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  1. 1. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257 Comparison of 2D and 3D Modeling of Hysteresis Motor with HTS Element in the RotorJoyashree Das (Research Scholar), Rup Narayan Ray (Associate Professor) Deptt. of Electrical Engg., National Institute of Technology Agartala, Agartala-799055, INDIA.Abstract efficient analysis method, various formulations are This paper presents 2D and 3D modeling compared for hysteresis region and it is proved thatof hysteresis motor using high temperature pseudo-permeability method is most effective [3].superconducting element Yttrium Barium D. Inacio et al., investigated the numerical andCopper Oxide (YBCO) in the rotor. These experimental techniques for the comparison of bothhysteresis motors aim to improve the conventional and high temperature superconductingperformance in comparison with that of hysteresis motor. High temperature superconductingconventional hysteresis motors. Various element (YBCO) is used as a rotor of HTSperformance parameters of high temperature hysteresis motor and simulations are performed insuperconducting hysteresis motor are computed finite elements software FLUX2D [4]. The drumfrom the proposed 2D and 3D modeling. The and disc type hysteresis machine withhysteresis loop thus obtained is used to find superconducting rotors is proposed to obtain thetorque and ac losses for variable applied current. optimal solution of the machine. For this analysis,The measured parameters are compared with the finite element modeling software Flux2D was usedexperimental data and both are found to be in [5]. The optimization technique of a coreless dualgood agreement. All the simulations are discs hysteresis motor (CDDHM) is developedperformed using MATLAB 7.5 and FEM based using genetic algorithm [6]. A high efficiencyCOMSOL Multiphysics software. operation scheme of a hysteresis motor is implemented which is driven by pulse widthKeywords: High Temperature Superconducting modulator (PWM) for a short duration over-(HTS) Hysteresis Motors, Yttrium Barium Copper excitation [7-9]. Changing magnetic property of theOxide (YBCO), Finite Element Method, COMSOL rotor using different types of rotor materials is oneMultiphysics. of the techniques to improve performance of the machine. Some of the examples are explained in this1. Introduction section using different materials. Now-a-days, high temperature In 1994, a new class of electromechanicalsuperconducting (HTS) hysteresis synchronous converters type hysteresis machines is designed withmotors have received attention because of their solid high temperature superconducting material ineconomical advantage as well as noiseless the rotors. The comparative analysis of both theoperation, small size, self-starting torque and traditional and superconducting motor performancelightweight compared to the conventional motors has been successfully carried out [10]. A cylindrical[1]. The possibility of incorporating HTS into power melt-textured YBCO blocks is used in the rotor ofapplications such as electrical motors, generators, hysteresis motor. This motor presents the detailedbearings and fault current limiters have attracted investigation on magnetic processes in these rotors.much attention. Hysteresis superconducting motors It is also found that the construction of electrooffer the simplest construction. Due to global motors with increased power density is possible ifinterest along with industrial applications, the HTS materials are used [11]. HTS electricaloptimal performance study of the motor is most machines (hysteresis and reluctance machines) withimportant. There are various techniques available to YBCO materials in the rotor are developed and it isimprove performance of the machine. The literature found that the specific output power of liquidstudy regarding the performance improvement of nitrogen cooled HTS motors with bulk YBCOthe machine is presented in this section. The elements can be higher than the conventional motorsmathematical technique with type-II [12]. Based on high temperature superconductorssuperconducting material in the rotor is developed such as YBCO and Ag-BSCCO elements in thebased on the critical state model for obtaining the rotor of various shape, a new type of electricalcurrent and field distributions within the motors is implemented. It is observed that the torquesuperconducting pieces using the finite element is linearly proportional to total hysteresis losses inmethod [2]. The finite element analysis of hysteresis the HTS rotor and independent on the rotor angularmotor using magnetization-dependent model is velocity [13-14]. An axial type HTS hysteresisemployed as a hysteresis model. To find the motor is designed. In this HTS hysteresis motor, the rotor consists of BSCCO element with the objective 1248 | P a g e
