Dual-Keel Electrodynamic Maglev System He, Jianliang, Rote, Donald M, Wang, Zian, and Coffey, Howard T DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor my of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. --- Argonne National Laboratory 9700 S. Cass Ave., Bldg. 362B232 Argonne, Illinois 60439, U.S.A.
Dual-Keel Electrodynamic Maglev System He, Jianliang, Rote, Donald M, Wang,Zian, and Coffey, Howard T Argonne National Laboratory 9700 S. Cass Ave., Bldg. 362B232 Argonne, Illinois 60439, U.S.A. Abstract This paper introduces a new concept for an electrodynamic-suspensionmaglev system that has a dual-keel arrangement. Each keel consists of a row of superconducting magnets aboard the vehicle. The keels move in troughs in the guideway that are each lined with pairs of figure-eight-shapednull-flux coils. Each pair of null-flux coils is cross-connected to produce null-flux suspension and guidance force. The cross-connected figure-eight null-flux coils in each trough are also energized by a three-phase power supply to produce propulsive force. Preliminary analysis shows that the new system has many advantages over other EDS systems in terms of system performance and dynamic stability. Introduction A modified version of the Japanese EDS maglev system uses the combined null-flux levitation, propulsion, and guidance (LPG)system. The system consists of two rows of figure-eight-shaped null-flux coils mounted on the side walls of the guideway, the ~ ~ energized by a three-phase coils are W S S - C O M ~ C ~and power supply. Several groups of superconducting magnets aboard the vehicle interact with the null-flux coils on the guideway to produce propulsive, null-flux levitation, and guidance forces [l-31. Advantages of the system include a high lift-to-drag ratio, a high guidance-to-dragratio, and elimination of propulsion coils. However, the system has several features that could be improved upon. First, the concentrated superconductingmagnets (SCMs) located at the ends of the vehicle require a large magnetizing current and introduce end-effects, that reduce the performance of the propulsion system and increase the magnetic field strength in the passenger compartment. Second, the null-flux coils interact only with one side of the SCMs;that is, the magnetic field generated by the SCMs is only partially used. Third, the need for cross connections across the entire guideway with increases the cable and installation costs. Fourth, typically, the motor section of the current Japanese system is only about several tens of meters; thus, extensive power switches are required along the entire guideway. Finally, the system may have some motion stability problems particularly at low speed due to unbalanced electromagnetic drag forces when the vehicle is laterally shifted. The system concept discussed in this paper is expected to reduce or eliminate these disadvantagesmentioned above. The new system concept consists of a dual-keel arrangement. Each keel consists of a row of SCMs aboard the vehicle [4]. The keels move in troughs in the guideway that are each lined with pairs of figureeight-shaped null-flux coils. Each pair of null-flux coils is cross connected to produce null-flux suspension and guidance forces. The cross-connected figure-eight-shaped null-flux coils in each trough are also energized by a three-phase power supply to form three-phase linear motors. In fact, one can view such a system as four double-sided linear motors or eight single-sided motors in parallel. Figures 1 and 2 show a cross-sectional view and a top view of the system, respectively. Because each trough is relatively narrow, typically smaller than one half meter, only very short connecting cables are required. The coils and cross connections can be installed in a trough as a single unit. The dual-keel maglev system has many advantages in terms of its dynamic stability and levitation, propulsion, and guidance performance. The system uses two sides or two poles of each SCM. Thus, when compared with conventional LPG system, all magnetic forces are expected to be doubled, if other parameters are the same. It is also possible to reduce the SCM current, which would thereby alleviate magnetic field shielding problems in the passenger compartment. The new system also allows for a longer motor section, thus simplifying the power supply and control systems and increasing the motor efficiency. Finally, by eliminating the high vertical walls on both sides of the vehicle, it improves passenger visibility and access and egress. Vehicle frontal cross section is also reduced Analysis The evaluation of the dual-keel maglev system is based on the dynamic circuit approach that has been discussed in previous papers [5-61. Because of symmetry, only one keel interacting with one trough needs to be considered. Furthermore, neglecting the
