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For a given rotor, the study of the impact of stator MMF from different winding distributions is usually carried out using analytical model under some simplifying hypotheses to limit time computation. To get more accurate results, finite element model is thus more suitable. However, testing different combinations of stator windings with the same rotor can be tedious when considering the stator slots. Indeed, this introduces mesh constraint, reluctance variation of the air gap and possibly taking into account of the connection between stator coils. To avoid this, a current sheet supplied such to represent the stator MMF and spread all around the inner slotless stator surface can be used. In addition, such an approach can be very useful to didactically assess the effect of each winding space harmonic on machine performance separately. The purpose of this paper is to use a current sheet coupled to an external analytical tool in order to easily test different windings or to quantify the effect of a given spatial harmonic of the winding.

In the proposed approach, the current sheet supply is obtained from an analytical tool that allows determining the spatiotemporal stator MMF of any winding considered. Moreover, stator teeth height is not modelled, and only the thickness of the stator yoke is considered along with the same air gap thickness. Results with the proposed approach are compared to the real stator modelling for two different winding configurations. Last, linear and non-linear magnetic material behaviours are investigated to validate the proposed approach in term of magnetic distribution.

For both studied cases, results in term of local and global physical quantities show good agreement between the real stator modelling and the proposed approach.

Current sheet is used with finite element model to study the inherent effect of different winding configurations on local and global physical quantities of an AC electrical machine. The proposed approach avoids the constraints in terms of stator slot geometry and electrical circuit definition. This is very useful to quickly test different winding configurations or to isolate a specific winding space harmonic to quantify its effect on the electrical performances. This cannot be performed using classical modelling as all space harmonics are taken into account.

The purpose of this paper is to analyse and compare the functional parameters of three- and six-phase permanent magnet synchronous motors (PMSM) with fractional-slot concentrated windings (FSCW).

The investigations are focused on the comparison of the distortions of back electromotive force (emf) and magnetomotive force (mmf) waveforms, as well as torque ripples, radial force spatial harmonics and motor performance studies. The finite element models of the test machine and a personally developed computer code have been used to calculate motor characteristics and analyse and synthesise multiphase winding layouts, respectively.

Compared with the traditional three-phase PMSM designs, the proposed six-phase machines are characterized by a significantly lower content of sub-harmonics in mmf waveform distribution. Moreover, the investigated six-phase machines exhibited a higher average value of electromagnetic torque, significantly lower torque ripples and a reduced value of low-order harmonics of the radial component of the electromagnetic force in the air-gap of the machine.

The analyses presented in this paper show that six-phase PMSM with FSCWs are advantageous to their counterpart three-phase machines. Specifically, they are more suited to working with multiple drives supplying a segmented winding system while simultaneously offering higher performance. This suitability to the use of a multi-drive supply for one motor offers flexibility and cost reduction while increasing the fault tolerance of a power train system.

The purpose of this paper is to investigate advantages of multiphase permanent magnet synchronous motors (PMSM) with fractional slot concentrated windings (FSCW). The investigation is based on comparative analysis and assessment of FSCW PMSM wound as 3, 6, 9 and 12 phase machines suited for low speed applications.

The investigations are focussed on distortions of back electromotive (emf) and magnetomotive force (mmf) with the torque ripples and motors’ performance taken into account. The finite element models with the aid of customized computer code have been adopted for motor winding design and back emf, mmf and motor performance analyses.

The novel multiphase winding layouts were found to offer lower content of sub-harmonics in the mmf waveforms compared with the traditional three-phase machine designs. Moreover, the investigated multiphase machines exhibited higher average value of the electromagnetic torque, while the multiphase PMSM machines with FSCW were further characterized by significantly lower torque pulsations.

The analyses presented in this paper demonstrate that PMSM with FSCW are advantageous to their counterpart three-phase machines. Specifically, they offer higher performance and are more suitable to work with multiple drives supplying segmented winding system. This ability of using multi-drive supply for one motor offers flexibility and cost reduction while increasing fault tolerant power train system.

