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Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors.

The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance.

The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation.

The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires.

The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.

The purpose of this study aims to focus on the detection and identification of the broken rotor bars (BRBs) of a squirrel cage induction motor (SCIM). The presented diagnosis technique is based on artificial neural networks (NNs) that use as inputs the results of the spectral analysis using the fast Fourier transform (FFT) of the reduced Park’s vector modulus (RPVM), along with the load values in which the motor operates.

First, this paper presents a comparative study between FFT applied on Hilbert modulus, Park’s vector modulus and RPVM to extract feature frequencies of BRB faults. Moreover, the extracted features of FFT applied to RPVM and the load values were selected as NNs’ inputs for the detection of the number of BRBs.

The obtained simulation results using MATLAB (Matrix Laboratory) environment show the effectiveness and accuracy of the proposed NNs based approach.

The current paper presents a novel diagnostic method for BRBs’ fault detection in SCIM, based on the combination between the signal processing analysis (FFT of RPVM) and artificial intelligence (NNs).

This study aims to deal with the problem of trajectory tracking control for the quadrotor under external environmental disturbance and variable payloads.

In the field of unmanned aerial vehicle (UAV) control, external environmental disturbance and internal variable payloads as two major interference factors lead to control performance degradation or even instability, thus a trajectory tracking controller which innovatively combines sliding mode control technology and model-free control technique is proposed. The proposed controller is constructed with a learning rate-based sliding mode controller and an ultra-local model. Based on the proposed controller, the nonlinear system model of variable load quadrotor is locally estimated and the system’s uncertainties and disturbances can be compensated.

The simulation and actual test results demonstrate the satisfactory control performance and the robustness of the proposed controller compared with the PID and Backstepping controller under external environmental disturbance and variable payloads. Moreover, the proposed controller solves the trajectory tracking control problem not only when payloads change at the center of gravity but also when the position of load variation deviates from the center of gravity.

In both military and civilian domains, the quadrotor may encounter such situations that the payloads change, such as transporting goods, aerial refueling and so on. As a large internal interference factor, variable load tends to lead to unstable control. The research results provide theoretical guidance and technical support for trajectory tracking control of quadrotor under variable payloads.

The proposed controller combines learning rate-based sliding mode controller and model-free control technique to achieve a more efficient and accurate trajectory control of the quadrotor when considering system uncertainties and the load variation that happens in the unknown location.

The purpose of this paper is to apply the method of separation of variables to obtain the current distribution in the slot of an electrical machine, taking into account the skin effect.

A slot in an electrical machine, filled with a solid conductor, and fed with an externally imposed density current, presents a current distribution that depends on the skin effect. The magnetic potential vector is formulated and solved using a separate representation as a finite sum of unidimensional (space and time) functions, taking into account the boundary conditions. The proposed method obtains the transient and permanent distribution of the current in the interior of the slot, both in transient and steady regime, and the results at the end of the transient are compared with the analytic ones in permanent regime.

The magnetic potential vector in the interior of a slot filled with a solid conductor can be expressed as a finite sum of just 16 modes, which capture the evolution of the field during the transient and permanent regime. These modes are expressed as the product of space and time functions, which have been obtained automatically by the separation of variables algorithm. Instead of solving multiple field problems, one for each time instant, the proposed method just solves two single‐variable differential equations, one in the time domain and other in the spatial one.

The application of the proposed method to non‐sinusoidal currents, such as those generated by variable speed‐drives, would allow to compute the field taking into account both the very small time scale of the pulse width modulation pulses, in the range of kiloHz, and the wide time scale of the currents envelope, in the range of 0‐100 Hz. Extension to 2D and 3D spatial configurations is also under consideration.

Using the method of separation of variables to solve electromagnetic problems provides a new method which can simplify and speed up the computation of transient fields in multidimensional time and space domains.

Comme pour les années précédentes, on voudra bien considérer que la participation au Congrès de l'AIEST des Experts Français s'inscrit dans la perspective d'une réflexion en commun à propos du thème choisi.

