2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media,

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1 007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any urrent or future media, inluding reprinting/republishing this material for advertising or promotional purposes, reating new olletive wors, for resale or redistribution to servers or lists, or reuse of any opyrighted omponent of this wor in other wors.

2 HTS Levitated Mobile Tehnology and Prototype Jianxun Jin and Luhai Zheng Youguang Guo, Jiaxin Chen and Jianguo Zhu Center of Applied Superondutivity and Eletrial Engineering Faulty of Engineering University of Eletroni Siene and Tehnology of China University of Tehnology ChengDu, SiChuan Provine, China Sydney, NSW 007, Australia Abstrat The speial reation phenomenon of a high tperature superondutor (HTS) to magneti fields provides an alternative tehnial solution for design of a levitated mobilization syst, in whih a linear motion drive with a HTS inorporated is a ritial issue. This wor presents the design and performane analysis of a HTS linear synhronous driving syst with a prototype built for verifiation. Magneti field finite elent analyses are onduted to ompute the ey parameters, and the steady state harateristi of the syst is predited by using the lassi phasor voltage equation. A simulation model is also built to analyze the syst dynami performane, and results show that the levitated HTS linear motion syst developed an be driven and ontrolled at the desired speed. Index Terms High tperature superondutor (HTS), HTS levitation, magneti field, maglev, linear motor. I. INTRODUCTION Linear motor is a ind of driving equipment for onverting eletrial energy into linear movent diretly without any inbetween transferring organization, and has advantages suh as simple struture, no abrasion, low noise, high auray, and easy to maintain. After a long-term exploration and experimental stages, linear motor has entered the pratial ommodity stage sine the 1970 s. The appearing of new inds of magneti material, ontrol tehnology, and oolant method, reate a solid ondition of linear motor for the eonomial appliation with high speed and high power. In 1990s, the low tperature superondutor (LTS) tehnology was applied to the linear synhronous motor (LSM) as to be the drive power of a maglev train in Japan, whih inreased speed signifiantly. Sine the disovery of high tperature superondutor (HTS) material [1], the HTS linear motor tehnology has soon developed and obtained a fast development as well as a great progress on the HTS applied to onventional rotating mahine and many other fields []-[10]. Now, the developed HTS linear motors mainly in the form of LSM, inlude the (i) HTS buls used in moving seondary [11]-[14], and (ii) the HTS oils applied in the stati primary [15] and an be subdivided into single-side [11],[15] and double-side [1]-[14] in strutures. Beause stable levitation fore an be generated by a permanent magnet (PM) lie NdFeB over a YBaCuO HTS bul [16], HTS levitation syst ontained with PMs and YBCuO buls an be used to develop a HTS linear driving syst. The main advantage of the HTS levitation is its strong levitating fore with passive and selfstabilizing feature [17],[18], leading to the roval of the sophistiated ontrol syst for regulating the air gap between guideway and levitated moving seondary, whih is neessary for other types of levitation transportation systs. So that the levitation syst integrated with HTS are suitable to be applied in a maglev syst for example, and many other transportations and mobilizations. Compared to the onventional linear motors, HTS linear motors have a number of obvious advantages, suh as smaller volume, less weight, bigger propulsion, and higher power fator. This paper presents the development of a HTS LSM driving syst with a small-sale prototype HTS levitated mobile. Both the woring priniples of the linear motor for driving and the PM-HTS buls for lifting the mobile are desribed. For design and performane analysis of the HTS LSM, magneti field finite elent analysis (FEA) is arried out for aurately alulating the major parameters suh as winding flux, ba eletromotive fore (f), winding indutane, and ogging torque. The steady state harateristi of the motor is predited by using the lassi phasor voltage equation, whih an provide a reasonable result if the fundamental omponents of the applied voltage, ba f and urrent are dominant. The lassi phasor voltage equation is used to predit the motor s steady state harateristi under the optimal brushless d ontrol (BLDC) ondition, i.e. the ba f is in phase with the stator urrent. A Matlab/Simulinbased model, apable of taing into aount the real urves of ey motor parameters against mover position, is ompiled to predit effetively the dynami drive performane under a BLDC ontrol she. II. PROTOTYPE AND MAGLEV FORCE Fig. 1 illustrates the she of the HTS prototype levitator propelled by a HTS LSM. The primary and the seondary of the HTS linear motor are omposed of 3Ф opper windings and HTS bul magnets, respetively. The levitated mobile is lifted by a levitation syst onsisting of field-ooled HTS buls on the mobile bottom and PMs plaed on the guideway along the mobile movent diretion. As shown in the Fig. 1, PMs, the same pole in longitudinal diretion and alternating poles of N and S in transverse diretion, are loated at both sides of the primary windings to levitate and guide the mobile. While the levitating fore is diretly proportional to the gradient of magneti field over the guideway, the lateral guiding fore depends on the trapped flux in the HTS buls. The HTS levitation syst has inherent stability in both vertial and lateral diretions, realizes selflevitation and self-guidane without any ative ontrol syst.

