Đang tải... (xem toàn văn)
Absfmct- Permanent magnet (PM) motors are attracting growing at- tention for a wide variety of industrial applications. In traction and spindle drives, constant power operation and wide speed range are de- sirable. With dc motor drives, these are achieved by the appropriate reduction of the field current as the speed increases. In the PM mo- tor, direct control of the magnet flux is not available. The air-gap flux, however, can be weakened by the direct axis armature current. In this operation, magnet demagnetization due to the direct axis armature reac- tion must be prevented, because the magnet torque decreases irreversibly if this demagnetization is very large. The current vector control method of PM motors is examined to expand the operating limits considering the inverter capacity. This control method is optimum in the sense of deriving maximum output torque within the voltage and current con- straints. The effects of motor parameters are examined by the computer simulation. The operating limits are examined considering the demag- netization of the permanent magnet.
I 866 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 26, NO. 5, SEPTEMBERIOCTOBER 1990 Expansion of Operating Limits for Permanent Magnet Motor by Current Vector Control Considering Inverter Capacity Absfmct- Permanent magnet (PM) motors are attracting growing at- tention for a wide variety of industrial applications. In traction and spindle drives, constant power operation and wide speed range are de- sirable. With dc motor drives, these are achieved by the appropriate reduction of the field current as the speed increases. In the PM mo- tor, direct control of the magnet flux is not available. The air-gap flux, however, can be weakened by the direct axis armature current. In this operation, magnet demagnetization due to the direct axis armature reac- tion must be prevented, because the magnet torque decreases irreversibly if this demagnetization is very large. The current vector control method of PM motors is examined to expand the operating limits considering the inverter capacity. This control method is optimum in the sense of deriving maximum output torque within the voltage and current con- straints. The effects of motor parameters are examined by the computer simulation. The operating limits are examined considering the demag- netization of the permanent magnet. I. INTRODUCTION RMANENT MAGNET (PM) motors are attracting p" growing attention for a wide variety of industrial appli- cations. The maximum steady-state torque of the PM motor depends on the continuous armature current rating. The maxi- mum speed attainable at this torque is limited by the available output voltage of the inverter. In traction and spindle drives, constant power operation and wide speed range are desirable. With dc motor drives, these are achieved by the appropriate reduction of the field current as the speed increases. In the PM motor, direct control of the magnet flux is not available. The air-gap flux, however, can be weakened by the demagnetizing current in the direct axis [ 11-[4]. This control method is called "flux-weakening.'' In this operation, magnet demagnetization due to the direct axis armature reaction must be prevented because the magnet torque decreases irreversibly if this demagnetization is very large. In this paper, the armature current control method expand- ing the operating limits is examined under the constant inverter capacity. The effects of motor parameters such as d- and q- Paper IPCSD 90-2 1, approved by the Electric Machines Committee of the IEEE Industry Applications Society for presentation at the 1989 Industry Ap- plications Society Annual Meeting, San Diego, CA, October 1-5. Manuscript released for publication March 6, 1990. S. Morimoto, Y. Takeda, and T. Hirasa are with the De7artment of Elec- trical Engineering, College of Engineering, University of Osaka Prefecture, 4-804 Mom-Umemachi, Sakai, 591 Japan. K. Taniguchi is with the Department of Electrical Engineering, College of Engineering, Osaka Institute of Technology, 5-16-1 Omiya, Asah-ku, Osaka, 535 Japan. IEEE Log Number 9037046. d-axis 'd 'a Fig. 1. Basic vector diagram for PM motor. axis inductances, flux linkage of the permanent magnet, and so on are examined by computer simulation. Furthermore, the control method and the output characteristics are examined considering the demagnetization of the permanent magnet due to the direct axis armature reaction. 