Simulation of High Temperature Superconducting Hysteresis Motor using MATLAB and COMSOL Multiphysics

Simulation of High Temperature Superconducting Hysteresis Motor using MATLAB and COMSOL Multiphysics

Joyashree Das* Dr. Rup Narayan Ray

Deptt. of Electrical Engineering, Deptt. of Electrical Engineering, NIT, Agartala, NIT, Agartala,

West Tripura-799055, India West Tripura-799055, India

Abstract

In this paper, a 2-pole, 50 Hz high temperature superconducting hysteresis motor has been numerically simulated using finite element method for its performance calculation. In this high temperature superconducting hysteresis motor, conventional copper winding is used in stator and the rotor consists of high temperature superconducting material which possess higher flux density consequently current density gets increased and the developed power also gets increased. To reduce the huge investments, errors and computational time for this work , numerical simulations are preferred over practical experiments. The performance parameters are compared with that of the conventional hysteresis motor in which ferro-magnetic material is used as a rotor. All the simulations are performed using MATLAB and partial differential

equation based module of COMSOL Multiphysics software with proper boundary conditions. The simulation result shows a good agreement with the experimental results.

1. Introduction

Hysteresis motor is special type of synchronous motor with uniform air gap and there is no dc e xcitation in the rotor because of the magnetic materia l used in the rotor. Initia lly the rotor starts rotating due to the combined effect of hysteresis and eddy currents induced in the rotor. The mechanical torque of this motor is produced in the hardened steel rotor by the action of rotating m.m.f. of the stator winding. The torque is proportional to

the area of hysteresis loop. The rotor of hysteresis motor has no winding, no teeth thus it has low noise operation. It has simp le structure with conventional stator winding, light weight, high self- starting torque during the run-up, constant speed, moderate start up current that is usually 180% less than the full load current and also pulls wide range of loads with different inert ia into synchronism [1-4]. These exc lusive advantages make the hysteresis motor especially suitable for wide range of industrial applications such as ATM, air conditioner, entry verificat ion, tele- printer, sound recorder etc. In spite of these advantages, the conventional hysteresis motor still suffers fro m some limitat ions. There are different techniques are available to imp rove performance of the machine. Therefore, improve ment in magnetic property of the rotor using different types of rotor materia ls is one of the techniques. Several international research groups have explored the use of HTS materia ls in the construction of rotor of hysteresis motors [2], as superconducting materia ls has the ability to trap the magnetic field as high as possible and carries greater current density at higher magnetic fie ld, high magnetic permeab ility, h igh saturation magnetizat ion and low losses . Some e xc lusive superiority of superconducting synchronous machines over its conventional mach ines have better torque to volume ratio [1], reduced size and losses for the same power [3],[4]. No wadays the applications of superconductors in rotating electrica l mach ines are getting more importance, resulting in greater overall efficiency,

increased current density, more power output, lower size and weight and better environmental impact. Hysteresis motor with high temperature superconducting rotor instead of rotor with conventional ferro magnetic material has been proved to be the most viable electrical machines with HTS materia l [4]. In conventional ferro magnetic material hysteresis is a non-linear magnetic property whereas in high temperature superconductors it is an ohmic property and related with the vortices dynamics [4].

The object of this investigation is to design a hysteresis motor with high temperature s uperconductor in the rotor. The studies of this type of motors through experiments involve huge cost, computational time, e rrors etc. Therefore fin ite ele ment based simulat ion techniques are opted here. Because it is much cheaper to design, simulate and correct the exact model in the computer than to build the real model with mistakes. The results are simu lated through the program written in MATLAB and using FEM based software COMSOL Mult iphysics.

2. Modeling of hysteresis motor

1. Conventional hysteresis motor

   The stator of hysteresis motor consists of copper winding and it is used to create the rotating magnetic field that drags the rotor. The rotor is made up of hard iron ring with a high degree of magnetic

   hysteresis. In this case motor shaft is made up of paramagnetic material [4]. The layout of hysteresis motor is shown in Figure (1).

   Figure 1. Hystere si s motor layout [4].

