Harmonic Torque Research Articles

New Simple High‐Quality Torque Control for Permanent‐Magnet Synchronous Motors: Compensating for Torque Ripple Caused by Nonsinusoidal Back EMF

SUMMARYThis paper proposes a new and simple torque‐sensorless torque control method for permanent‐magnet synchronous motors (PMSMs) with nonsinusoidal back EMF. The method suppresses the sixth and/or 12th harmonic torque ripples caused by the back EMF in a feedforward manner even at high speeds; it consists of two subordinate methods for compensation command generation and command‐tracking current control. The first subordinate method generates compensation current commands to cancel the torque ripples based on a mathematical model of PMSMs. The second method controls the stator current to track a current command containing both fundamental and compensatory components. In conjunction with the current control, a dedicated disturbance observer that employs a digital speed‐varying band‐pass filter as a disturbance filter is also proposed. The effectiveness and usefulness of the proposed method were verified through extensive experiments.

Geometrical optimization of SRM on operating mode for automotive application

This paper deals with double saliency switched reluctance motor for automotive application by offering simultaneously a design solution to the drawbacks of torque ripples and emitted noise caused by the important radial efforts. The work concerns the optimization of the motor structure, the main objectives is the reduction of the first harmonics of torque and radial force applied on the stator teeth. This geometric optimization is performed on operating points where the instantaneous computation of supply current is taken into account to resolve simultaneously both problems. This operating point is defined as torque–speed point by considering the instantaneous characteristics of the machine when the steady state is established.

Localization phenomena in annular-type oscillator arrays

This paper investigates intrinsic localized modes (ILMs) in a system where N nonlinear oscillators are arranged in a circle and connected by weak springs when the system is subjected to sinusoidal, harmonic excitation torque. These oscillators consist of point masses at the tip of pinned, massless rigid rods, nonlinear springs, and dashpots. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for the frequency response curves for fundamental harmonic oscillations. In the numerical calculations, the frequency response curves for N=3 are shown in the cases of both soft-spring and hard-spring nonlinear arrays and compared with the results of the numerical simulations. As a result, in the case of the soft-spring nonlinear arrays, eight stable oscillation patterns may appear when the connecting spring constants are comparatively small, and ILMs appear in six patterns depending on the initial conditions and the excitation frequency. The number of the oscillation patterns decreases as the connecting spring constants are increased. Comparatively, small values of the connecting spring constants may cause Hopf bifurcation to appear followed by amplitude modulated motions (AMMs), including regular ILMs, moving ILMs, and chaotic vibrations. In the case of the hard-spring nonlinear arrays, similar phenomena are observed except for moving ILMs. ILMs do not appear when the values of connecting springs exceed specific values in the both cases.

Analytical Prediction of Torque Ripple in Surface-Mounted Permanent Magnet Motors Due to Manufacturing Variations

In the production of surface-mounted permanent magnet machines, manufacturing tolerances also contribute to torque ripple. Additional harmonics of low electrical orders are created in the torque spectrum. Slight manufacturing variations develop asymmetry conditions in the rotor as well as in the stator. Finite element models can be used to analyze the magnitude of pulsating torque generated due to these asymmetries. However, due to its random nature, lack of periodicity, and symmetry, it is time consuming to study the problem with numerical methods for its uneven geometry that does not allow reduced geometrical models. Moreover, the experimental verification of all possible variations would be very challenging as it would require part dimensioning and part sorting a large quantity of motor builds and finally testing of all samples. Therefore, in this paper an analytical model is presented to study the effect of such imbalance on the torque ripple. The model shows an agreement against finite element models and also with experimental results when predicting torque harmonics that come from asymmetries.

