Strict Mathematical Model of Synchronous Reluctance Motors Considering Cross-Magnetic Saturation and Reciprocity Relation of Mutual Inductance

Yamamoto, S.; Kojima, Takuya; Hirahara, Hideaki

doi:10.23919/icems50442.2020.9290998

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…6) and ( 7) are substituted for Eqs. (10) and (11). It can be naturally confirmed that Mdq -id in Fig.…”

Section: Verification Of the Reciprocity Relation Of Mutual Inductancesupporting

confidence: 60%

“…(5) are substituted for Eqs. (10) and (11). It 0 1 0 2 0 0 0.05 0.1 D-axis and q-axis currents, i d and i q [A] D-axis and q-axis inductances,…”

Section: Verification Of the Reciprocity Relation Of Mutual Inductancementioning

confidence: 99%

“…In this paper, the effectiveness of considering the reciprocity relation of the mutual inductance has been verified. The detailed derivation process of the strict mathematical model of SynRM considering both the iron loss and cross magnetic saturation is clarified (11) . Moreover, a simplified mathematical model that can reduce amount of calculation by employing the equivalent inverse function is shown.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

2022

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A unique approximation function for the d-and q-axes inductances for a synchronous reluctance motor (SynRM) is shown. This inductance approximation function has excellent features, such as continuous and differentiable over the entire current range when taking into account cross-magnetic saturation and satisfactory reciprocity relation of the mutual inductance. It is also possible to derive an equivalent inverse inductance function that can estimate the d-and q-axes currents from d-and q-axes stator flux linkages. Using the proposed inductance approximation function, the authors derive two mathematical models. The first is a strict model in which the state and input variables are the respectively load current and stator voltage. The second is a simple model in which the state and input variables are respectively the flux linkage and stator voltage, which are derived using the equivalent inverse inductance function. These models are applied to simulate the transient performances considering the iron loss and cross-magnetic saturation. The experimental and simulated results with a flux-barrier SynRM validate the proposed method.

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“…6) and ( 7) are substituted for Eqs. (10) and (11). It can be naturally confirmed that Mdq -id in Fig.…”

Section: Verification Of the Reciprocity Relation Of Mutual Inductancesupporting

confidence: 60%

“…(5) are substituted for Eqs. (10) and (11). It 0 1 0 2 0 0 0.05 0.1 D-axis and q-axis currents, i d and i q [A] D-axis and q-axis inductances,…”

Section: Verification Of the Reciprocity Relation Of Mutual Inductancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

2022

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“…A lot of research has already been conducted to accurately model three-phase RSMs. In [11][12][13][14][15][16][17][18][19][20], nonlinear RSM models are provided in the (d, q)-reference frame. However, all of these papers assume a symmetric (balanced) system and, therefore, neglect the γ-component, which is generally obtained by the Clarke transformation in an unbalanced system and corresponds to a scaled 0-component.…”

Section: Introductionmentioning

confidence: 99%

“…However, all of these papers assume a symmetric (balanced) system and, therefore, neglect the γ-component, which is generally obtained by the Clarke transformation in an unbalanced system and corresponds to a scaled 0-component. In most publications, the magnetic behavior is described by nonlinear (apparent) inductances that depend on the stator currents or rotor position [11,12,14,15,17,18,20], while cross-coupling is mostly neglected (although present if not adequately considered during apparent inductance derivation). Other authors use flux linkage maps for modeling and, therefore, allow to include cross-coupling effects [12,13,16,19].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

Rossmann¹,

Monzen²,

Kamper³

et al. 2023

Preprint

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<p>Reluctance synchronous machines (RSMs) are characterized by high nonlinearities, cross-coupling effects and high torque ripple. This paper presents a nonlinear machine model of three-phase RSMs based on a nonlinear electromagnetic model including iron losses and a novel (extended) torque equation. The γ-component is used to consider asymmetries. The novel torque model provides a precise approximation of the machine’s torque ripple. Iron losses are covered as well. The nonlinear machine model with extended torque equation is implemented based on current, angle and speed dependent flux linkage and iron loss maps. Finally, the nonlinear and extended machine model is validated by comparing with state-of-the-art results obtained by finite-element analysis (FEA).</p>

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Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

Rossmann,

Monzen,

Kamper

et al. 2023

2023 IEEE 32nd International Symposium on Industrial Electronics (ISIE)

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Reluctance synchronous machines (RSMs) are characterized by high nonlinearities, cross-coupling effects and high torque ripple. This paper presents a nonlinear machine model of three-phase RSMs based on a nonlinear electromagnetic model including iron losses and a novel (extended) torque equation. The γ-component is used to consider asymmetries. The novel torque model provides a precise approximation of the machine's torque ripple. Iron losses are covered as well. The nonlinear machine model with extended torque equation is implemented based on current, angle and speed dependent flux linkage and iron loss maps. Finally, the nonlinear and extended machine model is validated by comparing with state-of-the-art results obtained by finite-element analysis (FEA).

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Strict Mathematical Model of Synchronous Reluctance Motors Considering Cross-Magnetic Saturation and Reciprocity Relation of Mutual Inductance

Cited by 5 publications

References 7 publications

Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

Nonlinear Three-Phase Reluctance Synchronous Machine Modeling With Extended Torque Equation

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