11. BASIC EQUATIONS OF PM MOTOR In the d-q coordinates which rotate synchronously with an electrical angular velocity w , the steady-state voltage equation is expressed as follows: d- and q-axis components of armature current, d- and q-axis components of terminal voltage, flux linkage of permanent magnet per-phase (rms), armature resistance, d- and q-axis components of armature self- inductances. = Erom (l), the basic vector diagram shown in Fig. 1 is ob- tained. The d- and q-axis components of the armature current are represented as id = -Ia sin0 i, =Ia cos0 (2) where Ia = die, I, is the armature current per-phase (rms), and /3 is the leading angle of armature current from the q-axis. The power P and the terminal voltage Va are given by P = + (Ld - Lq)idig} (3) V a- - J (W$a + WLdid + Ri,)2 + ( -wLqiq + Rid)*. (4) 0093-9994/90/09OO-0866$01 .OO 0 1990 IEEE MORIMOTO et al.: EXPANSION OF OPERATING LIMITS FOR PERMANENT MAGNET MOTOR 867 To examine the demagnetization of the permanent magnet due to the d-axis armature reaction, the demagnetizing coefficient C: is defined as the ratio of the d-axis armature reaction flux to the permanent magnet flux linkage [6]; If E is large and the coercivity of the magnet is not enough, then the permanent magnet demagnetization may create a se- rious problem and the magnet torque decrease irreversibly. In the per-unit expression, these basic equations are rewrit- ten as follows, where the armature resistance is neglected as the PM motor is used comparatively in high speed range and the resistance drop can also be neglected: Fig. 2. I. -" - Voltage-I imit Current-limit el I ipse _ * Increasing swed - Current-limit circle and voltage-limit ellipse for interior tor. magnet mo- P = w {Ed, + (1 - p)Xdidiq} (6) Fig. 2 shows the current-limit circle and the voltage-limit el- lipse in the id-iq plane. The voltage-limit ellipse becomes small as the speed w increases. The armature current vector i(id, iq) satisfying both conditions of the current limit and the voltage limit must be inside the current-limit circle and the voltage-limit ellipse. For example, the available armature cur- rent vector at w = WO is inside ABCDEF (hatched area) in (7) V, = (WE0 wxdid)2 + (WpXdiq)* f = -Xdid/EO where Eo =W'$,/v: xd =WrLdzL/v: x, =wrLqz:/v:, Fig. 2. p = xq/xd is the salient coefficient, and superscript r rep- resents its rated value. The salient coefficient p represents the saliency of the PM motor[6]. As the relative permiability of a permanent magnet is very nearly unity, the magnet space behaves like an air. The surface magnet motor exhibits negligible saliency, so that p = 1.0. On the other hand, the q-axis inductance of the interior magnet motor exceeds the d-axis inductance; hence p > 1. In this paper, the surface magnet motor and the interior magnet motor are examined. III. ARMATURE CURRENT VECTOR CONSIDERING INVERTER CAPACITY Considering the inverter capacity, the armature current I, and the terminal voltage Vu are limited as follows: The current limit Ilh is decided by the continuous armature current rating and the available output current of the inverter. The voltage limit Vlim is decided by the available maximum output voltage of the inverter. In this paper, the current and voltage limits are set as the ratings (Ilh = 1.0 pu, VI^ = 1.0 pu) for the simulation. From (2) and (9), the current-limit circle is given by ii + ii = I:, IV. OPTIMUM CURRENT VECTOR CONTROL From (6), the torque is represented as T = P/w = (Eo + (1 - p)Xdid)iq. (13) From this equation, the armature current vector il(id1, iql) producing maximum torque per current is derived as follows [51: (14) id1 = 0 iql =I,, id1 = -I, sin01 iql = I, cosP1, P # 1 where * (15) -Eo + JE; + 8(p - 1)2X:Zi 4(p - 1)xdIu 01 =sin-' The maximum torque-per-ampere current vector trajectory is shown in Fig. 3. If the armature current I, is limited by Ilim, the maximum torque is obtained at point A1 in Fig. 3. The d- and q-axis components of this point are derived by substituting I, = Ilim in ( 14) and (15). Until the terminal voltage Vu reaches its limited value Vlim at w = w1, the motor can be accelerated by this maximum torque. This maximum speed of the constant torque operation is given by From (7) and (lo), the voltage-limit ellipse is given by From (6) and (12), the armature current vector i2(id2, iq2) producing maximum output power under the voltage-limit condition is derived as follows, where the current-limit con- (Eo + xdid)2 + (pXdiq)2 = (Vli,/w)*. (12) I 868 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 26, NO. 5. SEPTEMBERIOCTOBER 1990 . itaxiaua Voltage-1 iaited aaximm-output 2. o'q torque-per-amp trajectory , J/ trajectory P =1.0 Voltage-1 imi t el I ipse Xd4.75 -2.01 (a) Uax i mu. torque-per-aap . trajectory 2. 