Nonsinusoidal Power Supply Analysis for Concentrated-Full-Pitch-Winding Multiphase Induction Motor

A nonlinear model is proposed representing air-gap magnetic flux density distribution in a synchronous machine with magnetic saturation in the pole tips. In order to explain the effect of magnetic saturation in a synchronous machine, the authors have measured air-gap flux in a specially designed synchronous machine, and recently proposed a model for the air-gap flux density distribution, concentrating on magnetic saturation in the field pole iron cores. In this paper, we propose an adaptation of our model for calculating air-gap flux, specifically addressing the magnetic saturation in the pole tips. By regarding the saturation as a consumer of m. m. f. similar to a virtual winding, we construct a magnetic circuit which represents the flow of magnetic flux inside the synchronous machine, and derive expressions which represent air-gap flux density distribution. Close agreement is obtained between the theoretically calculated results, and the results measured using search coils placed at the teeth of the armature.

The proposed technique focuses on the nonsinusoidal power supply control strategy aiming to obtain the optimal air gap flux density distribution. The electrical constraints for the alignment between rotated fundamental and harmonic air gap flux are illustrated in detail. The supporting simulation is performed to analyze the misaligned angles between fundamental and harmonic air gap flux for the traditional methods. Different from traditional flux-oriented methods, the improved algorithm for harmonic currents injection is designed based on rotor flux orientated control in fundamental plane and air gap flux orientated control in harmonic planes. The synchronous and aligned control of the fundamental and harmonic air gap flux is achieved regardless of load condition. The experimental verification is implemented based on a multiphase driving platform using a seven-phase induction machine as prototype. Various scenarios are provided for the proposed control strategy comparing with the traditional ones in terms of induced electromotive force waveforms, harmonic currents, and advance angles of air gap flux. The simulated and experimental results validate the theoretical assumption and the effectiveness of the proposed method.

Permanent magnet synchronous motors (PMSM) generate high-frequency electromagnetic vibration and noise when powered by inverters, and the cause is high-frequency electromagnetic exciting force (EMEF). In this paper, the frequencies and orders of EMEF are analyzed. The expression of EMEF acted on the stator inner surface is derived and the frequencies and orders of main components of vibration are listed. The high-frequency vibration experiments are conducted on a surface mounted 8-pole and 12-slot PMSM. The high-frequency vibrations near switch frequency and its multiples are main components of vibrations of motors when powered by inverters, and experiments are conducted to study the influence of switch frequency on the vibration acceleration. The impacts of periodic frequency PWM and random frequency PWM on the vibration acceleration and peak value of its frequency spectrum are studied by experiments. Introduction The vibration of motors is one of the most important performance indicators. The noise generated by vibration will pollute our working and living environment. A severe vibration can even destruct the machine structure. There are higher requirements for vibration in special applications. While the application of inverter improves the dynamic performance of the motor, it causes high frequency vibration and noise. Many researchers have done a lot of work about the vibration and noise of motors. The frequency of noise of inverter-fed induction machine is calculated[1,2]. The influence of inverters on the vibration of axial flux PM motors is studied by finite element method(FEM) and experiments. The impacts of random PWM and harmonic injection is studied[4-6]. The effect of pulse frequency modulation(PFM) in reducing noise of induction motor is studied[7]. When powered by inverters, the stator current has a lot of time harmonics which increases the complexity of air gap flux. The air gap flux determines the magnitude and frequency of electromagnetic exciting force (EMEF) acted on the inner surface of stator. In this paper, the flux distribution is derived by magnetic circuit method firstly. Then, the expression of radial of EMEF is obtained by Maxwell’s stress tensor. The frequency, order and sources of the main EMEF are listed. The high-frequency vibration experiments are conducted on a surface mounted 8-pole and 12-slot PMSM. The high-frequency vibrations near switch frequency and its multiples are main components of vibrations of motors when powered by inverters, and experiments are conducted to study the influence of switch frequency on the vibration acceleration. The impacts of periodic frequency PWM and random frequency PWM on the vibration acceleration and peak value of its frequency spectrum are compared by experiments. Calculation of EMEF in PMSM The vibration of stator of PMSM is mainly determined by radial EMEF acted on the inner surface of the stator. Neglecting the effect of magnetostriction and assuming 0 Fe μ μ  , the EMEF acted on the inner surface can be expressed as[8]: 2nd International Conference on Electrical, Computer Engineering and Electronics (ICECEE 2015) © 2015. The authors Published by Atlantis Press 1580 2 0 1 2 n n o F B μ = (1) where 0n B is the radial air gap flux density in the inner surface of stator. So the air gap flux distribution need to be obtained before calculating the EMEF. Neglecting the core magnetic reluctance, the air gap flux distribution can be expressed as ( ) ( ) ( ) , , , b t f t t θ θ λ θ = ⋅ (2) where θ is the mechanical angle, ( ) , f t θ is the air gap magneto-motive force(MMF) and ( ) , t λ θ is the air gap permeance. In a surface mounted PMSM (SPMSM), the air gap permeance does not change with time. It can be approximately expressed as ( ) 0 l θ λ λ = Λ +∑ (3) where 0 Λ is the constant part and l λ is the space periodic part caused by slots. l λ can be expressed as ( ) ( ) ( ) 0 ( 1) sin 1 cos cos ( 1) l l k l k k lZ lZ k l k k δ

