Q-axis Inductance Research Articles

Analytical Calculation of D- and Q-axis Inductance for Interior Permanent Magnet Motors Based on Winding Function Theory

Interior permanent magnet (IPM) motors are widely used in electric vehicles (EVs), benefiting from the excellent advantages of a more rational use of energy. For further improvement of energy utilization, this paper presents an analytical method of d- and q-axis inductance calculation for IPM motors with V-shaped rotor in no-load condition. A lumped parameter magnetic circuit model (LPMCM) is adopted to investigate the saturation and nonlinearity of the bridge. Taking into account the influence of magnetic field distribution on inductance, the winding function theory (WFT) is employed to accurately calculate the armature reaction airgap magnetic field and d- and q-axis inductances. The validity of the analytical technique is verified by the finite element method (FEM).

Speed Estimation with Parameters Identification of PMSM Based on MRAS

This paper deals with the permanent magnet synchronous motor (PMSM) speed estimation and parameters identification problems. It proposes a solution to estimate speed and identify stator resistance, d-axis and q-axis inductance simultaneously. In fact, there are a lot of methods for estimating the speed, for example high-frequency injection, Kalman filter, and model reference adaptive system (MRAS). However, with the PMSM running, some parameters will change such as the stator resistance will change with the increase in temperature. These parameters are useful for estimating the speed. So, it is necessary to identify parameters simultaneously to adapt to the changes of these parameters. In this paper, MRAS is the theoretical basis. First, the adaptive law of speed observer is constructed through Popov stability. Then, the adaptive laws of stator resistance, d-axis, and q-axis inductance are constructed through Lyapunov stability. The stability of the proposed observers is also discussed. Last, this paper uses field-oriented control strategy and illustrates the obtained results through simulation and experiment.

Comparisons of three‐phase and five‐phase permanent magnet assisted synchronous reluctance motors

This paper presents the comparison of three-phase and five-phase permanent magnet assisted synchronous reluctance motors (PMa-SynRM) in terms of their design and performance characteristics. With higher fault tolerant capability, efficiency, and reliability, the five-phase PMa-SynRM can be a better substitute when compared with the three-phase PMa-SynRM in critical applications where safety is top priority. In this study, for a fair comparison, same design procedure using in lumped parameter modelling is followed in developing the three-phase and five-phase PMa-SynRMs. The models are optimised to minimise cost and maximise efficiency. For further detailed comparison of the three-phase and five-phase PMa-SynRMs, two-dimensional finite element analysis (FEA) is utilised. Performance characteristics such as torque pulsation, back electromotive force, flux linkage, d- and q-axis inductances versus their respective currents, cogging torque, efficiency plot, and torque-speed characteristics are intensively simulated through FEA. The optimised three-phase and five-phase PMa-SynRMs are fabricated with the same power rating (3 kW) and same volume. Experimental tests are conducted on the prototypes to validate the simulation results.

Design of five‐phase permanent magnet assisted synchronous reluctance motor for low output torque ripple applications

This paper presents the design of five-phase permanent magnet assisted synchronous reluctance motor (PMa-SynRM) for integrated starter and generator (ISG) of hybrid electric vehicle with low torque ripple. When ISG works as starter in order to operate engine, PMa-SynRM produces 3 kW power at the rated speed of 1800 rpm with reduced vibration by multi-phase structure. PMa-SynRMs are similar to interior permanent magnet motors in structure but are more economical due to reduced permanent magnets. In this study, lumped parameter model (LPM) using magnetic circuit design is used in the approach to initially design the five-phase PMa-SynRM. Numerical equations are integrated with the LPM to design the machine with its given range of design parameter values. Thousands of designs are generated by LPM, which are then converged to optimised model using differential evolution strategy. In this study, optimisation is done with maximum efficiency and minimum torque ripple as objective. The optimised 3 kW five-phase PMa-SynRM is then analysed by finite element method for fine tuning. Simulation results for back electromotive force, flux linkage, developed torque, torque ripple, cogging torque, torque speed characteristics and d and q -axis inductances variation over respective axis currents are verified by fabricated prototype.

MTPA Trajectory Tracking Control for Interior PMSM Based on Adaptive Parameter Identification

For an interior permanent magnet synchronous motor (IPMSM) control system, the actual maximum torque per ampere (MTPA) trajectory may deviate from the ideal one with parameter variances, and thus the system may not obtain the maximum torque output. In view of this problem, a novel parameter identification method based on the model reference adaptive system (MRAS) is proposed in this paper. In this method, the deviations of MTPA trajectories with parameter variances are analyzed and evaluated firstly, and then the q-axis inductance and the rotor flux linkage are identified on-line in a full rank MRAS model according to Popov Hyper Stability Theorem. Finally, the feasibility and validity of the designed method are proved through simulation results.

