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Propagation of baseband voltage and current harmonics. (a) Voltage and current of the VFD. (b) Motor's air-gap torque. (c) Campbell diagram resulting from VFD.
Source publication
This paper analytically investigates expressions of oscillating motor's air-gap torque resulting simultaneously from dynamic electromagnetic and dynamic mechanical components. The electromagnetic torque is generated in the air-gap when the motor is supplied by variable frequency drives (VFDs) such as pulse-width-modulated voltage source inverters,...
Contexts in source publication
Context 1
... simplified form is given as follows: Fig. 3 summarizes the propagation of electrical baseband harmonics to the motor coupling zone, producing characteristic torque harmonics. The dot in Fig. 3 represents a possible location where the natural frequency of the shaft might be excited. And, Fig. 4 shows a specific example of how the 6th, 12th, and 18th torque harmonics are created ...
Context 2
... simplified form is given as follows: Fig. 3 summarizes the propagation of electrical baseband harmonics to the motor coupling zone, producing characteristic torque harmonics. The dot in Fig. 3 represents a possible location where the natural frequency of the shaft might be excited. And, Fig. 4 shows a specific example of how the 6th, 12th, and 18th torque harmonics are created from the corresponding positive- and negative-sequence electrical harmonics. ...
Citations
... And a multi-stator winding machine; in this case, it is a twelvephase synchronous machine supplied by identical power converters [ figure 5b]. In this case, the airgap torque is the sum of all individual torque generated by the converter supplying each three-phase stator windings [42]. The investigated families of back-to-back power converter topologies are shown in figure 6. [45]. ...
... All other harmonic components are reduced. Consequently, the resulting torsional stress will see a cancellation or drastic reduction on its corresponding harmonics [15], [42]. ...
Despite consistent maintenance and monitoring equipment installed in pumped storage hydropower (PSH) facilities, many shafts and electrical component failures are reported, possibly resulting from undetected sources. These sources include undetectable vibrations or, in certain conditions, high-frequency mechanical or electrical harmonics. This paper presents a direct method for plotting Campbell diagrams of large motors supplied by variable frequency drives (VFDs) for torsional analysis purposes in PSH systems. These diagrams display the precise locations where torsional stress components induced by VFDs can interfere with shaft resonance modes. The method simplifies the determination of the magnitude of stimulus forces in the motor airgap that may threaten the shaft. The method has been successfully applied to two-level, three-level neutral-point clamped, and seven-level cascaded H-bridge multilevel inverters, which are commonly used industrially available VFD topologies for pumped PSH plants. The paper also discusses the theoretical motor-pump voltage, current, and torque spectra when driven by a cascaded H-bridge multilevel converter operating with bypassed and faulty cells. The accuracy of the theoretical developments is supported by selected simulations results at different operating points and different fault conditions.
Hybrid experimental-numerical VFD-induced harmonic stress analysis is also performed to demonstrate
the relevance of the proposed study.
... The hypothesis advocated in numerous scientific publications [6] [7] [8] is that various harmonics cause mechanical vibrations in the synchronous generator shaft as well as in the prime mover shaft. The various harmonics manifest as a pulsating electromagnetic torque as well as induce a voltage at the frequency of the harmonics in the generator rotor and more specifically in the excitation and damping coils. ...
... The pulsating torque, in turn, causes harmonics to appear in the current spectrum. These dependencies are very well explained in [6] [7] [8]. In this report, experimental confirmation of the theoretical formulation is shown. ...
Autonomous power supply systems are widespread in industry and households. Part of the electric transport vehicles and marine power supply systems are also autonomous systems. A characteristic of these systems is their operation with a load of comparable power. A major share of the load is on the controllable electric drive. Variable frequency drives are complex power electronics devices that draw non-sinusoidal current. This, in turn, leads to non-stationary electromagnetic processes and a complex situation in terms of electromagnetic compatibility. More in-depth research into the operation of autonomous synchronous generators is needed. The harmonics on the stator side of the synchronous generator cause mechanical vibrations in its shaft as well as in the prime mover shaft. In this study, the instantaneous values of the voltages and currents are experimentally measured in an autonomous power supply system with a synchronous reluctance motor equipped with a variable frequency drive. Based on these values, quantitative and qualitative indicators of electrical energy are determined, as well as the pulsating torques of the shafts of electrical machines are analyzed.
... This result is also evident because the voltage harmonics generated by each PWM method are converted to current harmonics through the motor impedance. In addition, it is to be noted that the pulsating torque components are created by voltage and current harmonics resulting from the PWM process of each method [19]. Finally, the comparison of motor, LL-voltage, and current THDs produced by the investigated PWM strategies at different values of fundamental frequency ranging from 35 to 60 Hz are summarized in Fig. 12. ...
