Variable Flux Reluctance Machines Research Articles

Torque Ripple Suppression in the 6/4 Variable Flux Reluctance Machine with Open Winding Configuration by Using Harmonic Injection

High torque ripple can be observed with a 6/4 variable flux reluctance machine (VFRM). In order to minimize the torque ripple in VFRMs, this paper presents a harmonic injection method for 6/4 VFRMs with an open-winding configuration. By analyzing the impact of harmonics on VFRMs, the method involves detecting the third harmonic using a first-order low-pass filter (FLPF). Subsequently, the extracted harmonics are controlled and shifted to counteract the voltage harmonics in both inverters without inducing phase imbalance or overvoltage. With the proposed method, the torque ripple can be significantly reduced by about 50% under load conditions. The effectiveness of the harmonic injection method is validated through a prototype VFRM.

Influence of DC-Field Current on Short-Circuit Current in Variable Flux Reluctance Machine

DC-field windings of variable flux reluctance machine are wound on the same teeth with armature winding, which increases the short-circuit probability among the armature and field windings. Therefore, in this article, the various short-circuit faults of single phase, phase-to-phase, single field and phase-to-field are illustrated, and the influence of dc-field current on short-circuit current (SCC) and braking torque (BT) with consideration of initial rotor position are investigated. The SCC with dc-field current is analytically established, where the SCC and BT in transient and steady states are analyzed. The maximum SCC and BT are comprehensively compared by finite element method. It is found that the influence of dc-field current on the SCC and BT under transient conditions can be neglected. However, when the machine under un-saturated conditions, the SCC in steady states is associated with the saturation of iron core, i.e., the more saturated of the core excited by dc-field current in prefault, the smaller of the SSC in post fault. Both the SCC and BT are accompanied by the 12/14-pole VFRM prototype experimental verification.

Diagnosis of Open-Circuit Faults in DC-Field Excited Variable Flux Reluctance Machine Utilizing Armature and Field Currents

More electric aircraft has high reliability requirements, and the DC-field excited modular variable flux reluctance machine (MVFRM) is its key component. The MVFRM has both armature and field windings, in which AC (alternating currents) and DC (direct currents) are supplied. Hence, traditional fault diagnosis is not applicable for MVFRM. In this paper, the diagnostic methodology for open-circuit faults in both windings is proposed by utilizing armature currents and field currents. Based on the internal relationship between the armature currents with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> -axis currents and the field currents, the characteristics and diagnosis mechanisms of armature winding and field winding open-circuit faults are analyzed. The per-unit threshold setting method is adopted to improve the rapidity of the algorithm without reducing robustness. The rapidity and effectiveness of the fault diagnosis algorithm are verified by different types of open-circuit fault diagnosis experiments. Furthermore, the robustness of the fault diagnosis algorithm is verified by the variable speed and different loads of open-circuit fault diagnosis experiments.

Analysis and Preliminary Design of Variable Flux Reluctance Machines: A Perspective from Working Field Harmonics

Variable flux reluctance machines (VFRMs) are increasingly attracting research interest due to their magnetless and robust brushless structure. Under the modulation effect of the airgap permeance, the VFRM operates with a series of field harmonics, distinguishing it from conventional AC synchronous machines. This paper deals with the analysis and preliminary design of the VFRM from the perspective of multiple working airgap field harmonics. Firstly, the spatial and temporal order of the working field harmonics are defined. The systematic winding theory, including the unified star of slots and winding factor calculation method, is established to consider all these working harmonics. Then, an average torque model is built and simplified. The key role of 1st-order rotor permeance, 1st- and 3rd-order polarized stator permeance is deduced. The relationship between key parameters and average torque is computed, providing a guideline for the preliminary design of the VFRM.

Advanced Diagnosis of Armature Winding Short-Circuit Faults in Variable Flux Reluctance Machines Using Information Fusion on Mechanical and Electrical Signals

Advanced Diagnosis of Armature Winding Short-Circuit Faults in Variable Flux Reluctance Machines Using Information Fusion on Mechanical and Electrical Signals

Novel Harmonic Current Controller for DC-Biased Vernier Reluctance Machines Based on Virtual Winding