  2. 2. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257of increasing power densities and reducing losses. performance analysis, which is not reported untilThe experimental results are also presented for HTS now. Hence, 3D modeling of HTS hysteresis motorhysteresis motor [1]. A HTS 150 kW reluctance is proposed which is more precise and realistic andmotor is constructed with YBCO material that very useful in simulations. This paper is organizeddiscussed the demands on YBCO bulk material in as follows: Section 2 describes about the modelingsuperconducting motor for high performance and of hysteresis motor. In Section 3, simulation andalso presents the conceptual design of a experimental results are shown, and finally,superconducting linear motor and future conclusions are drawn in Section 4.applications for superconducting motors of mediumpower range [15]. The performance of an axial type 2. Modeling of Hysteresis Motormotor with a Bi-2223 HTS bulk rotor is fabricated 2.1. Conventional hysteresis motorand tested. It shows both the characteristics of The topology of hysteresis motor is shownconventional induction and hysteresis motor [16]. in Fig. 1. The main parts of hysteresis motor areRadial flux type of hysteresis motor is also stator and rotor. In this motor, the armature windingdeveloped. In this motor, the rotor is made up of Fe- is built in the stator slots and it consists ofCr-Co magnet steel [17]. The operation principle conventional copper conductors to create theand theoretical aspects of both the conventional and magnetic rotating field and the stator core is made ofHTS hysteresis motors are discussed. In this type of iron. The rotor of this type motor consists of hardHTS hysteresis motor, YBCO element is used in the iron ring with a high degree of magnetic hysteresis.rotor. The characteristics of both motors are Due to the use of magnetic materials in the rotor,implemented and compared. It shows that the torque there is no dc excitation in the rotor. The shaft isand power ranges of HTS hysteresis motor are made up of paramagnetic material [4].usually higher than the conventional hysteresismotor [4]. Due to the simple construction of HTShysteresis machines, superconducting (YBCO) rotoris used in drum and disc type of hysteresismachines. The torque of HTS hysteresis motorproduces from the repulsion of the magnetic polesinduced into the HTS rotor by the rotating field ofthe stator winding [5]. Several international research groups haveexplored the use of HTS materials in theconstruction of rotor of hysteresis motors [5], assuperconducting materials has the ability to trap thehigher magnetic field, higher flux density andcarries greater current density at higher magneticfield, high magnetic permeability, high saturationmagnetization consequently the developed poweralso gets increased. Some exclusive superiority of Fig. 1. Hysteresis motor layout [4].superconducting synchronous machines over itsconventional machines have better torque to volume 2.2. 2D modeling of HTS hysteresis motorratio [4-5], compact size, light weight and reduced The schematic diagram of HTS hysteresislosses for the same power [4],[18]. During last two motor is shown in Fig. 2. Superconductingdecades, different types of hysteresis machines have hysteresis motor is almost identical withbeen constructed successfully [19-22]. conventional hysteresis motor but its rotor is made There are several simulation tools available up of HTS materials (YBCO). The rotor core isto model the HTS hysteresis motor using finite constructed with paramagnetic materials. In thiselement method (FEM) [5]. For the purpose of HTS hysteresis motor aluminum is used as aanalysis, 2D modeling of the machine is generally paramagnetic material only for mechanical supportadopted. However, 2D modeling of HTS hysteresis of the HTS elements [5]. In this case the shaft alsomotor has the limitation to analyze performance of consists of paramagnetic material and