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The following paper presents an analytical study of the air-gap magnetic field distribution produced by the armature reaction of a linear machine. Based on the method of images, the magnetic field generated by a current carrying conductor inside the air-gap between two smooth infinitely permeable iron surfaces is modeled as a complex 2D function. The conductor model then becomes a current sheet model and horizontally oriented current sheets are used to model the magnetic field produced by the armature reaction for smooth ferromagnetic surfaces. Focus will be given to the study of the slot opening function in front of energized slots in comparison to the not energized ones of the classical theory pointing out some remarkable differences. Later, the model is extended to slotted geometries using a complex slotting function adapted for energized slots. At last, the Maxwell tensor expressed in complex formulation will be integrated to obtain the force components acting on the machine tooth tips, quantities that will be compared with FEM simulations in order to validate the proposed analytical model.

This paper presents an analytical study of the air-gap magnetic field of a Surface Permanent Magnet (SPM) linear machine under no load. By means of the method of images, the complex expression of the magnetic field of a conductor, inside the air gap between two smooth iron surfaces, is retrieved. Then, integrating the conductor expression, the formulation of the magnetic field of a current sheet and thus the one of a SPM, using two vertical current sheets, is obtained. At last, the no-load magnetic field expression, for a generic time instant, of a slotless machine is retrieved. The novelty of the proposed approach is the availability, due to a different calculation approach, of a unique closed-form formulation for the slotless machine air-gap field, a quantity that, in literature, is usually present in Fourier series formulation. Additionally, as a means to calculate integral quantities and show the goodness of the method a complex slotting function is introduced to account for the slotted geometry. Finally, starting from Lorenz’s force formulation, the expression of the Maxwell tensor in complex form is retrieved and the contribution of forces, integral of the complex stress tensor quantity, will be calculated and compared with FEM simulations, showing a good agreement also with the analytical slotted model.

In this paper, an analytical approach is proposed in developing a lumped parameter thermal model for the stator coils of naturally cooled axial-flux tooth-coil permanent magnet machines. The model comprises one tooth, the coil around it, and the air channels between coils and the teeth supporting structure; each component is subdivided into cuboidal or arc subelements. An expression of the convective exchange coefficient is proposed to take into account the radial position of each tooth. Experimental results validate the proposed model, which can also be used in the design stage of a machine.

This paper evaluates the parasitic currents that can occur in the structural part of some types of yokeless and segmented armature axial flux permanent magnet machines, where the frame-supporting stator floating teeth can originate stray paths. In this paper, these paths are defined and modeled, and the consequent effects (induced electro motive forces and currents) are estimated. The amount of these effects depends on the machine geometry, the magnetic circuit structure, and the winding layout. In this paper, the analysis is performed on two different rating machines, comparing their results. The model is validated by measurements on the corresponding prototypes.

The paper concerns the study of multi-winding transformers (MWT), with inverter fed LV primary windings and one MV secondary winding connected to the mains. Typical application fields are medium power WECSs, consisting of modular components (multi-module generator and transformer). The transformer design and modeling aspects are considered, and its performances are estimated, considering inverter command parameters, current waveforms, copper and core losses, accounting for the effects due to harmonics.

This paper analyzes some operational issues of three-phase surface-mounted permanent magnet synchronous generators (PMSGs) connected to a diode rectifier. This simple configuration coupled to a single-switch dc–dc converter is used in small-scale wind energy conversion systems, as well as in energy harvesting systems, to reduce costs. The diode rectifier causes an intrinsic limit for the maximum convertible power, which is related to the load impedance matching, and additional joule losses due to the distorted currents. By using an analytical steady-state model of the rectifier and of the PMSG, this paper discusses how to achieve two particularly meaningful operating conditions characterized respectively by the maximum power transfer and the maximum power per ampere. The theory is validated by simulation and test results on a prototype.