Direct current-biased vernier reluctance machine (DC-biased VRM) adopts a doubly salient structure and sinusoidal phase currents. It has better performance than switched reluctance machines and variable flux reluctance machines. The back electromotive force (EMF) waveforms of DC-biased VRMs contain low-order harmonics. It leads to harmonic currents in phase windings. The current harmonics increase the losses and worsen controller performance. The suppression of current harmonics has become a hot research topic in literatures. However, the existing harmonic suppression methods have their inherent defects. In this paper, a novel harmonic current controller based on virtual winding is proposed. Harmonic currents are decoupled and transformed into different harmonic planes, and independent closed-loop control is realized. The characteristics of harmonic planes and the relationship between them are analyzed. According to the analysis, the method of choosing valid planes and harmonic distribution is introduced. The major advantage of the proposed method is that, harmonic current sampling and control can be realized without the use of filters, and it avoids complicated design of controller parameters. Experimental results based on a DC-biased VRM are presented. It verifies that the proposed current control strategy based on virtual winding shows excellent harmonic control performance.

Zero Sequence Voltage Modulation Strategy of Variable Flux Reluctance Machine Based on Single Leg Excitation Control

Conventionally, the variable flux reluctance machines (VFRMs) are controlled by armature current and field current, which can be generated through a separated H-bridge. However, high switching losses in the H-bridge are not avoidable. To reduce the switching losses and improve efficiency, a VFRM control system based on single-leg excitation control is proposed. The field winding of VFRM is connected to the neutral point of armature winding by using single-leg to utilize the zero-sequence current as the DC excitation. A novel zero sequence voltage modulation technique is developed to generate the equivalent DC field excitation, i.e., the DC bias in the current of the armature winding. Compared with the separated DC field excitation, lower copper losses and higher efficiency can be obtained. Finally, experimental results on a prototype VFRM are presented for verification.

Comparative Study of Linear Variable Flux Reluctance Machine with Linear Wound Field Flux Reversal Machine

As members of doubly salient magnetless linear machines, linear variable flux reluctance (LVFR) and wound field flux reversal (LWFFR) machines inherit the merits of conventional magnetless linear machines such as low cost, high flux adjustment capability and high reliability. Furthermore, like linear switched reluctance machine, they have a very simple and compact long secondary, which are very attractive for long stroke applications. However, low force capability is their major defect. To solve this issue, new LVFR and LWFFR machine topologies were proposed in recent work, while lacking studies on their force improvement mechanism and further force evaluation. In this paper, LVFR and LWFFR machines with improved force performance are comparatively studied with the emphasis on their force capabilities. The operation principle of the two machines is analyzed based on magnetic field harmonics produced by flux modulation. Contributions of air-gap flux density harmonic components to no-load back electromagnetic forces of the two machines are analyzed and the average force equation is derived. Moreover, force capabilities of the both machines are investigated by means of the time-stepping finite-element analysis to verify the theoretical analysis.

Parameter Identification of Variable Flux Reluctance Machines Excited by Zero-Sequence Current Accounting for Inverter Nonlinearity

To identify the parameters of variable flux reluctance machines (VFRMs), the input voltage value is usually obtained from the reference voltage indirectly. However, the reference and actual voltages may be different due to the nonlinearity of the open winding inverter when using zero-sequence current, leading to the inaccuracy of parameter identification. To solve this problem, this paper proposes an equivalent nonlinearity voltage error model of the open winding inverter to compensate for the input voltage of VFRM during the online parameter identification. Since in the proposed method the phase current direction is not required, the calculation time can be reduced. Moreover, in the developed parameter identification model of VFRM the derived equivalent nonlinear voltage error is used to correct the input of the identification model so as to improve the accuracy of parameters. Finally, the experimental results on the prototype VFRM are presented for verification.

Fault-Tolerant Operation of DC-Field Excited Modular Variable Flux Reluctance Machine Under Open-Circuit Faults

Dc-field excited modular variable flux reluctance machines (VFRM) are passive salient-pole rotor and independent stator winding, which makes it suitable for aerospace applications. Fault-tolerant operation is commonly required to improve its reliability. Hence, the performance under winding open-circuit faults is analyzed and the fault-tolerant control strategy is presented to increase the output capacity in this article. First, the dc-rectified output voltages and power of the VFRM under both normal and open-circuit faults are derived. Then, phase angle control strategy of the fault-tolerant operation for a 12-slot-14-rotor-pole (12s14r) modular VFRM is proposed, where the control sequence is optimized to achieve the maximum output power of the generation system. Compared with the classical fault-tolerant method, a higher applicability of the proposed method in terms of the types of fault-tolerant operations can be achieved. The electromagnetic properties, including the armature current and the capacity of electrical power output, are analyzed with finite-element analysis. The effectiveness and feasibility of the proposed fault-topology and control strategy are verified by the 12s14r VFRM prototype in normal, fault, and fault-tolerant operation.

