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International Journal of Enhanced Research in Science, Technology & EngineeringISSN: 2319-7463, Vol. 5 Issue 1, July-2017

A New Finite Element Model Analysis for Permanent Magnet Synchronous Machine Stator

FaultManel Fitouri 1, Wiem Zaabi2, Yemna Ben Salem1, Mohamed Naceur Abdelkrim1

1 Research Laboratory Modelling, Analysis and Control of Systems (MACS) LR16ES22, National Engineering School of Gabes, Tunisia

2 Research Laboratory Computer Electronic Smart Engineering System Design (CES), Sfax, Tunisia

ABSTRACT

This paper attempts to analyze the characteristics of the inter-turn short circuit fault for the Permanent Magnet Synchronous Motor (PMSM). Based on Finite Element Analysis (FEA), the influence of the stator faults on the behavior of the PM machine is studied. A simple dynamic model for a PM machine with inter-turn winding fault is presented. The precision of the proposed Finite Element (FE) model is verified by a comparison of the simulation results tests. Using the simulated model, a technical method, based on Fast Fourier Transform (FFT) analysis of stator current and electromagnetic torque, is exported to detect the inter turn fault. The technique used and the obtained results show clearly the possibility of extracting signatures to detect and locate faults.

Keywords: Finite element method (FEM), Permanent Magnet Synchronous Motor (PMSM), winding short-circuit, Fast Fourier Transform (FFT) analysis.

1. INTRODUCTION

Permanent Magnet Synchronous Motors (PMSM) are widely used in high performance application such us automotive, appliances, medicine and aerospace because of their efficiency, reliability, multiple fields and high dynamic response performance [1]. For more precise modelling of the PM motor, it is important to build a mathematical model of the PMSM.The analytical model, the Finite Element Analysis and the Coupled Electric Circuit model are the three motor modelling methods. For example, in [21], the dq model is an analytical model, which is given in following equations calculated with simple characteristics and parameters of the machine. The most accurate models are the two Dimensional (2-D) FEM of the PMSM model, which take into account the nonlinearity of the magnetic material for a detailed study of the machine [18-19-20]. Consequently, it is important to create a new model that relies the analytical model with the FE model coupling with an external electrical circuit. The machine models are usually used for fault diagnosis [2-13], include the FE model and the coupling electrical circuit model. PMSM faults can be classified into static and dynamic eccentricity, damaged bearings, demagnetization in rotor magnets, fault in connection of the stator windings and stator short-circuited turns. The inter-turn fault is one of the most frequent fault. It is caused by mechanical stress, discharge, environmental conditions and moisture. Modelling of PMSM with an inter-turn fault has been shown in references [5-6]. In reference [25-27], the models of an inter-turn fault are deduced either from circuit models using Matlab/Simulink which present many disadvantages or with a combined model as proposed in this paper. The combined model is constituted of two components: The first is the stator windings which are designed with an external electrical circuit using Ansys Maxwell Circuit Editor, the second is the rotor already created by 2-D FE model [7-24]. In references [8-12], Vaseghi and Boileau presented a model which takes into account the effect of the inter-turn fault of the circuit of stator winding in the conventional Park’s model using Matlab and validate the results via experimental studies. However, the FE model is the non linear model that analysis the performance of the machine due to any fault can be observed without destroying the machine and experimenting in laboratories. So, the simulation results are more realistic that can be used to perform the machine for both cases healthy state and under faulty condition [15]. The impact of the inter-turn fault on the machine is very intensive. The fault can severely reduce the stator currents, the voltages and the electromagnetic torque. In addition, this fault leads to the variations of the electromotive force (EMF) of the PMSM [17].

