Three-phase Permanent-magnet Machines Research Articles

Open-Circuit Fault Diagnosis of Three-Phase Permanent Magnet Machine Utilizing Normalized Flux-Producing Current

In this paper, an open-circuit fault diagnostic method is proposed for three-phase permanent magnet machines. By individually applying inverse coordination transformation to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> - and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis currents, per-phase current can be decomposed into flux- and torque-producing currents. Their post-fault behaviors are found to be highly related with the fault types and locations. Hence, the normalized flux-producing current can be used as a single fault index to detect and identify both open-switch and open-phase faults. Since the established fault index is close to zero, the proposed fault diagnostic method is naturally robust to load/speed variations. In addition, a low decision threshold can be set to reduce fault diagnostic time. The robustness and effectiveness of the proposed method are verified by the experiments on one prototype.

Performance of a Dual Three-Phase Permanent Magnet Machine for a Steer-by-Wire System Under Healthy and Faulty Conditions

Performance of a Dual Three-Phase Permanent Magnet Machine for a Steer-by-Wire System Under Healthy and Faulty Conditions

Dual Three-Phase Permanent Magnet Synchronous Machines Vector Control Based on Triple Rotating Reference Frame

This paper presents a triple rotating coordinate transformed vector control method for dual three-phase permanent magnet (PM) machines. In the proposed scheme, the control variables are converted to three sets of αβ components directly, which are 120° electric degrees different from each other. It omits the complicated six-dimensional transformed matrix and reduces the computation greatly. The relationship with vector space (VSD) control was mathematically analyzed. By ensuring the consistency of control variables in the three stationary reference frames, the suggested method can not only achieve the same fundamental control performance as VSD but compensate for the imbalance current caused by the harmonics in the back electromotive force. In addition, the proposed method belongs to multi redundancy control in theory, which is maybe a good solution for fault-tolerant operation. Finally, a prototype dual three-phase PM machine was tested. The experimental results are in good agreement with the theoretical analysis.

Effect of Flux Barriers on Short-Circuit Current and Braking Torque in Dual Three-Phase PM Machine

This paper investigates the influence of stator flux barriers on the short-circuit current (SCC) and braking torque of a dual three-phase permanent magnet (PM) synchronous machine. By optimizing the position and width of stator flux barriers, the machine has a lower amplitude of short-circuit current and brake torque when the short-circuit fault occurs. First, the SCC and braking torque are analytically derived. The amplitude of SCC is proportional to the PM flux linkage and inversely proportional to the inductance. The braking torque is proportional to the square of the PM flux linkage and inversely proportional to inductance. Then, the equivalent magnetic circuit model of flux barriers is established. Its influence on flux linkage and inductance is analyzed, and the improvement mechanism of output torque and fault tolerance is revealed. Furthermore, the flux barriers’ width is optimized by finite element analysis and the theoretical analysis is verified. Finally, experiments on the prototype machine are carried out for the validation.

New magnetic isolation winding for modular multiple three‐phase permanent‐magnet machine with mixed‐layer

In large scale permanent magnet (PM) machines, such as direct drive wind power generators, stator modularity is widely used for easy manufacturing and to protect the winding from mechanical damage due to being exposed to air. Multiple three-phase systems that use commercial inverters provide not only a fault-tolerant operation but also price competitiveness. Although the conventional modular structure of a concentrated single-layer or distributed winding shows good performance, a large magnetic mutual interference between coils is inevitable. Consequently, if conventional windings are applied to multiple three-phase systems, complexity and difficulty for controlling the machine can arise. This study proposes a new magnetic isolation winding scheme for modular multiple three-phase PM machines with a mixed layer to deal with the abovementioned limitation. For comparison, five different modular multiple-three phase PM machines with a mixed-layer winding (MMPM) are presented and three conventional modular types are selected. Then, several simulation results and experimental data confirm the validity of the proposed structure.