The paper analyses torsional vibrations caused by electromagnetic torque harmonics in permanent magnet synchronous generators. A vibration mitigation method is proposed based on changing the phase angle of the carrier signal of sinusoidal PWM in order to invert the phase of the torque harmonic causing resonance. Since the frequency has not changed, the system is still in resonance. Thus, after a given time, the torque harmonic should be inverted again. The process is repeated as long as the system is at or near resonance. A criterion is presented to select the exact phase shift of the carrier needed in order to invert the torque harmonic. A method to calculate both the toggle time needed and the frequency range to apply such technique is presented. With the mitigation technique applied, two cases are considered on Matlab/Simulink, namely sustained operation at resonant frequency and accelerating the machine over some critical points.

The paper analyzes a torque and DC-current ripple mitigation strategy in a modular axial-flux permanent magnet synchronous generator for multi-MW Wind Energy Conversion Systems (WECSs). The machine modules are aligned with one another and driven by the same shaft. Each module is connected to its own two-level converter and the converters are paralleled at the DC side. In order to reduce the DC-side current harmonics and the ripple in the resultant torque, a phase shift between the converters' PWM carrier signals is implemented. The converters are operated within the linear PWM modulation range. A mathematical analysis is carried out. A criterion for the best choice of the phase shift in two- and three-module configurations is developed. Theoretical results are compared with those from simulations in Matlab/Simulink, verifying the soundness of the method.

The paper presents a method to reduce both the torque ripple and the dc current ripple in the machine side converter, in a multi megawatt Wind Energy Conversion System, based on a PM Synchronous Generator which has a multi modular structure. Each converter module consists of a three-phase, two level inverter, operating as a rectifier, with PWM sinusoidal modulation. The first aim of the method is exploiting not only the linear PWM region but also over modulation region, in order to allow a higher AC voltage, with the same dc link voltage. The ripple mitigation is gained by means of a suited shifting among the carrier signals and the control signals in the several modules. The paper describes the method, and discusses the criteria that can be adopted to choose the suited shifting angles. Some simulation results are reported.

Electrical machines are generating and using most of the electrical energy converted worldwide from fossil fuels or renewable sources. An optimized electrical machine means not only less input energy used but also higher electromechanical energy available as output. This is translated into getting more with less and having an impact on the total amount of greenhouse gases released into the atmosphere, thus mitigating global warming. Benefiting from the latest developments in the electrical machine field are various industries such as electric propulsion [new electric vehicles (EVs) and plug-in hybrid EVs (HEVs)], renewable energy harvesting, consumer applications, and military and aerospace products. This article brings together the contributions from several authors working in academia and industrial research and development centers and comprises a collection of short analyses dedicated to the hottest topics in the electrical machine research community. The article focuses on special and difficult problems to be solved in the design process of the most important electrical machine topologies. The topics discussed cover new machine topologies such as fractional slot winding motors and synchronous reluctance motors; electromagnetic, mechanical, and thermal problems in permanent magnet (PM) machines design; operation of high-speed machines and high-power turbo generators; noise and vibration reduction in switched reluctance motors (SRMs) for automotive applications; high-efficiency induction machines (IMs) configurations compatible with the new international standard and a comprehensive analysis of universal motors (UMs).

This study deals with the analytical modelling of the steady-state operation of a three-phase diode rectifier whose dc bus is connected to a constant voltage source. Such a system exhibits several operation modes that are fully investigated. Analytical expressions of the boundaries of each mode as well as the average dc and the rms ac currents are deduced as a function of the ac and dc parameters, including voltage drops across diodes. They allow us to evaluate the power delivered to the dc bus as well as the efficiency of the conversion in each mode of operation. These results can also be extended to practical rectifiers with bulk dc capacitors and allow for performing parametric analyses and optimisation in the design of drives or permanent magnet synchronous generators directly connected to a diode rectifier. The theoretical results are validated by experimental tests.

This paper reviews the design procedure of wound-type Inter-Phase Reactors used in high power rectifier systems, and gives some guidelines for an optimized sizing aimed at minimizing costs and active mass. In particular, the paper proposes a design algorithm to identify the optimal number of coils and turns and clarifies the role of the air-gap in minimizing the magneto-motive force unbalance and affecting the column peak flux density.

