Characteristic Analysis of Surface Permanent-Magnet Vernier Motor According to Pole Ratio and Winding Pole Number

Shi, Hongda; Niguchi, Noboru; Hirata, Katsuhiro

doi:10.1109/tmag.2017.2702278

Cited by 31 publications

(20 citation statements)

References 13 publications

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“…9. Ampere's circuital law is applied to these three loops to Applying Ampere's circuital law, the fluxes in the three loops can be calculated as (see Appendix 1 for more detailed derivations) ( where is the electrical loading, is the phase number, is the stator slot height, is the stator slot opening and is the effective airgap length, is the Carter's coefficient given by [20], [30] A- It is worth noting here that the magnitudes of fluxes flowing in Loop1 and Loop2 are the same [see (12) and (13)]. For validating the armature flux calculation, total flux linking with the phase C is estimated directly by FEA by doubling the flux extracted from contour [marked in yellow dotted line in Fig.…”

Section: Armature Flux Calculationmentioning

confidence: 99%

“…The power factor equation can then be given as (19) where is the factor which represents the ratio of armature flux linkage to PM flux linkage. Substituting the values of PM and armature flux linkages from (10), (16) and 18, can be expressed as (20) where , representing the permeance term.…”

Section: Power Factor For Different Slot/pole Numbersmentioning

confidence: 99%

“…The airgap permeance created by the stator open slot structure is given by

normalΛ ()(, θ_{s}) = Λ_{0} + \sum_{J = 1, 2, 3 \dots}^{\infty} Λ_{j} \cos ()(, j Z θ_{s})

where Z is the number of stator slots,

Λ_{0}

is the constant airgap permeance value and

Λ_{j}

is the amplitude of jth order harmonics of the permeance function. For simplicity, considering only the interaction between the fundamental magnet MMF

()(, F_{1})

and the constant

()(, Λ_{0})

as well as the first order

()(, Λ_{1})

components of the airgap permeance, the airgap flux density

(][, B_{g} ()(, θ_{s}, t))

is given by [7, 18, 19]

\begin{matrix} right leftthickmathspace.5em \\ B_{normalg} (θ_{normals}, t) & = B_{P_{normalr}} \cos (P_{normalr} θ_{normals} - ω_{normale} t) \\ + B_{z - P_{normalr}} \cos [((Z - P_{normalr}) θ_{normals} + ω_{normale} t)] \\ + B_{z + P_{normalr}} \cos [((Z + P_{normalr}) θ_{normals} - ω_{normale} t)] \end{matrix}

With…”

Section: Basic Working Principle Of Vernier Machinementioning

confidence: 99%

“…Ampere's circuital law is applied to these three loops to estimate the magnitudes of the armature fluxes. The following assumptions have been made for this calculation: The stator and rotor core are infinitely permeable. Airgap flux density is constant along the radial direction. Applying Ampere's circuital law, the fluxes in the three loops can be calculated as (see Appendix 1 for more detailed derivations)

ϕ_{1} = \frac{\sqrt{2} μ_{0}}{m} \frac{G_{normalr}^{2} {\bar{τ}}_{r} τ_{r} Q L_{normalstk}}{K_{normalc} (G_{normalr} + 1)}

ϕ_{2} = \frac{\sqrt{2} μ_{0}}{m} \frac{G_{normalr}^{2} {\bar{τ}}_{r} τ_{r} Q L_{normalstk}}{K_{normalc} (G_{normalr} + 1)} = ϕ_{1}

ϕ_{3} = \frac{μ_{0}}{\sqrt{2} m} G_{normalr} τ_{r} Q L_{normalstk} (\frac{h_{t}}{b_{o}})

where Q is the electrical loading, m is the phase number,

h_{t}

is the stator slot height,

b_{o}

is the stator slot opening and

g^{normal′ normal′} = K_{c} ()(, g + ()(, h_{m} / μ_{rec})) = K_{c} g^{'}

is the effective airgap length,

K_{c}

is the Carter's coefficient given by [19, 30…”

Section: Armature Flux Linkage Calculationmentioning

confidence: 99%

“…where Z is the number of stator slots, Λ 0 is the constant airgap permeance value and Λ j is the amplitude of jth order harmonics of the permeance function. For simplicity, considering only the interaction between the fundamental magnet MMF F 1 and the constant Λ 0 as well as the first order Λ 1 components of the airgap permeance, the airgap flux density B g θ s , t is given by [7,18,19]…”

Section: Basic Working Principle Of Vernier Machinementioning

confidence: 99%

See 4 more Smart Citations

Investigation of scaling effect on power factor of permanent magnet Vernier machines for wind power application

Padinharu

Zhu

et al. 2020

IET Electric Power Applications

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This paper investigates the scaling effect on power factor of surface mounted permanent magnet Vernier (SPM-V) machines with power ratings ranging from 3kW, 500kW, 3MW to 10MW. For each power rating, different slot/pole number combinations have been considered to study the influence of key parameters including inter-pole magnet leakage and stator slot leakage on power factor. A detailed analytical modelling, incorporating these key parameters, is presented and validated with 2D Finite Element Analysis (FEA) for different power ratings and slot/pole number combinations. The study has revealed that with scaling (increasing power level), significant increase in electrical loading combined with the increased leakage fluxes, i.e. (a) magnet leakage flux due to large coil pitch to rotor pole pitch ratio, (b) magnet inter-pole leakage flux and (c) stator slot leakage flux, reduces the ratio of armature flux linkage to PM flux linkage and thereby has a detrimental effect on the power factor. Therefore, unlike conventional SPM machines, the power factor of SPM-V machines is found to be significantly reduced at high power ratings.

