Harmonic Torque Research Articles

Investigation of Torque Production and Torque Ripple Reduction for Six-Stator/Seven-Rotor-Pole Variable Flux Reluctance Machines

This paper investigates the torque production and the torque ripple reduction of a six-stator/seven-rotor-pole (6/7) variable flux reluctance machine (VFRM). As a main advantage, the 6/7 VFRM produces higher torque density, but less torque ripple compared with the 6/4 VFRM. The instantaneous torque equation of the 6/7 VFRM is derived by considering the spectra of the winding inductance and current. Based on the derived equation, the average torque is found to be mainly produced by the mutual inductance between the field and armature windings. The even-order harmonics of self-inductance and odd-order harmonics in mutual inductance between the field and armature windings are eliminated due to the opposite polarity connection of the armature coils in each phase. This results in the elimination of the third harmonic torque ripple, while a multiple of the sixth harmonic torque ripple exists. In order to mitigate the sixth harmonic torque ripple, the harmonic current injection method is implemented into the field winding. The field harmonic current is calculated from the analytical torque ripple equation. The performance of the proposed methods is verified by both finite element analysis (FEA) and experiment.

Analysis of Stator Slots and Rotor Pole Pairs Combinations of Rotor-Permanent Magnet Flux-Switching Machines

This paper investigates the influence of stator slots and rotor pole pairs combinations on torque performances in rotor permanent magnet flux switching (RPM-FS) machines. Based on a magnetomotive force (MMF) permeance model, the candidates of stator slots and rotor pole pairs combinations with higher torque capability can be determined by analyzing the PM-MMF and winding factor. Meanwhile, the candidates with a lower torque ripple can be obtained by referring to the cogging torque, which is related to the greatest common divisor of stator slots and rotor pole pairs. In addition, from the field modulation principle, the RPM-FS machines with the same fundamental magnetic loadings and winding factors exhibit identical fundamental harmonic torque, but different modulation harmonic components. Finally, four candidates with attractive torque performance are chosen, and the characteristics are verified by finite-element analysis and experiments.

Design of Dual Skewed Rotor in Cage Induction Motor for Reducing Synchronous Parasitic Torque

Dual skewed rotor is an improved skewed rotor pattern in suppressing the slot harmonics. However, in order to lessen synchronous parasitic torque, the relevant structural parameters should be modified for different slot combinations. According to the unified expressions of magnetic flux densities, the general harmonic torque could be calculated with the virtual displacement method. Then, the synchronous torque ratio is proposed to reflect the effect of synchronous parasitic torque on the starting torque. Under the premise of the assumed parameter range, the rotor type and minimized skewed angle are determined for three kinds of slot combinations. The normal skewed rotor could be seen as a special topology of dual skewed rotor. Finally, the validity of designing process is verified by the comparison of simulation study and experimental results.

Cancelation of Torque Ripples in PMSM via a Novel Minimal Parameter Harmonic Flux Estimator

This paper presents a novel approach for treating the harmonic torque in permanent magnet motors at selected harmonic orders. The method is based on the online estimation of the motor harmonic flux. For this purpose, a novel minimal parameter harmonic flux estimator (MPHFE) is developed. The MPHFE is formulated such that the inductance, resistance, and stator current and its derivative are not necessary for the estimation of the harmonic flux. This was achieved by forcing the harmonic current to zero through the combined action of a field-oriented controller (FOC) and a feedforward controller. Subsequently, the harmonic flux can be obtained directly from the estimated harmonic back EMF without the involvement of other motor parameters. Finally, the estimated flux is used in conjunction with a comprehensive model of the motor harmonic torque to determine the stator current compensation for eliminating the torque harmonic. Experimental results presented from a permanent magnet motor confirm the theoretical claims in this paper as well as demonstrate the effectiveness of the proposed method to reduce the magnitude of the harmonic torque significantly.

Influence of motor harmonic torque on wheel wear in high-speed trains

With the increase of train speed, the harmonic torque of the traction motor of a high-speed train is not a negligible source of excitation. In order to explore the influence of the harmonic torque of the motor on wheel wear, a high-speed EMU vehicle model was established based on the multibody dynamics theory. FASTSIM was used to calculate the wear parameters, and the Zobory wear model was used to calculate the depth of the wheel wear. The influence of the harmonic torque of the motor on the wear parameters and wear depth of high-speed trains under straight and curve conditions is calculated, respectively. The simulation results show that the harmonic torque has a large influence on the wheel rail vertical force and the longitudinal creep force and has little influence on the lateral creep force. With the 30% harmonic torque, the wheel rail vertical force increases by 7.6%, the longitudinal creep force increases by 15%, and the lateral creep force increases by 4%. The amplitude of the longitudinal creepage increases by 14.2% when the harmonic torque is 10%, and increases by 34.4% when the harmonic torque is 30%. When the harmonic torque increases, the wheel wear depth increases, the 10% harmonic torque increases by 3% and the 30% harmonic torque increases by 8%, and the increase of the motor harmonic component accelerates the wheel wear. At the same time, small longitudinal positioning stiffness can help to reduce the influence of the harmonic torque, and the selection of the longitudinal positioning stiffness needs to consider the dynamic performance of the vehicle.

