One of the most common requirement in modern industrial applications is to minimize costs associated with repair and exploitation. Recently, in the industrial processes, induction motors are most often used as drive systems. Therefore, providing them continues and failure-free work is closely linked to the aforementioned cost minimization. The development of electronics as well as low cost of production will increase the number of induction motors which are used in industrial applications . The use of semiconductor devices to control induction motors makes it easy to adjust the system and thus greatly improves its flexibility. With the variety of uses of induction motors, the importance of fault diagnostics is also increased. Diagnosis of faults has to ensure reliable and continuous operation of the motors . One of the most common damage of induction motors are damage of the stator circuit. Stator circuit damage accounts for about 36% of damages [3, 4]. Damage to the stator circuit is very often triggered by inter-turn short-circuits [3, 5]. Inter-turn short-circuits are caused by insulation damage between the single windings of coil and this can lead to spread short-circuit to the whole coil and even between adjacent coils. Damage to the insulation may be associated with mechanical stress, over-current or thermal impact. In addition, inter-turn short-circuits may cause asymmetry of the magnetic field that can lead to the generation of vibration and the occurrence of higher harmonics in a torque waveform, which can significantly affect the reduction of system performance. As a result of the process described above, it may be possible to stop the motor which can involve high costs of a production process.
Current trends in the field of diagnostics of electrical machines focuses on early and non-invasive failure detection. Most common non-invasive diagnostic techniques use such methods as Discrete Variation Transform (DFT) or Fast Fourier Transform (FFT). The input signal to the above mentioned methods is usually the current, the pulsation of the torque or the machine vibrations. One of the most popular methods is motor current signature analysis (MCSA). The MCSA method allows to monitor the state of machine without the use of additional sensors and thus does not interfere with its operation [2, 6]. Another example of a diagnostic method related to inter-turn short-circuit is a method that is similar to the MCSA method which involves analysis of back-electromotive force (emf) in the frequency domain. This method is more fully described in . The above mentioned methods, apart from numerous advantages, also have disadvantages, frequency analysis can be used only for stationary signals. Analysis of non-periodic signals that occur, for example, during start-up of a motor, it is necessary to use another method which allows analysis of non-stationary signals such a method is based on wavelet transform. Furthermore, modern diagnostic systems use artificial neural networks as decision support systems to automate the diagnostic process [8, 9, 10].
In the paper, a finite element method (FEM) which is shown, among others, in the paper [11, 12, 13, 14, 15] and a field-circuit model were used. The use of a field-circuit model of the machine makes it unlike the circuit model to take into account such electromagnetic phenomena as for example: eddy currents or a saturation of magnetic core. For the field-circuit model equations of motion, supply system and magnetic field were formulated. These equations allow to describe the magnetic fields distribution as well as description of stator connection with power supply. As mentioned earlier, the finite element method was used. The FEM is one of the most popular methods used in the analysis of electrical machines. The advantage of FEM is the ability to determine in a simple way mechanical and electrical parameters or response of the motor. An additional argument for using FEM was the simplicity that it gives with modelling of motor faults. Other methods are, for example: winding function theory (WFT), magnetic equivalent circuit (MEC) or dq0 conversion method .
The paper focuses on the analysis of torque pulsation of an induction motor. The presented results concern two cases: the first in which the machine is unloaded and the second when the load is equal to 15 Nm. Moreover, the paper describes the effect of inter-turn short-circuit on torque pulsations in transient state. Furthermore, results of the learning process of two types of neuronal networks were presented: the first GRNN and the second MLP. This paper presents an extension of the methods described in article .
2 Modeling of inter-turn short-circuit
The result of the inter-turn short circuit in a phase winding is a division of the phase winding into two parts (Figure 1).
In the Figure 1, the phase stator windings are highlighted as follows: phase A is highlighted in red, phase B in green, and phase C in blue. However, the part of phase A winding, which has been shorted is in yellow. The red part denotes the faulty phase winding with the number of turns equal to NAf, the resistance RAf and the inductance LAf. The yellow part represents shorted turns has a number of turns equal to Nf, the resistance Rf and the inductance Lf. The short circuit has been treated as a metal-metal connection. Therefore, there is no additional resistance in the shorted circuit.