The present work proposed a methodology to estimate the iron and copper losses of a three - phase, squirrel cage induction motor for both sinusoidal and inverter-fed power supply, based on a two - dimensional finite element analysis software (Maxwell 2D - V16). The three-dimensional effect of stator end winding, rotor end ring, and rotor bars skewing were included by coupling with RMxprt software. The inverter simulation was done by Simulink. The modeling was done based on the design documents of a 2.2 kW, 2 pole test motor. The values of iron and copper losses estimated by Maxwell 2D at full load condition, sinusoidal power supply was compared with that extracted from solving the motor equivalent circuit parameters, and that taken from RMxprt with a good agreement. Both copper and iron losses were increased when motor operated with an inverter-fed power supply with respect to sinusoidal power supply. Also, these losses were decreased with increasing of inverter carrier frequency. The loss results will make a good roadmap for the motor designers, and operators to achieve the goal of an efficient inverter-fed induction motor operation.

This paper proposes an effective assistant model for considering the stator slot-opening effect on air gap flux density distribution in conventional interior-type permanent magnet (IPM) motor. Different from the conventional slot-opening effect analysis in surface-type PM (SPM) motor, a composite effect of slot-opening uniquely existing in IPM motor, which additionally causes enhancement of air gap flux density due to magnet flux path distortion in iron core between the buried PM and rotor surface. This phenomenon is represented by a proposed assistant model, which simply deals with this additional effect by modifying magnetic pole-arc using an effective method. The validity of this proposed analytical model is applied to predict the air gap flux density distribution in an IPM motor model and confirmed by finite element method (FEM).

The pole phase modulation (PPM) technique is an effective method to extend speed range and torque capabilities for an integrated starter and hybrid electric vehicles applications. In this paper, the five pole-phase combination types of a multiphase induction motor (IM) with 36 stator slots and 36 stator conductors are presented and compared quantitatively by using the time-stepping finite element method (TS-FEM). The 36 stator conductors of the proposed multiphase IM are fed by a 36 leg inverter and the current phase angle and amplitude of each stator conductor can be controlled independently. This paper focuses on the winding connection, the PPM technique and the performance comparative analysis of each pole-phase combination types of the proposed multiphase IM. The flux distribution, air-gap flux density, output torque, core losses and efficiency of five pole-phase combination types have been investigated.