steel is usedthe machine. Due to the rotation of the magnetic as a paramagnetic material. A singledomains, magnetic material shows 3D magnetic superconducting cylinder cannot be constructed dueproperty even under 2D rotating magnetic to the brittle nature of YBCO materials. So theexcitation. The modeling and analysis of segments are assembled with epoxy resin [4], [5].magnetization process of the motor can be Huge numbers of segments are advantageous forcompleted if 3D properties are properly considered. large shielding [2]. If the numbers of the circularIt calculates the magnetic fields around and inside sectors are increased, the flux distribution inside thethe motor. A better precision may be obtained if 3D HTS rotor is also increased because of the presencemodeling is incorporated for the purpose of of paramagnetic materials between them. But the 1249 | P a g e
  3. 3. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257numbers of circular sectors are limited, otherwiseflux leakage increases with increase of the number  Therefore,  H  μσ H t  0 2    (2)of sectors and thus the developed torque of the  Hxhysteresis motor will decrease [5]. Here, H is magnetic field (A/m), H =   and  Hy 2D  Hx   Hy     Hz  3D   Where, μ is permeability (H/m), σ is conductivity (S/m) and B r is residual flux density (T) respectively. After determine the value of H, the value of current density (J) is obtained using the following equation   J   H (3) Then the electric field E is calculated using the E-j power law  Fig. 2. Schematic diagram of HTS hysteresis motor  nin COMSOL MULTIPHYSICS. E  Ec J J c (4) Where, Ec is critical electric field (V/m), Jc is critical2.3. Proposed 3D modeling of HTS hysteresis current density (A/m2) and n is power indexmotor respectively. 3D HTS hysteresis motor has the same After determining E and J, total ac loss Q ismaterials and specifications as 2D HTS hysteresis obtained bymotor except the motor is replaced by the 3- Tdimentional model. The 3D view of HTS hysteresis Q 1 T   (J  E)dsdt (5)motor is shown in Fig. 3. 0 s Where, T is time period.Fig. 3. 3-dimentional view of HTS hysteresis motorin COMSOL MULTIPHYSICS. The hysteresis loop is the most importantphenomenon in any hysteresis motor and E-Hformulation is the most useful expression of anelectromagnetic field [23]. Therefore, the basicelectromagnetic equation for the HTS hysteresismotor is Fig. 4. Flow chart   E   B t 3. Simulation and Experimental Results (1) Both 2D and 3D high temperatureWhere, E is electric field (V/m) and B is magnetic superconducting hysteresis motors are numericallyflux density (T). simulated using the software COMSOL Multiphysics and based on finite element method. 1250 | P a g e
  4. 4. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257The E-j power law derived in Eq. (4) and it is used shows the mesh of a 2D and 3D HTS hysteresisto calculate the ac losses of HTS hysteresis motor. motor.The specifications of the high temperaturesuperconducting material used in the rotor of theHTS hysteresis motor is shown in Table 1 and alsothe dimensions of the conventional and HTShysteresis motor is shown in Table 2.Table 1. Specifications of the HTS material used inthe rotor. Name of the sample YBCOOuter radius(cm) 2.17Inner radius(cm) 1.82Thickness(cm) 0.35Critical electric field(V/m) 104Initial Conductivity (S/m) 2D 1016Critical current density(A/m2) 4  10 7Table 2. Dimensions of HTS and conventionalhysteresis motor. Dimensions HTS Conventional hysteresis hysteresis motor (cm) motor (cm)Stator Outer Radius 4 6Rotor Outer Radius 2.17 2.8Rotor Inner Radius 1.82 2.625Air-gap 0.1 0.1 The mesh statistics are applied to 3Ddiscretized the HTS hysteresis motor into finiteelements. In order to have high level of accuracy the Fig. 5. Mesh of 2D and 3D HTS hysteresis motor.automatic mesh diagram is not used and a meshdiagram is designed manually. In this simulation, 3.1. Magnetic flux distribution in HTS hysteresisthe numbers of nodes are higher around the air gap motorand hysteresis rotor. From this mesh statistics, Fig. 6 shows the streamline plot ofvarious parameters are known, shown in Table 3. magnetic flux density in a 2D and 3D HTS hysteresis motor. It is observed that two poles haveTable 3. Mesh statistics of HTS hysteresis motor been created in both 2D and 3D HTS hysteresis motor and also three-dimensional model calculates Mesh statistics 2D 3D magnetic fields