Effective Current Limitation for Multifrequency Current Control With Distortion-Free Voltage Saturation and Antiwindup

In three-phase converters, it is frequently important to control current components other than the positive-sequence fundamental. Adequate voltage saturation and antiwindup (VSA) should also be included to prevent malfunction under output-voltage saturation due to, e.g., large voltage disturbances or dc-link-voltage reduction. A multifrequency VSA technique was recently proposed, based on modifying the current references so that the control output voltage is brought back to within the hexagonal boundary. Thus, it avoids the additional distortion that would arise if the control output surpassed (even partially) the hexagon. However, no current limitation was considered. If the current references demanded by the VSA are saturated, windup of the integrator contained in said VSA scheme may occur. Furthermore, current saturation also causes steady-state overmodulation; then, the actual current differs from that fed back to the control (due to the internal-model-control structure included in the VSA), and hence it is not effectively limited. This article adds current-saturation functionality to the multifrequency VSA by several relevant modifications. Windup of the integrator of the VSA when current saturation occurs is prevented. The actual current is effectively limited to the desired value also when there is steady-state overmodulation. Experimental results with a three-phase permanent-magnet machine are provided.

Effect of angle displacements on electromagnetic performance of dual three‐phase consequent‐pole permanent magnet machine

The machine with consequent pole (CP) rotor can improve the utilisation ratio of permanent magnet (PM). However, all the N poles or S poles are replaced by salient rotor iron, leading to the asymmetric air-gap flux density. It potentially results in even-order back electromotive force (back-EMF) harmonics and unbalanced magnetic force. This study aims to investigate the influence of various angle displacements (i.e. 0°, 15°, 30° and 60°) on the electromagnetic performance of the dual three-phase PM machine with CP rotor. The electromagnetic characteristics, including air-gap flux density, back-EMF, torque performance, short circuit current, braking torque and PM demagnetisation under both healthy and fault conditions are compared comprehensively. Finally, the 24-slot/22-pole prototype machine is manufactured. The back-EMF waveforms and static torque are measured and compared to the finite-element predicted results to validate the theoretical analysis.

Numerical Calculation of Stator End Leakage Reactance of Permanent Magnet Machines with Concentric Winding

Concentric winding has been widely used in small capacity AC motors due to its excellent performance. In this paper, a numerical calculation method based on the magnetic vector potential is proposed to calculate the stator end leakage reactance of concentric winding. In this case, the basic unit of numerical calculation becomes the coil group rather than the coil since concentric windings have different coil sizes. The calculated stator end leakage reactance of a prototype three-phase permanent magnet machine with concentric winding is validated using the finite element method. Compared to 3D electromagnetic field calculation, the proposed method does not require a complex modeling process and is therefore highly efficient computationally, requiring only a fraction of the calculation time.

A Novel Synthetic Loading Method for Multiple Three-Phase Winding Electric Machines

This paper develops a version of the synthetic loading method, suitable for the testing of multiphase machines with multiple three-phase distributed windings. The method is at first discussed in general terms for a structure with k three-phase stator windings (i.e., total number of phases is n = 3 k ). Subsequent detailed development is described for a dual three-phase (six-phase) stator winding configuration. With a control architecture that allows the use of half of the three-phase windings as a motor and the other half as a generator, the machine (and/or the converter) can be tested under full rated power without the need for any mechanical load. Moreover, the power consumed from the grid is in essence equal only to the total losses of the system. Modeling, based on the double d-q approach, and the control layout that includes full cross-coupling decoupling are described for a permanent magnet (PM) synchronous machine. An experimental test rig with a double three-phase PM machine of 150 kW rating is detailed and the samples of experimental results are provided to verity the theoretical considerations.

Effects of Harmonics Into Magnet Shape and Current of Dual Three-Phase Permanent Magnet Machine on Output Torque Capability

The harmonics can be utilized in the outer frame of a permanent magnet and phase current waveform in a multiphase machine to improve the output torque capability. The relationship between the output torque and harmonics in both the shape of the permanent magnet and phase current waveform is mathematically established in this paper. Consequently, the optimum harmonics are quantitatively identified and verified by the finite-element (FE) method. It is found that the incremental output torque decreases with the order of the harmonics. However, the output torque does not increase when the harmonic order is higher than seventh. It is also shown that the harmonics in the shape of the permanent magnet and phase current waveform influenced each other. The optimum of the interacted harmonics is dependent on the fundamental and harmonic winding factors. For the dual three-phase surface-mounted permanent magnet (SPM) machines with tile rotors, sinusoidal field rotor, and sinusoidal with third harmonic field rotor, their airgap flux density, back electromotive forces, and torque characteristics are compared. It is demonstrated that the average torque with the optimal harmonics into both the shape of the permanent magnet and phase current waveforms can be enhanced while the torque ripple remains similar to that of the one with the sinusoidal field rotor. Finally, the prototype machine is built and measured to verify the analytical and FE analysis.