Due to their numerous benefits, multi-modulation single-carrier pulse width modulation (MSC-PWM) approaches are becoming more prevalent in multilevel converter topology control systems. Compared to traditional multi-carrier PWM techniques, MSC-PWM methods present more straightforward real-time implementation, while achieving acceptable harmonic performances. However, their application remains limited to grid integration of photovoltaic converter systems, and no literature examines their suitability and effectiveness in multilevel converters supplying electrical machines. This paper uses the traditional and modified MSC-PWM methods to discuss the design and implementation of vector control for an induction motor fed by a multilevel cascaded H-bridge inverter. First, the vector control scheme is briefly introduced, and then each MSC-PWM method’s implementation scheme is thoroughly described. Then, the effectiveness of the investigated MSC-PWM methods is evaluated through steady-state and dynamic computer simulation results. Finally, a performance comparison of different PWM methods is conducted based on the spectra and THDs of the motor voltage, current, and electromagnetic torque. According to the comparison study, the modified MSC-PWM technique is superior to the conventional MSC-PWM method in reducing the motor voltage THD by up to 30%, motor current THD by up to 40%, and subsequently reducing the torque ripple in the motor air gap.
... Because of the decoupling effects of the DC-link capacitor, the current at the rectifier input can be simplified as (9) [13]. ...
... For this type of converter, it is also assumed that the grid and generator side dynamics are decoupled. Therefore, the generator current resulting from the pulse-width-modulation (PWM) commands of the rectifier is given in (12) [13], [14]. ...
... Consequently, the electromagnetic torque in the airgap can be expressed by (13) C ...
... As a result, they can threaten the equipment insulation in a very short time [17]. It is crucial to take necessary precautions to minimize the voltage and current harmonics generated by VFD topologies, as they combine in the machine's air gap, producing oscillating torque components, some of which may have high magnitudes [18]. If their frequencies are close to one of the shaft's eigenfrequencies, there is a risk of excitation of the shaft's ...
... As a result, they can threaten the equipment insulation in a very short time [17]. It is crucial to take necessary precautions to minimize the voltage and current harmonics generated by VFD topologies, as they combine in the machine's air gap, producing oscillating torque components, some of which may have high magnitudes [18]. If their frequencies are close to one of the shaft's eigenfrequencies, there is a risk of excitation of the shaft's eigenmodes, which could lead to mechanical shaft failures [19,20]. ...
This paper proposed a simplified modeling approach for a power quality (PQ) assessment of Electric Submersible Pumps (ESP) systems supplied by the two-level, the neutral-point-clamped three-level, and the cascaded H-bridge (CHB) multilevel inverter VFD topologies. The VFD switching function models and their analytical expressions are proposed to understand how they can create high-frequency components that might excite the resonance mode in a transmission cable or a rotating shaft system. Voltage, current, and motor airgap torque harmonics induced by each VFD topology in a balanced operation mode are derived and correlated to the PWM carrier and motor operating frequencies. The motor airgap harmonics are calculated based on Concordia's transformation of voltages and currents in αβ-plan. These harmonic components are represented in the form of Campbell diagrams. An analysis of harmonics under unbalanced conditions was also conducted in a CHB VFD topology-powered ESP system with failed and bypassed cells. The investigated modulation technique is a neutral-shift PWM method that enables the system to operate balanced line-line voltages even if the line-neutral voltages are unbalanced. The effects of modifying the electrical spectrum using the neutral-shift PWM method on electrical and mechanical spectra are analyzed. The results of the Matlab/Simulink-based simulation show that the proposed full ESP system model is highly accurate in both normal and failure modes. The results are consistent with theoretical predictions and are graphically shown in the time and frequency domains for easy analysis. Hybrid experimental-numerical results on a reduced-scale laboratory setup are also discussed to confirm the correctness of the suggested developments.
... The equipment needs to meet the high bandwidth and high-precision loading and measurement of a variety of different waveforms, including step signal, square wave, trapezoidal wave, and sine wave. The measurement error should not be higher than 0.5%, and the loading error should not be higher than 0.2% [11][12][13]. According to the above analysis, the key technical points of the transient performance test of the motor and driver mainly include the following two aspects: First, the loading function of any load curve, that is, it can provide step, sine wave, square wave, sawtooth wave, and even arbitrary waveform loading of torque or speed [14][15][16][17]. ...
In view of the problem that the traditional motor test system cannot directly test the transient parameters of the motor and the dynamic arbitrary load loading requirements during motor loading, as well as the high cost of implementation, this research uses STM32+FPGA as the core to form the main control of the motor test system unit, combining the superior control performance of the ARM processor and the high-speed data processing advantages of FPGA. FPGA and STM32 are controlled by the FSMC bus communication and data ping-pong algorithm. Using this method, a small-size control core board in the motor test system is manufactured. It can be embedded in the existing traditional dynamometer system to improve the dynamometer transient parameter test and the dynamic motor loading performance. The experimental results show that the system can basically meet the requirements of the motor transient test and dynamic loading, and can achieve the fastest data refresh rate of 1 ms when measuring the motor’s speed and torque, as well as arbitrary waveform loading within a 100 M sampling frequency, with a loading error of 0.8%. It satisfies the motor transient test and dynamic loading requirements.