The effect of coupled lateral and torsional vibrations of an unbalanced Jeffcott rotor supported by roller bearings

In this paper, an unbalanced Jeffcott rotor supported by the roller bearings is modelled, and the dynamic differential equations are obtained by the Lagrange’s equations. The fourth order Runge–Kutta method is employed to simulate this system in two cases. Simulation results show the combined effect of the coupled lateral and torsional vibrations and the variable compliance vibration of the rotor. In the case of that only a large and constant radial force is applied, the sum and difference between variable compliance and rotational frequency components of the torsional vibrations of the disk are induced because of the roller bearings’ rotation. And when they are near to the natural frequency of the torsional vibration, the resonance peaks appear. In the case of that a large and constant radial force and a harmonic torque are simultaneously applied, the two components, the sum and difference between rotational frequency and the frequency of the external torque, of the lateral vibrations of the disk are induced. When the frequency of the external harmonic torque approximatively equal to a special value, the two frequency band lines, variable compliance and the sum of rotational frequency and the frequency of external torque, intersect near the natural frequency of the lateral vibration, and the vibration may aggravate.

A study of the matching of impellers and motors for contra-rotating fan based on electromagnetic-fluid coupling analysis

The contra-rotating fan is an electromechanical device in which electromagnetic force and aerodynamic force coordinate together. Its operation process is affected by multiple factors and is also coupled with multiple variables. In order to further reveal its working mechanism, electromagnetic-fluid coupling model for contra-rotating fan was presented and relevant numerical computations were performed by the combination of the motors’ electromagnetic-field simulation and the fan’s fluid-field simulation. Curves of electromagnetic torque and aerodynamic torque in time domain, respectively, for two motors and two impellers of the fan were obtained, and then fast Fourier transform algorithm was used to analyze their harmonic components. Meanwhile, the resonance effect induced by the same-frequency components between the harmonic electromagnetic and aerodynamic torques was investigated. Moreover, the impeller–motor interaction and matching performance were explored so as to determine the optimal combination scheme of blade number in two-stage impellers. The reasonableness of this scheme was validated experimentally. This heterogeneous physical-field simulation method targeted at electromagnetic-fluid coupling condition offers an important reference for optimizing the fan system.

DC Bus Voltage Pulsation Suppression of the Permanent Magnet Synchronous Generator With Asymmetries Accounting for Torque Ripple

This paper proposes an effective method for suppressing the second harmonic dc bus voltage pulsation accounting for the second harmonic torque ripple in the permanent magnet synchronous generator (PMSG) system with asymmetric impedance. Neither the balanced current control nor the instantaneous power control can cope with the second harmonic dc bus voltage pulsation and the second harmonic torque ripple simultaneously in an asymmetric PMSG system. In this paper, the average power control is employed and only the positive sequence currents appear in the system, thus the second harmonic torque ripple will be avoided with balanced back electromagnetic forces. The second harmonic power and dc link voltage pulsations are then reduced by a compensation unit in parallel with dc bus diverting the second harmonic power. The effectiveness of the proposed method is verified through a small-scale wind turbine PMSG prototype with inherent asymmetry and deliberately introduced asymmetries.

Magnetic Gear: Radial Force, Cogging Torque, Skewing, and Optimization

Magnetic gears are able to transmit torque between an input and an output shaft without mechanical contact. As for electrical drives, torque density, acoustic noise, and torque ripple are of primary concern. This paper describes the influence of the pole numbers on the radial forces and the cogging torques. We show how continuous and discrete skewing can suppress torque harmonics effectively. Further, we investigated different simulation modes for magnetic gears using finite-element software. A multiobjective optimization was conducted to find a Pareto-optimal magnetic gear, whose cogging torque was minimized by skewing one rotor. Finally, we present a prototype with a gear ratio of 1:21, and compare finite-element results with the measurements of unskewed and skewed magnetic gears.

Model Predictive Torque Control for Torque Ripple Compensation in Variable-Speed PMSMs

This paper presents a new and simple finite-control set model predictive control strategy to reduce the torque ripple in permanent-magnet synchronous machines (PMSMs). The method is based on minimizing a cost function that considers the flux linkage torque harmonics obtained from a discrete-time model of the machine. The power converter switching state that minimizes this cost function is selected and applied during a whole sampling period. Additionally, it is proposed to mitigate the other source of torque ripple, known as cogging-torque, using a feed-forward signal applied to the torque control loop. A hybrid method that uses the output information from an observer and look-up table is presented to obtain a good cogging-torque estimation and thus an accurate mitigation of this disturbance torque at low rotational speed. Experimental results demonstrate the good performance of the torque ripple compensation methods presented in this paper.