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One major reason for diagnosis of this fault at the initial stage of its occurrence is the ever-increasing cost of the Permanent Magnets. Many methods have been used to detect inter-turn fault in PMSM [2-8-27]. These methods can be categorized as frequency analysis methods. They are based on the Fast Fourier Transform which is applied to the stator currents or electromagnetic torque by comparing the healthy to the faulty case. The main advantage of the FFT is that it uses for the detection of the short circuit of turns for a PMSM analyzed by means of FEA and advanced signal processing [3-16]. The main contribution of this work is to include a new model using 2D FEA software with a coupled electrical circuit in order to study the effect of stator winding inter-turn faults. Specifically, the FE model of the PMSM with inter-turn fault is developed. The parameters, the electromagnetic torque, the Stator winding currents, the stator induced voltage and the fault current are obtained from the solutions of the FE computation of the machine under the same type of fault conditions. The FFT analysis is applied to detect the fault of the machine using Ansys Maxwell Software. The proposed model is denoted that all the simulations are realised by FEM and the diagnosis of the fault is performed for both healthy and faulty machine.This work is organized as follows: Section II describes the FE model of the motor in Ansys Maxwell and the electric Circuit of Permanent Magnet Motor coupled in Ansys Maxwell Software and Ansys Circuit Editor Software. Permanent magnet model with stator winding short-circuit fault and the simulation results of the proposed model are shown in Section III. In Section IV, the proposed fault detection technique (Fast Fourrier Transform ) is analysed. Section V concludes the paper.

2. The Finite Element Method

The FEM is a computer based numerical technique to calculate the parameters of the electromagnetic devices. It can be used to calculate the flux density, the flux linkages, the inductance, the torque, the induced EMF etc. A FEM, which addresses dynamic material properties of the magnets and yet can be implemented readily in the software, is presented to find the parameters of the magnetization circuit. It offers unlimited flexibility in the geometrical shape, the material properties and the boundary conditions in different regions of the machine [22].The magnetic field distribution inside the machine is calculated using the FEM. This distribution can be used to calculate other properties such as the induced voltage of the machine. Also, it provides detailed information about the nonlinear effects of the machine (based on its geometry and material properties). This modelling approach is able to obtain an accurate and a complete description of an electrical machine [23]. The magnetic circuit is modelled by a mesh of small elements. There field values are assumed to be a simple function of the position within these elements, enabling interpolation of results [10].

A. The Finite Element Model of PMSM

A model of the PMSM was constructed using Ansys Maxwell Software that is one of the well known Ansoft software for the FEM modelling. This software solves complex electromagnetic field problems and considers the nonlinearity of the study domain [4]. Maxwell Software solves the electromagnetic field problems by solving Maxwell’s equations in a finite region of space with an appropriate boundary conditions. Maxwell’s equations are given by the following equations [26]:

(6) (7)

(8) (9)

with H is the magnetic field intensity, J is the surface current density, D is the electric flux density, E is the electric field intensity, B is the magnetic flux density and ρ is the volume charge density. In this work, the Maxwell Software is mainly used to build and analyze the interior of PMSM. Figure 1 illustrates the RMxprt model of the PMSM model.

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Figure 1. RMxprt model of the PMSM machine.When the RMxprt model was analysed, it was exported to the 2-D model using the Ansys Maxwell, it only computes solution for only one of the symmetries. In this case, the machine has been divided into four equal parts and only one part is represented on 2D model as shown in figure 2. The geometrical of 2-D model and the mesh division is depicted in figure 2.

Figure 2. Finite Element Model of PMSM and the mesh division.The coupling of the electrical circuit with the magnetic field domain is essential for the dynamic modelling of the electrical motors using FEM.

Figure 3. The analysis procedure for coupling an electrical circuit of PMSM using Ansys Maxwell and Ansys Maxwell Circuit Editor.

The analysis procedure of the FE model coupled with an electrical circuit is shown in figure 3. There are three important steps to validate the co-simulation of FE model of PMSM with the electrical circuit: Firstly, the machine geometry is created in Ansys RMxprt/Maxwell, which is an analytical machine solver where the user specifies the electrical parameters (output power, frequency and voltage) and the geometrical dimensions of the machine. Secondly, when the RMxprt model was analysed, it was exported to the 2D model using the Ansys Maxwell. Then, the machine takes a long time to simulate the model. Finally, the machine is first created in Ansys Maxwell, then exported in Ansys Maxwell Circuit Editor for co-simulation by establishing interface between Circuit Editor and Maxwell. Therefore, all the simulation results are validated by the dynamic model and the co-simulation of the two environment Maxwell and Circuit Editor.