coupling between figure-eight-shaped null-flux coils that are separated by the SCMs, one can apply the model developed in previous papers to the dual-keel system. A complete motor section (an energized guideway block), in general, consists of two sections: one that couples with the magnet system of the vehicle and another that comprises the balance of the block. By letting nb be the total number of poles in the block, nm be the number of poles that couple with the vehicle magnet system, and z be the pole pitch of the vehicle magnet system, one can express the length of the energized block and the length of the vehicle magnet system as q,z and nmt, respectively. In a three-phase system, each pole interacts with three figure-eight-shapedguideway coils that belong to three different phases. Two cross-connected figure-eightshaped coils can be represented by a circuit containing four branches connected in parallel, each of which represents a single loop of the figure-eight-shaped coils. Null-flux lift and guidance forces are generated when circulating currents exist. By applying the information provided in references [5-61, one can represent one phase of the figure-eight-shapednull-flux coils in one keel side shown in Figures 1 and 2 by an equivalent circuit, as shown in Fig. 3, where R and L, (L - Mi2 - Mab) are the resistance and the equivalent inductance of a loop of the figure-eight-shaped coil, M12 is the mutual inductance between the upper and lower loops, Mab is the mutual inductance between the two longitudinal neighboring loops that beiong to different phases, and Ei (i = 1,4) is the voltage induced in the loop in phasor notation. The terms nb and nm are used to modify the circuit for single-phase representation. The equivalent circuit consists of two parts: the left part, which represents the figure-eightshaped coils per phase that couple with the magnet system of the vehicle, and the right part, which represents the remaining guideway coils per phase that do not couple with the magnet system of the vehicle. The system can be viewed as four linear synchronous motors operating in parallel. (That is, the upper loops of the figure-eight-shapedcoils in each side form one motor, and the lower loops of the coils on the same side form another motor.) On the other hand, the dualkeel system can be viewed as eight such motors in parallel. The terms Il,I2,I3, and I4 are the currents flowing in each loop of the figure-eight-shapedcoils. They are also the currents flowing in four different motors because the loop coils belonging to the same phase are connected in series. The sum of 11,12,13, and I4 is the phase current, Iph, that produces propulsive force, and the differences between I1 and I2 and between 13 and 14 generate null-flux lift. The applied phase voltage is indicated by Vph. The null-flux guidance force is generated from the current difference between the sum of 11 and 12 and the sum of 13 and 14. To determine propulsive force, one can simplify the equivalent circuit in Fig. 3 by using the Thevenin equivalent circuit technique, as shown in Fig. 4, where Rph and xph are the resistance and reactance for each equivalent phase and where EPh is the induced phase voltage. These quantities are calculated as follows: Eph = 7 (E1 + E2 + E3 + E4), (3) Xe + h M 1 2 andxe= 6.)(L- M12 - Mab). It is important to note that El, E2, E3, and E4 are in phase, although their amplitudes may be different because the two cross-connected figure-eight-shaped coiis experience the same SCM phase as the vehicle moves forward. Thus, one can conclude from Eq. (3) that Eph is in phase with E l, E2, E3, and E4. By assuming the applied voltage Vph as a reference phasor, one can introduce a power angle 6 by which the induced voltage EPh lags Vph. Thus, Eq. (3) may be rewritten as w&g= (4) The root mean square (rms) value of the induced voltage may also be expressed in terms of the mutual inductance between the moving SCM and the loop coil: where Is is the current of superconducting coil and M s i is the mutual inductance between the superconducting coil and the ith loop of the figureeight-shaped null-flux coils as shown in Fig. 4. The term Msi represents functions of y and z, depending upon lateral and vertical vehicle motions. The flux linking the figure-eight-shaped coils lags the induced voltage by 90'. Dividing the flux by the SCM current (which is assumed to be constant), one can express the mutual inductances and their derivatives in phasor notation by the following equation
The propulsive force can be readily determined from the equivalent circuit shown in Fig. 4. The real power delivered to a single-keel system is and the reactive power is m Neglecting circuit resistance, the propulsive force is obtained in terms of the mutual inductances from Eqs. (1) and (7): Fp=P V If one assumes a total required propulsive force of 200 kn (100kN for each keel), the required phase voltage is 1.33 kv for nm/nb = 1, 2.7 kv for nm/nb = 0.5, and 5.3 kv for nm/nb = 0.25. Thus, to keep the applied phase voltage within 10 kv, the energized block length should be around 150-225 m for a vehicle having a 20- to 30-m-long magnet system. 'Ihis shows that if the applied voltage is kept the same as that of the modified Japanese LPG system, the block length can be doubled, or the current in the SCM can be reduced to one half. However, when the current in the SCM is reduced by one half, the levitation and guidance forces become one fourth. The levitation forces, FL, can be derived from the equivalentcircuit [6]: [: FL = 3nmLRe I+- = FLL+ FLP+ FLG. Because only the fundamentalwave in the longitudinal direction is considered, the total force, which is a The simple relation shown in Eq. (9) relates the propulsive force for one keel side, Fp of the combined system to the system parameters. It is important to note from Eq. (9) that for a given vehicle speed v, the propulsive force depends upon several major factorsthe ratio of the length of the vehicle magnet system to the length of the energized block, the sum of the coupling coefficients (Msi/Le) between vehicle magnets and the guideway coils, the applied voltage, and the current flowing in the superconductingcoils. One important point that follows from symmetry, but. not evident from Eq. (9),is that the propulsive force, Fp, from each keel is an even function of y; that is, Fp(y)=Fp(-y). Consequently, there are no torque induced by variation of the propulsive force with lateral position. Further more, because of the use of the two keels, there is no induced torque