... Han [21] established an electromechanical coupling model in openloop voltage to frequency control mode and calculated and analyzed the effect of factors such as multi-stage inverters on fatigue life. Song-Manguelle [22] considered pulsewidth modulation, inverters, while simplifying a dynamic mechanical load to a variable frequency drive containing harmonics, and investigated the interaction between electrical and mechanical harmonics. The above studies show that inverters have an important influence on the drive system when studying the dynamic characteristics of electromechanical coupling. ...
... In the dynamic characteristics analysis method, most scholars [12][13][14][15][16][17][18][19][20][21][22] mainly focus on the dynamics of electromechanical inter-coupling of systems in the steady state, and some scholars also study the dynamic characteristics of electromechanics under transient conditions for some electrical systems with transients [11] or sudden changes in mechanical loads [10,23]. However, for differential speed regulation systems, it is very basic and common for the variable frequency drive to produce smooth changes in the mechanical load. ...
... Therefore, it is necessary to carry out transient analysis of the start-up and speed regulation stages in addition to the study of the steady state characteristics of the differential speed regulation system. Some of the above-mentioned scholars [10][11][12][13][14][15][16] have studied the dynamic characteristics of motor-gear system coupling, while others [17][18][19][20][21][22] have analyzed the dynamic characteristics of inverter-motor coupling or invertermotor-pump coupling. These studies only consider part of the electromechanical drive system and do not provide a complete reflection of the overall coupling dynamic characteristics of the electromechanical coupling system. ...
The differential speed regulation system driven by inverters, motors and differential gear trains is a complex electromechanical system that achieves speed regulation and energy savings efficiently and economically. In this paper, the complete drive trains dynamic model of the differential speed regulation system with the inverter power supply-motor-differential gearbox-load is established. The inverter power supply considers constant voltage to frequency ratio control, sinusoidal pulse width modulation and inverter, the motors are modeled based on the equivalent circuit method, and the differential gear trains consider a lateral-torsional model with time-varying meshing stiffness and damping. The dynamic properties of the system are analyzed and compared with the variable frequency drive model considering inverter power supply and the direct drive model using ideal power supply under variable operation conditions. The results show that the variable frequency drive model varies more smoothly in the time domain and contains additional harmonic components in the frequency domain resulting from the coupling of the inverter triangle carrier frequency to the fundamental frequency of the power supply than the direct drive model. It also shows that the variable frequency drive model is a more realistic and rational model than the direct drive model. The complex coupling relationship can be seen in the inverter power supply-motor-differential gearbox-load system, where both inverter harmonics and mechanical meshing force harmonics are found in the dynamic response of the motor’s electromagnetic torque, rotor speed; the inverter harmonics are also reflected in the mechanical meshing force harmonics.
... As presented that source of ripple in torque is harmonics present in three-phase voltage source inverter which induces torsion of components and sometimes creates defects or even catastrophic failure of the transmission shaft . Manguelle et al. (2018) Shen et al. present vibration analysis of two stage gear system considering shaft crack into consideration to make system reliable (Shen et al. 2020). Hence, to make system power efficient and reliable, it is very important to analyse the torsional vibration and stresses induced due to harmonics in power supply and ripple in source torque. ...
... PMSM (M) is considered as first lumped element in the present system. S 1 shaft along with disc C 1 of claw coupler A as 2nd element, C 2 -S 2 -C 3 as 3rd, C 4 -S 3 as 4th and generator as 5th element respectively (Manjibhai et al. 2021). In this way, 5 degrees of freedom lumped system is established. ...