3 The levitation fore and guidane fore are generated based on the pinning fore or the shielding fore of the HTS bul [17]-[19]. The magneti levitation fore and guidane fore between a HTS bul and PM are modelled as Fig. and illustrated as Fig. 3. When the materials and dimensions of the PM-HTS buls are properly hosen, an appropriate levitation fore and guidane fore an be generated for levitating and guiding the designed prototype. The levitation fore and guidane fore between a PM and an HTS bul an be alulated based on the Lorentz fore F, whih is related to urrent density J as F = J B (1) Then the HTS-PM levitation fore F Lev and guidane fore F Gui are given by (, ) = ( ', ') ( ', ') F x z J x z B x z dv () Lev y x VSC (, ) = ( ', ') ( ', ') F x z J x z B x z dv (3) Gui y z VSC where v is volume, V SC is the HTS volume, J y (x,z ) is the superonduting urrent density distribution at (x,z ) in the superondutor and in the y diretion of Fig. 1, B x (x,z ) is the magneti flux density generated by the PM in the x diretion at (x,z ) without superondutor applied, B z (x,z ) is the PM magneti flux density in the z diretion at (x,z ) without superondutor applied. To solve the above equation, it is neessary to now the applied field B x (x,z ) and B z (x,z ), and the urrent distribution J y (x,z ). Fig. 1 Shati diagram of an HTS maglev vehile prototype. Fig. Illustration of HTS levitation theoretial model [17]. Fig. 3 Illustration of interation between HTS bul and PM. III. LINEAR MOTOR DRIVE While the levitation fore and guidane fore are produed by the PM-HTS buls, the driving fore is produed by the interation of magneti fields of the bul superondutor (BSC) magnets mounted on the mover sides and the urrents flowing in the oils plaed in the slots of stationary sidetras. The prototype HTS linear motion driving syst an be seen in Fig. 4, and Table 1 lists its major dimensions and parameters. The thrust fore vetor df, ating on an infinitely thin stator ondutor elent vetor ds arrying stator urrent I s, is given by df = Is ds B (4) If the stator ondutor annot be onsidered as infinitely thin and the flux density vetor B is averaged with respet to the axis y, then (4) leaded to df = Js Ye s BavdA (5) where B av is the flux density vetor averaged with respet to the axis y, J s is the urrent density in the stator ondutor, Y is the ondutor length in the y diretion, e s is the unity vetor pointing in the diretion of flowing urrent in the stator ondutor, and da is a differential elent of the stator ondutor ross setion. The total fore vetor F produed by two poles of the HTS linear drive an be alulated by integration over ross setions of all stator ondutors. TABLE I MAJOR PARAMETERS AND DIMENSIONS OF THE HTS LINEAR MOTOR Dimensions and parameters Quantities BSC magnet length (magnetization diretion) (mm) 0 BSC magnet width (movent diretion) (mm) 30 BSC magnet height (mm) 10 Gap between adjaent BSC magnets (mm) 10 Thiness of bul ba iron (mm) 5 Tooth length (mm) 5 Tooth width (mm) 10 Tooth depth (mm) 10 Slot width (mm) 10 Main air gap (mm) 5 Number of turns of stator winding 35 Diameter of opper wire (mm) 0.75 Resistane per phase ( Ω ) 0.41

