Research Journal of Applie Sciences, Engineering an Technology 4(7): 846-85, ISSN: 4-7467 Maxwell Scientific Organization, Submitte: November, Accepte: December 9, Publishe: September, Moelling of Permanent Magnet Synchronous Motor Incorporating Core-loss K. Suthamno an S. Sujitjorn Control an Automation Research Unit, Power Electronics, Machines an Control Research Group, School of Electrical Engineering, Suranaree University of Technology, Nakhon Ratchasima,, Thailan Abstract: This stuy proposes a q-axis moelling of a Permanent Magnet Synchronous Motor (PMSM) with copper-loss an core-loss taken into account. The propose moels can be applie to PMSM control an rive with loss minimization in simultaneous consieration. The stuy presents simulation results of irect rive of a PMSM uner no-loa an loae conitions using the propose moels with MATAB coes. Comparisons of the results are mae among those obtaine from using PSIM an SIMUINK software packages. The comparison results inicate very goo agreement. Key wors: Dq-axis, losses, moelling, permanent magnet synchronous motor INTRODUCTION Present-ay inustry has wiely utilize Permanent Magnet Synchronous Motors (PMSM) because of their several avantages. These inclue high efficiency, low maintenance, high power-factor an ruggeness. Some applications, such as hybri vehicles, aircrafts, automate machines etc., usually require accurate control of spee an position. Control ifficulty arises since a PMSM has complex ynamic that results in complicate moelling. In classical machine textbooks, reaers often fin equivalent circuit, phasor an ifferential equation moels, for instance books authore by Fransua an Magureanu (984) an Ong, (998). DQ-axis moels, or q-moels, of PMSMs are also available (Pillay an Krishnan, 989; Monajemy an Krishnan, ; Krishnan, ). The q-moels are useful for machine control in the sense that relevant ac-signals are presente as c-signals. To achieve minimum loss rive of a PMSM, its moels with core-loss taken into account is esire. Equivalent circuit moels for the purpose are available (Morimoto et al., 994; Fernanez-bernal et al., ; Cavallaro et al., 5; in et al., 9). The equivalent circuit moels provie an insight for loss minimization, however cannot provie accurate ynamic performances of the machines. In contrast, the q-moels provie accurate information concerning machine ynamic an control. However, the available q-moels o not incorporate loss terms. Use of the moels is thus limite to machine control an rive without an extension to cover loss minimization. This stuy proposes the q-moels of PMSMs that incorporate core-loss as well as the equivalent circuit moels. The propose moels are applie to simulations using MATAB TM. The results are compare with those of commercial software packages incluing PSIM TM an SIMUINK TM with PowerSim Blockset. MATERIAS AND METHODS Moelling of a PMSM herein consiers both copperan core-losses esignate as R S an R C, respectively. Figure illustrates the iagram representing a PMSM, the symbols in which are liste by the en of the stuy. v Sabc = [v sa v sb v sc ] T an i = [i sa i sb i sc ] T Sabc are the voltage an the current vectors, respectively, at the motor terminals. The voltage an the current vectors at the motor cores are represente by v =[v ca v cb v cc ] T an = [i ca i cb i cc ] T Sabc i Cabc, respectively. i = [i a i b i c ] T oabc is the rotor current vector. The following matrices esignate the inuctances an flux: msabc ms cos ( re ) o ms cos re o mscos re ms re ms re cos cos ms cosre ms cosre ms cosre ms cos re () Corresponing Author: S. Sujitjorn, Control an Automation Research Unit, Power Electronics, Machines an Control Research Group, School of Electrical Engineering, Suranaree University of Technology, Nakhon Ratchasima,, Thailan 846
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, Fig. : Diagram representing a PMSM ls ls ls ls PM abc PM PM PM () sin( re ) sin re sin re () R S = iag [R S R S R S ] an R C = iag [R c R c R c ] represent the wining an the core resistances, respectively. Therefore, Eq. (4) expresses the motor voltage: v R i t i v Sabc S Sabc ls Sabc Cabc (4) an Eq. (5) expresses the voltage across the motor cores: T qo v sabc cos( re ) cosre cos re ( re ) sin( re ) sinre sinre (6) Therefore, we can state that v sqo = T qo ( re ) v sabc an = T - qo ( re ), where ( re ) stans for an electrical v sqo reference angle of the rotor shaft. Since: v R i t i v S S sqo ls S C qo qo qo i re ls Sqo (7) the rate of change of the motor current wrt time in q- frame can be expresse as: v t or R i C abc abc C C abc (5). et v sqo, = [v sq v s v s ], i sqo, = [i sq i s i s ] an qo = [8 q 8 8 ] T be the terminal voltages, currents an magnetic flux in q-frame, respectively. Transformation from the three-phase abc-frame to the q-frame utilizes the transformation matrix: t i v R R i sq ( ( ) R i ls sq s c sq i C oq re ls s t i v R R i s ( ( ) Ri ls i C o re ls sq ) s S C s ) (8) (9) 847