Performance Analysis and Modeling of a Tubular Staggered-Tooth Transverse-Flux PM Linear Machine

This paper investigates the performance analysis and mathematical modeling of a staggered-tooth transverse-flux permanent magnet linear synchronous machine (STTF-PMLSM), which is characterized by simple structure and low flux leakage. Firstly, the structure advantages and operation principle of the STTF-PMLSM are introduced, and a simplified one phase model is established to investigate the performance of the machine in order to save the computation time. Then, the electromagnetic characteristics, including no-load flux linkage, electromotive force (EMF), inductance, detent force and thrust force, are simulated and analyzed in detail. After that, the theoretical analysis of the detent force, thrust force, and power factor are carried out. And the theoretical analysis results are validated with 3-D finite-element method (FEM). Finally, an improved mathematical model of the machine based on d-q rotating coordinate system is proposed, in which inductance harmonics and coupling between d- and q-axis inductance is considered. The results from the proposed mathematical model are in accordance with the results from 3-D FEM, which proves the validity and effectiveness of the proposed mathematical model. This provides a powerful foundation for the control of the machine.

MTPA control of mechanical sensorless IPMSM based on adaptive nonlinear control

In this paper, an adaptive nonlinear control scheme has been proposed for implementing maximum torque per ampere (MTPA) control strategy corresponding to interior permanent magnet synchronous motor (IPMSM) drive. This control scheme is developed in the rotor d–q axis reference frame using adaptive input–output state feedback linearization (AIOFL) method. The drive system control stability is supported by Lyapunov theory. The motor inductances are online estimated by an estimation law obtained by AIOFL. The estimation errors of these parameters are proved to be asymptotically converged to zero. Based on minimizing the motor current amplitude, the MTPA control strategy is performed by using the nonlinear optimization technique while considering the online reference torque. The motor reference torque is generated by a conventional rotor speed PI controller. By performing MTPA control strategy, the generated online motor d–q reference currents were used in AIOFL controller to obtain the SV-PWM reference voltages and the online estimation of the motor d–q inductances. In addition, the stator resistance is online estimated using a conventional PI controller. Moreover, the rotor position is detected using the online estimation of the stator flux and online estimation of the motor q-axis inductance. Simulation and experimental results obtained prove the effectiveness and the capability of the proposed control method.

Robust Diagnosis Method Based on Parameter Estimation for an Interturn Short-Circuit Fault in Multipole PMSM under High-Speed Operation.

This paper proposes a diagnosis method for a multipole permanent magnet synchronous motor (PMSM) under an interturn short circuit fault. Previous works in this area have suffered from the uncertainties of the PMSM parameters, which can lead to misdiagnosis. The proposed method estimates the q-axis inductance (Lq) of the faulty PMSM to solve this problem. The proposed method also estimates the faulty phase and the value of G, which serves as an index of the severity of the fault. The q-axis current is used to estimate the faulty phase, the values of G and Lq. For this reason, two open-loop observers and an optimization method based on a particle-swarm are implemented. The q-axis current of a healthy PMSM is estimated by the open-loop observer with the parameters of a healthy PMSM. The Lq estimation significantly compensates for the estimation errors in high-speed operation. The experimental results demonstrate that the proposed method can estimate the faulty phase, G, and Lq besides exhibiting robustness against parameter uncertainties.

Performance investigation of hybrid excited switched flux permanent magnet machines using frozen permeability method

This study investigates the electromagnetic performance of a hybrid excited switched flux permanent magnet (SFPM) machine using the frozen permeability (FP) method. The flux components due to PMs, field excitation windings and armature windings have been separated using the FP method. It has been used to separate the torque components due to the PMs and excitations, providing a powerful insight into the torque generation mechanism of hybrid excited SFPM machines. It also allows the accurate calculation of d- and q-axis inductances, which will then be used to calculate the torque, power and power factor against rotor speed to compare the relative merits of hybrid excited SFPM machines with different types of PMs (i.e. NdFeB, SmCo and Ferrite). This offers the possibility of choosing appropriate PMs for different applications (maximum torque or maximum speed). Although only one type of hybrid excited PM machine has been employed to carry out the investigations, the method used in this study can also be extended to other hybrid excited PM machines. The predicted results have been validated by tests.

