## What is/are Flux Linkages?

Flux Linkages - Finally, a scheme of setting auxiliary teeth in the primary component is adopted to suppress the unbalance of the three phase flux linkages.^{[1]}At first, the cross coupling effect between the axes in dq reference is analyzed, by measuring the flux linkages for different current combinations.

^{[2]}The second measure is to further enhance the open circuit flux linkages, back electromotive force (EMF) and thus the torque density by adopting the proposed ASP structure.

^{[3]}This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.

^{[4]}Moreover, to obtain an efficiency map, a data map of the d-q flux linkages based on the d-q currents should be established.

^{[5]}The theoretical expressions of flux linkages are derived, which are closely related to the eccentric distance and angle.

^{[6]}Then, the variables are collected and used to estimate the flux linkages and consequently the machine torque.

^{[7]}Based on its special rotor structure, the magnetic flux linkages of the worm stator windings are deduced with its structural and kinematic parameters.

^{[8]}, they share the same current but their flux linkages and forces differ in tilted positions.

^{[9]}The linearization is exemplified for flux linkages and machine torque, respectively.

^{[10]}In this article, the general mechanism of the even order harmonics elimination in various stator-PM machines is investigated, and it is found that either the opposite PM polarities or the opposite coil polarities of the two adjacent phase coils can guarantee the elimination effect, and hence, the symmetrical phase flux linkages.

^{[11]}The stator currents in the rotor frame of reference are given as inputs to a reduced FE model, which computes the nodal values of the magnetic vector potential and thereafter the flux linkages.

^{[12]}The focus of this work is on the experimental measurement and the proper finite-element prediction of stator and rotor flux linkages for induction machines.

^{[13]}For illustration, and to support the analysis with quantitative results, it exemplarily investigates the effects of this saturation interaction on the flux linkages and the torque during the postfault operation of a rotor flux-oriented drive.

^{[14]}After electromagnetic analysis utilizing Finite Element Analysis (FEA) software package, expressions combining Lumped Parametric Magnetic Equivalent Circuits, vector potential governed by Laplace Equations, and Maxwell Stress Tensor method are used to develop 2-D analytical model for open circuit flux linkages, no-load and on-load Magnetic Flux Density, detent force and thrust force.

^{[15]}The electromagnetic properties like flux linkages, back EMF, detent force and thrust force of the proposed machine is investigated.

^{[16]}This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.

^{[17]}The ripple minimization is achieved primarily through rotor segment shaping, which has a strong influence on stator flux densities, flux linkages, and torque harmonics.

^{[18]}The BLDC motor’s DTC has simultaneous control over torque and flux linkages.

^{[19]}The equations are resolved with respect to the derivatives of flux linkages.

^{[20]}It is based on: (i) a generic transformer-like machine model in an arbitrarily rotating (d,q)-reference frame, considering nonlinear flux linkages and iron losses in the stator laminations; (ii) machine identification by evaluating steady-state measurements over a grid of (d,q) stator currents, producing frequency-dependent machine maps for e.

^{[21]}Various options for estimation these quantities are considered using the calculation of flux linkages in the stator reference frame based on measured phase voltages and stator currents.

^{[22]}In this approach, a non–conventional extended dual dq–frame model that accounts for higher order space harmonics in inductances and flux linkages has been developed and used for accurate computation of average torque and torque ripple of six–phase PMSM.

^{[23]}To illustrate the proposed concept in this torque controlled drive, torque and mutual flux linkages are applied as external inputs and speed of the machine is kept fixed.

^{[24]}Finally, 12S-6P stator rotor configurations has been selected as the best contenders which deliver the highest flux linkages, peak torque and maximum power of 4.

^{[25]}The idea of the steady-state mode calculation consists in determining vectors of currents and flux linkages of the motor circuits, using which makes it possible to evaluate the electromagnetic torque, active and reactive powers, etc.

^{[26]}The selected methods are compared with regard to spatial distributions of radial air-gap magnetic flux density and of exemplary flux linkages for a theoretical movable coil.

^{[27]}Those parameters are also required for the estimation of the electromagnetic torque together with the magnetic flux linkages in the direct torque control (DTC) as well as for observers of the angular position and speed of the rotor in sensorless applications of the field-oriented control (FOC).

^{[28]}On the one hand, the SWFFS generator topology with unequal stator pole pitch is proposed to enhance the power density by changing the flux linkages’ phases of the equivalent armature coils based on the virtual coil flux linkages.

^{[29]}Based on the optimal reverse saliency, the machine performances are analyzed and compared with the existing machine in detail, including flux linkages, inductances, torque performances, and operation performances.

^{[30]}Neural network-based algorithms are good candidates for modeling the current-to-flux linkages curves of synchronous reluctance (SynR) motors, but so far their use was limited by the inherent complexity and the computational burden.

^{[31]}A limited, by no means complete, analysis of the two dominant types of AC machine (the AC induction and the synchronous) dynamics is included with a view to guide the reader to appreciate the necessity for transformations of voltages and currents and flux linkages of a three-phase machine to one of the rotating axes, in order to appreciate how current controls are used for controlling the torque and flux linkages independently of each other.

^{[32]}Measurements performed on the prototype endorse the assumptions regarding the linearization of the flux linkages as well as the negligible impact of the magnetic field harmonic content.

^{[33]}In addition, flux linkages and instantaneous powers characteristics were analyzed by connecting the two main coils in parallel and in series.

^{[34]}The relations among the Fourier coefficients of flux linkages and electromagnetic torque/thrust are presented for the models written in dq reference frame.

^{[35]}Analysis on fundamental magnetic flux characteristics, armature and FEC magnetic flux linkages, cogging torque, back-Emf, various torque capabilities, refinement of unbalance magnetic flux, and torque-power versus speed characteristics are conducted using 2D FEA through JMAG Designer version 15.