Some electromagnetic and thermal aspects concerning special permanent magnet machines, employed in damping seismic oscillations in structural systems, are examined. The power generated by the machine during a seismic event is regulated by a suited converter and delivered to an external resistor. Some modeling features and selected simulations are examined, together with test results obtained by a prototype. Some special tests, aimed to identify the thermal parameters of the machines, are presented and discussed.

In some topologies of yokeless and segmented armature (YASA) axial flux permanent-magnet (AFPM) machines, the particular frame structure required to fasten floating teeth can originate stray paths where parasitic currents may circulate. This paper investigates how the amplitude of these currents and the related additional Joule losses depend on the machine size. Reference is made to wind energy generators, rated from some tens of kilowatts up to a few megawatts. The developed model is mainly based on wind turbine basic data of vendor data sheets, and on the quantities evaluated and tested in two YASA AFPM prototypes, rated 50 and 200 kW.

High power Permanent Magnet Synchronous Generators for wind applications may be made of modular subsystems, connected to the same shaft. The paper mathematically analyses the DC-side current and the torque ripples of a particular configuration: the stator phase axes of the several modules are axially aligned while the rotors are reciprocally shifted by a suited angle. Moreover each module is connected to a two-level AC-DC converter; such converters are paralleled on the DC-side. For now, just square wave rectifier operation has been considered: the necessary phase shift of the voltages among the converters is found out in order to reduce the ripple of the resultant DC-side current and of the total torque. Such a phase shift coincides with that among the rotors. Some calculations are checked through a simulation, proving the effectiveness of the proposal.

Some design and operation aspects of axial flux permanent magnet synchronous machines, employing armature windings with concentrated coils wound around the stator teeth, are presented. The e.m.f. control is based on the variation of the windings flux linkage, obtained by modifying the stator (or rotor) configuration. Thanks to the high number of poles and the excellent waveform quality, even with deep field weakening, these machines exhibit a satisfactory operation at low speed, both as generators and motors. In the paper, the main constructive machine features are discussed, together with some design and FEM results. A test on a prototype has also been carried out.

An equivalent electrical circuit, characterized by the minimum coil sections number necessary to analyze the commutation in a universal motor, is discovered. The model parameters are also determined: in particular, the self and mutual inductance coefficients and the electromotive force induced in the coil sections (taking into account the magnetic saturation), the brush-commutator voltage drop, the electric arc. By means of a numerical solution of the equivalent circuit, the current waveforms are analyzed; the comparison between the computed and measured waveforms of the brush-commutator voltage drops allows to verify the model.

Due to the high torque capability, axial flux (AF) permanent-magnet (PM) machines are an interesting solution for direct driven wind energy conversion systems and low-speed motors. However, the structure of such machines makes them sensitive to geometrical imperfections due to manufacturing process. This paper analyzes the effects that various types of geometrical imperfections produce in concentrated coil AF PM generators. In particular, a case study is presented, where the mechanical stresses, the resulting axial force, and the bending torques on the shaft, as well as the circulation current in the winding parallel paths, are calculated. The results obtained by means of an analytical approach are compared with those based on finite element method simulations and are validated by some experimental results on a prototype.

This paper investigates the optimal arrangement of the coils in a wound-type interphase reactor to avoid the decreased inductance due to local saturation in the core when operated with high dc current. In theory, the direct currents and the related magnetomotive forces in the two ways of an interphase reactor are equal, and this compensation leads one to conclude that the global flux in the yokes is zero. However, the dc currents in the coils produce a significant leakage flux that flows locally in the core. If the coils are not suitably arranged and if the dc current is high, the leakage flux causes local saturation, a drop in the inductance, and noticeable circulation of a triple harmonic current through the reactor. Such a phenomenon is investigated by means of both a simplified field model and three-dimensional magnetostatic simulations. A number of criteria for the arrangement of the coils to improve operation are derived and applied to a real rectification system used in an electrolysis plant. Some in situ operational measurements of both the original and the improved interphase reactor are reported.