2. Proposed high temperature

superconducting hysteresis motor

Superconducting hysteresis motor is almost identical with conventional hysteresis motor but its rotor is constructed fro m HTS materia ls (YBCO). In this motor, stator consists of conventional copper conductors. However, the rotor core is made up of paramagnetic materials, alu minum is used as a paramagnetic materia l, they provide the mechanica l support to the HTS e le ments [2] and the shaft consists of para magnetic material such as steel. The cross-sectional view of HTS hysteresis motor is shown in Figure (2). Due to the brittle nature of YBCO materia ls, a single superconducting cylinder cannot be constructed. So the segments are assembled with non- magnetic materia ls [2], [4] Figure (3). For la rge shielding, mo re segments are

advantageous [5]. If the nu mbers of the circula r sectors are increased, the flu x distribution inside the HTS rotor is also increased because of the presence of paramagnetic materials between them. But the numbers of circular s ectors are limited otherwise flu x leakage increases and thus the developed torque of the hysteresis motor will decrease Table (1) with increase of the number of sectors [2].

Figure 2. Cross-sectional view of HTS hysteresi s motor.

Figure 3. Segmented HTS hystere si s rotor, with two or four segments [4].

Nu mber of segments, n

Table 1. Analytical high field limits of torque [5]

High fie ld

torque limit/ Tma x

3. Proble m formulation

The alternating current of diffe rent magnitudes is applied in the non-HTS stator of a high temperature superconducting hysteresis motor and thus the rotating magnetic field is produced in the air-gap and trapped field produced in the HTS rotor due to high current carrying property. Then the various parameters of a HTS hysteresis motor are ca lculated using finite ele ment method that provides a wide range of simu lation options for controlling the comple xity of both modeling and analysis of a system and similarly, the desired level of accuracy required and associated computational time require ments can be managed simu ltaneously to address most engineering applications [6]. The simu lations are done using MATLAB and finite e le ment method based COMSOL Mult iphysics software.

3.1. Formulation of

electromagnetic problem

It is knownthat E-H formu lation is the most useful exp ression of an electro magnetic field [7]. Therefore, the basic electromagnetic equation for the HTS hysteresis motor is e xp ressed as

H

×E=

t

Where, E is electric field vector [V/ m] and is magnetic permeability of the materia ls [H/ m].

Therefore,

2 H H 0

t

Here, H is magnetic fie ld vector [A/ m].

4. Simulation and results

The HTS hysteresis motors are numerically simu lated using finite ele ment method based software COMSOL Mult iphysics that internally compiles a set of PDEs representing the entire model and also provides tools for plotting and post-processing any model quantity or parameter such as surface plot, contour plot, stream-line plot, cross – section plot and animation etc [8],[9]. The specifications of the high temperature superconducting materia l used in the rotor of the HTS hysteresis motor is shown in Table (2).

Table 2. Specifications of the HTS material used in the rotor.

For the simulation of the HTS hysteresis motor, time dependent solver parameter is used. Where the time stepping is 0:0.001:0.02 (second) and the relative and absolute tolerance is 0.001 second. Figure (4) shows the cross -sectional view of a HTS hysteresis motor and Table (3) gives the geometric data of a HTS hysteresis motor. In Figure ( 4), C1 is stator outer radius, C2 and C3 is outer and inner radius of HTS rotor respectively, C4 is shaft radius and C5 is the copper conductor radius respectively.

Figure 4. Cross-sectional view of HTS Hystere si s Motor in COMSOL MULTIPHYSICS.

Table 3. Geometry of a HTS hystere si s motor in COMSOL Multiphysics

To discretize the HTS hysteresis motor into fin ite ele ments, mesh statistics are applied. Fro m this mesh statistics Table (4), various parameters are known. Figure (5) shows the mesh of a HTS hysteresis motor.

Table 4. Mesh stati sti cs of HTS hystere si s motor

Figure 5. Mesh of a HTS hystere si s motor.

The solution time is changed due to change in the values of various

parameters but the number of ele ments and number of degrees of freedom will re main same unless the geometry is changed. Dirichlet condition is applied in the outer boundary and shaft and Neu mann condition is applied in other boundaries.