^{[36]}The flux linkages at five special mover positions are calculated by magnet tube method and Gauss–Seidel iteration method which takes the saturation into consideration.

^{[37]}Two MTPC strategies are investigated: (i) MTPC using linearised flux linkages; and (ii) MTPC using measured, nonlinear flux linkages.

^{[38]}This paper first proposes a comprehensive torque model considering the harmonics in PM flux linkages, inductances and stator currents to investigate the induced torque components, which are neglected in existing approaches.

^{[39]}Then, the extended model is transformed into dq–axis using MRF rotating at speeds of dominant harmonics in PM flux linkages and inductances, the fundamental being the electrical rotor frequency.

^{[40]}The paper deals with the flux linkages estimation of a synchronous motor during speed or load transients.

^{[41]}(i) the flux linkages stemming from permanent-magnet (PM) poles, or the so-called PM flux linkages, and (ii) the magnetising inductances related to the stator–rotor magnetic couple.

^{[42]}Compared with conventional flux linkage calculation methods, the proposed observer can provide desirable flux linkages, which increases the robustness of the sensorless DTFC system.

^{[43]}Assuming a linear magnetic behaviour and a constant air-gap length, analytical approximations of the flux linkages are derived using the mathematical properties of Fourier series.

^{[44]}Three sets of interpolation tables were computed using two-dimensional finite element analysis, calculated flux linkages and electromagnetic torque were used for development of Simulink model.

^{[45]}By applying Park transformation, the fundamental harmonic components of stator phase currents, flux linkages, and voltages during steady-state operation, become constants under rotor synchronous reference frame, while the currents in the rotor damper cage are still alternating.

^{[46]}The overall system performance and effectiveness of the proposed method are evaluated via comprehensive simulations results where lower ripples associated with both thrust and flux linkages waveforms and better speed tracking.

^{[47]}The relation between flux linkages, phase currents and rotor position is studied in the rotor reference frame considering three different phenomena, namely saturation, cross-saturation, and magnetic saliency.

^{[48]}The FEA results show that inner stator structure machine has greater output power and voltage because of low flux linkages but in the inner rotor structure has less performance due to the high flux linkages.

^{[49]}Consequently, the zero sequence flux linkages are reduced by the resultant zero sequence current.

^{[50]}

## Magnetic Flux Linkages

Based on its special rotor structure, the magnetic flux linkages of the worm stator windings are deduced with its structural and kinematic parameters.^{[1]}Those parameters are also required for the estimation of the electromagnetic torque together with the magnetic flux linkages in the direct torque control (DTC) as well as for observers of the angular position and speed of the rotor in sensorless applications of the field-oriented control (FOC).

^{[2]}Analysis on fundamental magnetic flux characteristics, armature and FEC magnetic flux linkages, cogging torque, back-Emf, various torque capabilities, refinement of unbalance magnetic flux, and torque-power versus speed characteristics are conducted using 2D FEA through JMAG Designer version 15.

^{[3]}Moreover, five situations of PMSM models with different magnetic flux linkages are simulated by using the finite element analysis method.

^{[4]}The proposed control method does not need to know the motor two-axis inductances, the rotor permanent magnetic flux linkages, and the rotor position.

^{[5]}

## Pm Flux Linkages

This paper first proposes a comprehensive torque model considering the harmonics in PM flux linkages, inductances and stator currents to investigate the induced torque components, which are neglected in existing approaches.^{[1]}Then, the extended model is transformed into dq–axis using MRF rotating at speeds of dominant harmonics in PM flux linkages and inductances, the fundamental being the electrical rotor frequency.

^{[2]}

## Rotor Flux Linkages

The focus of this work is on the experimental measurement and the proper finite-element prediction of stator and rotor flux linkages for induction machines.^{[1]}There are two such control methods: using the proportional law of controlling the motor power supply frequency and voltage and using the law that maintains constant stator and rotor flux linkages and the main flux linkage in the air gap.

^{[2]}

## Phase Flux Linkages

Finally, a scheme of setting auxiliary teeth in the primary component is adopted to suppress the unbalance of the three phase flux linkages.^{[1]}In this article, the general mechanism of the even order harmonics elimination in various stator-PM machines is investigated, and it is found that either the opposite PM polarities or the opposite coil polarities of the two adjacent phase coils can guarantee the elimination effect, and hence, the symmetrical phase flux linkages.

^{[2]}

## Circuit Flux Linkages

The second measure is to further enhance the open circuit flux linkages, back electromotive force (EMF) and thus the torque density by adopting the proposed ASP structure.^{[1]}After electromagnetic analysis utilizing Finite Element Analysis (FEA) software package, expressions combining Lumped Parametric Magnetic Equivalent Circuits, vector potential governed by Laplace Equations, and Maxwell Stress Tensor method are used to develop 2-D analytical model for open circuit flux linkages, no-load and on-load Magnetic Flux Density, detent force and thrust force.

^{[2]}

## Stator Flux Linkages

This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.^{[1]}This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.

^{[2]}

## flux linkages waveform

The overall system performance and effectiveness of the proposed method are evaluated via comprehensive simulations results where lower ripples associated with both thrust and flux linkages waveforms and better speed tracking.^{[1]}Comprehensive simulations and experimental results have demonstrated that the proposed control scheme has a better performance in reducing the ripples associated with both thrust and flux linkages waveforms.

^{[2]}

## flux linkages neglected

This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.^{[1]}This transient phenomenon of a power system utilizing synchronous generator and modelling by fully three-phase model with changes in stator flux linkages neglected is analyzed by employed single machine infinite bus taken to the power system.

^{[2]}