Induction and Permanent-Magnet Synchronous Machines for High-Speed Applications

Induction and Permanent-Magnet Synchronous Machines for High-Speed Applications A. Arkkiol, T. Jokinen', E. Lantto2 'Laboratory of Electromechanics, Helsinki University of Technology, Finland 2High Speed Tech Oy Ltd., Espoo, Finland Abstract Solid-rotor induction motors are mechanically very robust and therefore potential candidates for highspeed electric drives. Permanent magnet machines offer better electromagnetic characteristics. These two types of machine are compared for high-speed applications. Electromagnetic, thermal and mechanical aspects are discussed. The permanent magnet machines are considered to be the best solution for applications in which the surface speed of the rotor remains below 250 m/s. For very large speeds and powers, a solid-rotor induction motor is preferred. I. INTRODUCTION The modem frequency converters can provide power up to 0.5-1 MW at frequencies 1-2 khz. Using such a power source, an electrical machine can be run within the speed range of 20 000-120 000 rpm. The converter does not any more restrict the power of a high-speed drive. It is the mechanical and thermal constraints of electrical machines that limit the maximum power and speed of an electrical high-speed application. A large-power, high-speed electrical machine is typically needed for a gas turbine drive. When the turbine wheel is attached directly on the shaft of an electrical machine, the conventional gearbox is eliminated and savings are obtained in volume, losses and costs. The reliability increases, and when active magnetic or gas bearings are used, the drive is oil-free. Other applications for highspeed machines are compressors, vacuum pumps, machine tools and flywheel energy storages. The position of the standard cage induction motor is very strong within the slow and medium speed applications. The permanent magnet machines are slowly gaining some floor because of their better efficiency and powerweight ratio, but on the other hand, the induction machines are much cheaper because of the lower material costs and because their production lines have been refined to top efficiency. Within the high-speed applications, the situation is more open. The market is still quite small, and the highly efficient production lines do not exist. Even the induction motor requires a frequency converter for the high-speed operation. The door is open for machines but do they meet the challenges of the high-speed drives? Fig. 1 shows some operation points reported for highspeed electrical machines. The literature search was made in IEEE/IEE Electronic Library and internet. These points should be taken as indicative, only, as it was often impossible to find out whether the reported powers were steady state rated values or some other maximum values. The older sources typically dealt with induction machines, the newer ones with permanent magnet machines. 14 10000 1000 100 104 20000 40000 60000 80000 100000 120000 Rotation speed [rpm] Fig. 1. Power-speed data published of high-speed electrical machines. The comparison of electromagnetic characteristics, only, would probably show that a synchronous machine is always a better choice than a solid-rotor induction machine. The problem becomes more complicated when the mechanical and thermal constraints are taken into account. The data of Fig. 1 slightly suggest that a highspeed permanent magnet machine may produce somewhat larger shaft power than a high-speed induction machine. To study this question in more detail, some high-speed and induction machines will be designed and their simulation results compared and discussed. Induction machines equipped with different types of solid rotors have been studied based on experimental [1], analytical [2-4] and numerical [5-6] methods. A solid steel rotor is very robust. It can stand surface speeds larger than 400 m/s as well as high operation temperatures. When a solid rotor is used, the high-speed application can often be realised as subcritical, i.e. the first bending critical speed of the rotor is above the rotation speed range of the drive. The relatively large rotor losses and low power factor are the main weaknesses of a solidrotor induction machine. The electrical characteristics of a solid rotor can be improved by making axial and/or circumferential grooves on the rotor surface [1] or by coating the rotor with a copper layer [6]. When the surface speed of the rotor exceeds 300 m/s, the gas friction losses often become the dominant loss component of a highspeed machine. 871