0Iq Voltase- I imi ted\ Rlxium-output Current-I imit P =2.0 Eo'O. 6 Xd=0.75 ellipse A4(-EO/Xd.0) -2.0 (b) Fig. 3. Maximum torque-per-ampere current vector trajectory and voltage- limited maximum-output current vector trajectory for Eo < X,Jlirn. (a) Surface magnet motor (p = 1). (b) Interior magnet motor (p > 1). dition is not considered, where I Pfl The current vector trajectory of the voltage-limited maximum- output is shown in Fig. 3. The current vector approaches the point A4 (id = -Eo/Xd,iq = 0) as the rotor speed increases and reaches the current-limit circle at w = w2 (point A2 in Fig. 3). The rotor speed w1 is the maximum speed for the constant torque operation with the maximum torque considering the current limit. The rotor speed w2 is the minimum speed for the voltage-limited maximum-output operation. Below this speed, the voltage-limited maximum-output operating point cannot be reached, because the voltage-limited maximum-output tra- jectory intersects the voltage-limit ellipse outside the current- Lxiaua torque-per-aap 2.07 trajectory Yo I tage-1 imi ted axiauroutput x,4.5 ellipse -2.01 Fig. 4. Maximum torque-per-amp current vector trajectory and voltage- limited maximum-output current vector trajectory for Eo > Xdlli,,,. DC SUPP~Y Inverter Fig. 5. Scheme of flux-weakening control system. limit circle. To produce the maximum output power in all speed ranges considering the conditions of both the current and the voltage limits, the optimum current vector is choosen as follows. Region Z (w 5 wl): id and i, are constant values given by (14). The current vector is fixed at A1 in Fig. 3. Region ZZ (a1 < w w2): id and i, are chosen as the cross point of the current-limit circle and the voltage-limit ellipse. The current vector moves from A1 to A2 along the current- limit circle as the rotor speed increases. Region ZZZ (a 5 w2): id and i, are given by (17). The current vector moves from A2 to A4 along the voltage-limited maximum-output trajectory. Region I corresponds to Z, = Zli,, Vu < Vlim. Region I1 corresponds to Z, = Zlim, Vu = Vlim. Region I11 corre- sponds to I, < Zlirn, Vu = I/lim. If &/Xd is larger than Zlimr the voltage-limited maximum-output trajectory is outside the current-limit circle (see Fig. 4). Therefore, Region I11 does not exist, and the output power becomes zero at w = w3 (point A3 in Fig. 4): (19) Fig. 5 shows the scheme of the flux-weakening control sys- tem in which the current vector is controlled according to the Vlim EO - Xdzlim * w3 = MORIMOTO et al. : EXPANSION OF OPERATING LIMITS FOR PERMANENT MA( U2 Region II I Region 111 I 0 -0.5 ,;' I 1:b Speed 2 w (PU) 3:O 4!i'" Fig. 6. Output power characteristics for surface magnet motor. - with flux weakening; - - - - - - without flux weakening. foregoing algorithm. The relationships between the current commands iC;, i;, the torque command T * , and the rotor speed w are preliminarily obtained by the simulation based on the knowledge of the motor parameters. These relationships are stored in the memory of the microprocessor as a lookup table. The current commands are decided by the torque command and the detected speed using the lookup table. The commands iC; and i; are transformed to the phase current commands i; and i: using the rotor angle feedback 0. The closed-loop cur- rent controller is responsible for controlling the PWM volt- age excitation so that the instantaneous phase currents follow their commanded values. The current commands are always kept inside the voltage-limit ellipse and the current-limit cir- cle. Therefore, the current regulators are not saturated in all operating regions, and the resultant currents follow the com- manded currents. Fig. 6 shows the output power characteristics for the sur- face magnet motor (nonsalient machine: p = 1). The motor parameters used in Fig. 6 are the same in Fig. 3(a). The terminal voltage reaches its limited value at w = w1. Below this speed, the torque is kept constant and the output power is proportional to the rotor speed. The output power without the flux-weakening control (id = 0 control) decreases rapidly over this speed (see the broken lines). On the other hand, the output power with the flux-weakening control is large and kept almost constant by controlling the d- and q-axis components of the armature current according to the rotor speed (see the solid lines). The operating limits are greatly enlarged by the optimum current vector control. V. EFFECTS OF MOTOR PARAMETERS Fig. 7 shows the effects of the motor parameters such as Eo and Xd. If Eo 5 XdZlim (Xd = 0.7, 0.8 in Fig. 7), the output power does not decrease at high speed. If