4 Fig. 4 Top view of the HTS linear motor. The oils wound around stator teeth are onneted to form 3 phase windings, whih are supplied by a standard 3-phase inverter. It an be seen that only the windings faing the moving seondary would produe the driving fore, while the others only ause additional resistane, power loss, and flux leaage. To deal with this probl, the windings an be divided into setions. The inverter is only onneted to the ative setions [0]. IV. MAGNETIC FIELD FEA AND PARAMETER CALCULATION Magneti field FEA an aount for the detailed linear motor struture and the nonlinear properties of ferromagneti materials and hene an aurately ompute the field distribution and motor parameters. In this paper, twodimensional field omputation in one pole-pair region is arried out, whih an be suffiient for theoretial analysis. It should be noted that three-dimensional analysis within the whole motor ould be onduted for onsidering the fringing effet and non-symmetry among three phases, at the expense of longer omputational time. The waveform of BSC magnet flux, defined as the winding flux produed by the mover BSC magnets, an be obtained from the no-load field solutions at different mover positions. To inrease the omputational auray and effiieny, the stator and mover are meshed separately from the middle of the air gap. When the mover moves to a speified position, the meshes are stithed along the middle air gap line. Periodial boundary onditions are applied. Fig. 5 shows the BSC magnet flux versus the mover position, whih is almost sinusoidal. When the mover moves, an f is indued in the stator windings. The magnitude of fundamental flux omponent is omputed as φ 1 = mwb, so the ba f and fore onstants, K E and K F, an be determined as 1.47 Vs/m and 4.41 N/A respetively by K E = π N e N s φ 1 / (τ ) (6) K F = m K E (7) where N e = 6 is the number of ative oils per phase, N s the number of turns of a oil, τ the pole pith and m = 3 the number of phases. By using a modified inrental energy method [1], the self and mutual indutanes of the three phase windings are omputed as and 0.06 mh, respetively. Due to the large effetive air gap in the surfae mounted linear motor, the indutanes rain onstant at different mover positions. Fig. 5 BSC magneti flux of one turn of one oil. The ogging fore an be obtained from the no-load field solutions by the Virtual wor or the Maxwell stress tensor method. It is found that the ogging fore is negligible. V. STEADY-STATE CHARACTERISTIC When the HTS linear drive operates in synhronous mode, its steady-state harateristi an be predited by the phasor equation V = E + R I + ω (8) j 1L1I 1 where V 1, E 1 and I 1 are rms values of the applied voltage, the indued f, and the urrent of a phase winding, respetively, R 1 is the phase winding resistane, ω 1 is the angular frequeny, and L 1 is the synhronous indutane whih equals the selfindutane plus half mutual indutane here. The LSM is assumed to operate in the optimum BSDC mode, i.e. I 1 in phase with E 1, so that the eletromagneti power and fore an be alulated by F P = me 1 I 1 (9) = P / v K I 1 (10) = where v is the mover speed, and E 1 = K E v. Fig. 6 Steady-state mehanial harateristis of the prototype. F

5 For a given terminal voltage V 1, the relationship between the mover speed and eletromagneti fore is determined by (11) v = R1F m πl1 F R1F + K E V1 K + T K τ T πl1 F + K E K τ T R1F m (11) The HTS levitator steady-state mehanial harateristis with different phase voltages are illustrated in Fig. 6. VI. PERFORMANCE ANALYSIS BY PHASE VARIABLE MODEL The dynami performane of the linear motor under BLDC ontrol an be analyzed by the following equationbased phase variable model [],[3] F V = r i + dλ / dt + e, =a, b, (1) λ = L i (13) q= a q q ei + ei + ei v a a b b = + Fog (14) dv m F Bv F L dt = (15) All above variables are used as their onventional meanings [3]. The profiles of L, e and F og an be obtained from a series of nonlinear FEA solutions, in whih the mover position dependene and saturation effet are onsidered. Suppose the eletrial potentials of terminals a, b, and N-the neutral point of the Y-onneted three phase windings are U a, U b, U and U N, respetively, one an obtain V = U U, =a, b, (16) Assuming that the hard swithing is applied, at the moment when phase a is positively exited and phase b is negatively exited, the following equations an be obtained U N 1 3 = 1 = a b = a ( U ( U N E ) E ) i 0 i = 0 (17) Aording to (1)-(17), a Matlab/Simulin-based simulation model, as shown in Fig. 7, an be built to analyze the HTS linear drive s dynami performane. Fig. 7 Matlab/Simulin-based simulation model of the BSCDC motor with sinusoidal ba f. As an example, Fig. 8 shows the start-up speed urve of the HTS LSM with full load when the rated voltage of the inverter is applied. The developed prototype an drive the levitated mobile at the rated speed of 3 m/s as example.

6 Fig. 8 Speed urve during start-up. VII. CONCLUSION This paper presents a design and analysis of a HTS levitator with a HTS LSM driving syst for the tehnology verifiation. The HTS an speially funtion in the design as magnets for levitation, guidane, and driving. Different omputing methods are used for its performane analysis. Results show that the HTS levitated syst with proposed design and its driving she an be effetively operated and ontrolled, and the simulated results show that the designed HTS driving syst is apable of driving the prototype at the desired speed. HTS well developed allows the levitated mobiles built in various sales to suit different appliations. Both eletromagneti properties and operational harateristis of the ritial elent HTS in this tehnology are suitable to pratial appliations with the superior performane whih an not be ahieved using other tehniques to date. ACKNOWLEDGMENT The authors would than Mr. J. Wen for providing assistane to the wor. 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