This paper focuses on a dual-motor series system of a double-Y shifted 30° permanent magnet synchronous motor (PMSM) with a salient-pole rotor structure driven by a single inverter. A mathematical model is established considering the non-sinusoidal distribution of the air gap flux density (including the 5th harmonic). A vector control system based on the i d=0 strategy and incorporating torque compensation is proposed. Simulation studies under variable load conditions demonstrate that the series system can achieve decoupled control for PMSMs with a salient-pole rotor structure and non-sinusoidal air gap flux density distribution.

Outer rotor permanent magnet machines have been applied to low-speed and high-torque applications for their high moment of inertia and torque density. The 12-slot/10-pole outer rotor fractional slot permanent magnet machine model is established by the finite element analysis (FEA) in this paper, and the no-load back EMF, air-gap flux density and flux distribution of the machine are preliminarily simulated and verified. The stator tooth width of outer rotor permanent magnet machine is analyzed, and five different schemes of stator tooth width are designed. It is proved that the torque density can be effectively improved by using reasonable armature tooth width and auxiliary tooth width by FEA. At last, the reason of improving the output torque is explained by the analysis of the magnetic density and the winding coefficient of the armature tooth.

I. IntroductionThere are many studies on axial flux permanent magnet machines (AFPMMs) due to their compactness [1]. The conventional AFPMMs comprise a stator and two rotors. In general, the stator with toroidal windings or overlapping windings is sandwiched between two rotors [2][3]. Toroidal windings have shorter ends than overlapping windings, which can reduce copper loss and ending effect. However, this structure also wastes the ends of windings, which means that the windings are not utilized sufficiently. To some extent, it reduces the torque density of the machine.This paper proposes a novel axial-radial flux permanent magnet machine (ARFPMM) to solve the problem. In the ARFPMM, the endings of windings are also used to produce torque with little increase of volume, which results in the improvement of torque density.II. Structure of ARFPMMThe proposed ARFPMM integrates both axial-flux and radial-flux machines in a compact space, which improves the torque density. As shown in Fig. 1(a), the ARFPMM is composed of one stator, two axial rotors and one radial rotor. Because the end of overlapping windings is useless, the machine adopts toroidal windings. Thus, the stator is equipped with opening slots on three faces. Permanent magnets are mounted on the surface of rotors. The radial rotor is fixed and aligned with two axial rotors, which can avoid the tilt of axial rotors and generation of harmonics in flux density per phase. The inner and outer diameters of permanent magnets on axial rotors are the same as those of stator. Similarly, the height of permanent magnets on radial rotor is equal to that of stator.In order to suppress air-gap flux density harmonics and get more sinusoidal waveform of air-gap flux [4], the permanent magnets are arranged as Halbach-array. It can also increase the flux density in the air gap. The magnetization direction of PMs is related to the number of segments per pole pair. As shown in Fig. 1(b), each pole pair is divided into six segments, so the magnetization direction of each segment varies 60° in turn.III. Design and AnalysisCompared with integer-slot concentrated windings, fractional-slot concentrated windings can enhance flux-weakening capability and reduce cogging torque [5]. Therefore, a 20 pole 24 slot fractional-slot concentrated-winding machine is chosen. In the case, the winding factor is 0.966. It is related to the no load back electromotive force (EMF) which can be calculated as equation (1). E0=4.44fkwNΦ10 (1)Where f is the electric frequency of the machine, kw is the winding factor, N is the number of coils per phase in series, Φ10 is the magnetic flux. In the ARFPMM, three rotors are used to increase the magnetic flux in air gap. The result of 3D FEA for back EMF is shown in Fig. 2(a). Fig. 2(b) is the fast Fourier transform of back EMF. It shows that the maximum harmonic is the third order harmonic, which can be neglected due to the star-connection of three phase windings.Because the magnetic flux in air gap is increased under the same operating state, the torque of ARFPMM is also increased. Fig. 2(c) shows the torque of the machine at rated conditions when the current is 7 A and rotor speed is 600 rpm. In the condition, the average torque is 41.63 Nm and the torque density is 28.58 Nm/L. The torque ripple is 3.4 Nm, 8.1% of the rated torque. As shown in Fig. 2(c), the peak-peak value of cogging torque is 3.26 Nm.IV. ConclusionThis paper proposes a novel ARFPMM with a unique structure of two axial rotors and one radial rotor, and implements its design and FEA. Due to the Halbach-array PMs, the main harmonics of back EMF is the third order harmonic, which is negligible when the windings are connected in star-connection. Compared with conventional AFPMM, the structure increases the torque through increasing the magnetic flux through windings per phase. Thus, the ARFPMM reaches an extremely high torque density of 28.58 Nm/L. On the other hand, fractional-slot concentrated winding configuration reduces the cogging torque, of which the peak-peak value is only 3.26 Nm.AcknowledgeThis work is supported in part by NSFC (52077186&51677159), in part by STIC of Shenzhen Municipality (JCYJ20180307123918658), and in part by ITF (ITP/027/19AP), HK. **