3 Wavelet analysis of torque waveforms
3.1 The torque waveforms during the start of the machine
Calculations were made for a squirrel cage induction machine. Its rated parameters were: the power was 2.2kW, the speed was 1410 rpm, the supply voltage was 400 V (stator windings connected in a star configuration), and the frequency of supply system was 50 Hz. The machine had 24 stator slots, and 22 rotor slots. The number of coils per phase winding was 4, the number of turns per winding was 220. The rotor cage was made of aluminum. The nonlinear B-H curve of the stator and rotor core was taken into account. The skewing of the rotor was included into the field-circuit model. It was assumed that the supply voltage was sinusoidal, symmetrically and mutually displaced by the angle of 2/3π. On the basis of the technical documentation of the tested machine, the FEM model of a machine was developed.
Simulations were performed for two cases: the first at no-load test (TL = 0 Nm) and the second at rated load (TL = 15 Nm). In the first step, the torque waveforms for a healthy motor was calculated. In the second step, the torque waveforms for a faulty motor were calculated. The calculations were performed for a set of selected numbers of shorted turns from Nf = 0 turns to Nf =55 turns. The obtained waveforms as results of calculations in case of TL = 0 Nm and TL = 15 Nm are presented in Figure 2a and Figure 2b, respectively. The amplitudes of the torque waveforms are presented in Table 1. The calculations were carried out in Maxwell computing software.
3.2 Wavelet analysis torque waveforms
The obtained waveforms of torque have been analysed using wavelet transform. In this analysis, the Discrete Wavelet Transform using the wavelet Daubechies “db3” was used . The analysis relies upon a decomposition process which split the signal (torque waveform) into approximation and detail. The calculations were performed up to the 5th level of the decomposition tree (Figure 3). The results of decomposition, i.e. approximation “A” and detail “D”, for number of shorted turns equal to 55 at no-load and nominal load, are presented in Figure 4 and Figure 5, respectively.
4 Implementation of generalized regression neural network
The numerical technique in signal analysis, classification problems and deduction is a difficult task. The artificial neural network could be very helpful and stand in for this task.
In this paper a generalized regression neural network (GRNN) was developed. The GRNN consist of two-layers and two types of activation function (Figure 6a). A radial basis function was used as an activation function for neurons in the first layer of network. Neurons in the second layer were activated using a linear function. The radial basis function of neurons of the first layer is defined as:
where ci is the center, and σi is the spread.
An issue related to the classification of faults in a machine as the number of shorted turns through the neural network was based on a sum of radial basis functions which can be described by following formula:
where φ is the activation function and wi is the weight.
Expected value of a number of shorted turns as well as the answer of GRNN and MLP in cases of TL = 0 Nm and TL = 15 Nm are shown in Figure 7. The multilayer perceptron network (MLP) was chosen as the reference for performance of GRNN. The structure of MLP was as follows: ten neurons with a sigmoid activation function in the first layer and one neuron with a linear activation function in the second layer of network (Figure 6b). The elaborated MLP network was trained using Levenberg-Marquardt algorithm.
The process of training an artificial neural network consists in modifying network parameters such as weights and biases. The learning process ends when the objective function reaches its minimum value. The objective function can be describe by following formula:
where di is the target value.
The performance of ANN (GRNN, MLP) was determined by the answer error. The error was calculated as a relative difference between the answer of the ANN and the expected value in the following form:
where Nf is expected value, NANN is answer of ANN (GRNN, MLP).
This error indicates how well the ANN has been trained. The goal of training process it to get the lowest value of the error. The results of training process are presented in Figure 8.
One of parameters of GRNN which can be modified is a spread σ(1). Therefore, the results of error of GRNN answer are presented as a function of spread in case of selected number of shorted turns (Figure 9).
In the paper, the analysis of the torque of the squirrel cage induction motor with use of DFT and ANN was shown. Torque waveforms were obtained from finite element analysis for two cases: first one when induction motor was loaded by rated torque equal of 15 Nm and second for a load equal 0 Nm. The wavelet decomposition of torque waveforms was made up to 5th level of decomposition tree. Results presented in Figure 7. i.e. answer of ANN in relation to expected value, show advantage GRNN over MLP. It should be noted that in the case in which motor is loaded by rated torque, the error of MLP is lower than in the case of an unloaded motor. Furthermore, one can observe that the biggest error of answer is in case of few shorted turns at rated torque. Regardless of the load of the motor, MLP generates larger errors than GRNN which is shown on Figure 8. Moreover, it should be noticed that for GRNN influence of spread on mean square error (mse) is significant only for small number of shorted turns. Increasing the number of shorted turns reduces the effect of the spread parameter on the mse.