High-speed permanent magnet machines have been studied in [7-10], among others. The mechanical constraints have limited the use of machines to applications with moderate surface speeds, typically less than 250 m/s. In the electromagnetic design, care must be taken to minimise the eddy-current loss of the rotor, and especially, of the permanent magnets. These losses easily raise the temperature higher than allowed for the material. The strengths of a machine, when compared with a solid-rotor induction machine, are the good power factor and electrical efficiency, which lead to a high power per volume ratio. The mechanical strength of electrical steels limits the surface speeds of laminated rotors to about 200 m/s. This restricts the rotor volume and torque available from laminated-rotor high-speed machines. In this study, electrical machines with laminated rotors are not considered. II. DESIGN PROCESS Fig. 2 shows a flow chart of a typical design process of a high-speed machine. The process starts with the design of the load machine. It is usually on the same shaft as the rotor of the electrical machine and sets the power and speed requirements for the electrical machine. Mechanical aspects couple the designs of the load and electrical machine together, and the design becomes an iterative process in which optimal characteristics are sought for both the machines. In the present paper, the design process is simplified by only considering the electrical machine. Three operation points are chosen: (30 000 rpm, 540 kw), (60 000 rpm, 95 kw) and (100 000 rpm, 30 kw), and for each of these speed-power points a radial-flux solid-rotor induction motor and a radial-flux surface-mounted permanent magnet motor is designed. A. Structural Design As the load machine is not known, a comprehensive structural design cannot be made. The active length of the electrical machine (stator core length) is chosen to be 2.5 times the diameter of the stator bore. If only the rotors of the electrical machines could be considered, their freebody critical speeds would be much higher than the planned rotation speeds but as the load machine and bearings must be included, the full rotors may be supercritical. Fig. 3 shows the basic rotor construction of the machines. The shaft of the machine is solid steel on which the permanent magnets are mounted. On and between the permanent magnets, there is an aluminium screen for reducing eddy-current losses. The system is supported against the centrifugal forces by a carbon fibre sleeve or retaining ring. The dimensions of the permanent magnets, aluminium screen and carbon fibre sleeve were chosen to keep the maximum stress in the sleeve below 800 MPa. The solid rotors of the induction machines are simple steel cylinders coated with thin layers of copper. To get the required power from a solid-rotor machine, a somewhat larger rotor will be needed than the corresponding rotor. As the solid rotors are robust enough, increasing the rotor size and surface speed does not cause any special mechanical problems. Aluminium screen >< Steel shaft,.carbon fibre \ sleeve N Fig. 3. Basic construction of the rotors considered. Fig. 2. Flow chart of a high-speed application design. B. Electromagnetic Design The calculation of the magnetic field and operating characteristics is based on time-stepping, finite-element analysis. The details of the method have been reported by Arkkio [11]. The magnetic field in the core region of the motor is assumed to be two-dimensional. End-winding impedances are added to circuit equations of the windings to approximately model the 3D end-winding fields. The Crank-Nicholson time-stepping scheme is used to model the time-dependence of the variables. The field and circuit equations are discretised and solved together. The magnetic field, currents and potential differences of the windings are obtained in the solution of the equations. The motion of the rotor is achieved by changing the finite-element mesh in the air gap. Second-order, isoparametric, triangular elements are used. A typical finite element mesh for a pole pitch of a machine contains 5 000-8 000 nodes, and 600 time steps per one period of supply frequency is used in the numerical simulations. 872

Several simplifications are made in order to keep the amount of computation on a reasonable level. The magnetic field in the core of the machine is assumed to be two-dimensional. The laminated iron core is treated as a non-conducting, magnetically non-linear medium, and the non-linearity is modelled by a single valued magnetisation curve. The eddy-currents in the stator winding are neglected when solving the magnetic field. These eddycurrent losses as well as the losses in the laminated iron core are estimated in the post-processing phase based on the time-variation of the magnetic field. C. Thermal Design Open circuit air-cooling is considered as shown in Fig. 4. The outer surface of the frame is ribbed and cooled by an axial airflow. Some air must be blown into the air gap to remove the friction losses. The hot spots of the machines are in the end windings, which require an extra cooling flow. The design of heat transfer is