This paper summarizes the results of an experimental and analytical investigation of the slot ripples in the damper windings of a salient-pole synchronous machine under steady state operation. A new method of measuring damper winding currents and voltages directly has been established and used to examine the ripples due to the stator slot openings, which appear in the damper bar currents and voltages, air gap flux density distributions and terminal voltages. By examining the physical relationship between air gap fluxes and damper winding currents and voltages both at no load and on load, slot ripples phenomena have been made clearer than before. >

This paper studies the effects of the flux modulation poles (FMPs) on the radial magnetic forces in permanent magnet vernier (PMV) machines. The air-gap flux density distribution in the PMV machine is analyzed by using a combination of the finite element analysis and analytical methods. And then, the radial force density is calculated by Maxwell's stress method. At no-load condition, the permeance harmonics by FMPs generate various air-gap flux density harnmonics by interacting with the magneto-motive force (MMF) harmonics of the magnet. As a result, the low order harmonics of the radial force density which may induce significant vibration is caused in the PMV machine. Furthermore, the characteristics of the radial force density under the load condition will be investigated.

This paper investigates what effects different cogging torque reduction techniques, have on the cogging torque waveforms and air-gap flux density of surface mounted PMSMs with distributed windings and large number of slots per pole. Methods such as magnet step skew, stator teeth dummy slots and magnet pole shaping are the main scope of the paper, as they do not result in unwanted rotor unbalances. The effects of different number of magnet pole segments and different skew angles on the cogging torque waveforms are also depicted. Two dimensional Finite element analysis (FEA) is performed in order to obtain the cogging torque peak-to-peak variations and air-gap flux density distribution.

The induction motor with skewed rotor bars is an effective motor structure for eliminating the slot harmonic fields, and the resulting noise and vibration. 2-D multi-slice finite element method (FEM) is typically used to analyze the performance of the induction motor with skewed rotor bars. However, in order to achieve high accuracy, the number of the slices is generally very high, which is also a time-consuming work. In this paper, a fast identification method of air-gap flux density (AGFD) is proposed. In the proposed method, the AGFD calculated by the 2-D multi-slice FEM is post-processed by a skewed factor. In order to achieve a relatively high accuracy, the number of slices of the 2-D multi-slice FE models can be significantly reduced by using the proposed method. And in this paper, based on the proposed method, the influence of the skewed rotor bars on the air-gap force of a 5.5 kW motor are also studied.