around and inside the hysteresis Mesh Triangular Tetrahedral motor. The transport current of non-HTS stator Number of elements 17432 23564 produces rotating field in the air gap between the Number of degrees of 34754 100531 stator and the rotor of the motor, which in turn freedom induces currents in the superconductor and thus the Number of boundary 1234 5012 HTS rotor is magnetized. Because of the high elements current leading ability of the HTS material, most of Solution time (s) 26.219 94.9282 the fluxes are trapped in the HTS hysteresis rotor. This phenomenon is shown in the plots of flux density (B) and magnetic field (H) in 2D and 3D The solution time is changed due to change HTS hysteresis motor in Fig. 7 and Fig. 8. From the values of various parameters but the number 7 and Fig. 8, it is observed that compared to theof elements and number of degrees of freedom will other region the magnetic flux concentration is moreremain same unless the geometry is changed. Fig. 5 inside the HTS rotor and the flux density and magnetic field in 3D HTS hysteresis motor is higher 1251 | P a g e
  5. 5. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257than 2D HTS hysteresis motor for the samecondition. b 2D c d Fig.7. a. Magnetic flux density (B) plot of a 2D HTS hysteresis motor, b. Magnetic flux density (B) (Top view) plot of a 3D HTS hysteresis motor, c. 3D Magnetic flux density (B) [at (1,1,1)] plot of a 3D HTS hysteresis motor, d. Magnetic flux density (B)Fig. 6. Streamline plot of magnetic flux density of a plot of a 3D HTS hysteresis motor (at level 5).2D and 3D HTS hysteresis motor. a a 1252 | P a g e
  6. 6. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257 0.8 2D 3D 0.6 0.4 Magnetic flux density(B) (T) 0.2 0 b -0.2 -0.4 -0.6 -0.8 -3 -2 -1 0 1 2 3 4 Magnetic field(H) (A/m) 5 x 10 Fig. 9. B-H loop of a 2D and 3D HTS hysteresis motor. 3.3. Effects of applied current on torque of a HTS c hysteresis motor The area of hysteresis loop isFig. 8. a. Magnetic field (H) plot of a 2D HTS approximately proportional to the applied currenthysteresis motor, b. Magnetic field (H) [at (1,1,0)] that is calculated in the last section. It is also knownplot of a 3D HTS hysteresis motor, c. Magnetic field that the torque is directly proportional to the area of(H) at (1,1,1) plot of a 3D HTS hysteresis motor. the hysteresis loop. Therefore, the torque is directly proportional to the current. The torque in hysteresis3.2. Hysteresis loop of HTS hysteresis motor motor is calculated using the Due to the application of variable transport  1 currents of different magnitudes in the non-HTS relation, T    PVr Ah , [3] where, P isstator conductors, different flux plots are obtained.  2Π The values of magnetic fields (H) and the flux number of pole pairs, V r is volume of the HTSdensities (B) at different positions on the HTS rotorhave been taken and then the hysteresis loops are rotor and A is area of the hysteresis loop in the hplotted. The areas of the hysteresis loops Fig. 9 are HTS rotor. MATLAB program has been developedchanged at different stator current. Due to the higher to draw the hysteresis curves and the correspondingvalue of magnetic field and flux density in 3D HTS torque developed in the motor. As shown in Fig. 10,hysteresis motor than 2D HTS hysteresis motor, the the torque changes almost linearly with the appliedarea of the 3D hysteresis loops are larger than the current and that is the common feature of any2D hysteresis loops shown in Fig. 9. When the hysteresis motor [3], because of the area of theapplied current in the stator is increased resulting hysteresis loop is approximately proportional to thethe increase of field strength of rotating magnetic applied current. It is also observed that the value offield in the air gap, more fluxes are trapped into the torque in 3D HTS hysteresis motor is higher thanHTS material. The area of the hysteresis loop is also 2D HTS hysteresis motor as well as conventionalincreased and thus the power density of the hysteresis motor. The simulation result shows ahysteresis motor is increased. good agreement with the experimental results of a conventional hysteresis motor [3], [24-25] as shown in Table 4. 1253 | P a g e