Toumi D., Boucherit M.S., Tadjine M., Observer-based fault diagnosis and field oriented fault tolerant control of induction motor with stator inter-turn fault, Archives of Electrical Engineering, 2012, 61(2), 165-188 Google Scholar
Qi Y., Zafarani M., Akin B., Fedigan S.E., Analysis and Detection of Inter-Turn Short-Circuit Fault Through Extended SelfCommissioning, IEEE Transactions on Industry Applications, 2017, 53(3), 2730 - 2739 CrossrefGoogle Scholar
Wolkiewicz M., Tarchała G., Kowalski C. T., Stator windings condition diagnosis of voltage inverter-fed induction motor in open and closed-loop control structure, Archives of Electrical Engineering, 2015, 64(1), 67-79 Google Scholar
Berzoy A., Mohamed A.A.S., Mohammed O., Impact of Inter Turn Short-Circuit Location on Induction Machines Parameters Through FE Computations, IEEE Transactions on Magnetics, 2017, 53(6), 1-4 Web of ScienceGoogle Scholar
Grubic S., Aller J.M., Lu B., Habetler T.G., A Survey on Testing and Monitoring Methods for Stator Insulation Systems of Low45 Voltage Induction Machines Focusing on Turn Insulation Problems, IEEE Transactions on Industrial Electronics, 2008, 55(12), 4127-4136 CrossrefGoogle Scholar
Cusido J., Romeral L., Ortega J.A., Rosero J.A., Espinosa A.G., Fault detection in induction machines using power spectral density in wavelet decomposition, Transactions on Industrial Electronics., 2008, 55(2), 633-643 CrossrefWeb of ScienceGoogle Scholar
Sarikhani A., Mohammed O.A., Inter-turn fault detection in PM synchronous machines by physics-based back electromotive force estimation, IEEE Transactions on Industrial Electronics., 2013, 60(8), 3472-3484 Web of ScienceCrossrefGoogle Scholar
Demenko A., Nowak L., Pietrowski W., Calculation of magnetization characteristic of a squirrel cage machine using edge element method, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2004, 23(4), 1110-1118 CrossrefGoogle Scholar
Pietrowski W., Application of radial basis neural network to diagnostics of induction motor stator faults using axial flux, Przegląd Elektrotechniczny, 2011, 87(6), 190-192 Google Scholar
Naderi P., Inter-turn short-circuit fault detection in saturable squirrel-cage induction motor using magnetic equivalent circuit model, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2016, 35(1), 245-269 Web of ScienceCrossrefGoogle Scholar
Hongbo Q., Wenfei Y., Shuai Y., Bingxia T., Cunxiang Y., The influence of inter-turn short circuit fault considering loop current on the electromagnetic field of permanent magnet synchronous motor, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2017, 36(4), 1028-1042 Web of ScienceGoogle Scholar
Lubin T., Hamiti T., Razik H., Rezzoug A., Comparison between finite-element analysis and winding function theory for inductances and torque calculation of a synchronous reluctance machine, IEEE Transactions on Magnetics, 2007, 43(8), 3406- 3410 Web of ScienceCrossrefGoogle Scholar
Smith A.C., Williamson S., Smith J.R., Transient currents and torques in wound-rotor induction motors using the finiteelement method, Proc. Inst. Elect. Eng.–Elect. Power Appl., 1990, 137(3), 160–173 Google Scholar
Faiz J., Ebrahimi B.M., Akin B., Toliyat H.A., Finite-Element Transient Analysis of Induction Motors Under Mixed Eccentricity Fault, IEEE Transactions on Magnetics, 2008, 44(1), 66–74 Web of ScienceCrossrefGoogle Scholar
Naderi P., Shiri A., Rotor/Stator Inter-Turn Short Circuit Fault Detection for Saturable Wound-Rotor Induction Machine by Modified Magnetic Equivalent Circuit Approach, IEEE Transactions on Magnetics, 2017, 53(7), 1-13 Web of ScienceGoogle Scholar
Pietrowski W., Górny K., Wavelet torque analysis and neural network in detection of induction motor inter-turn short-circuit, Proceedings of 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering, 2017, 1-2 Google Scholar
Kia S.H., Henao H., Capolino G.A., Diagnosis of Broken-Bar Fault in Induction Machines Using Discrete Wavelet Transform Without Slip Estimation, IEEE Transactions on Industry Applications, 2009, 45(4), 1395-1404 Web of ScienceCrossrefGoogle Scholar
About the article
Published Online: 2017-12-29
Citation Information: Open Physics, Volume 15, Issue 1, Pages 851–856, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2017-0101.
© 2017 Wojciech Pietrowski and Konrad Górny. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0