Computationally Efficient Method for Identifying Manufacturing Induced Rotor and Stator Misalignment in Permanent Magnet Brushless Machines

A computationally efficient method is presented to investigate additional cogging torque harmonics resulting from misalignment of the rotor and stator caused by assembly and manufacturing tolerances in an axial flux fractional pitch permanent magnet synchronous machine (PMSM). The superposition method creates a complete cogging torque profile by using a library of pole transitions over a single stator slot. The method extends previously published work, and is used to predict the effect of eccentricity misalignment in combination with pole and slot placement inaccuracies on cogging torque. Experimental data are presented supporting the superposition data indicating that static and dynamic eccentricity produce first- and second-order sidebands about the rotor and stator affected harmonics, respectively. There is good agreement between the hybrid superposition method, FEA, and measured experimental data.

Cage-rotor induction motor inter-turn short circuit fault detection with and without saturation effect by MEC model

The inter-turn short fault for the Cage-Rotor-Induction-Machine (CRIM) is studied in this paper and its local saturation is taken into account. However, in order to observe the exact behavior of machine, the Magnetic-Equivalent-Circuit (MEC) and nonlinear B–H curve are proposed to provide an insight into the machine model and saturation effect respectively. The electrical machines are generally operated near to their saturation zone due to some design necessities. Hence, when the machine is exposed to a fault such as short circuit or eccentricities, it is operated within its saturation zone and thus, time and space harmonics are integrated and as a result, current and torque harmonics are generated which the phenomenon cannot be explored when saturation is dismissed. Nonetheless, inter-turn short circuit may lead to local saturation and this occurrence is studied in this paper using MEC model. In order to achieve the mentioned objectives, two and also four-pole machines are modeled as two samples and the machines performances are analyzed in healthy and faulty cases with and without saturation effect. A novel strategy is proposed to precisely detect inter-turn short circuit fault according to the stator׳s lines current signatures and the accuracy of the proposed method is verified by experimental results.

UPSC SVPWM controlled multi‐level inverter topology for multiple pole‐pair induction motor drive for minimising torque ripple

The demand for multi-level inverters is increasing progressively in motor control applications. Many pulse width modulation (PWM) techniques are proposed in the literature and one of the popular modulation methods is unipolar phase shifted carrier (UPSC) PWM. This PWM technique is commonly used in uninterrupted power supply applications where transformer multiple primary windings are connected to two-level inverters. However, this modulation technique is not popularly used in drives applications because a conventional induction motor consists of only two terminals per phase. In this study, a multi-level inverter configuration for four pole induction motor drive is presented, where it is compatible to use the above mentioned PWM technique. By using this multi-level inverter configuration and UPSC PWM technique, all lower order harmonics are shifted to four times the switching frequency, which in turn reduces the torque ripple considerably. The proposed concept is tested on 5hp four-pole induction motor in MATLAB/Simulink and finite element analysis and is also experimentally verified with a laboratory prototype. The simulation and experimental results show the effectiveness of the proposed topology and demonstrate the improvement in harmonic profile and torque ripple.

Analysis of the dynamic performance of a variable-frequency induction motor drive using various control structures and algorithms

A comparative analysis of the dynamic characteristics of field-oriented induction motor drive control systems relying on the main magnetic flux linkage vector reference, space-vector pulse width modulation (SVPWM) of the voltage inverter output, and direct torque control (DTC) is carried out using the Matlab/Simulink program package, with the parameters of the induction motor model used being the same. A changeover from stepless vector control systems to systems using microprocessors and modern controllable frequency converters operating on the principle of relay control entails possible changes in the properties of the electric drives being controlled. In this connection, there is a need to compare the dynamic performance characteristics of an electric drive with a slave vector control system (with an idealized frequency converter), referred to as electric drive 1 (ED1), an electric drive with a DTC system (ED2), and an electric drive using direct torque control and SVPWM (ED3). Modeling has shown that the response time of the torque control loop in all the control systems considered is the same, the time delay being no more than 0.01 s. On the whole, speed control transients in all of the above systems take their course in one and the same way. The differences in flux linkage control transients between ED2 and ED3, on the one hand, and ED1, on the other hand, are due to the differences between the methods used to form the electromagnetic torque. No provision is made in the above control systems for the stabilization of the magnitude of the flux linkage vector. At low loads, the flux linkage automatically follows the load. In an ED3 with direct torque control, the calculation of the necessary instant magnitudes of the voltage vector projections and the SVPWM based formation of the voltages applied to the motor allows implementation of a fast-response control system with minimal harmonic distortions and torque pulsations. The control system coefficients are calculated beforehand. The speed controller is adjusted to the technical optimum. In the main flux linkage oriented control system, it is also desirable to use an SVPWM-based formation of the motor voltage.