Characteristic analysis and diagnosis of short-circuit fault in armature winding of four-phase variable flux reluctance machine

Characteristic analysis and diagnosis of short-circuit fault in armature winding of four-phase variable flux reluctance machine

Flux-Weakening Control for Variable Flux Reluctance Machine Considering the Second Order Harmonic in Phase Voltage

Due to the second order harmonic in the phase voltage, the voltage peak value is much higher than the amplitude of its fundamental component in the 6/4 variable flux reluctance machines (VFRMs). Conventionally, the amplitude of the fundamental component in the phase voltage is used to calculate the voltage constraint in flux-weakening control, which results in a large voltage margin and reduces the DC link voltage utilization. To deal with this problem in the VFRMs, the flux-weakening control considering the second order harmonic of the phase voltage is proposed in this paper. In this method, the voltage peak value is used to calculate the current operating points, by using which the maximum voltage utilization in flux-weakening region can be achieved. It shows by using the proposed method a wider the constant torque region owing to the lower voltage margin in the VFRMs, which exhibits higher power output in flux-weakening region. Finally, the method is verified by the test results in the VFRM.

Permanent magnet-assisted variable reluctance machines: An analysis of the working mechanism and characteristics

<p indent=0mm>Variable flux reluctance (VFR) machines are very reliable and have a wide field-regulation range, but their torque density is low due to the absence of a permanent magnet (PM). Therefore, in this paper, a PM-assisted VFR (PMa-VFR) machine is proposed, and, focusing on the operation mechanism of the PMa-VFR machine, the air-gap flux density values for field winding, PM winding, and armature winding are deduced. The matching rule of various harmonics under magnetic-field modulation is revealed, and the action mechanism behind field winding and PM excitations with respect to influencing torque are explored. Then, the contribution of each working harmonic to the torque is obtained by Maxwell’s stress tensor method. Finally, a prototype is developed, and the operation mechanism and theoretical analysis are verified by experiments.

A New Loop-Based Hybrid Analytical Modeling Formulation and the Selection of Its Nonlinear Solver

This article presents a comprehensive comparative study between two nonlinear solvers for the hybrid analytical modeling (HAM) formulation. The Newton-Raphson method (NRM) and the fixed-point method (FPM) are compared in terms of their convergence rate, computational time, and accuracy. A new HAM formulation using the loop-based magnetic equivalent circuit (MEC) instead of the node-based one is proposed to improve the convergence and condition number. The loop-based formulation is coupled with both NRM and FPM nonlinear solvers to perform the magnetostatic analysis of a 12/10 variable flux reluctance machine (VFRM) under local magnetic saturation. It is shown that both methods can achieve convergence for various saturation levels, mesh, and harmonic refinements. However, FPM exhibits a 0.4 larger convergence rate than NRM. It is also observed that the accuracy of NRM decreases under deep magnetic saturation, and the number of required iterations of NRM increases with the model refinement. However, FPM is able to converge for all analyzed refinements with less than six iterations.

Effects of DC-Field Excitation on the Incremental Inductance of a Variable Flux Reluctance Machine

This article presents a method for the computation of the incremental inductances in a 12/10 variable flux reluctance machine (VFRM) using the hybrid analytical modeling coupled with a fixed-point nonlinear solver. The variation of incremental and apparent inductance with respect to the dc-field excitation is investigated for both zero and non-zero ac-field excitations. The results show that the difference between both inductance values is not negligible after 25 A/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> dc-current density for the investigated benchmark without the ac field. Moreover, when a non-zero ac field is introduced in addition to the dc-field, the apparent inductance becomes misleading not only under magnetic saturation but also under low excitation in the linear region of the saturation curve. The results obtained with the proposed nonlinear hybrid model are compared with the finite element method in terms of magnetic flux density distribution and incremental inductance value. The root-mean-square discrepancy of magnetic flux density distribution is found to be 37.6 mT. Furthermore, the discrepancy between incremental inductance results of the proposed method and the finite element model is calculated as 1.43%, while the proposed approach requires less post-processing and necessitates ten times less number of degrees-of-freedom.