The purpose of this paper is to present a detailed advanced dynamical model of induction machine (IM) with unskewed rotor bars, including rotor slot harmonics.

Procedure of IM modeling using results from finite element analysis (FEA). Series of magneto-static FEA simulations are used to obtain matrix of IM inductances as a function of rotor angular position and geometry. Each element in this matrix is represented by Fourier series (FS) and incorporated in proposed dynamical model. Using or neglecting various elements in FS of inductance matrix may be useful for determining which component of the series has dominant influence on harmonic content of stator currents, torque ripple or speed variation. The usefulness of application of presented model is verified comparing with time-stepping FEA simulations.

Although the model is not suitable for usage in on-line regulation of IM drives, but the results of simulations may be used to thoroughly explain origins of higher order harmonics in stator currents of IM and help improve sensorless speed estimation algorithms and fault diagnostics.

This paper shows an approach to the modeling of IM which includes effects of non-uniform air gap and non-sinusoidal distributions of magneto-motive forces. Inductance matrix elements are complex functions of rotor position, geometry and winding distributions and it gives an opportunity for detail analysis of IM behavior in numerous applications.

The purpose of this paper is to present three novel techniques aimed at increasing the efficiency of the polarization fixed point method for the solution of nonlinear periodic field problems.

Firstly, the characteristic B‐M resulting from the constitutive relation B‐H is replaced by a relation between the components of the harmonics of the vectors B and M. Secondly, a dynamic overrelaxation method is implemented for the convergence acceleration of the iterative process involved. Thirdly, a modified dynamic overrelaxation method is proposed, where only the relation B‐M between the magnitudes of the field vectors is used.

By approximating the actual characteristic B‐M by the relation between the components of the harmonics of the vectors B and M, the amount of computation required for the field analysis is substantially reduced. The rate of convergence of the iterative process is increased by implementing the proposed dynamic overrelaxation technique, with the convergence being further accelerated by applying the modified dynamic overrelaxation presented. The memory space is also well reduced with respect to existent methods and accurate results for nonlinear fields in a real world structure are obtained utilizing a normal size processor notebook in a time of about one‐half of one minute when no induced currents are considered and of about one minute when eddy currents induced in solid ferromagnetic parts are also fully analyzed.

The originality of the novel techniques presented in the paper consists in the drastic approximations proposed for the material characteristics of the nonlinear ferromagnetic media in the analysis of periodic electromagnetic fields. These techniques are highly efficient and yield accurate numerical results.

This paper aims to obtain a symmetrical step-down topology with lower equivalent capacity and wider step-down range under the condition of the same output. Two new symmetrical step-down topologies of star-connected autotransformers are proposed in this paper. Taking the equivalent capacity as the main parameter, the obtained topologies are modeled and analyzed in detail.

This paper adopts the research methods of design, modeling, analysis and simulation verification. First, the star-connected autotransformer is redesigned according to the design objective of symmetrical step-down topology. In addition, the mathematical model of two topologies is established and a detailed theoretical analysis is carried out. Finally, the theoretical results are verified by simulation.

Two symmetrical star-connected autotransformer step-down topologies are designed, the winding configurations of the corresponding topology are presented, the step-down ranges of these three topologies are calculated and the influence of step-down ratio on the equivalent capacity of autotransformer are analyzed. Through analysis, the target step-down topologies are obtained when the step-down ratio is [1.1, 5.4] and [1.1, 1.9] respectively.

Because the selected research object is only a star-connected autotransformer, the research results may lack generality. Therefore, researchers are encouraged to further study the topologies of other autotransformers.

This paper includes the implications of the step-down ratio on the equivalent capacity of autotransformers and the configuration of transformer windings.

The topologies designed in this paper enable star-connected autotransformer in the 12-pulse rectifier to be applied in step-down circumstances rather than situations of harmonic reduction only. At the same time, this paper provides a way that can be used to redesign the autotransformer in other multi-pulse rectifier systems, so that those transformers can be used in voltage regulation.

The purpose of this paper is to investigate torque ripple and magnetic force on the teeth in interior permanent magnet (IPM) machines over a wide range of speed operation for electrical power steering (EPS) applications.