Analytical Evaluation and Reduction of Torque Harmonics in Induction Motor Drives Operated at Low Pulse Numbers

Induction motor drives operated with a low ratio of the switching frequency to the fundamental frequency (i.e., pulse number) are prone to have high magnitudes of low-order torque harmonics. This paper proposes a method to analytically evaluate the harmonic torque spectrum based on the pulsewidth-modulated voltage waveforms for low pulse number operation. The predicted torque harmonic spectra for different pulsewidth-modulated waveforms are validated through simulations and experiments. This paper also reports optimal switching angles to minimize the total rms value of torque harmonics of order 6, 12, 18 $,\dots,$ $6(N-1)$ , considering the number of switching angles per quarter ( $N$ ) to be 4 and 5. Compared to sine triangle pulsewidth modulation and selective harmonic elimination pulsewidth modulation with the same pulse number, the proposed optimal switching angles significantly reduce the total rms value of all harmonic torques of order lower than $6N$ . Extensive simulation and experimental results on a 3.7-kW induction motor drive are presented to demonstrate the superior performance of the proposed optimal pulsewidth modulation.

Analysis of generalized continual-clamp and split-clamp PWM schemes for induction motor drive

Continual-clamp pulse width modulation (CCPWM) clamps each phase of a three-phase inverter to one of the two dc buses continually for \(60^{\circ }\) duration in each half of the fundamental cycle. Split-clamp pulse width modulation (SCPWM) divides the \(60^{\circ }\) clamping interval into two sub-intervals, which are not necessarily equal, and falling in two different quarter cycles. Whether continual clamp or split clamp, the positioning of the clamping interval in case of CCPWM, and the ratio of splitting the clamping interval in SCPWM – all influence the waveform quality of the inverter output. This paper derives analytically closed-form expressions for the total RMS harmonic distortion factor and torque ripple factor pertaining to CCPWM with any arbitrary position of the clamping interval (i.e., generalized CCPWM) and also corresponding to SCPWM with any arbitrary ratio of splitting of the clamping interval (i.e., generalized SCPWM). The analytical results are well supported by experimental results on 3-hp and 5-hp induction motor drives.

Research on Vibration Characteristics and Stress Analysis of Gearbox Housing in High-Speed Trains

Gearbox housing in high-speed trains has two kinds of excitation sources: the internal excitation of gear mesh excitation and the external excitation that contains the wheel polygonization and the input torque. To study the effect of the torque on the vibration and stress of the gearbox housing, a multibody dynamic model is established by the Simpack, in which the elastic deformation of the wheelset and the gearbox housing are considered. A traction drive system is modeled by the MATLAB/Simulink to calculate the traction torque, which is transformed to drive the high-speed train to overcome the basic resistance and run with a constant speed. The accuracy of the model is verified by comparing the simulation results with the measurement results. Based on the electromechanical model, the vibration acceleration of the gearbox housing in the case of without torque, with ideal torque, and with harmonic torque is calculated and analyzed, as well as its dynamic stress. The results show that the traction torque plays a role in amplifying the vibration acceleration and dynamic stress. When the fatigue damage of the gearbox housing is calculated, it will obtain a more accurate result to consider the effect of the traction torque.

PMSG-based Wind Turbine Torque Harmonic Reduction Through LPV Control of EKF-Based Disturbance Estimation

Torque disturbance is imposed by the non-stationary wind profile, tower shadow, and wind shear propagate along the drive train to reach wind turbine generators. This is the main cause of several detrimental effects to several mechanical components specifically bearings, gearboxes, drive train, generators, etc. This paper applies Linear Parameter Varying (LPV) control technique based on harmonic estimation and torque reconstruction using the Extended Kalman filter for wind turbine torque ripple cancellation.