show abstract

Section: Armature Flux Calculationmentioning

confidence: 99%

Section: Power Factor For Different Slot/pole Numbersmentioning

confidence: 99%

“…The airgap permeance created by the stator open slot structure is given by

normalΛ ()(, θ_{s}) = Λ_{0} + \sum_{J = 1, 2, 3 \dots}^{\infty} Λ_{j} \cos ()(, j Z θ_{s})

where Z is the number of stator slots,

Λ_{0}

is the constant airgap permeance value and

Λ_{j}

is the amplitude of jth order harmonics of the permeance function. For simplicity, considering only the interaction between the fundamental magnet MMF

()(, F_{1})

and the constant

()(, Λ_{0})

as well as the first order

()(, Λ_{1})

components of the airgap permeance, the airgap flux density

(][, B_{g} ()(, θ_{s}, t))

is given by [7, 18, 19]

\begin{matrix} right leftthickmathspace.5em \\ B_{normalg} (θ_{normals}, t) & = B_{P_{normalr}} \cos (P_{normalr} θ_{normals} - ω_{normale} t) \\ + B_{z - P_{normalr}} \cos [((Z - P_{normalr}) θ_{normals} + ω_{normale} t)] \\ + B_{z + P_{normalr}} \cos [((Z + P_{normalr}) θ_{normals} - ω_{normale} t)] \end{matrix}

With…”

Section: Basic Working Principle Of Vernier Machinementioning

confidence: 99%

ϕ_{1} = \frac{\sqrt{2} μ_{0}}{m} \frac{G_{normalr}^{2} {\bar{τ}}_{r} τ_{r} Q L_{normalstk}}{K_{normalc} (G_{normalr} + 1)}

ϕ_{2} = \frac{\sqrt{2} μ_{0}}{m} \frac{G_{normalr}^{2} {\bar{τ}}_{r} τ_{r} Q L_{normalstk}}{K_{normalc} (G_{normalr} + 1)} = ϕ_{1}

ϕ_{3} = \frac{μ_{0}}{\sqrt{2} m} G_{normalr} τ_{r} Q L_{normalstk} (\frac{h_{t}}{b_{o}})

where Q is the electrical loading, m is the phase number,

h_{t}

is the stator slot height,

b_{o}

is the stator slot opening and

g^{normal′ normal′} = K_{c} ()(, g + ()(, h_{m} / μ_{rec})) = K_{c} g^{'}

is the effective airgap length,

K_{c}

is the Carter's coefficient given by [19, 30…”

Section: Armature Flux Linkage Calculationmentioning

confidence: 99%

Section: Basic Working Principle Of Vernier Machinementioning

confidence: 99%

See 3 more Smart Citations

Investigation of scaling effect on power factor of permanent magnet Vernier machines for wind power application

Padinharu

Zhu

et al. 2020

IET Electric Power Applications

View full text Add to dashboard Cite

show abstract

Single stator‐single rotor permanent magnet Vernier machine topologies for direct‐drive applications: Review and case study

Faiz

Ghods

Arianborna

et al. 2021

Int Trans Electr Energ Syst

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Stator and rotor structures, arrangement of permanent magnets (PMs), and type of coils of PM Vernier machines are reviewed and classified. Then, electromagnetic performance and the energy conversion process in the machine are described. Determination of magnetic field distribution and air-gap permeance of the machine is very complicated than that of other PM machines. Impacts of variations of dimensions in the machine such as the number of modulators on the modulus width and the rotor PMs thickness on the load characteristics (cogging torque, back-EMF, and power factor) are investigated. In addition, principles of flux modulation machines operation are presented and the shape and dimensions of the modulators are optimized. The two-phase and four-phase winding types are used to improve the output power of the machine. Finally, a 150 W PM Vernier generator is designed and prototyped to feed the road speed camera.electric machines and drives, power quality | INTRODUCTIONDirect-drive systems are widely used in various applications, such as wind generators and electric vehicle (EV) propulsion. 1,2 To regulate speed in low-speed applications, different structures of direct-driven machines have been so far proposed in which the gearbox is removed from the machine, which is considered as the main advantage. [3][4][5] In recent years, many types of direct-driven machines have been introduced, such as transverse flux permanent magnets (PM), flux switching, and flux reversal machines whose performances are based on the properties of flux

show abstract

Comparison of Conformal Mapping Models in Permanent-Magnet Vernier Machines

Huang

Chen

et al. 2022

Lecture Notes in Electrical Engineering

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Characteristic Analysis of Surface Permanent-Magnet Vernier Motor According to Pole Ratio and Winding Pole Number

Cited by 31 publications

References 13 publications

Investigation of scaling effect on power factor of permanent magnet Vernier machines for wind power application

Investigation of scaling effect on power factor of permanent magnet Vernier machines for wind power application

Single stator‐single rotor permanent magnet Vernier machine topologies for direct‐drive applications: Review and case study

Comparison of Conformal Mapping Models in Permanent-Magnet Vernier Machines

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