The requirement of stringent environment and fuel efficiency target on automotive demand the use of lighter, smaller and efficient motors. The advantages like higher magnetic properties than ferrite, near net shape magnet production, and no use of heavy rare earth elements makes the use of bonded neo magnet in an automotive accessory motors very attractive. The isotropic nature of bonded neo magnets offers a feasibility to obtain wide range of magnetization profiles. The magnetization of the magnet influences the air-gap flux distribution and hence the motor performance 1. The performance of permanent magnet motors using isotropic bonded neo magnet can be improved by optimizing the air-gap flux profile using magnetization. Based on the magnet circumference touching the motor air-gap and the desired magnetization profile, an appropriate magnetization fixture needs to be designed. In an external rotor permanent magnet brushless (PMBL) DC motor and brushed DC motors, the inner circumference of the magnet touches the airgap and hence the magnet is magnetized using an inner-only fixture which has magnetization coils next to the inner circumference of the magnet. When the radial magnetization is desired, a double sided magnetization can also be used to magnetize bonded neo ring magnets 2. The use of double sided magnetization helps in enhancing the motor performance 3. To ensure that the bonded neo magnet is fully saturated a minimum magnetizing field of around 3T is to be generated throughout the magnet thickness 4. Considering this required magnetizing field, a fixture each offering inneronly and inner-outer magnetization (double sided magnetization) is designed using Finite element analysis (FEA) to achieve the radial magnetization. The simulation based results on the performance comparison of two fixtures is summarized. Figure 1 shows the simulated mid airgap flux density when magnet is magnetized with inner-only and inner-outer magnetizing fixtures. From this figure it is observed that, compared to inner-only fixture, the inner-outer fixture results in flat topped radial wave shape of flux density. Both designed fixtures are fabricated and the measured performance is used to validate the simulation results. It is observed that the peak magnetizing current and the energy required to achieve the magnet saturation in an innerouter fixture is 19.8% and 26.5% less respectively compared to inner only fixture. The reduction in peak magnetizing current and magnetization energy requirement will lead to reduced thermal stress and improved fixture reliability. It will also help in reducing the magnetization cycle time due to better heat dissipation in inner-outer fixture. During magnetization of the magnet, the effectiveness of the inner-outer fixture depends highly on the alignment of the inner and outer magnetization coils. The alignment and hence the performance of the fixture is influenced by the fabrication tolerances 5. Even a small misalignment between the coils on either side of the magnet will result in flux waveform distortion and reduction in magnetic flux. Considering the manufacturing tolerances, the effect of the various misalignment angles between the inner and outer magnetization coils on the magnet flux is arrived at using the FEA based simulation. The magnetization result is also measured by creating various misalignments between the inner and outer magnetization coils in the fabricated inner-outer magnetization fixture. Table I gives the measured magnet flux integral for various misalignment angles. It is observed from Table I that the $\pm 2 ^{circ}$ mechanical misalignment between the coils will not result in significant change in magnet flux and higher misalignment angles will result in considerable reduction of flux per pole. It is also observed that the misalignment effect is symmetric about the aligned position and higher degree of misalignment causes drooping wave shape on one side and a hump on the other side in any given pole depending on the direction of misalignment.

In this paper, comparisons are made on various parameters of electromagnetic fields like air gap flux density (radial), flux distribution, phase currents, speed and torque of a healthy and stator inter-turn fault induction motor (IM). Using FEM (Finite Element Method), the inter-turn short circuit fault analysis of PWM (Pulse Width Modulated) inverter fed 3 phase IM is analyzed. The inter-turn fault is the initial stage of a short circuit in the stator winding and it progresses to a phase to phase fault or phase to ground fault if left undetected. When the IM is directly fed from the mains, the inter-turn fault can be identified using a popular technique known as MCSA (Motor Current Signature Analysis). But this method fails when the IM is fed from a PWM inverter due to rich noise content observed in the current spectrum due to high frequency inverter switching making it difficult to detect the fault. The electromagnetic field analysis of PWM inverter fed 3 phase IM with 12.5% and 25% stator winding inter-turn fault is carried out on a 7.5kW IM using ANSYS Maxwell FEA (Finite Element Analysis) tool. The spatial FFT spectrum of air gap flux density (radial) indicates the presence of stator winding inter-turn fault with rich noise content compared to healthy motor.