Suppression of Even-Order Harmonics and Torque Ripple in Outer Rotor Consequent-Pole PM Machine by Multilayer Winding

The fractional slot concentrated winding consequent pole (CP) permanent magnet (PM) synchronous machines can improve the PM utilization ratio. However, the even-order harmonics exist in phase back electromotive forces (EMFs) for specific slot and pole number combinations, resulting in high torque ripple. Therefore, the multilayer winding is employed in this paper to reduce the torque ripple by suppressing the even-order harmonic back EMFs. The principles of both even-order harmonic back EMFs and torque ripple suppression by the four-layer windings are illustrated. The electromagnetic characteristics of the CP PM machine with four-layer windings are compared with that of PM machines with the traditional and CP rotors by finite-element analysis. It is demonstrated that the four-layer winding can suppress the even-order harmonic back EMFs and torque ripple in the machine with CP rotor. The prototypes of both the traditional rotor and CP rotors with four-layer wingdings are manufactured and tested to verify the theoretical analysis.

Modeling for solar array drive assembly system and compensating for the rotating speed fluctuation

A dynamic model of the solar array drive assembly (SADA) system consisting of a stepper motor and two flexible solar arrays is investigated. The fluctuation compensation of the rotating speed and vibration suppression is studied by integrating the sliding mode control (SMC) method and input shaping (IS) technique. The dynamic equations of the system are derived by the Hamiltonian Principle. The linearized form of the nonlinear dynamic equations with boundaries conditions is adopted to obtain the natural frequencies and global modes of the solar arrays. Based on the electromechanical dynamics model of the stepper motor, a cooperative compensation scheme is designed to achieve the stability of solar arrays and the suppression of system vibration. Numerical results show that the driving speed is significantly influenced by the harmonic torque and the structural vibration of payload. The SMC method compensates for the rotating speed fluctuation much better than the pure feed-forward operation used in the traditional stepper motor. The system with SMC method and IS technique performs much better than the case without vibration suppression.

Cancellation of harmonic torque disturbance in permanent magnet synchronous motor drives by using an adaptive feedforward controller

The effects of disruptive harmonic torque disturbances on permanent magnet synchronous motor drives originating at the mechanical load or from cogging can be mitigated by producing a counteracting electric torque. The study proposes using an adaptive feedforward controller (AFC) for this purpose. The AFC is designed to operate as an auxiliary loop in parallel with a field-oriented controller, which provides speed control. The AFC input is the motor speed control error. The loop is tuned at the frequency of the harmonic torque and its output is added to the q -axis current reference as a variation current of the same frequency. The main advantage of the proposed method is that it does not require an estimation of the disturbance torque. The theoretical analysis of the scheme is presented in the study. Experimental results are also presented in the study from a motor drive system where the mechanical load produces harmonic torques. The results demonstrate the effectiveness of the AFC in significantly reducing speed oscillations by cancelling the effect of the torque harmonic disturbance.

A Nonlinear Analytical Model for the Rapid Prediction of the Torque of Synchronous Reluctance Machines

The synchronous reluctance motor works under heavy saturation. This paper presents a nonlinear analytical model of the reluctance machine, which is used to derive both average and torque harmonics as a function of the rotor geometry. Maps showing the torque harmonics as a function of the rotor barrier angles are derived. These maps are useful tools for the machine designer to get a proper rotor geometry. The torque maps are compared with those obtained from both linear analytical and finite element models. The maps computed analytically show good agreement with those derived by means of finite element analysis, and they are obtained in a much smaller computing time.

Planetary Gear Fault Detection Based on Mechanical Torque and Stator Current Signatures of a Wound Rotor Induction Generator

In this paper, an approach for tooth localized fault detection in the sun gear of a planetary gear, using the measured mechanical torque and the stator current of a wound rotor induction generator (WRIG), is proposed. A theoretical background is developed to demonstrate that the faulty sun gear produces periodic fault signatures in the mechanical torque and consequently fault-related frequencies in the stator current of the WRIG. The employed technique needs knowledge of mechanical system torsional natural frequencies, which aid in identifying the most sensitive fault characteristic harmonics in both mechanical torque and stator current spectra. It is illustrated by simulation and experimental results that the amplitude of these harmonics can be used as a fault index for diagnosis of tooth localized defect in planetary gears. A test rig based on a 5.5 kW WRIG, shaft connected to the sun gear of a planetary gear through a high-speed shaft and couplings, was utilized for validation of the proposed technique.

Effects to System Performance of Different PWM Techniques in Field Oriented Speed Control with back-to-back Converter of PMSG

In this paper, the performance of space vector pulse width modulation (SVPWM), sinusoidal pulse width modulation (SPWM) and hysteresis current control (HCC) techniques used in speed control with back to back converter of permanent magnet synchronous generator (PMSG) used in wind turbines are comparatively analyzed. The comparative analysis includes dynamic response, total harmonic distortion (THD), torque ripple and current ripple. Furthermore, SVPWM and SPWM are compared in terms of the using DC link voltage. Analysis of system is realized with MATLAB/Simulink program. PMSG used in simulations is surface mounted, bipolar and its power is 1.8 kW. Also, the energy of PMSG is transferred to grid with Field Oriented Control (FOC). According to analysis results, it has been observed that SVPWM generally has more effective results than both HCC and SPWM control techniques. Finally, it is observed that SVPWM can produce about 15 percent higher than SPWM in output voltage.