in the yaw direction resulting from a variation of drag force with lateral position. The example in our earlier analysis of the dependence of the magnetic forces on vertical and lateral displacements indicated the sum of coupling coefficient was about 1.44 [6]. The maximum thrust is obtained at a load angle of. ' 0 9 By assuming a vehicle speed of 500 km/h (139 m/s), a magnet current of 700 ka, and a load angle of 30, one obtains the following relation: function of lateral and vertical displacements, can be expressed without further approximationas the sum of three terms. These terms are defined as the force components: FLL,resulting from the vertical offset and following the null-flux principle; FJJ, resulting from the applied voltage; and F m,resulting from the lateral displacement. One may neglect the second and the third terms because they are relatively small. The term FLL, in terms of mutual inductances and their derivatives, is given by the following equation: One can show numerically that for a vertical offset of z < 0, Ms2 is greater than Msl and Ms4 is greater than Ms3. The derivatives of Msl and Ms3 are positive and those of Ms2 and Ms4 are negative. Thus, one can see from Eq. (12) that a positive nullflux lift is induced at a vertical offset of z c 0. Similarly, one can show that a negative restorative force is induced at a vertical offset of z > 0. By letting yo be the equivalent air gap (the distance from the center of the SCM to the center of the figureeight-shaped coil) and y be the lateral offset, one can
r define two air gaps: y1= yo + y and y2 = yo - y, as shown in Fig. 5. Equation (12) can be rewritten as where f(y,z) is a general function, depending upon the lateral and vertical offsets, the dimensions of the guideway coils and SCMs, and the coupling between the SCMs and guideway coils. Function f has a unit of Henry per meter, and a large change of inductance in vertical direction will lead to a large levitation force. It follows from Eq. (13) that levitation force F u is an even function of y because FLL(Y)=FLL(-Y). Therefore, the levitation force produced by each keel of the dual-keel maglev system is independent of the direction of the lateral motion. A lateral shift in either direction results in a slight rise in the vehicle's verticai position. Consequently, there is no induced roll motion resulting from a variation of levitation force with lateral position. A similar approach can be used to determine the guidance force. However, the guidance force depends on the two different air gaps (y1, y2); therefore, the guidame force can be expressed as follows: the above equations. One can conclude that the dualkeel maglev system can either save half of the SCMs, nm, or reduce SCM current by 70.7% when compared with the Japanese LFG system (if the dimensions of the figure-eight-shaped null-flux coils and the SCMs are not changed). Clearly, one can also show that if the SCM current, Is, and the number of SCM, nm. are the same, then the dimensions of SCMs and the fip-eight-shaped null-flux coils can be reduced, such as one reducing the height of SCMs (and of course the vehicle cross section) and the height of the guideway coils. CONCLUSIONS The dual-keel EDS maglev system described in this paper uses both sides of the superconducting magnets, a design that can improve system performance. For specified design parameters, such as levitation, propulsion, and guidance force requirements, the dualkeel maglev system can have the following design benefits, as compared with the Japanese LPG system: (1) reduce SCM current to 70.7% and increase the block length by 1418, (2) reduce the number of SCMs by one half, (3) reduce the applied phase voltage, and (4) reduce guideway coil or SCM dimensions. Maglev design depends on many critical issues, including cost analyses. In the future, a more detailed design needs to be generated in tums of system cost. References = FGG+ FGP+ FGL, where F m denotes the guidance force resulting from the lateral offset. This term follows the null-flux principle and is a dominant part of the guidance force, while the second and the third terms resulting from the vertical offset and the propulsion current, respectively, are relatively small. FGG is given by = Le + 2M12. Note from Eqs. (12) and where (15) that both FLLand FGGare proportional to the square of the SCM current. Total system levitation and guidance forces are two times the forces given by [41 Fujiwara, S.; Fujie, J.: United States Patent, No. 4779538, Oct. 1988 Fujiwara, S.; Fujimoto, T.: Proc. of International Conference on Maglev '89, Yokohama, Japan, July 1989, pp. 241-244 Fujiwara, S.; Fujimoto, T.: Institute of Electrical Engineers of Japan, Vol. 112-D, No. 5, June 1992, pp. 459-466. He, J.L., Wang, Z.; Rote, D.; et al.: Argonne National Laboratory, invention report, DOE Case No. S-78,763. He, J.L.; Rote, D.M.; Coffey, H.T.: Proc. of the 13th International Conference on Magnetically Levitated Systems and Linear Drives, May 1993, pp. 64-69 He, J.L.; Coffey, H.T.; Rote, D.M.: IEEE Transactions on Magnetics, Vol. 31, No. 2, March 1995, pp. 981-987 ACKNOWLEGEMENT This work was supported by the Federal Railroad Administration through interagency agreement DTFR53-93-X-OOO47 with the U.S. Department of Energy.
SCMs Aboard Vehicle CTOSS-connecttd NuU-FIUXW i s far RDpulsion Fig. 1 Front View of the Invented System coils coupling with S C M S I Fig, 2 Top-View of the Invented System *I4 coils without coupling with SCMs L Fig. 3 Circuit Diagram of One Phase of the Combined System t" Fig. 4 Equivalent Circuit Representing Circuit in Fig. 2 Fig. 5 Cross-Sectional View of the Vehicle Magnet and the Figure-Eight-ShapedCoil Relations.