Analysis of Split-Tooth Stator Slot PM Machine

In this article, split-tooth stator slot permanent magnet (PM) machines, which have high fault-tolerant capability, are proposed. Compared with the existing 12-slot 10-pole (12S10P) stator slot PM machine, the torque can be improved by 66% by properly choosing the split tooth number and other geometric parameters. It is found that two split teeth stator slot PM machine (ST2) shows the best torque characteristics among the stator slot PM machines with different split tooth number. To further illustrate the merits and demerits of ST2, a conventional 6S4P surface mounted PM machine (SPMM) and a 6S4P variable flux reluctance machine serve as the benchmarks to compare with the 6S11P ST2, at both open circuit condition and load condition. The 6S11P ST2 shows 68% higher torque over the 6S4P VFRM. Although the torque of the 6S11P ST2 is around half of the 6S4P SPMM, the former has 70% higher torque per PM volume than the latter. Furthermore, demagnetization analyses under three-phase short-circuit and pure d-axis currents show that the 6S11P ST2 has much better demagnetization withstand capability over the 6S4P SPMM. A Prototype is manufactured and tested to validate the theoretical analyses.

DC-Field Excitation Variable Flux Reluctance Starter Generator With Modular Structure for Fault-Tolerant Capability Improvement

In this article, a variable flux reluctance machine (VFRM) with dc field excitation and modular structure is proposed and it exhibits controllable flux, simplified manufacture, better fault tolerant capability, and potentially reduced material consumption. Its operational theory is illustrated by using flux modulation principles, and the working harmonics considering the modular structure are analyzed. Besides, the winding factors of modular VFRM are derived considering the flux gap width. The parameters are optimized by two-dimensional finite element method to maximize the back electromotive force (back-EMF) and the ratio of phase self-inductance to mutual inductance. Moreover, the electromagnetic performance including open circuit air-gap flux distributions, open circuit air-gap flux densities, flux linkage, back-EMF, inductance of armature windings, output characteristics, loss, power factor, and efficiency-map are compared for 12s10r and 12s14r nonmodular and modular VFRM. Additionally, the fault including short circuit and open circuit fault are analyzed. Finally, a modular 12s14r VFRM prototype is manufactured and tested to validate the theoretical and finite-element analyses.

Flux-Weakening Control for Variable Flux Reluctance Machine Excited by Zero-Sequence Current Considering Zero-Sequence Resistive Voltage Drop

In the control of variable flux reluctance machine (VFRM) excited by zero-sequence current, neglecting the zero-sequence resistive voltage drop would cause a large calculation deviation of the stator voltage, which can saturate the inverter and influence the switching from constant torque region to flux-weakening region. To solve with this problem, a flux-weakening control method considering the zero-sequence resistive voltage drop for VFRM is proposed. Firstly, the relationship between dq-axis voltages, zero-sequence voltage and the maximum voltage is presented. Secondly, based on the deduced voltage constraint, the calculation of optimal reference currents in flux-weakening region is presented by using Lagrange multiplier method. Since the zero-sequence voltage is considered, the calculation accuracy of the stator voltage and the utilization rate of DC link voltage are improved, which improves the output power capability. Finally, the proposed method is verified by the experimental results.

Feasible Stator/Rotor Pole Combinations of Variable Flux Reluctance Machines With Second Harmonic Current Injection Method

The second harmonic current injection method is recently developed to enhance the torque density of variable flux reluctance machines (VFRMs). This article investigates the feasibility and effectiveness of the second harmonic current injection method in VFRMs with different stator/rotor pole combinations. By using magnetic gearing effect, it is found that the second harmonic injection method can only be applied to the 6 j /(6 i ± 2) j ( i , j = 0, 1, 2…) stator/rotor pole VFRMs for the torque density enhancement. For the other stator/rotor pole combinations, the second harmonic current has no contribution in average torque production but only leads to excessive torque ripple. Further, by using global optimization method and finite element analysis, 6/8 stator/rotor pole combination is proved to be the optimal stator/rotor pole combination for 6-stator-slots VFRMs with the second harmonic current injection method, being able to exceed the maximal torque density of conventional VFRMs by 12% at a fixed copper loss.

Torque Density Enhancement of 6/4 Variable Flux Reluctance Machine With Second-Harmonic Current Injection

Variable flux reluctance machines (VFRMs) are developed as magnetless electrical machines. To extend the application of VFRMs, the enhancement of torque density is a key during machine design. In this paper, a novel second-harmonic current injection method is developed for torque density enhancement for 6-stator-slot/4-rotor-tooth (6/4) VFRM. By using the analytical method, the optimal current profile with injected second-harmonic current is obtained. The average torque of 6/4 VFRM is improved by 20% with the proposed method under all load conditions. Moreover, the proposed current profile has fixed harmonic proportions and is easily applicable to machines with different specifications. All the conclusions are confirmed by both finite-element analyses and experimental results.