When solving the cogging torque of complex electromagnetic structures, such as consequent pole hybrid excitation synchronous (CPHES) machine, traditional methods have a huge computational complexity. The notable feature of CPHES machine is the symmetric range of field-strengthening and field-weakening, but this type of machine is destined to be equipped with a complex electromagnetic structure. The purpose of this paper is to propose a hybrid analysis method to quickly and accurately solve the cogging torque of complex 3D electromagnetic structure, which is applicable to CPHES machine with different magnetic pole shapings.

In this paper, a hybrid method for calculating the cogging torque of CPHES machine is proposed, which considers three commonly used pole shapings. Firstly, through magnetic field analysis, the complex 3D finite element analysis (FEA) is simplified to 2D field computing. Secondly, the discretization method is used to obtain the distribution of permeance and permeance differential along the circumference of the air-gap, taking into account the effect of slots. Finally, the cogging torque of the whole motor is obtained by using the idea of modular calculation and the symmetry of the rotor structure.

This method is applicable to different pole shapings. The experimental results show that the proposed method is consistent with 3D FEA and experimental measured results, and the average calculation time is reduced from 8 h to 4 min.

This paper proposes a new concept for calculating cogging torque, which is a hybrid calculation of dimension reduction and discretization modules. Based on magnetic field analysis, the 3D problem is simplified into a 2D issue, reducing computational complexity. Based on the symmetry of the machine structure, a modeling method for discretized analytical models is proposed to calculate the cogging torque of the machine.

About 13 to 44 per cent of motor faults are caused by bearing failures in induction motors (IMs), where lubrication plays a significant role in maintaining rotating equipment because it minimizes friction and prevents wear by separating parts that move next to each other, and more than 35 per cent of bearing failures can be attributed to improper lubrication. An excessive amount of grease causes the rollers or balls to slide along the race instead of turning, and the grease will actually churn. This churning action will eventually wear down the base oil of the grease and all that will be left to lubricate the bearing is a thickener system with little or no lubricating properties. The heat generated from the churning, insufficient lubricating oil will begin to harden the grease, and this will prevent any new grease added to the bearing from reaching the rolling elements, with the consequence of bearing failure and equipment downtime. Regarding the case of grease excess in bearings, this case has not been sufficiently studied. This work aims to present an effective methodology applied to the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the Margenau-Hill distribution (MHD) and artificial neural networks (ANNs), where the obtained results demonstrate the correct classification of the studied cases.

This work proposed an effective methodology applied to the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the MHD and ANNs.

In this paper, three cases of study for a bearing in an IM are studied, detected and classified correctly by combining some methods. The marginal frequency is obtained from the MHD, which in turn is achieved from the stator current signal, and a total of six features are estimated from the power spectrum, and these features are forwarded to the designed ANN with three output neurons, where each one represents a condition in the IM: healthy bearing, mechanical bearing fault and excessively lubricated bearing.

The proposed methodology can be applied to other applications; it could be useful to use a time–frequency representation through the MHD for obtaining the energy density distribution of the signal frequency components through time for analysis, evaluation and identification of faults or conditions in the IM for example; therefore, the proposed methodology has a generalized nature that allows its application for detecting other conditions or even multiple conditions under different working conditions by a proper calibration.

The lubrication plays a significant role in maintaining rotating equipment because it minimizes friction and prevents wear by separating parts that move next to each other, and more than 35 per cent of bearing failures can be attributed to improper lubrication and it negatively affects the efficiency of the motor, resulting in higher operating costs. Therefore, in this work, a new methodology is proposed for the detection and automatic classification of mechanical bearing faults and bearing excessively lubricated conditions in an IM through the MHD and ANNs. The proposed methodology uses a total of six features estimated from the power spectrum, and these features are sent to the designed ANN with three output neurons, where each one represents a condition in the IM: healthy bearing, mechanical bearing fault and excessively lubricated bearing. From the obtained results, it was demonstrated that the proposed approach achieves higher classification performance, compared to short-time Fourier transform, Gabor transform and Wigner-Ville distribution methods, allowing to identify mechanical bearing faults and bearing excessively lubricated conditions in an IM, with a remarkable 100 per cent effectiveness during classification for treated cases. Also, the proposed methodology has a generalized nature that allows its application for detecting other conditions or even multiple conditions under different working conditions by a proper calibration.