In recent years, the market of the brushless Permanent Magnet (PM) motors, such as Permanent Magnet Synchronous Motor (PMSM) and Brushless Direct Current Motor (BLDCM) drives, has become huge due to demand of the Electric Vehicles (EVs) and Hybrid Electric Vehicles (HEVs). However, brushless PM drives are less robust compared to other types of motor drives due to the high acoustic noise, vibrations, and de-magnetization risk of the PM (Chan. Proc IEEE 95:704–718, 2007; Report, Implementing Agreement for Co-operation on Hybrid and Electric Vehicle Technologies and Programmed. International Energy Agency, 2016). These shortcomings pose important restrictions for critical applications. Initially, to run PMSM, Sinusoidal Pulse Width Modulation (SPWM) is implemented. But this technique generates current harmonics and high torque ripples, which ultimately leads to Acoustic Noise and Vibration (ANV) in PMSM drive. Hence, for analysis purpose, a framework based on lumped model along with effective mass and mass participation factor technique for prediction of torsional vibration in case of SPWM technique is elaborated to show detailed methodology for vibration response caused by high torque ripples. This framework is generalized in a way that can be easily extended to any mechanical power transmission system having shaft-coupler or geared system especially for EV and HEV application. Also, vibration prediction modelling is integrated with optimum number of modes or degree of freedom selection technique, which help to enhance the accuracy of model along with computationally efficient, which is the novelty of present work, which usually researchers took earlier randomly based on their setup and mass distribution without any specific technical justification. The vibration analysis reveals high torsional twisting and untwisting of shaft in case of SPWM, because of high source torque ripple. Henceforth, a Random Pulse Width Modulation (RPWM) technique for reduction of ANV is discussed in this chapter. The proposed RPWM method brings a significant reduction in torque ripples which directly influence ANV in the motor, thereby enhancing the performance of the complete drive system under operation. The relationships between the stator current harmonics feed by drive and non-sinusoidal magnetic field flux distribution, with torque ripples is developed and detailed analysis is discussed in this chapter. An extensive simulation and experimental work are carried out on a 1.07- kW, 4-poles, 36-slots, 3-phase PMSM drive for validation of proposed control strategy. In the end, experimental validation part is presented for all analytical modelling and simulation results presented in this chapter.
... The flux is approximated as the time integral of the voltage. The voltage drops resulting from the stator impedance can be neglected because the stator impedance does not influence the location of torque components in the frequency domain; it only slightly modifies their magnitudes [34]. This model does not consider the air gap torque resulting from the process dynamic load. ...
... Process-induced mechanical torque components, such as gas slugs, are supplied to the shaft model as an externally controlled voltage source. These torque components may induce current pulsations flowing from the motor windings back to the VFD [34]. The air gap torque model is inserted between the electrical and mechanical subsystems such that it becomes easy to emulate the reversible propagation of electrical and mechanical harmonics. ...
... The air gap motor torque errors are slightly higher than the errors obtained for the other variables because the voltage drop caused by stator windings has been neglected when calculating the electromagnetic torque with the proposed approach. As discussed in Section III-C, the stator impedance does not influence the location of torque components in the frequency domain; it only slightly modifies their magnitudes [34]. Finally, it can be concluded that the proposed model is a simple and accurate computer tool to simulate the steady-state behavior of the ESP systems, regardless of the type of VFD topology involved. ...
This paper proposes a high-level engineering guide to develop an integrated system model for power quality analysis in electrical submersible pump (ESP) applications with variable frequency drives (VFDs). Such analyses are troublesome in industry due to the complexity of these systems. In this paper, simple steps to perform system integration analyses of such arrangements, including torsional analysis are developed. A simplified VFD-ESP model suitable for coupled electrical and mechanical analysis in steady-state is proposed in all their configurations of practical interest. Such a model can be easily implemented in common simulation softwares, significantly reducing engineering efforts for implementation and analysis. The focus of the proposed model is the prediction of ESP failures which might result from a poor power quality caused by VFDs. Analytical expressions of different types of harmonics in these systems, as well as their accurate locations in the frequency-domain, including their inter-harmonics and common-mode
harmonics are derived for this purpose. Effectiveness of the proposed model is verified through offline and real-time hybrid simulation results. Finally, a comparison between simulation results obtained using the proposed model and measurements collected on a down-scale laboratory prototype is carried out to demonstrate the accuracy of the suggested modeling approach.
... From the analytical point of view, it is to be noticed that all motor construction induced torque components are dependents on the machine speeds and can be classified as baseband harmonics, with frequencies proportional to the stator current and motor poles (i.e., motor speed), and magnitudes dependent on the machine construction [21]. ...
This paper proposes time-domain analytical expressions of the instantaneous pulsating torque components in a synchronous machine air gap when supplied by a load-commutated-inverter (LCI) system. The LCI technology is one of the most used variable frequency drives when very high power and low speed are required in applications such as pipeline recompression and decompression, as well as liquefied natural gas compression. In such applications, synchronous motors are used because of their high efficiency resulting from a separated supply of the current to their rotor through the excitation circuit. These applications usually have long and flexible shafts, which are very sensitive to torsional vibration excitation when their natural frequencies interact with any external torque applied to the shaft. A torsional analysis is required by international standards to assess the survivability of the shaft through the overall speed range of the motor. Therefore, the magnitude and frequencies of the motor air-gap torque are needed for such evaluation. The proposed developments are supported by numerical simulations of LCI systems in a large range of operation range. From the simulation results, torque harmonic families are derived and expressed in a parametric form, which confirm the accuracy of the proposed relationships.