based on a thermal network model. The details of the model have been reported by Saari [5]. After solving the network equations, for instance, the constraining temperature rise of the stator endwindings is obtained as a linear combination of the losses ATw= klpres-ew + k2pres-cr + k3pcore + k4prot + ATfric (1) where Pres-ew is the resistive loss in the end windings, Pres-cr is the resistive loss in stator slots, Pcore is the stator core loss and Prot is the rotor loss. The coefficients k1-k4 and ATfri, obtained for the three machines are given in Table I. The temperature rise of the stator end-windings was kept below 105 K. The magnetic characteristic of the NdFeB permanent magnet material is strongly temperature dependent. It was assumed to be a straight line with a remanence fluxdensity of 1.0 T and coersive field strength of -750 000 A/m. The rotor losses were minimised to keep the temperature rise of the magnets below 50 K. D. Bearings These high-speed machines are typically equipped either with active magnetic bearings or airfoil bearings. We assume that the bearings do not significantly affect the characteristics or comparison of the electrical machines. The mechanical or thermal aspects related to the bearings are not considered. E. Power Supply When used for low or medium speed machines, a switching frequency around 15 khz typically allows tens or hundreds of voltage pulses per half a cycle of the fundamental frequency and leads to an almost sinusoidal stator current. For a high-speed machine, the best voltage waveform available from a modem frequency converter may contain only a few pulses per half cycle. Such a voltage generates a lot of additional eddy-current losses in the machine. From loss point of view, a voltage waveform having only one pulse per half cycle may be a better choice than a voltage with 3-7 pulses [6]. The losses are reduced both in the motor and frequency converter. All the simulations of this study are performed using a pulseamplitude-modulated six-step voltage, i.e. one 1200 pulse per half cycle. III. RESULTS Fig. 5 shows the cross-sectional geometry of the 30 000 rpm permanent magnet machine and Fig. 6 the 100 000 rpm solid-rotor induction machine. Tables Ila - Ilc give the main parameters and Fig. 7 shows the losses computed for the six motor designs. In the tables and figures, refers to a permanent magnet motor, to an induction motor. The losses and efficiencies presented include the friction losses on the rotor surface but not in the bearings. Fig. 4. Cooling air flow. TABLE I COEFFICIENTS OF THE THERMAL MODEL Speed of the k1 k2 k3 k4 ATfric machine [K/W] [K/W] [K/W] [K/W] [K] 30 000 rpm 0.0426 0.0190 0.0132 0.0033 7.3 60 000 rpm 0.1124 0.0664 0.0479 0.0055 5.1 100 000 rpm 0.2402 0.1598 0.1190 0.0110 4.9 Fig. 5. Cross-sectional geometry of the 30 000 rpm, 540 kw motor. 873

20 15 0 10 n n0 0 5-0 a)n =30000rpm,P =540kW. 5.0 Fig. 6. Cross-section of the 100 000 rpm, 30 kw induction motor. 4.0 TABLE Ila. PARAMETERS OF THE 30 000 rpm MACHINES Rated speed [rpm] 30 000 30 000 Rated Power [kw] 540 540 Number of poles 4 2 Number of stator slots 36 36 Chording 7/9 5/6 Inner stator diameter [mm] 135 165 Core length [mm] 338 413 Radial air-gap length [mm] 2.5 4.0 Surface speed of the rotor [m/s] 204 250 Displacement factor; cos4 0.98 0.74 Efficiency [%] 98.6 96.9 - le n 3.0, 2.0 -J 1.0 0.0 b)n =60000rpm,P =95kW. TABLE Ilb. PARAMETERS OF THE 60 000 rpm MACHINES Rated speed [rpm] 60 000 60 000 Rated Power [kw] 95 95 Number of poles 4 2 Number of stator slots 36 36 Chording 7/9 5/6 Inner stator diameter [mm] 68 83 Core length [mm] 170 208 Radial air-gap length [mm] 1.5 2.25 Surface speed of the rotor [m/s] 204 250 Displacement factor; cos4 0.98 0.68 Efficiency [%] 97.7 95.2 - le 2.5 2.0 1.5 o 1.0-0 0.5 TABLE lic. PARAMETERS OF THE 100 000 rpm MACHINES Rated speed [rpm] 100 000 100 000 Rated Power [kw] 30 30 Number of poles 4 2 Number of stator slots 24 24 Chording 5/6 5/6 Inner stator diameter [mm] 41 50 Core length [mm] 103 125 Radial air-gap length [mm] 1.0 1.5 Surface speed of the rotor [m/s] 204 250 Displacement factor; cos4 0.98 0.63 Efficiency [%] 96.9 93.1 Fig. 7. 0.0 c)n= 100000rpm,P =30kW. Losses of the motor designs. refers to a permanent magnet motor, to an induction motor. In Table II and Fig. 7 the electromagnetic and friction losses of a motor are considered, only. The power taken by the cooling fan is neglected, and in a high-speed drive, also the frequency converter always consumes some power. A realistic efficiency of a state of the art frequency 874