The purpose of this paper is to introduce an algorithm based only on local extreme analysis of a time sequence to further the detection and diagnosis of inter-turn short circuits and unbalanced voltage supply using vibration signals.

The upper and lower extreme envelopes from a modulated and oscillatory time sequence present a particular characteristic being of, theoretically, symmetrical versions with regard to amplitude reflection around the time axis. Thus, one may say that they carry the same characteristics in terms of waveforms and, consequently, frequency content. These envelopes can easily be built by an interpolation process of the local extremes, maximums and minimums, from the original time sequence. Similar to modulator signals, they contain more detailed and useful information about the required electrical fault frequencies.

Results show the efficiency of the proposed algorithm and its relevance to detecting and diagnosing faults in induction motors with the advantage of being a technique that is easy to implement in any computational code.

A laboratory investigation carried out through an experimental setup for the study of faults, mainly related to the stator winding inter-turn short circuit and voltage phase unbalance, is presented.

The main contribution of the work is the presentation of an alternative tool to demodulate signals which may be used in real applications like the detection of faults in three-phase induction machines.

Pulsating torques cause a number of problems in electrical machines, including mechanical vibrations, acoustic noise and the depreciation of mechanical equipment. In induction motors, the slot skewing method is an effective way to solve these issues; however, it has some drawbacks such as output torque drop, stray loss intensification due to inter-bar currents and iron loss increment. Besides, slot skewing may not be practical in higher-rated induction motors. In this regard, this paper introduces a modified non-skewed rotor (MNSR) structure as a possible alternative to the skewed designs.

The proposed structure includes a two-segmented rotor with an intermediate ring between the rotor parts that are mounted on the shaft with a relative shift angle. Detailed information about the idea and structure of the MNSR as well as its manufacturing aspects will be presented in the second section of the paper. First, the working principle of the proposed design is described via analytical equations to provide an insight into the concept. The shifting angle will then be calculated by analyzing the harmonic contents of the electromagnetic torque. Finally, the validity of the analytical method will be verified by developing three-dimensional finite element models.

It is demonstrated that by using the proposed rotor structure, the torque ripple has been reduced to a satisfactory level without significantly affecting the mean torque, unlike the skewing method. Furthermore, the new method could avoid the disadvantages of the skewing method while enhancing other motor characteristics such as iron loss. Also, the total volume of the MNSR is equal to the initial design, and the mass and material differences are also negligible.

In this paper, a MNSR is introduced as a possible alternative to the skewed patterns. The study mainly focused on electromagnetic torque profile characteristics, i.e. the mean torque enhancement and the ripple reduction. The MNSR structure can be used for general purposes and high-performance applications, especially where excellent torque characteristics are required.

The purpose of this paper is to inspect strategic placing of different signal processing techniques like wavelet transform (WT), discrete Hilbert transform (DHT) and fast Fourier transform (FFT) to acquire the qualitative detection of rotor fault in a variable frequency drive-fed induction motor under challenging low slip conditions.

The algorithm is developed using Q2.14 bit format of Xilinx System Generator (XSG)-DSP design tool in MATLAB. The developed algorithm in XSG-MATLAB can be implemented easily in field programmable gate array, as a provision to generate the necessary VHDL code is available by its graphical user interface.

The applicability of WT is ensured by the effective procedure of base wavelet selection, which is the novelty of the work. It is found that low-order Daubechies (db) wavelets show decent shape matching with current envelope rather than raw current signal. This fact allows to use db1-based discrete wavelet transform-inverse discrete wavelet transform, where economic and multiplier-less design is possible. Prominent identity of 2sf_s component is found even at low FFT points due to the application of suitable base wavelet.

The proposed method is found to be effective and hardware-friendly, which can be used to design a low-cost diagnostic instrument for industrial applications.