Theoretical and Experimental Evaluation of Pulsating Torque Produced by Induction Motor Drives Controlled With Advanced Bus-Clamping Pulsewidth Modulation

This paper investigates possible reduction of pulsating torque in open-loop and vector-controlled induction motor drives through deployment of certain advanced bus-clamping pulsewidth modulation (ABCPWM) method. Toward this goal, a simple and machine-independent method is proposed to analyze the torque harmonic spectrum of a voltage source inverter fed induction motor, operated with any real-time pulsewidth modulation (PWM) method. The analytically evaluated torque harmonic spectra, pertaining to conventional space vector PWM (CSVPWM), bus-clamping PWM (BCPWM), and ABCPWM, are validated through simulation and experimental results. Theoretical and experimental studies bring out the superiority of the ABCPWM in terms of torque harmonics over CSVPWM and BCPWM. The magnitude of the dominant torque harmonic with the ABCPWM scheme is shown to be significantly lower than that with CSVPWM, over a wide range of speed. The rms torque ripple (i.e., total rms value of all harmonic torques) is lower with ABCPWM than with BCPWM over the entire range of speed.

Parametric investigation for rigid circular foundations undergoing vertical and torsional vibrations

This study derives the vertical and torsional responses of a rigid circular foundation resting on unbounded soil. The rigid foundation is subjected to vertical incident P-waves, torsional incident waves, vertical harmonic forces, and harmonic torques, respectively. The solutions of the proposed method are found to agree well with existing solutions of previous research. Results of dimensionless parameter analysis show that the vertical response of the rigid surface foundation can be simplified to a function of the Poisson ratio, the dimensionless frequency and mass ratio, and that the torsional response can be further simplified to a function of dimensionless frequency and mass ratio. As the dimensionless mass ratio increases, the vertical and torsional responses increase at low frequencies but decrease at high frequencies, while the fundamental frequency of the foundation-soil system also decreases. As the Poisson ratio increases, the vertical response increases at low frequencies but increases at high frequencies, while the fundamental frequency of the system increases. As the damping ratio of the viscoelastic half-space increases, the vertical and torsional responses rapidly decrease, and the fundamental frequency of the system slightly decreases. The study found significant characteristics of dynamic responses for the foundation undergoing vertical and torsional vibrations, which can provide helpful physical insights for foundation designs.

Inter-turn short-circuit fault detection in saturable squirrel-cage induction motor using magnetic equivalent circuit model

Purpose – The purpose of this paper is to obtain an integrated method for inter-turn short circuit fault detection for the cage-rotor induction machine (CRIM) considering saturation effect. Design/methodology/approach – The magnetic equivalent circuit (MEC) is proposed for machine modeling and nonlinear B-H curve is considered for saturation effect. The machine has some differential equations which are converted to algebraic type by trapezoidal method. On the other hand, some nonlinear equations are present due to saturation effect. A set of nonlinear algebraic equation should be solved by numerical method. Therefore, the Newton-Raphson technique is used for equation solving during of the considered time step. Findings – Generally, the operating point of electrical machines is close to the saturation zone due to designing considerations. Moreover, some current and torque harmonics will be produced due to time and space harmonics combination, which cannot be studied when saturation modeling is neglected. Considering both space and time harmonics, a method is proposed for inter-turn short circuit fault detection based on the stator current signatures and the machine performance is analyzed in healthy and faulty cases. In order to obtain the integrated method, two sample machines (two and also four-pole machines) are modeled and finally the accuracy of the proposed method is verified through the experimental results. Research limitations/implications – The calculations have been done in this work is limited to CRIM considering. However, the presented modeling method can be used for another types of electrical machines by some minor modifications. Originality/value – Obtaining of an integrated formula for the inter-turn short circuit fault detection which has been presented for first time is the more advantages of present work. Moreover, in order to saturation effect considering, a new method is presented for solving of nonlinear equations which is another novelty of paper.