1. Magnetic flux distribution in HTS hysteresis motor

   The surface plot of electric field (V/ m) in a HTS hysteresis motor is shown in Figure (6). It is observed that two poles have been created. The stator current produces rotating field in the air gap between the stator and the rotor, which in turn induces currents in the superconductor and the HTS rotor is magnetized. Due to the high current leading ability, most of the flu xes are trapped in the HTS hysteresis rotor. This phenomenon is shown in the plots of magnetic flu x density (B) of a HTS hysteresis motor in Figure (7) and

   Figure 7. Magnetic flux density of a HTS hysteresi s motor.

   Figure 8. Magnetic field of a HTS hystere si s motor.

2. Effects of applied current on torque of a HTS hysteresis motor

The torque in hysteresis motor is calculated using the

1

magnetic fie ld (H) plot of HTS hysteresis motor in Figure (8). It is observed that

relation, T

2

PVr Ah , [10],[11]

the magnetic flu x d istribution is

ma ximu m inside the HTS rotor compared to the other region.

where, P is number of pole pairs, Vr is volume of the HTS rotor and Ah is area

Figure 6. Electric field of a HTS hystere si s motor.

of the hysteresis loop in the HTS rotor. MATLAB progra m has been developed to draw the torque in the motor. As shown in Figure (9), the torque changes almost linearly with the applied curren t, that is the common feature of any hysteresis motor [10]. The simulat ion result shows a good agreement with the e xperimental results [11],[12].

0.36

0.34

0.32

0.3

0.28

0.26

0.24

0.22

0.2

0.18

0.16

100 105 110 115 120 125 130 135

Applied current (mA)

Numerical Experimental

Torque (Kg-cm)

Figure 9. Simulation and experimental results of torque vs. current plot of a HTS hysteresi s motor.

5. Conclusion

In this paper, modeling of high temperature superconducting hysteresis motor is presented and numerically simu lated using MATLAB and COMSOL Multiphysics and then compared with the e xperimental results of conventional hysteresis motor. All the simu lation results are verified with the e xperimental results . So the application of MATLAB and COMSOL

Multiphysics software for performance calculation of hysteresis motor with high temperature superconducting element in the rotor is justified and helps in the numerical ana lysis of various parameters with different geometrica l configurations.

6. References

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2. A. Leao Rodrigues, Drum and Disc Type Hysteresis M achines with Superconducting Rotors, IEEE, 2009, pp. 55-59.

3. M atch, L., and M organ, J., Electromagnetic and electromechanical machines,Wiley & Sons, New-York, 1986.

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5. J. G. Barnes, D. M. M cCulloch, and D. Dew-Hughes, Torque from Hysteresis M achines with Type-II Superconducting Segmented Rotors, Physica C: Superconductivity, vol.331 (Issue 2), 2000, pp. 133-140.

6. J. S. Penn, N. M cN.Alford, D. Bracanovic, and A. Ashraf, Thick Film YBCO Receive Coil for Very Low Field M RI, IEEE Vol.9 No.2, 1999.

7. Chari, M . V. K., and Silvester, P. P., Finite elements in electrical and magnetic field problems, John Willy and Sons, 1980.

8. Hanke, M ichael, Short Introduction to COM SOL M ultiphysics, 2006, pp. 1-6.

9. P. Togni, M. Cifra, and T. Drizdal, COM SOL M ultiphysics in ndergraduate Education of

   Electromagnetic Field Biological Interaction, 2008, pp. 433436.

10. Hong-Kyu Kim, Sun-Ki Hong, and J. Hyun-Kyo, Analysis of Hysteresis M otor using Finite Element M ethod and M agnetization-Dependent M odel, IEEE Transactions On Magnetics, vol.36 No.4, 2000, pp. 685-688.

11. Sun-Ki Hong, Hong-Kyu Kim, Hy eong- Seok Kim, and J. Hyun-Kyo, Torque Calculation of Hysteresis M otor using Vector Hysteresis M odel, IEEE Transactions On Magnetics, vol. 36, no. 4, 2000, pp. 1932-1935.

12. Lee Hak-Yong, Hahn Song-yop, Park Gwan-Soo, and Lee Ki-Sik Torque Computation of Hysteresis M otor using Finite Element Analysis with Asymmetric Two Dimensional M agnetic Permeability Tensor, IEEE Transactions On Magnetics, vol. 34, no 5, 1998, pp. 3032-3035.