B. Electric Circuit of Permanent Magnet Motor and coupling Component

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The circuit was created using the Ansys Maxwell Circuit Editor, a program for designing an electric circuit which is used to solve the problems of transient Maxwell. The electrical coupled circuit of the PMSM model is shown in figure 4, where the parameters of the machine and the electric sources are coupled with FEM model in Ansys Maxwell. In this circuit, the three winding, called LPhaseA, LPhaseB and LPhaseC, from the Maxwell 2D model was implemented. The resistances (RA, RB and RC) and the inductances (LA, LB and LC) must have the same name in FE model. The power source is considered as a voltage source connected in the series with the inductances and resistances of the stator windings. The voltage relations for the three phases are defined as follow:

(10)

Figure 4. External electric circuit coupled to Ansys Maxwell.

Simulation results of the PMSM in healty operating conditions are depicted in figure 5.It shows the electromagnetic torque, the stator winding currents and the stator induced voltage from the FE model in healthy operating conditions. It can be noted that the mean torque is about 50 Nm as expected. The peak value of the currents and the induced voltage are respectively 43.55 A and 150 V.

(a)

(b)

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(c)Figure 5. Simulation results of PMSM in normal operating conditions: (a) Electromagnetic torque,(b) Stator

winding currents and (c) Stator induced voltage.

Analyzing the flux distributions density in the machine’s core reaches satisfactory values without any highly saturated regions is given in figure 6.

Figure 6. Flux distributions of the PMSM in healthy case.

3. PMSM inter-turn Fault Model

Before you begin to format your paper, first write and save the content as a separate text file. Keep your text and graphic files separate until after the text has been formatted and styled. Do not use hard tabs, and limit use of hard returns to only one return at the end of a paragraph. Do not add any kind of pagination anywhere in the paper. Do not number text heads-the template will do that for you.The inter-turn short circuit in the one of the stator coils is the most common fault in the permanent motor [17]. This type of fault is a major reason for the stator winding failures to prevent further damage to the machine. In this work, the stator winding of a PMSM with inter-turn fault is represented in figure 7. The fault is occurred in the

phase A and represents the fault insulation resistance. When fault resistance varies, the insulation fault evaluates toward an inter-turn full short circuit.

Figure 7. External electric circuit coupled to Ansys Maxwell with inter turn fault.

For three different values of fault insulation resistances: : , and , the electromagnetic

torque, the Stator winding currents, the stator induced voltage and the fault current ( ) of the circuit model and the FEM are presented respectively in figure 8, figure 10 and figure 12.

C. Abbreviations and Acronyms

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Define abbreviations and acronyms the first time they are used in the text, even after they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, sc, dc, and rms do not have to be defined. Do not use abbreviations

in the title or heads unless they are unavoidable. :

(a)

(b)

(c)

(d)

Figure 8. Simulation Results of the PMSM in faulty conditions with :(a) Electromagnetic torque, (b) Stator winding currents, (c) Stator induced voltage and (d) fault currents.

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Figure 9. Flux distributions of PMSM in faulty case .

(a)

(b)

(c)

(d)

Figure 10. Simulation Results of the PMSM in faulty conditions with : (a) Electromagnetic torque,(b) Stator winding currents ,(c) Stator induced voltage

and (d) fault currents.Page | 7



(a)

(b)

(c)

(d)

Figure 12. Simulation Results of the PMSM in faulty conditions with :

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(a) Electromagnetic torque, (b) Stator winding currents, (c) Stator induced voltage and (d) fault currents.