Modeling and Analysis of Variable Frequency Inverted Sine PWM Technique for a Hybrid Cascaded Multilevel Inverter

In cascaded H-bridge multilevel inverter, a variable frequency inverted sine PWM technique is modeled for hybrid electric vehicles. It has a particular advantage of increasing power which is achieved using series connection of H-bridge and also this topology is capable to produce superior spectral quality with considerable improvement of fundamental voltage. The variable frequency inverted sine PWM technique produces lesser torque ripple and enhances the fundamental output voltage mainly at lower modulation index ranges. The topologies of multilevel inverter are flying capacitor, diode clamped and cascaded inverter. In the paper, we will discuss about the cascaded multilevel inverter based on inverted sine PWM technique. The two switching strategies widely used to control multilevel inverters are constant frequency inverted sine PWM (CF-ISPWM) and variable frequency inverted sine PWM (VF-ISPWM). This implies that switch utilization substantially reduces 32.35% of the constant frequency inverted sine PWM switching technique. The performance of the technique is validated in terms of Total Harmonic Distortion (THD) and Torque ripple which significantly reduces when compared to constant frequency ISPWM. The analysis of conventional triangular PWM inverter and inverted sine PWM inverter using constant and variable switching scheme is done in MATLAB Simulink and verified experimentally by FPGA Spartan 3E processor.

Minimization of Torque Ripple in PMBLDC Motor using different PWM Techniques based Variable Frequency Drives

In this paper, torque ripple minimization for high performance of Indirect Field Oriented Control (IFOC) of multi level based five phase PMBLDC motor is presented. The independent control of stator flux, position, speed and electromagnetic torque based on hysteresis control as employed in conventional DTC and FOC are applied to retain the simplicity and provide quick instantaneous control. The decoupling control between the rotor flux and the torque is no longer achieved in terms of stator current component this paper introduces a decoupled rotor flux and torque control based on the reference generation of magnetizing current components by incorporating PI control system and using space vector (SVPWM) technique. It is able to perform high performance IFOC control in BLDC drives using SVM technique. The various PWM techniques based variable frequency controller (VFC) for minimization of torque ripples are considered and discussed. This paper proposes the five levels based five phase inverter with reference current generation techniques to reduce the harmonic distortion and torque ripple. The Total Harmonic Distortion (THD) is evaluated based on Fast Fourier Transformation (FFT) analysis for torque ripple minimization. The proposed controller and simulation results are discussed with a comparative study in different PWM techniques based variable frequency strategies of PMBLDC drive. A simulation model has been built using MATLAB/SIMULINK and also to investigate the proposed system under different PWM Techniques.

PMSMのための簡易高品質トルク制御

This paper proposes a new and simple torque-sensorless torque control method for permanent-magnet synchronous motors (PMSMs) with nonsinusoidal Back EMF. The method suppresses the sixth and/or 12th harmonic torque ripples caused by the back EMF in a feedforward manner even at high speeds; it consists of two subordinate methods for compensation command generation and command-tracking current control. The first subordinate method generates compensation current commands to cancel the torque ripples based on a mathematical model of PMSMs. The second controls the stator current to track a current command containing both fundamental and compensatory components. In conjunction with the current control, a dedicated disturbance observer that employs a digital speed-varying band-pass filter as a disturbance filter is also proposed. The effectiveness and usefulness of the proposed method were verified through extensive experiments.

Обеспечение электромеханической совместимости в частотно-регулируемых асинхронных электроприводах при регулировании частоты ШИМ

Provision of electromechanical compatibility of asynchronous drive is considered. A computer drive model has been developed to investigate electromechanical processes in systems with PWM-inventors and asynchronous motors. Model calculations show that continuous change in the reference voltage frequency enables a multiple decrease of the amplitude of higher harmonics and electromagnetic torque with constant distortion factor. Vibrations of the electric drive may be decreased due to the reduced amplitudes of the torque harmonics. Motor losses change insignificantly. Variation of the reference voltage frequency within the given range should not to be implemented with frequency of motor supply currents.