the existing slot/pole combinations, the proposed ones could result in a higher winding factor, lower torque ripple, and lower cogging torque. This diversity in the number of the slot/pole combinations brings the designers more alternative solutions. To reach such slot/pole combinations three-slot pitch coils are applied. The existing slot/pole combinations are limited to the designs with an integer number of slots per phase in one periodicity of the FSPM machine. In the presented work, FSPM machines with fractional numbers of the slots per phase in one periodicity of the machines are introduced. However, the phase back electromotive force signals are balanced. Moreover, to achieve a slot/pole combination with small unbalance magnetic force (UMF) and low THD value of the armature MMF, the multilayer winding technique is applied. In addition, a simple technique is presented to find an arrangement of the multilayer winding with very small UMF. Extensive finite element simulations are used to compare the FSPM machines with the proposed slot/pole combinations with the traditional FSPM machines. [ABSTRACT FROM AUTHOR]

In this work, an analytical technique is developed for modeling of the air gap flux density in the slotless eccentric surface-mounted permanent magnet (PM) machines. In the developed model, a 2-D solution for the Poisson equation is provided. In the modeling process, the eccentric stator is replaced with an equivalent current sheet at the stator bore. This current sheet is selected such that the overall tangential flux density caused by the PMs and the current sheet at the removed stator bore is zero. To find the contribution of current sheet on the air gap flux density, a conformal transformation is applied. The obtained exact values of the instantaneous air gap flux density components are used to compute the variables of the eccentric machine such as the back-EMF, the electromagnetic torque, and the unbalanced magnetic force. The provided model is valid for static, dynamic, and even mixed rotor eccentricity conditions. Finally, finite-element analysis is applied to verify the proposed model. [ABSTRACT FROM PUBLISHER]

An analytical model is proposed for the prediction of the no‐load air gap magnetic flux density and the armature reaction in the slotless surface‐inset PM machines. For this purpose, the exact 2D solution of the Poisson equation is derived. In the modelling process, the rotor salient poles are taken away and some surface magnetisation currents are considered at the borders of the removed salient poles. The contribution of this work is finding the value of the surface magnetisation currents such that the rotor saliency is accurately considered. The field solution in the provided surface‐mounted PM machine is simply obtained by the separation of variables method. The machine back‐EMF and its inductances is obtained by the predicted flux density due to the PMs and the stator currents, respectively. In addition, using the resultant air gap flux density in the Maxwell stress tensor, the developed electromagnetic torque is computed. Finally, the ability of the proposed model is evaluated by finite element analysis as well as experimental tests. [ABSTRACT FROM AUTHOR]

In this paper, a complex vector model is provided for an integrated three‐phase shell‐type rotating transformer. The equivalent magnetic circuit is used to obtain the transformer parameters. Furthermore, using vector representation of the dq transformation, the voltage equations of the rotating transformer in double‐reference synchronous frame are obtained. Thanks to the developed model, the transformer design parameters are selected such that the voltage equations in double‐reference frames are decoupled. For the first time, the machine complex vector representation is exploited to design a symmetrical rotating three‐phase transformer. For this purpose, two separated equivalent circuits in double‐reference frames or two decoupled sequences networks are developed. The decoupled circuits simplify the analysis of the rotating transformer in the unbalanced conditions as well as balanced circuits. Being symmetrical is an important issue for the rotating transformer connected to the rotor winding of a doubly‐fed induction generator. Moreover, the steady‐state performance and sequence analysis of the rotating transformer are discussed. Finally, the validity of the obtained model and accuracy of the presented analysis are verified by finite element analysis and experimental tests. [ABSTRACT FROM AUTHOR]

A fully laminated shell-type three-phase rotating transformer, appropriate for the most brushless applications, is proposed. The stationary and rotary parts of the proposed machine include both radially and axially laminated magnetic cores. Thanks to the special construction, the mechanical assembling of the proposed device in an integrated three-phase unit is very simple. In addition, a high permeance, low eddy current magnetic path is provided for the magnetic flux in the machine volume. However, to limit the core eddy currents in a normal range, a special geometry is selected for the radially laminated parts. Using the transformer magnetic equivalent circuit, the self and mutual inductances are obtained analytically. Based on the developed analytical model, geometrical dimensions are selected such that, a balanced three-phase machine is provided. Finally, finite-element analysis and experimental results are used to verify the obtained analytical model. [ABSTRACT FROM AUTHOR]

Abstract—In this work, an electromagnetic design procedure for a line-start synchronous reluctance motor is presented, and the main considerations are highlighted. To improve the steady-state performance of this motor, the geometry of the flux barriers as well as their number are optimized using an automatic optimization algorithm. For this purpose, two types of flux barriers, arc shaped and trapezoidal shaped, are formulated and studied by finite-element analysis. Analyzing the average cage torque during synchronization, effectiveness of the dq-axis rotor resistances on successful synchronization is discussed. To validate the results of this analysis, dynamic simulations are used, and the impact of the dq-axis rotor resistances on synchronization is investigated. In addition, the effect of the rotor bar position on the value of the dq-axis rotor resistances is discussed and analyzed by finite-element analysis. Finally, the impact of small pieces of permanent magnet in the flux barriers is studied. It is shown that against the permanent magnet-assisted motor, permanent magnets always enhance the motor performance; the steady-state characteristic of the line-start permanent magnet assisted motor could be deteriorated by permanent magnet. [ABSTRACT FROM PUBLISHER]

This paper compares two methods to compute the parameters of a line-start synchronous reluctance (LSSR) machine, by means of finite element analysis. In both methods, both the impact of the skin effect on the rotor parameters and the impact of saturation on magnetizing inductances are taken into account. The first method is based on an equivalent single-phase model of the machine. A pulsating flux is imposed along the d- and q-axes separately, so as to compute the machine parameters along both d- and q-axes. Magnetizing inductances are achieved as a function of the flux, and the rotor resistances and leakage inductances are obtained as a function of rotor frequency. The second method is based on the d-q axis model of the LSSR machine. A rotating magnetic field is imposed, and the d-q axis parameters are estimated simultaneously from the field solution. In addition, such a method allows the cross-saturation to be considered as well. [ABSTRACT FROM PUBLISHER]