EO > XdZlim (Xd = 0.5, 0.6 in Fig. 7), the output power decreases as the rotor speed increases. In the speed range of Fig. 7 (w 5 4.0 pu), it can be seen that the output characteristics for xd = 0.6 is the best. The same results are obtained in case of the interior magnet motor (p > 1). From Fig. 7, it has been seen that the ideal constant power operation can be obtained with the condition of Eo 2 XdZlim [7]. ;NET MOTORS 869 Xd=O. 6 1.0 b B 0.6 c B d 0.4 0.2 0 1.0 2.0 3.0 4.0 Speed w (PU) Fig. 7. Effects of motor parameters. b 0.6 *: 0.4 0.2 1.0 U4 4 a 0.5 .O 8 L I J -1.0 OO 1.0 2.0 3.0 4.0 Seed w (PU) Fig. 8. Effects of saliency. Fig. 8 shows the effects of saliency. The output powers of the different type motors are nearly the same at high speed range (w > 2.0), but the output power of the interior magnet motor (p = 2 .O or 3 .O) is larger than that of the surface magnet motor (p = 1 .O) at low speed range because the reluctance torque is available in the interior magnet motor. The maximum values of the demagnetizing coefficient are about 0.8. In some cases, the permanent magnet is demagnetized irreversibly by the flux-weakening control. VI. DEMAGNETIZATION OF PERMANENT MAGNET If the PM motor is controlled by the foregoing flux- weakening control method, which uses the negative d-axis armature current, it is very important to examine the demagne- tization of the permanent magnet, because the magnet torque decreases irreversibly if the demagnetization is very large. Fig. 9 shows the equivalent d-axis magnetic circuit for the PM motor. The following nomenclature applies in Fig. 9: po permeability of air, pr Pu Plm Pla recoil permeability ( G! po) =PuIm/Arn, where Pu = pOAg/Ig, permeance of air gap, =P/mlm/Am, where Plm = leakage permeance of magnet, =PIaIm /A m , where pio = leakage permeance of ar- mature, I 870 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 26, NO. 5. SEPTEMBERIOCTOBER 1990 B Air gap B, B, Permanent magnet Armature reaction Fig. 9. Equivalent d-axis magnetic circuit for PM motor B Load line .=urllc Fig. 10. Demagnetization curve for rare-earth permanent magnet. I, magnet length, Am magnet area, I, air gap length, A, effective gap area, H, coercivity, H, magnetic field intensity by armature reaction. Fig. 10 shows the demagnetization curve for a rare-earth permanent magnet where the sign of magnetic field intensity H is reversed. With the permanent magnet that has a straight demagnetization curve, such as a rare-earth permanent mag- net, the recoil line coincides with the demagnetization curve. Therefore, the operating point of the magnet moves along the demagnetization curve. Using the demagnetizing coefficient C; defined in (8), the operating point (H,, B,) is given as follows: where U (pU +P/m)/Pu, leakage factor of flux, x Ho, Bo (pu +pl,,)/p,, leakage factor of MMF, operating point at no-load, The d-axis armature current can be safely increased until the resultant flux density at the trailing edge of the magnet becomes approximately zero. This safe operating condition is represented as follows: t 5 him. (22) - : without demagnetization-limit ___ : E Iim=o.a 0 '2.0 0.2 -0.5 -1.0 1.0 2.0 3.0 4.0 Speed w (PU) Fig. 1 1. Output characteristics c0nsiderir.g demagnetization limit. From (8) and (22), the d-axis armature current considering the demagnetization is limited as follows: id 2 - EOhim /Xd (23) The demagnetization-limit C;lim is given by substituting Bm = 0 in (21): The leakage factors U, h are larger than 1.0; therefore, Elirn > 1.0. If the demagnetization curve is not straight, the demagnetization-limit Elim may be smaller than 1 .O. &im must be carefully desided according to the permanent magnet ma- terial and the design of magnetic circuit. Fig. 11 shows the output characteristics considering the de- magnetization limit. The d-axis armature current id is limited according to the demagnetization limit. As a result, the out- put power decreases at high speed range as the demagnetizing limit decreases. Therefore, a magnet material that has a linear demagnetization curve must be used for the PM motor if wide speed range or constant power operation is desirable. VII. CONCLUSION In this paper, the current vector control method for ex- panding the operating limits is examined under the constant inverter capacity. On the basis of the simulation, the following conclusions can be obtained. 1) The operating limits are greatly expanded by controlling the d- and q-axis components of the armature current accord- ing to the rotor speed. 