Optimisation of current harmonics for three‐level VSI based induction motor drive suitable for traction application

A method for minimisation of current harmonics spectrum for asynchronous traction motor fed from three-level neutral point clamped voltage-source inverter is described in this study. A selective harmonic elimination and mitigation-based algorithm using particle swarm optimisation has been utilised. Since the load is an induction motor suitable for traction application, a modified objective function with constraint of individual current harmonics has been proposed in this study to obtain improved harmonic elimination and control with low switching frequency. The proposed method has been compared with conventional technique considering only torque spectrum as objective function. Moreover, a suitable formulation for loss calculation has been proposed to optimise both the motor losses and torque harmonics. Suitable simulations along with experiments are performed with a practical induction motor of cage type to justify the proposed method.

Harmonics reduction in standalone DFIG-DC system by shunt active filter controlled in stator flux reference frame

The presence of diode rectifier in standalone Doubly Fed Induction Generator-Direct Current (DFIG-DC) system leads to considerable current, voltage and torque harmonics and requires reactive power from the machine. A unique shunt active filter arrangement is proposed for addressing these requirements. The DC Link of DFIG-DC itself acts as input to shunt active filter and there is no requirement of creating and regulating a separate one. Since the stator flux reference frame is known in FOC of DFIG-DC system; the same can be used as PLL for the generation of current references for harmonics and reactive compensation in active filter control scheme. Hence, the AC voltage sensing is not needed in the proposed active filter control. In this paper, it is shown that current, voltage and torque harmonics are reduced with the help of shunt active filter, which have lower rating compared to the rotor side converter. The proposed scheme is verified by detailed experiments on a 5.5 kW slip-ring induction machine.

Torque Ripple Minimization in Neutral-Point-Clamped Three-Level Inverter Fed Induction Motor Drives Operated at Low-Switching-Frequency

Neutral-point-clamped (NPC) multilevel inverter fed high power drives operating at low switching frequency are prone to low-order torque pulsations. For a case of $N$ switching angles per quarter, apart from maintaining the fundamental component, $(N-1)$ voltage harmonics can be eliminated. Consequently, ${\frac{N-1}{2}}$ or lower number of torque harmonics could be eliminated. This paper proposes an optimal pulse-width modulation (PWM), which minimizes the combined root mean square (RMS) value ( $\tau _{{\rm RMS}}$ ) of torque harmonics of order lower than $6N$ at any modulation index ( $M$ ) for an induction motor drive fed from an NPC three-level inverter. This paper considers cases of two, three, and four switching angles per quarter cycle of the pole voltage. Compared with synchronized sine-triangle PWM and selective harmonic elimination (SHE) PWM, the proposed PWM reduces the first ( $N-1$ ) torque harmonics (i.e., $\tau _6$ , $\tau _{12}, \ldots, \tau _{6(N-1)}$ ) over a wide speed range. Simulation and experimental results are presented on a 3.7-kW open-loop constant volts-per-Hertz induction motor drive.

Low‐noise design of fault‐tolerant flux‐switching permanent‐magnet machines

The high variable flux density in the air-gap of fault-tolerant flux-switching permanent-magnet (FT-FSPM) machine results in rich harmonics of the magnetic field, thus generating large vibration and noise. This study proposes two novel FT-FSPM machines which can effectively reduce the radial pressure, thus reducing the vibration and noise. First, the radial pressure of the initial FT-FSPM machine is analysed. Second, the novel proposed FT-FSPM machines are introduced and analysed. Third, the electromagnetic performance, including back electromotive force, output torque, inductance, and radial pressure harmonics, of the initial and the two proposed machines are compared by finite element method. Then, the vibration modes with corresponding natural frequencies are predicted. The vibration and noise are simulated by boundary element method. Finally, the effectiveness of the low-noise design is verified by measurement results.

Torque Harmonic Minimization for Load Commutated Inverters in Pulse Mode

This paper considers the operation of a load commutated inverter (LCI) fed synchronous machine when the stator voltage is too low to ensure commutation of the machine side thyristors. Under such low-voltage conditions, the LCI is operated in a so-called pulse mode, accompanied by higher drive torque harmonics than during standard operation. Following a theoretical analysis, an alternative pulse mode is proposed, describing how to operate the LCI during pulse mode in order to keep the excitation of the natural frequencies of the drive shaft at a minimum.