Design And Rotor Geometry Analysis Of Permanent Magnet–Assisted Synchronous Reluctance Machines Using Ferrite Magnet

Abstract Various electric machines can be the candidate for electric vehicles applications, including induction machines, permanent magnet synchronous machines, switched reluctance machines, etc. Another class of machine, which has been relatively ignored, is synchronous reluctance machines. In order to enhance and increase torque density of pure synchronous reluctance machines, the low cost permanent magnet can be inserted into rotor lamination to contribute torque production, which is so-called permanent magnet-assisted synchronous reluctance machines. This paper presents the design and rotor geometry analysis of low cost ferrite permanent magnet-assisted synchronous reluctance machines with transversally-laminated rotor. The advanced finite element method will be employed to calculate d-axis and q-axis inductance variation with rotor geometric parameters. The electromagnetic performance of optimized permanent magnet-assisted synchronous reluctance machines will be evaluated as well.

Increasing the saliency ratio of fractional slot concentrated winding interior permanent magnet synchronous motors

In permanent magnet synchronous motor (PMSM) servo systems, the saliency ratio is an important factor in sensorless control and flux-weakening control. Compared with the interior PMSM (IPMSM) with distributed windings, the IPMSM with concentrated windings gains more popularity in servo system applications. However, the saliency ratio of current fractional slot concentrated windings (FSCWs) IPMSM is low and hard to increase, without much literature investigating how to improve the ratio. In this paper, the components of d - and q -axes inductances of FSCW IPMSM are determined, a novel concept named mechanical phase region is introduced and the key parameters influencing the saliency ratio of FSCW PMSMs have been investigated through thorough theoretical analysis and simulation. The design principles on increasing the saliency ratio of FSCW IPMSMs are proposed and the maximum saliency ratio of a 10 poles 12 slots motor is obtained. On the basis of the theory, a novel rotor structure with higher saliency ratio is designed. A new experimental method of measuring d - and q -axes inductances closes this paper with three experimental prototypes built to verify the theory and simulation results.

Permanent-Magnet Temperature Estimation in PMSMs Using Pulsating High-Frequency Current Injection

The injection of a high-frequency signal in the stator via inverter has been shown to be a viable option to estimate the magnet temperature in permanent-magnet synchronous machines (PMSMs). The variation of the magnet resistance with temperature is reflected in the stator high-frequency resistance, which can be measured from the resulting current when a high-frequency voltage is injected. However, this method is sensitive to d- and q-axis inductance (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> ) variations, as well as to the machine speed. In addition, it is only suitable for surface PMSMs (SPMSMs) and inadequate for interior PMSMs (IPMSMs). In this paper, the use of a pulsating high-frequency current injection in the d-axis of the machine for temperature estimation purposes is proposed. The proposed method will be shown to be insensitive to the speed, L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> , and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> variations. Furthermore, it can be used with both SPMSMs and IPMSMs.

Design and optimisation of interior PM machines with distributed and fractional-slot concentrated-windings for hybrid electric vehicles

This paper presents an optimisation of an interior permanent magnet (PM) machine with fractional-slot concentrated-windings (FSCW) based on a machine with integer-slot distributed windings (ISDW), and a performance comparison between the two machines for use in hybrid electric vehicles. Finite element analysis (FEA) is used to investigate the characteristics of the two machines which have the same dimensions and rated power. The effect of the number of slots on the back-EMF, cogging torque, d- and q-axis inductances and efficiency is analysed for the two machines. The measured results have good agreement with the FEA results.

Modeling and Implementation of MTPA Control Strategy for SynRM Variable Speed Drives

The correct modeling and control of synchronous reluctance motors (SynRMs) requires a suitable representation and identification of the machine parameters. Accordingly, simple experimental offline approaches are presented in this paper for the calculation of the viscous friction coefficient, constant friction load, iron loss resistance and d- and q-axes inductances. The motor behavior under vector control is analyzed considering both saturation and iron losses. The simulation results of a vector-controlled 2.2 kW SynRM are compared with experimental tests in order to demonstrate the effectiveness and accuracy of the proposed parameter identification methods. Then, a maximum torque per ampere (MTPA) control strategy is derived using the SynRM validated model, showing the importance of both magnetic saturation and iron losses in the control performance of the SynRM drive.

Analysis and Design of a Novel-Shape Permanent Magnet Synchronous Motor for Minimization of Torque Ripple and Iron Loss

This paper presents the shape optimization of a permanent magnet synchronous motor to reduce the torque ripple and iron loss. Specifically, the harmonics of the electromotive force and cogging torque are decreased by adjusting the permanent magnet arrangement and non-uniform air gap length. In addition, an additional flux path along the q-axis is proposed with a unique rotor shape to increase the q-axis inductance and reluctance torque. The improvement in the performance of the proposed model is verified with simulated and experimental results.