2) The output characteristics are affected by the parame- ters such as Eo and Xd . If Eo Xdllim, the operating limits become very large. When Eo Xdllim, the ideal output char- acteristics can be obtained. If Eo > Xdllim, the output power is large in the low speed range but the wide speed range cannot be obtained. 3) In the interior magnet motor, in which the q-axis induc- tance is larger than the d-axis inductance, the large output torque can be obtained as the positive reluctance torque is available. MORIMOTO et al.: EXPANSION OF OPERATING LIMITS FOR PERMANENT MA( 4) The control method considering the demagnetization- limit is analyzed. If the permanent magnet has a straight de- magnetization curve, as does a rare-earth permanent magnet, the PM motor can be safely operated until the demagnetiz- ing coefficient becomes 1.0. If wide speed range or constant power operation is desirable, the permanent magnet with a high coercivity and a linear demagnetization curve must be used for the PM motor. REFERENCES [l] B. Sneyers, D. W. Novotny, and T. A. Lipo, “Field weakening in buried permanent magnet ac motor drives,” IEEE Trans. Ind. Appl., vol. IA-21, pp. 398-407, Mar./Apr. 1985. T. Sebastian and G. R. Slemon, “Operating limits of inverter-driven permanent magnet motor-drives,” IEEE Tins. Ind. Appl., vol. IA- 23, pp. 327-333, Mar.lApr. 1987. T. Jahns, “Flux-weakening regime operation of an interior permanent- magnet synchronous motor drive,” IEEE Trans. Ind. Appl., vol. IA- B. K. Bose, “A high-performance inverter-fed drive system of an in- terior permanent magnet synchronous machine,” IEEE Trans. Ind. Appl., vol. IA-24, pp. 987-997, Nov./Dec. 1988. T. M. Jahns, G. B. Kliman, and T. W. Neumann, “Interior permanent- magnet synchronous motor for adjustable speed drives,” IEEE Trans. Ind. Appl., vol. IA-22, pp. 738-747, JulylAug. 1986. Y. Takeda and T. Hirasa, “Current phase control methods for per- manent magnet synchronous motors considering saliency,” in PESC Conf. RE., Apr. 1988, pp. 409-414. R. Schiferl and T. A. Lipo, “Power capability of salient pole permanent magnet synchronous motors in variable speed drive applications,” in IEEE IAS Annu. Meeting Conf. Re., 1988, pp. 23-31. [2] [3] 23, pp. 681-689, July/Aug. 1987. [4] [5] [6] [7] Shigeo Morimoto was born on June 28, 1959. He received the B.E. and M.E degrees from Univer- sity of Osaka Prefecture, Japan, in 1982 and 1984, respectively. He joined the Mitsubishi Electric Corporation, Tokyo, Japan, in 1984. Since 1988, he has been a Research Associate in the Department of Electri- cal Engineering at the University of Osaka Prefec- ture, engaged in research on inverter systems and ac servo control systems. Mr. Morimoto is a member of the Institute of Electrical Engineers of Japan, the Society of Instrument and Control Engi- neers of Japan, and the Japan Society for Power Electronics. ;NET MOTORS 87 1 Yoji Takeda was born in Osaka, Japan, on Novem- ber 10, 1943 He received the B.E., M.E., and Ph.D. degrees from the University of Osaka Prefec- ture, Japan, in 1966, 1968, and 1977, respectively In 1968, he joined the Department of Electncal Engineering, University of Osaka Prefecture He is presently an Associate Professor. Dr. Takeda is a member of the Institute of Elec- trical Engineers of Japan, the Institute of Systems, Control and Information Engineers, and the Japan Society for Power Electronics. Taka0 Hirasa (M’85) was born on May 13, 1930. He received the B.E. and Ph.D. degrees from the University of Osaka Prefecture, Japan, in 1958 and 1965, respectively Since 1953, he has been with the Department of Electrical Engineenng at the University of Osaka Prefecture, where his areas of interest are power system stability, motor controls, and power elec- tronics applications. Since 1976 he has been a Pro- fessor of Electrical Engineering. Dr. Hirasa is a member of the Institute of Elec- trical Engineers of Japan, the Institute of Systems, Control and Information Engineers, and the Japan Society for Power Electronics. Katsunori Taniguchi (M’75) was born in Na- gasalu, Japan, on April 21, 1943. He received the B.S. degree in electrical engineering from Osaka In- stitute of Technology, Osaka, Japan, and the M.S. and Ph.D degree from University of Osaka Pre- fecture, Osaka, Japan, in 1966, 1970, and 1974, respectively. Since 1966, he has been with the Department of Electrical Engineering, Osaka Institute of Technol- ogy, where he is currently a Professor. He is en- gaged in research on PWM power conversion sys- tem and its application to the motor control. Dr. Taniguchi is a member of the Institute of Electrical Engineers of Japan, the Society of Instrumentation and Control Engineers, and Japan Society for Power Electronics.