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This paper details how the equations describing the magnetic field inside the motor and the equations of its electric circuit can be integrated in one only system, which can be solved using the Finite Element Method (FEM). When a model of a circuit is used, the solution of the magnetic field equation is the input to calculate the currents of the machine windings. As the magnetic field depends on these currents, it is necessary to follow an iterative process until initial and final currents match. With the technique proposed in this paper, because both magnetic field equations and electric circuit equations are integrated in the system, just in one step, the currents and induced voltages can be obtained with high accuracy and considerable time saving.

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.

The aim of this paper is to present an approach, able to deal with different models for anisotropy in the finite element method, and how it can be integrated in its formulation.

This approach is to apply this to the study of power transformers, in which grain‐oriented steel sheets are usually used. In this type of analysis, magnetic characteristics of the steel sheets such as non‐linearity and anisotropy, or even the hysteresis, must be taken into account.

The Newton‐Raphson method is generally used to solve the system of equations, but it is a CPU‐time‐consuming task, especially when finite element models and circuit equations are coupled and therefore, time is considered in the analysis.

An approach able to deal with different models for anisotropy in the finite element method is presented.

Electrical machine slots cause an undesirable effect on the m.m.f. wave in the airgap. This effect consists of the occurrence of high frequency harmonics. When the rotor turns, the movement of rotor slots in relation to the stator slots produces cycle variations in the magnetic circuit reluctance. This effect results in high frequency harmonics in the current wave spectrum. Simultaneously high frequency harmonics torques appear. These are known as slot harmonics. To avoid slot harmonics, both in the rotor and in the stator slots, the slots are skewed. When this technique is used, the simplified hypothesis of the finite element model (FEM) in 2D cannot be employed, as it is based on the concept that the magnetic field possesses translational symmetry along the machine shaft. In this paper a method for analysing electrical machines with skewed slots is presented without using the 3D analysis.

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 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.

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).

The purpose of this paper is to present a diagnosis technique, for rotor broken bar in double cage induction motor, based on advanced use of wavelet transform analysis. The proposed technique is experimentally validated.

The proposed approach is based on a combined use of frequency sliding and wavelet transform analysis, to isolate the contribution of the rotor fault components issued from vibration signals in a single frequency band.

The proposed technique is reliable for tracking the rotor fault components over time-frequency domain. The quantitative analysis results based on this technique are the proof of its robustness.

The validity of the proposed diagnosis approach is not limited to the analysis under steady-state operating conditions, but also for time-varying conditions where rotor fault components are spread in a wide frequency range.

The developed approach is best suited for automotive or high power traction systems, in which safe-operating and availability are mandatory.

The paper presents a diagnosis technique for rotor broken bar in double cage induction motor base on advanced use of wavelet transform which allows the extraction of the most relevant rotor fault component issued from axial vibration signal and clamping it in a single frequency bandwidth, avoiding confusions with other components and false interpretations.

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.