Analysis of Dual Three-Phase Permanent-Magnet Synchronous Machines With Different Angle Displacements

In this paper, a novel nonconventional angle displacement (i.e., 15°) between two sets of three-phase windings is proposed for dual three-phase permanent-magnet (PM) machines. First, all feasible angle displacements between the two three-phase winding sets for various slot/pole number combinations of dual three-phase machines are discussed in general. Then, an in-depth investigation is carried out on a 24-slot/10-pole dual three-phase PM machine as an example covering various electromagnetic performances. The investigation shows that under healthy and three-phase open-circuit conditions, the proposed 15° configuration has a comparable electromagnetic performance to the 30° configuration, and a better performance than the 0° counterpart. Furthermore, under three-phase short-circuit (SC) condition, the proposed 15° configuration has the lowest SC current, smallest braking torque, and the best PM demagnetization withstand capability. Finally, three prototype 24-slot/10-pole surface-mounted PM machines are built and tested to verify the theoretical analyses.

Conversion of Three-phase Commercial Machines into Six- phase Machines for Didactic and Research Purposes

Generally poly-phase machines are called those with more than three phases (> 3ph), these have acquired importance in recent years in specific applications such as wind power, electric vehicles, aeronautics, boat propulsion, etc. Its main advantage lies in fractionate power in large machines (ships, wind) and fault tolerance to low power machines (aeronautics, electric vehicles). Because they are special machines, it is complex to acquire them in our country. Therefore, the conversion of two three-phase permanent magnet machines into two six-phase poly-phase machines with two different winding configurations is presented. They are aimed at didactic purposes in the Electrical Machines course and in research tasks. In the present work the process of construction of two poly-phase machines from commercial three - phase machines is detailed.

Torque Improvement of Dual Three-Phase Permanent-Magnet Machine With Third-Harmonic Current Injection

This paper presents dual three-phase permanent magnet (PM) machines utilizing third-harmonic back electromotive force (EMF) and current to improve the output torque, but the torque ripple remains almost similar. The feasibility and practical issues of dual three-phase machines with third-harmonic EMF and current are first discussed, and the output torque is analytically derived. Furthermore, the optimal value of the third harmonic injected into a current waveform for maximum torque improvement is also analytically derived and validated by finite-element analysis (FEA) with the consideration of the constraints of both the peak and root-mean-square currents. For feasible dual three-phase PM machines, torque characteristics, including the average torque and the torque ripple, are compared without and with third-order harmonic injection. It is found that, for a dual three-phase machine without third-harmonic back EMF, the optimal third harmonic into the current is 1/6 of the fundamental current, and the average torque with the current having the optimal third harmonic injected can be improved by 15%. However, for the dual three-phase PM machines with third-harmonic back EMF, the optimal third harmonic into the current is dependent on the ratio of the third-harmonic back EMF to the fundamental back EMF, and the interaction of the third-harmonic current and the third-harmonic EMF results in the further improvement of the output torque. Finally, the experiments on a prototype are given to verify both the analytical and FEA methods.

Low Space Harmonics Cancelation in Double-Layer Fractional Slot Winding Using Dual Multiphase Winding

One of the main drawbacks of nonoverlapped coils in fractional slot concentrated winding permanent magnet (PM) machines are the high eddy current losses in both rotor core and permanent magnets induced by the asynchronous harmonics of the armature reaction field. It has been shown in the literature that the reduction of low space harmonics can effectively reduce the rotor eddy current losses. This paper shows that employing a combined star-delta winding to a three-phase PM machine with fractional slot windings and with a number of slots equal to 12, or its multiples, yields a complete cancellation to the fundamental magneto-motive force (MMF) component, which significantly reduces the induced rotor eddy current. Besides, it offers a slight increase in machine torque density. A case study on the well-known 12-slot/10-pole PM machine is conducted to explore the proposed approach. With the same concept, the general n-phase PM machine occupying 4n slots and with a dual n-phase winding is then proposed. This configuration offers a complete cancelation of all harmonics below the torque producing MMF component. Hence, the induced eddy currents in both rotor core and magnets are significantly reduced. The winding connection and the required number of turns for both winding groups are also given. The concept is applied to a 20-slot/18-pole stator with a dual five-phase winding, where the stator winding is connected as a combined star/pentagon connection. The proposed concept is assessed through a simulation study based on 2-D finite element analysis.