동기릴럭턴스전동기의 자기포화를 고려한 최대토크제어

This paper presents a synchronous reluctance motor drive for maximum torque to current (MTC) considering magnetic saturation. Measured d-axis and q-axis inductances are used to obtain current angle vs. maximum torque curve using torque equation. Maximum torque to current control is achieved by the current angle and stator current for maximum torque from the current angle vs. maximum torque curve at a given torque reference.

Investigation of $d$- and $q$-Axis Inductances Influenced by Slot-Pole Combinations Based on Axial Flux Permanent-Magnet Machines

Flux-weakening capability of permanent-magnet synchronous machines (PMSMs) is fundamentally determined by <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> -axis inductances. Based on axial flux permanent-magnet machines (AFPMs), this paper extracts the intrinsic factors that influence the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $q$</tex></formula> -axis inductances of PMSMs, meanwhile revealing the fact that the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex></formula> -axis inductances of fractional slot concentrated winding machines are not inevitably larger than that of distributed ones. The proportion of each of the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$d$</tex></formula> - and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$q$</tex> </formula> -axis component inductances for multigap AFPMs is first studied. By analyzing armature inductance in conjunction with differential leakage inductance, this paper introduces a novel parameter to decouple the influence of slot-pole combinations and physical dimensions so that the “inductance ability” of different slot-pole combinations can be quantified. An improved method of calculating the slot leakage inductance of semiclosed slots is then put forward, which proves to be more accurate than the conventional method. The investigations and conclusion in this paper are not restricted to AFPMs but applicable to radial flux permanent-magnet machines as well. Validations of various slot-pole combinations are carried out with finite-element analysis and experiments.

Signal-Injection-Assisted Full-Order Observer With Parameter Adaptation for Synchronous Reluctance Motor Drives

A back-electromotive-force-based position observer for motion-sensorless synchronous reluctance motor (SyRM) drives is augmented with parameter adaptation laws for improved operation at all speeds, including standstill. The augmented observer is theoretically analyzed under various operating conditions. The analysis indicates that the stator-resistance adaptation should be enabled only at low speeds, the d-axis inductance adaptation should be enabled only at medium and high speeds near no load, and the q-axis inductance adaptation should be enabled only at high speeds under high load. The augmented observer is experimentally evaluated using a 6.7-kW SyRM drive.

Torque ripple analysis for IPM AC motors

Purpose – The purpose of this paper is to investigate a new cause of torque ripple in interior permanent magnet (IPM) alternating current (AC) motors, which is common but has hardly been studied. The paper also proposes a new method to suppress the total torque ripple. Design/methodology/approach – Besides the well-known cogging torque and mutual torque ripple, a new ripple which exists in the reluctance torque is found. It is verified with both analytical model and finite element analysis. Also, a novel method is proposed to reduce the reluctance torque ripple, with experimental validation. Findings – It is usually said that the winding inductances of an IPM AC motor vary sinusoidally with the rotor position, thus, the d-axis and q-axis inductances are constant, whilst the reluctance torque is smooth. However, in most practical motors, the inductances vary irregularly, causing a significant ripple in the reluctance torque. Moreover, in machine design, it is always desirable to suppress the cogging torque as much as possible. However, in this paper, it is proved that the cogging torque can remain and be used to cancel the reluctance torque ripple. Originality/value – Torque ripple in the IPM AC motors is usually reduced by suppressing the cogging torque and making both back electromotive forces and currents sinusoidal. However, this paper reveals the new cause of the torque ripple due to the irregular variation of winding inductances. Moreover, the paper gives a new method to cancel the reluctance torque ripple with the cogging torque.

Direct-Driven Interior Magnet Permanent-Magnet Synchronous Motors for a Full Electric Sports Car

The design process of direct-driven permanent-magnet (PM) synchronous machines (PMSMs) for a full electric 4 × 4 sports car is presented. The rotor structure of the machine consists of two PM layers embedded inside the rotor laminations, thus resulting in some inverse saliency, where the q-axis inductance is larger than the d-axis one. An integer slot stator winding was selected to fully take advantage of the additional reluctance torque. The performance characteristics of the designed PMSMs were calculated by applying a 2-D finite-element method. Cross saturation between the d- and q-axes was taken into account in the calculation of the synchronous inductances. The calculation results are validated by measurements.