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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.

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 paper is to propose applications of advanced signal-processing techniques for the diagnosis and detection of rotor fault in an induction machine. Two techniques are used: spectral analysis techniques and time frequency techniques for the diagnosis of an electrical machine. One is based on the power spectral density estimation techniques, such as periodogram and Welch periodogram. The second method is based on Hilbert transform (HT) to extract the envelope for the stator current. Then, this signal is processed via discrete wavelet transform (DWT) for determining the faulty components in the spectrum of the stator current envelope and identifying the eigenvalues of energies (HDWT).

First, this paper focused on theoretical development and a comparative study of these signal-processing techniques, which are based on the periodogram, Welch periodogram, HT and the DWT to extract the envelope for the stator current; it is used to compute the energy stored in each decomposition level obtained by the stator current envelope (HDWT). Moreover, the Welch periodogram is applied to obtain the envelope spectrum.

The simulation obtained and the experimental validation results of the proposed methods through MATLAB environment show the effectiveness of the proposed approaches with a good accuracy by power spectral density estimation techniques (periodogram and Welch periodogram). Moreover, the faults are manifested through the appearance of new frequencies components, as well as the envelope for the stator current (HT and DWT). This approach is effective for non-stationary and stationary signal to extract useful information for the detection of broken bar fault.

The current paper proposes a new diagnosis method for the detection and characterization of broken rotor bars defects early; it is founded primarily on theoretical development, and the comparison is based on the power spectral density technique (periodogram and Welch periodogram) and the computation of the energy stored in each decomposition level (precisely the HT and DWT). Moreover, the Welch periodogram is applied to obtain the envelope spectrum. The main advantages of the proposed techniques increase their reliability and availability.

Nowadays, an extra consumption of electric energy in the Colombian houses is generated due to electric or electronic elements plugged into the electric network. This fact produces a cost overrun in the user’s electricity bills. To reduce this extra cost, and also with a plus of reducing greenhouse gas emission, a monitoring system for the consumption of electric energy in a household will be designed and implemented to make electricity users realize how much money and energy is being wasted due to the unnecessary electric elements plugged into the network. This paper aims to show a monitoring system that allows the client to supervise the consumption of some appliances inside his/her home, remotely. It is also considered the HMI to be able to log in, choose the intervals of data and generate reports and graphics. The monitoring system is based on the integration of several technologies that are already used and implemented in houses and buildings, such as: measuring and treatment of data electronically using microcontrollers, Wi-Fi technology and dynamic graphic interface (website).

The methodology consists of several tasks, starting from documentation of the variables, instrumentation and methods for getting to the solution; the first part of the methodology focuses on selecting the electric and/or electronic elements to be monitored, so the instrumentation is able to monitor. Then, the power stage was implemented in this stage to measure signals from the sensors while sensing the electric nodes are adjusted, so does the transmission and reception. In the third stage, the design information system was implemented; this is where the received data from the sensors are stored and managed for further organization and visualization. Activities included the following: Analysis of the model of use cases: Identification of actors and actions that are involved in the system. Server selection: Study of the different server to manage the database. Design of the database: The variables, tables, fields, profiles are determined for managing the information. Connection between sensors and database: Correct data transmission and managing to the database from the sensors. Finally, the system is validated in a rural house for a month.

The monitoring system satisfies the main objective of making a tracing of the behavior of some appliances inside a house, showing graphically the instant current generated while connected, the cumulated energy consumed and the cost in Colombian pesos of the energy consumed so far, in real time.

The monitoring system requires the correct functioning of the sensors connected to each household appliance in the home.

The main approach in the monitoring platform is the real-time measurement of energy consumption by nodes (in each appliance) that allows the user to control the money. The innovative impact of the project will be based on the use of hardware and information systems in the measurement of electrical consumption.

This research has a direct impact on the economic aspects of the low-income population by allowing them to manage their energy consumption through the proposed system.

The main approach in the monitoring platform is the real-time measurement of energy consumption by nodes (in each appliance) that allows the user to control the money.

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 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).

Squirrel cage induction motors suffer from several faults such as rotor broken bar. One of the powerful methods to detect induction motor faults is the line current signature analysis. This paper aims to present a novel algorithm based on continuous wavelet transform (CWT) to diagnose a rotor broken bar fault.

The proposed CWT has high flexibility in monitoring any frequency of interest in a waveform. Based on this transform, stator current frequency spectrum is analyzed to diagnose the rotor broken bar fault. The algorithm distinguishes the healthy motor from the faulted one based on a proper index. The method can be used in steady-state running time of induction motor and under different loading conditions. Experimental results are presented to show the validity of the proposed approach.

The proposed index considerably increases at the broken bars conditions compared to the healthy conditions. It can clearly diagnose the faulty conditions. The experimental results are found to be in good agreement with the theoretical and simulated results. The proposed method can reduce the noise and spectral leakage effects.

The main contribution of the paper are as follows: using CWT for detection of broken bar faults; introducing a proper index for diagnosing broken bars; and introducing a supplementary index to reduce the noise and spectral leakage effects.

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.

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.

The purpose of this paper is to prevent the destruction of other parts of a wind energy conversion system because of faults, the diagnosis of insulated-gate bipolar transistor (IGBT) faults has become an essential topic of study. Demand for sustainable energy sources has been prompted by rising environmental pollution and energy requirements. Renewable energy has been identified as a viable substitute for conventional fossil fuel energy generation. Because of its rapid installation time and adaptable expenditure for construction scale, wind energy has emerged as a great energy resource. Power converter failure is particularly significant for the reliable operation of wind power conversion systems because it not only has a high yearly fault rate but also a prolonged downtime. The power converters will continue to operate even after the failure, especially the open-circuit fault, endangering their other parts and impairing their functionality.

The most widely used signal processing methods for locating open-switch faults in power devices are the short-time Fourier transform and wavelet transform (WT) – based on time–frequency analysis. To increase their effectiveness, these methods necessitate the intensive use of computational resources. This study suggests a fault detection technique using empirical mode decomposition (EMD) that examines the phase currents from a power inverter. Furthermore, the intrinsic mode function’s relative energy entropy (REE) and simple logical operations are used to locate IGBT open switch failures.

The presented scheme successfully locates and detects 21 various classes of IGBT faults that could arise in a two-level three-phase voltage source inverter (VSI). To verify the efficacy of the proposed fault diagnosis (FD) scheme, the test is performed under various operating conditions of the power converter and induction motor load. The proposed method outperforms existing FD schemes in the literature in terms of fault coverage and robustness.

This study introduces an EMD–IMF–REE-based FD method for VSIs in wind turbine systems, which enhances the effectiveness and robustness of the FD method.