The flux-weakening capability of IPM machines has been analysed by finite element method considering the effect of cross-coupling between d- and q-axis current. The traditional method of analysing torque ripple is based on constant torque and flux-weakening region. However, the cross-coupling need to be considered when applying this technique to flux-weakening region. Meanwhile, the torque ripple with current amplitude and angle and with different speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth due to the separated teeth with stator yoke is also investigated during the constant torque and flux-weakening region.

The torque ripple and magnetic force on teeth in IPM machine are dependent on current and current angle. Both the lowest torque ripple and magnetic force on teeth exist over the whole torque-speed region.

The purely sinusoidal currents are applied in this analysis and the effects of harmonics in the current on torque ripple and magnetic force on teeth are not considered in this application. The 12-slot/10-pole IPM machine has been employed in this analysis, but this work can be continued to investigate different slot/pole number combinations.

This paper has analysed the torque ripple and magnetic force on the teeth in IPM machines for EPS application over a wide range of operation speed, which are the main cause of vibration and acoustic noise. The variation of torque ripple with current amplitude and angle as well as speed in the flux-weakening region is also investigated. In addition, the magnetic force on the teeth is also investigated over the whole torque-speed region.

The specific modulation methods are used to control different kind of single-phase, as well as three-phase, inverters to ensure flexibility and high quality of the output waveform. This paper aims to present a combination of two classical methods, namely, pulse width modulation method and direct digital synthesis modulation method.

The total harmonic distortion of output waveforms of single-phase inverter based on elaborated modulation method has been determined by means of fast Fourier transform analysis. Tests have been carried out by using standard low-frequency application and also a wireless resonant energy link system.

Applying appropriate timer parameters of microcontroller enables to obtain a waveform for given output parameters (amplitude, frequency, frequency modulation index, etc.). The only limitation is the computing power of a microcontroller.

The elaborated method can be successfully used in both low- and high-frequency application ensuring high level of output waveform quality. Additional signal generators and the control of amplitude modulation ratio are no longer indispensable, what simplify immensely a control system.

This study aims to focus on the grid connected inverter.

The grid connected inverter for harmonic suppression was designed, the topological structure of the inverter and the design of LCL filter were analyzed, then a PIR controller was proposed and finally simulation and experiment were carried out.

The simulation results showed that the distortion rates of the 5th, 7th and 11th harmonics under PIR control were 0.14%, 0.13% and 0.06%, respectively, which were significantly lower than that under PI control. The system test results also showed that the current waveform under PI control was rough and total harmonic distortion (THD) content was 3.8%; under PIR control, the grid connected current waveform was relatively smooth, with fewer spikes and burrs, and the THD content was 1.9%, indicating that the harmonics were effectively suppressed.

The experimental results verify that the inverter and PIR controller designed in this study are effective for harmonic suppression. This work makes some contributions to the improvement of the effect of harmonic suppression and promotion of the better application of grid connected inverter.

This study aims to predict the unstable period-1 orbit (UPO-1) of DC–DC converters and find analytical expressions to describe it.

Nonlinear dynamical phenomena of a peak–current–mode controlled direct current–direct current (DC–DC) Boost converter are discussed briefly first. Then fast fourier transform (FFT) analysis of state variables under different dynamic states is provided, and the characteristic of the harmonic content in different states is summarized. Following these, a scientific hypothesis on the harmonic content of the UPO-1 is presented, and the Equivalent Small Parameter method is adopted then, thus analytic-form expressions of the UPO-1 can be derived.

According to results of theoretical analysis, numerical simulations and experiments, this paper illustrates that, like stable period-1 orbit, the UPO-1 is also made up of the DC component and harmonics with integer times of switching frequency.

This work provides an unreported approach for extracting the UPO-1 of DC–DC converters, which is mainly based on predicting the harmonic structure information of the orbit. According to experimental parts of the work, it shows that the stabilizer can be designed easier by using the proposed method. Additionally, from a broader perspective, the results could also have implications in a wide class of forced oscillation systems.