  7. 7. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257 0.38 Experimental 0.36 2D Numerical 3D Numerical 0.34 0.32 Torque (Kg-cm) 0.3 0.28 a 0.26 0.24 0.22 0.2 100 105 110 115 120 125 130 135 Applied current (mA)Fig. 10. Torque vs. current of 2D and 3D HTShysteresis motor. bTable 4. Comparison between 2D, 3D HTS andconventional hysteresis motor.Parameter 2D 3D Experimental (HTS) (HTS) (Conventional) Torque 0.2664 0.2679 0.2647 (Kg-cm)3.4. Current density plot in a HTS hysteresismotor The Fig. 11 shows the current density plot cof a 2D and 3D HTS hysteresis rotor. Due to thetrapped field effect in the HTS hysteresis rotor, the Fig. 11. a. Current density plot of a 2D, b. currentcurrent density also more in that region but it is not density (top view), c. current density plot 3D HTSuniform due to the anisotropic conductivity of the hysteresis rotor.superconducting material. When the trapped fieldsare gradually decreased in the inner part of the HTS 3.5. Losses in a HTS hysteresis motorrotor, the current density also gradually decreases It is known that the torque is directlyand becomes minimum in the inner part of the rotor. proportional to the hysteresis loss in theIn both of the HTS hysteresis motors, the value of superconducting element [4]. Thus, the loss canpower index (n) is 15 and the value of integral of also be calculated from the torque and it iscurrent density in the 2D HTS rotor independent of the field rotational frequency [1]. This torque is already calculated in last 3.07691610 A/m and 3D HTS rotor is 6 2 When the applied current is increased, the HTS have8.34053 10 A/m . It is observed that the value 6 2 the trend to either have a larger amount of current orof integral of current density is less compared to the greater volume of current. When the HTS is incritical current density ( 4 10 A / m ) and it is maximum current carrying condition, there is no 7 2also observed that the current density in 3D HTS additional volume for the new current to flow, thushysteresis motor is higher than 2D HTS hysteresis the magnitude of current will increase. According tomotor. E-j power law, when applied current increases, the current density and electric field is also increased as a result of this the value of AC loss (Q) is also increased following eq. (5), which is proportional to the product of E and J. The AC losses have been calculated with different peak values of applied current, shown in Fig. 12. This is because the E-j power law is used with the power index n=15. From this plot, it is observed that the AC loss increases with the increase of applied current. 1254 | P a g e
  8. 8. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257 x 10 -3 segmented rotors. Physica C: 1.7 2D Superconductivity, 331(2), 133-140. 1.65 3D [3] Hong-Kyu, Kim, Sun-Ki, Hong, & Hyun- Kyo, J. (2000). Analysis of hysteresis 1.6 motor using finite element method and 1.55 magnetization-dependent model. IEEE AC loss (W/m) Transactions On Magnetics, 36(4), 685- 1.5 688. 1.45 [4] Inacio, D., Inacio S., Pina, J., Goncalves, 1.4 A., Ventim, Neves, M., & Rodrigues, Leao, A. (2007). Numerical and 1.35 experimental comparison of 1.3 electromechanical properties and efficiency 100 105 110 115 Applied current (mA) 120 125 of HTS and ferromagnetic hysteresis motors. 8th European Conference On Applied Superconductivity (EUCAS 2007),Fig. 12. AC loss vs. applied current of 2D and 3D 1-7.HTS hysteresis motor. [5] Rodrigues, Leao, A. (2009). Drum and disc type hysteresis machines withTable 5. Comparison between 2D and 3D HTS superconducting rotors. IEEE, 55-59.hysteresis motor. [6] Sadeghi, H., M., & Darabi, A. (2010). Optimization of a new type of hysteresis Parameters 2D 3D motor using genetic algorithm. EEEIC, 479-482.AC loss(W/m) 1.4348e-3 1.4753e-3 [7] Kubota, T., Tamura, T., & Kurihara, K. (2009). High-efficiency operation of PWMCurrent density 3.076916 8.340531 inverter-driven hysteresis motor with short- 2 duration overexcitation. Proc. Int. Conf.