converter is 97 00. The total efficiency of a 30 000 rpm electric drive would be approximately 95.2 00 with a motor and 93.5 00 with an induction motor. Fig. 8 shows the line-to-line supply voltage and terminal-current waveforms from the FE simulations of the 60 000 rpm machine. All the machines were studied in delta connection. Fig. 8. (D 1000 500-500 0 - -1000 _ 0.0)o 100 50 0-50 lil K 0.20 0.40 0.60 0.80 1.00 Time [ms] -100 0.00 0.20 0.40 0.60 0.80 1.00 Time [ms] Voltage and current waveforms from the FE simulations of the 60 000 rpm machine. IV. DISCUSSION The proper choice of some design parameters is discussed below. A. Rotor losses l.. 0 The rotors of the machines studied are covered with carbon fibre sleeves that fasten the magnets on the rotor yoke. Thermally, the sleeve is an insulation layer. Special care has to be taken to minimize the rotor losses and maintain a low enough operating temperature for the magnets. An aluminium shield was used over and between the magnets. It reduced the rotor losses, especially the eddy-current losses in the magnets, roughly to one fourth of the losses obtained without using a shield. The eddy-current losses in the rotor are mainly caused by stator-slot harmonics and time harmonics associated with the non-sinusoidal supply voltage. Both these harmonics can be reduced by increasing the air gap. The relatively large air gaps used are given in Tables Ila-Ilc. Removing the friction losses from the air-gap region also requires a large air gap. The drawbacks related to the large air gaps are a low power factor in induction motors and a relatively large amount of magnet material needed for the machines. A third measure to reduce the rotor losses is to use a chorded stator winding. Chording reduces the low order spatial harmonics of the stator winding. It also slightly reduces the power obtained per magnet volume from the machines but chorded windings were used for both the machine types as the reduction of the eddy-current losses was considered more significant. In addition, chording shortens the end windings and may reduce the resistive losses of the stator winding. B. Number ofpoles The rotation speeds and supply frequencies of the machines studied are so high that the choice of the pole number has to be made between two and four poles. The smaller stator frequency and lower core losses are obtained with a two-pole machine. However, the stator yoke of a two-pole machine is thick, which leads to a large machine and possible problems with stator cooling. In a permanent magnet machine, the armature reaction is much larger in a two-pole machine than in a four-pole machine. Because of this effect, considerably more power could be obtained from a four-pole machine than from a two-pole machine of the same rotor size. Therefore, all the motors were chosen to be four-pole machines. As already mentioned, the air gap of a high-speed machine has to be large to reduce the rotor losses and allow efficient cooling. Such an air gap in a four-pole induction motor leads to a very low power factor. To avoid this, all the induction motors were chosen to be two-pole machines. C. Stator core material In high-speed machines, the flux-densities are typically relatively small. The fundamental air-gap flux densities for the induction motors were within 0.33-0.41 T and for the motors within 0.43-0.48 T. The frequencies are high, and the eddy-current losses of the steel sheets are significant. To reduce these losses, an electrical steel sheet of 0.20 mm thickness was chosen for all the machines. D. Circulating and eddy-current losses in stator winding The diameters of the stator conductors have to be relatively small to keep the eddy-current losses of the stator winding under control. This means that there are tens of parallel conductors in the stator winding. It is difficult to mix the positions of these wires perfectly so that the electromotive forces induced in all of them would be equal. Circulating currents start to flow between the parallel conductors. Some cases have been measured in which the circulating currents cause an additional loss that is of the same order of magnitude as the loss calculated based on the dc resistance of the winding [6]. In the present study, the eddy-current loss of the stator winding has been included in the analysis. The possible circulating currents have been neglected. E. Utilisation factors A utilitisation factor C, defines how much electromagnetic torque Te can be obtained from the volume of the stator bore Te = CUDst st (2) where Dst is the diameter of the stator bore and Ist is the length of the stator core. A utilisation factor provides useful dimensional information at the beginning of a design process of a high- 875