The results in figure 8, figure 10 and figure 12 prove that the average values of electromagnetic torque decrease with the increase of the fault resistance. It can be seen that when the fault resistance decreases, the current magnitude of the affected phase and the fault current magnitude increase and the phase current became more unbalanced and nonsinusoidal.The results in figure 9, figure 11 and figure 13 show the flux distributions that the magnetic flux concentration is observed around the phase’s short circuit. We can notice that the region around the phase’s short circuit of the stator has a higher degree of saturation. The magnetic density of the faulty motor is higher than the healthy one where the significant change in the magnetic flux density in the stator slots is saturated and highlighted in red circles.

4. Fast Fourier Transform (FFT) Analysis

More frequently, the fault detection in PMSM has been studied by analyzing the stator current harmonics by the mean of the well-known Fast Fourier transform . This analysis has been extended to the PMSM, which frequency analysis of a signal highlights many important hidden features and extracts some useful information [9-14]. Figure 14 shows the FFT of the phase A current and the electromagnetic torque of a healthy machine obtained by Ansys Maxwell simulation.

(a) (b)

Figure 14. (a) FFT of the electromagnetic torque and (b) FFT of the

phase currents (Phase A) of healthy machine.

In this section the results of the FEM simulations, presented respectively in figure 15, figure 16 and figure 17, show the electromagnetic torque and the stator current harmonic content for an inter turn fault with different values of the fault

resistance ( , and ). When the inter-turn fault occur, the phase A current fundamental wave magnitude significantly reduces relative to the stator normal condition. With the increase of the electromagnetic torque, the fundamental wave magnitude gets smaller and smaller. As it can be seen through figure 15, figure 16 and figure 17, the occurrence of the inter-turn fault increases significantly the magnitudes of several sidebands around the fundamental and their magnitude increases.

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(a) (b)

Figure 15. (a) FFT of the electromagnetic torque and (b) FFT of

the phase currents (Phase A) .

(a) (b)


the phase currents (Phase A) .

(a) (b)


the phase currents (Phase A) .cursor up to highlight all of the above author and affiliation lines. Go to Column icon and select “2 Columns”. If you have an odd number of affiliations, the final affiliation will be centered on the page; all previous will be in two columns.

Table 1 presents the stator currents of phase A spectral harmonics of a healthy machine and for inter-turn fault machine

for respectively fault resistances , and . The value of current in phase A has been

increased when the fault resistance was increased.

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Table 1: The spectral components and the average value of thecurrent in phase A.

Current Phase A Spectral

ComponentsCurrent Phase A

Values(A)50 Hz 100 Hz

Healthy 43.587 - 43.557Fault1 ( )

58.334 1.316 59.240

Fault2 ( ) 72.853 1.634 70.213

Fault3 ( ) 79.696 2.676 81.402

5. CONCLUSION

In this paper, a dynamic model coupling 2D FEM in Ansys Maxwell Software and equivalent circuit simulation in Ansys Maxwell Circuit Editor Software is proposed to compute the performances of a PMSM with an intern-turn fault. The nonlinear magnetization characteristics have been considered and calculated using the FEM. Connecting the Ansys Maxwell and the Ansys Maxwell Circuit Editor, the dynamic model of the PMSM is constituted and a co-simulation is performed. The detection of the short circuit of turns for a PMSM has been analyzed by means of FEA and advanced signal processing. In order to highlight the effect of the inter turn fault, the harmonic spectral analysis and the symmetrical components for the phase current and the electromagnetic torque are carried out.

Table 2: Specification Adopted of PMSM.Parameters Values

Number of poles 4Output power 15 K wRated voltage 127 V

Speed 1500 rpmFrequency 50 Hz

Operating temperature 75 ° C

Table 3: Stator parameters. Table 4: Rotor parameters.Parameters Values

Outer diameter 180 mmInner diameter 92 mm

Length 101 mmStacking factor 0.95

Steel type D23-50Number of slots 24

Parameters Values Outer diameter 91 mmInner diameter 40 mm

Length 101 mmStacking factor 0.95

Steel type D23-50

6. ACKNOWLEDGMENT

This work was supported by the Ministry of the Higher Education and Scientific Research in Tunisia.

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