Current Control for Dual Three-Phase Permanent Magnet Synchronous Motors Accounting for Current Unbalance and Harmonics

This paper proposes an improved vector space decomposition current control scheme for dual three-phase permanent magnet (PM) synchronous motors having two sets of three-phase windings spatially shifted by 30° electrical degrees. A proportional-integral (PI) and resonant (second) controller is developed for eliminating the current unbalance in αβ subplane, which is effective irrespective of the degree of current unbalance, while PI plus multifrequency resonant (second and sixth) control is employed to eliminate the current unbalance, fifth and seventh current harmonics in z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane. Compared with existing methods only accounting for current unbalance in z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> subplane, the proposed method has considered the current unbalances in both z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and αβ subplanes and can eliminate them simultaneously at the steady-state of operation. Consequently, the full compensation of current unbalance can be achieved, by which both the current unbalance between two sets and current unbalance between phase windings in each set are eliminated. Meanwhile, the fifth and seventh current harmonics caused by nonsinusoidal back electromotive force and inverter nonlinearity can also be fully compensated. The effectiveness of proposed method is verified by a set of comparative experiments on a prototype dual three-phase PM machine system. It shows that fully balanced currents without the fifth and seventh current harmonics at the steady state of operation can be achieved.

Determination of the inductance parameters for the decoupled d – q model of double‐star permanent‐magnet synchronous machines

Analytical models are the key tools in the model-based control design of electric drives. The inductances together with the stator resistance are the fundamental parameters of these models. In this study three methods to determine the inductances of the decoupled d–q model of double-star permanent-magnet (PM) synchronous machines are studied. These methods have commonly been used to determine the inductances of conventional three-phase PM machines. Two of the evaluated methods are based on the phase-variable inductance waveforms and flux linkages and are thus analysed with finite-element analyses only. The third method, based on the analytical stator voltage equations, can be applied straightforwardly with the real drive system supplied with voltage-source inverters (VSIs). This method requires only the knowledge of the rotor position and the existing current measurements of the VSIs that are used for the current control. Experimental results are provided to verify the applicability of the voltage-equation-based method to determine the inductances. On the average, the presented methods provide similar values, but also some discrepancies between the obtained values can be observed. The measured inductance parameters are validated using model-based closed-loop controllers.

An Improved Performance Direct-Drive Permanent Magnet Wind Generator Using a Novel Single-Layer Winding Layout

Direct-drive permanent magnet (PM) generators have become a strong contender in medium and large rating wind energy conversion systems as they not only provide higher efficiency and annual energy production, but also reduce the operational and maintenance cost. PM generators with nonoverlap single-layer windings provide a cost-effective design variation that eases manufacturing, reduces torque ripples, enhances voltage quality, and provides fault tolerant capability. The performance of such machines depends mainly on the proper selection of the pole and slot numbers, which results in negligible coupling between phases. The preferred slots per phase per pole (SPP) ratios eliminate the effect of low order harmonics in the stator magnetomotive force (MMF), and thereby the vibration and stray loss are reduced. This paper proposes a new three-phase winding configuration based on the 20 slots/18 poles five-phase PM machine. The proposed design is compared with the well-known 24 slots/20 poles three-phase PM machine. The comparison shows that the proposed generator offers reduced torque ripples, improved output voltage quality, and less core loss for the same machine volume.

Modeling magnetic saturation and saliency effects via Euler-Lagrange models with complex currents for three-phase permanent magnet machines

Permanent magnet machines with both magnetic saturation and saliency effects can be directly described via Euler-Lagrangian formulation with complex currents. The Lagrangian is the sum of a mechanical kinetic energy and a magnetic Lagrangian. This second term is expressed in terms of rotor angle, complex stator and rotor magnetizing currents. Via simple modification of magnetic Lagrangian we derive a non-trivial dynamical model describing permanent-magnet machines with both saturation and saliency. We propose an experimental validation of such models on a customized torque machine of 1.2 kW. This first validation relies on injections of high frequency oscillations on the stator voltage. According to the proposed saturation model, the resulting amplitudes of the current-ripples is an increasing function of the current offset. Such dependance is effectively observed experimentally and confirmed by simulations.