speed application. Table III gives the utilisation factors obtained for the induction and permanent magnet machines designed in this study. TABLE III UTILISATION FACTORS FOR THE MACHINES [N/m2] Operation point 30 000 rpm, 540 kw 60 000 rpm, 90 kw 100 000 rpm, 30 kw F. Economic aspects T 28 000 19 000 17 000 15 000 11 000 9 000 When mass-produced electrical machines are considered, their costs can be roughly estimated based on the amounts of materials used. The manufacturing of the stators for the designed solid-rotor and -rotor machines is very similar, only the stator of a solid-rotor machine is larger weighting about twice as much as the stator of a machine of equal power. The material and manufacturing costs of a rotor are higher than those of a solid rotor. Very roughly estimated, a rotor will be twice as expensive as a solid rotor. These considerations lead to the conclusion that the total material plus manufacturing costs of these two types of machine will be about equal. The frequency converter for a machine will be smaller and cheaper due to the better power factor of the machine. In operation, the better efficiency of a machine leads to lower energy costs. G. machine contra induction machine The electrical characteristics are clearly in favour of the machine. The mechanical, rotordynamic and thermal aspects are for the solid-rotor machine. It will probably be easier to cover the largest powers and speeds using solid-rotor machines [5]. Factors related to the load machine, bearings and operation environment will finally define, which one of these two machines will be chosen for a certain application. V. CONCLUSIONS Solid-rotor induction motors and permanent magnet synchronous motors were studied for high-speed applications. To get a reliable comparison, three induction machines and three machines were designed for the operation points (30 000 rpm, 540 kw), (60 000 rpm, 95 kw), (100 000 rpm, 30 kw) using similar designing methods, tools and constraints. The electromagnetic design was based on time-stepping, finite element analysis. The thermal design was done using thermal network models. The mechanical analysis was not complete as only the electrical machine (no bearings or load machine) was considered. However, the designed rotor structures should stand the loading of the centrifugal acceleration. The solid-rotor induction motors are mechanically very robust. If needed, they can be run at surface speeds larger than 400 m/s. As the mechanics allows using large rotor volumes, these motors can deliver quite large powers. Solid-rotor induction motors suffer, however, from a low power factor which leads to large resistive stator losses. The utilisation factors of the induction machines were almost 50 0 lower than the corresponding factors of the machines. The mechanical and thermal design of a high-speed permanent magnet rotor is a challenge. If the design is done successfully, the permanent magnet machine provides the best operating characteristics for most highspeed applications. REFERENCES [1] H. Peesel, "Uber das Verhalten eines Asynchronmotors bei verschiedenen Laufern aus massivem Stahl," Dissertation of Technische Hochschule Carolo-Wilhelmina zu Braunschweig, 1958, 57 p. + Appendices. [2] B. J. Chalmers and I. Woolley, "General theory of solid-rotor induction machines," Proc. IEE, vol. 119, no. 9, 1972, pp. 1301-1308. [3] D. Bergmann, "Betriebseigenschaften von warmerohrgekuhlten Asynchron-maschinen mit gerillten Massivrotor und Kurzschlusskafig unter besonderer Berucksichtigung der Stromrichterspeisung," Dissertation of Technische Hochschule -Aachen, 1982, 145 p. [4] J. Pyrhonen, "Calculating the effects of solid rotor material on machine characteristics," European Transactions on Electrical Power Engineering, vol. 1, no. 6, 1991, pp. 301-310. [5] J. Saari, "Thermal analysis of high-speed induction machines," Acta Polytechnica Scandinavica, Electrical Engineering Series, no. 90, Espoo 1998, 73 p. http:hlib.tkk.fi/diss/199x/isbn9512255766. [6] J. Lahteenmaki, "Design and voltage supply of high-speed induction machines," Acta Polytechnica Scandinavica, Electrical Engineering Series, no. 108, Espoo 2002, 140 p. http:hlib.tkk.fi/diss/2002/ isbn951226224x. [7] P. Chudi and A. Malmquist, "Development of a small gas turbinedriven high-speed permanent magnet generator," Dissertation of Royal Institute of Technology, Stockholm, Sweden; Dept. of Electrical Machines and Power Technology, 14 January 1990, 174 p. [8] J. L. F. van der Veen, L. J. J. Offringa and A. J. A. Vandenput, "Minimising rotor losses in high-speed high-power permanent magnet synchronous generators with rectifier load," IEE Proceedings - Electric Power Applications, vol. 144, no. 5, 1997, pp. 331-337. [9] T. Jokinen, J. Larjola and I. Mikhaltsev, "Power Unit for Research Submersible," International Conference on Electric Ship, 1st September 1998, Istanbul, Turkey, pp. 114-118. [10]0. Aglen and A. Andersson, "Thermal analysis of a high-speed generator," Conference Record of the 38th IAS Annual Meeting. 12-16 Oct. 2003, vol. 1, pp. 547-554. [11]A. Arkkio, "Analysis of induction motors based on the numerical solution of the magnetic field and circuit equations," Acta Polytechnica Scandinavica, Electrical Engineering Series, no. 59, Helsinki 1987, 97 p. http:hlib.hut.fi/diss/198x/isbn951226076x. 876