( A/mm ) Elect. Mach. And Systems, 1-4. [8] Kubota, T., Tamura, T., & Kurihara, K.4. Conclusion (2010). New scheme for high-efficiency In this work, modeling of 2D and 3D operation of PWM inverter-drivenhysteresis motors using HTS material are presented hysteresis motor with short-durationand the computed parameters are compared with the overexcitation. International Conferenceexperimental ones. All the simulated results show a on Electrical Machines, 1-6.good matching with the experimental results and it [9] Kubota, T., Tamura, T., & Kurihara, K.also shows that the bulk HTS material can trap (2010). Characteristics of PWM inverter-higher value of magnetic field compared to ferro- driven hysteresis motor with short-durationmagnetic material. The three dimensional model overexcitation. ICEMS, 1429-1433.calculates magnetic fields around and inside the [10] Kovalev, L., K., Ilyushin, K., V., Penkin,motor and gives better results of motor performance. V., T., & Kovalev, K., L. (1994).It has been observed that the developed torque Hysteresis machines with high temperatureincreases almost linearly with the increase of the superconducting rotors. Elsevier Science,applied current. Three dimensional modeling of 145-170.HTS hysteresis motor is proposed which is more [11] Habisreuther, T., Strasser, T., Gawalek, W.,precise and realistic and very useful in simulations. Goorner,t P., Ilushin, K., V., & Kovalev,The proposed 3D modeling of HTS hysteresis motor L., K. (1997). Magnetic processes ingives superior results compared to 2D modeling as hysteresis motors equipped with melt-far as the experimental results are concerned. textured YBCO. IEEE Transactions On Applied Superconductivity, 7(2), 900-903.References [12] Kovalev, L., K., Ilushin, K., V., Koneev, [1] Muta, I., Jung, H. J., Hirata, T., Nakamura, S., M., A., Kovalev, K., L., Penkin, V., T., T., Hoshino, T., & Konishi, T. (2001). Poltavets, V., N., Gawalek, W., Fundamental experiments of axial-type Habisreuther, T., Oswald, B., & Best, K., J. BSCCO-bulk superconducting motor (1999). Hysteresis and reluctance electric model. IEEE Transactions On Applied machines with bulk HTS rotor elements. Superconductivity, II (I), 1964-1967. IEEE Transactions On Applied [2] Barnes, G. J., McCulloch, M. D., & Dew- Superconductivity, 9(2), 1261-1264. Hughes, D. (2000). Torque from hysteresis [13] Kovalev, L., K., Ilushin, K., V., Kovalev, machines with type-II superconducting K., L., Penkin, V., T., Poltavets, V., N., 1255 | P a g e
  9. 9. Joyashree Das, Rup Narayan Ray / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1248-1257 Gawalek, W., & Habisreuther, T. et al. Material Science and Engineering B53, (1998). Hysteresis electrical motors with 211-215. bulk melt texture YBCO. Material Science [20] Chun, Y. D., Kim, Y. H., Lee, J., Hong, J. and Engineering, 216-219. P., & Lee, J. W. (2001). Finite element[14] Kovalev, L., K., Ilushin, K., V., Koneev, analysis of magnetic field in high S., M., A., Kovalev, K., L., Penkin, V., T., temperature bulk superconductor. IEEE Modestov, A., K., Larionoff, A., S., Trans. On Applied Superconductivity Gawalek, W., & Oswald, B. (2001). HTS 11(1), 11(2), 2000-2003. electrical machines with YBCO bulk and [21] Suguira, T., Shashizume, H., and Mika, K. Ag-BSCCO plate-shape HTS elements: (1991). Numerical electromagnetic field recent results and future development. analysis of type II superconductors. Int J. Physica C: Superconductivity, 354(1-4), of Applied Electromagnetics in Materials 34-39. 2, 183.[15] Oswald, B., Krone, M., Strasser, T., Best, [22] Nakamura, T. et al. (2004). K., J., & Soil, M. et al. (2002). Design of Synchronization of an axial type Bi2223 HTS reluctance motors up to several bulk motor operated in liquid nitrogen. hundred kW. Physica C: Superconductor Science and Technology Superconductivity, 372-376 (2), 1513- 17, 1319-1323. 1516. [23] Chari, M. V. K., and Silvester, P. P. (1980).[16] Muta, I., Jung, H., Nakamura, T., & Finite Elements in Electrical and Magnetic Hoshino, T. (2002). Performance of axial- Field Problems. New York: John Willy and type motor with Bi-2223 HTS bulk rotor. Sons, 31-36. Physica C: Superconductivity, 372-376(3), [24] Sun-Ki, Hong, Hong-Kyu, Kim, Hyeong- 1531-1534. Seok, Kim, & Hyun-Kyo, J. (2000). Torque[17] Wakui, G., Kurihara, K., & Kubota, T. calculation of hysteresis motor using vector (2007). Radial flux type hysteresis motor hysteresis model. IEEE Transactions On with rotor ring of sprayed surface layer. Magnetics, 36(4), 1932-1935. Electrical Engineering in Japan, 112(4), [25] Lee, Hak-Yong, Hahn, Song-yop, Park, 132-143. Gwan-Soo, & Lee, Ki-Sik (1998). Torque[18] Match, L., & Morgan, J. (1986). computation of hysteresis motor using Electromagnetic and Electromechanical finite element analysis with asymmetric Machines. Wiley & Sons. two dimensional magnetic permeability[19] McCulloch, M., & Dew-Hughes, D. tensor. IEEE Transactions On Magnetics, (1998). Brushless ac machines with high 34(5), 3032-3035. temperature superconducting rotors. 1256 | P a g e