The paper describes an algorithm for the design of a special current transformer (C.T.), suited to measure the residual harmonic content of fluctuating direct currents, generated by static convertors on their D.C. side. The use of a suitably proportioned C.T. allows the galvanic insulation and the filtering of the D.C. component (without employing high-pass filters). The design of the C.T. is affected by the high value of the D.C. component, which implies the use of a gapped magnetic core. An in-depth study of a C.T. model has been carried out: particular attention is devoted to the effects of the distributed capacitances of the windings. The paper also analyses the experimental results obtained during tests carried out on a prototype C.T., comparing them with the values calculated from the theoretical model.

This paper deals with the ac-dc interface conversion in grid-connected wind energy conversion systems based on modular permanent-magnet synchronous generators. In particular, some solutions based on diode rectifiers are extensively analyzed as for the waveforms, the efficiency, and the torque ripple, by considering several connections, which are allowed by the inherent modularity of the considered generators. Rectifier schemes with a high number of pulses can be easily realized without using special shifter transformers so that these solutions can be attractive for low- and medium-power applications.

An analytical method is presented to evaluate the field and global quantities for the operation and design analysis of axial flux permanent-magnet (PM) machines. The method, of general applicability, is based on the definition and superposition of suited field functions, able to accurately model the different singularities of the studied device: PM field distribution, effects of slotting, and radial end effects. Selected explorative FEM analyses are used in order to investigate the field functions shape and to help in identifying their structure and parameters. Then, the flux density distribution is obtained, as a function of the rotor position, taking into account some manufacture dissymmetry effects, such as air-gap offsets and PM rotor disk inclinations. This approach allows to analyze the effect of dissymmetry on the circulation of current among winding parallel paths in no-load operation. Moreover, by using the Maxwell stress tensor, the stress distribution is evaluated, as well as the resultant axial forces and the bending torques on the shaft due to the rotor disk tilts. Several FEM simulations show the soundness of the proposed method, which exhibits high accuracy and great evaluation speed.

Some design and operation aspects of axial flux permanent magnet synchronous machines, wound with concentrated coils, are presented. Due to their high number of poles, compactness, and excellent waveform quality and efficiency, these machines show satisfactory operation at low speeds, both as direct drive generators and as motors. In this paper, after a general analysis of the model and design features of this kind of machine, the attention is focused on wind power generation: The main sizing equations are defined, and the most relevant figures of merit are examined by means of a suitable parametric analysis. Some experimental results obtained by testing a three-phase, 50-kW, and 70-rpm prototype are presented and discussed, validating the modeling theory and the design procedure.

A new method for the synthetic determination of the losses of three–phase induction motors by means of direct tests is described. The tests are carried out with a reduced supply voltage and a reduced braking torque: subsequent calculations to refer the results to rated values are then applied. Using this procedure, a considerable extension of the power range over which direct methods can be employed becomes possible, whilst avoiding the use of correspondingly more powerful braking devices. A few experimental tests confirm the validity of the proposed method. Moreover, the potentialities of the method are discussed; then a few error analysis considerations are developed; finally, some possible thermal referring procedures are proposed.

An equivalent circuit of universal motors is developed, based on the design data. After representing the magnetomotive force distribution in the air gap, an analytical expression of the flux linkage of the armature winding coils is derived; this allows for the determination of the expressions of the speed and transformer EMFs induced in the armature winding and their representation by means of circuit parameters, as a function of the magnetic core saturation. The motor performances are computed, using the circuit parameters determined both analytically (by the design data) and by measurements. Some quantities are also compared with the ones obtained by finite-element analyses. Finally, the model is validated by experimental tests.

The technique for the simulation of the dynamic behaviour of rotating machines presented in the paper is based on an equivalent circuit representation of the magnetic configuration. The circuit parameters are obtained by a preliminary automated sequence of magnetostatic FEM analyses and take into account the local magnetic saturations. The adopted solution technique is based on an invariant network topology approach: its application, presented for the operation analysis of a low‐power synchronous generator, allows a great reduction of the calculation time in comparison with a commercial FEM code for the transient simulation.