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, Fig. : Equivalent circuits of a PMSM taking account of core-loss an separate inuctances (a) (b) 848
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, Fig. : Simulation iagrams, (a) PSIM, (b) internal simulation iagram of the PMSM coupler moule in (a), (c) SIMUINK with PowerSim Blockset (c) Table : Parameters of a PMSM for simulations Parameters Propose moe SIMUINK PSIM R S (e).9.9.9 R C (e) NA NA ls (mh).77 NA NA m (mh) 5.75 NA NA mq (mh).5 NA NA (mh) NA 6.5 6.5 q (mh) NA.8.8 8 PM.*.*.45** J (kg-m ).5.5.5 B(Nm.s / ra)... *:in V. s / ra; **:in V peak - /Krpm Since an t i v so ( vso R Siso ) ls qo t M C qo re qo qo one can obtain that: t mq i m i i oq o o PM qo R C ( is i re M qo ) qo qo () () () () Hence, the rate of change of the torque generating currents in q-frame wrt time can be expresse as: t i oq mq Ri Csq Ri Coq i re m o re PM (4) t i o Ri Ri i m C S C o re mq oq (5) Base on the erive voltage an current equations, the equivalent circuits as shown in Fig. can be obtaine. Eq. (6) to (9) express the input power, output power, electromagnetic torque an the rate of change of spee of the motor, respectively. ls sq sq s s R i i R i i Pin vsq isq vs is i l i l mq i sq lsq m ls is S sq sq C cq c P Pout re PM ioq m mq ioq io ( ( ) ) P i i i r ( em loa Br) J em PM oq m mq oq o out (6) (7) (8) (9). The evelope moels escribe so far were coe in MATAB to simulate the machine ynamic base on a set of parameters (Ong, 998; in et al., 9) tabulate in Table. The results are compare to those obtaine from using PSIM an SIMUINK with PowerSim Blockset, respectively. Figure shows the simulation iagrams. In an actual rive, the supply frequency is varie in stepwise manner such that the machine graually gains its spee. This was conucte accoringly with a frequency-step of Hz in our simulations. For the simulate PMSM, the supply is Vrms, 6 Hz. The 849
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, 5 Torque (N.m) 5 5 Psim 9.. -5.5.5.5 (a) 5 Velocity (ra/s) 5 5 Psim 9.. -5.5.5.5 (b) current magnitue(a) 6 5 4 Psim 9...5.5.5 Fig. 4: Motor responses, (a) torque, (b) spee, (c) magnitue of the resultant current (c) machine was riven at no-loa from stan-still up to a spee of 5 ra/s within.6-.7 s. At the moment of s, Nm loa was suenly applie to the machine shaft. At s, the supply frequency was reuce from 5 to 4 Hz. RESUTS AND DISCUSSION Figure 4 illustrates the simulation results incluing torque an spee of the motor as well as the magnitue of the resultant current of the q-currents. The results obtaine from the three simulation approaches agree well except that PSIM gives the mechanical torque at shaft while the other two approaches give the electromagnetic torque. Therefore, the torque curve from PSIM shown in Fig. 4a is lower than the other two curves. The curves inicate oscillatory transient responses at the instant the frequency an the loa-torque are change. Figure 5 shows the motor phase-voltages an -currents. Notice that 85
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, 5 Psim 9.. voltage (V) 5-5 - -5 -.5.5.5 5 Psim 9.. voltage (V) 5-5 - -5 -.5. 5.5 5 Psim 9.. voltage (V) 5-5 - -5 -.5.5.5 (a) current (A ) 6 4 - Psim 9.. -4-6.5.5.5 85
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, current (A) 6 4 - Psim 9.. -4 current (A) -6.5.5.5 6 4 - Psim 9.. -4-6.5.5.5 (b) Fig. 5: (a) motor phase-voltages, (b) motor phase-currents (top, mile an bottom winows for phase-a, -b an -c, respectively) when the motor is riven at 5 Hz, it is almost unstable uring which the torque is about rate. The motor can prouce a stable rate torque with somewhat lower riving frequency, i.e. 4 Hz, as inicate by the response curves from s onwar. CONCUSION This paper has presente the erivation of the q-axis moels of a PMSM with copper- an core-losses uner consieration. The propose moels are useful for optimize efficiency rive evelopment of a PMSM. Using MATAB, PSIM an SIMUINK, simulations of irect-riven machine have been conucte. Comparisons of the results have inicate very goo agreement among the three approaches. R S R c ls, ms m, mq, q NOMENCATURE Stator wining resistance Core loss resistance Stator leakage inuctance Self an mutual inuctances - an q-axis mutual inuctances - an q-axis inuctances 8 PM Permanent magnet flux T r, T re Mechanical an electrical rotor spees J em Electromagnetic torque v s, v sq - an q-axis stator voltages v o, v oq - an q-axis core-loss voltages i s,i sq - an q-axis stator currents i c, i cq - an q-axis core-loss currents i o,i oq - an q-axis torque generating currents P in, P out Input power an output power B Viscous friction coefficient vs, i abc sabc Three-phase stator voltage an current vectors v, i Three-phase core-loss voltage an current Cabc Cabc vectors Three-phase torque generating current vectors. i oabc 7 abc Three-phase stator flux leakage vector 7 qo q-axis stator flux leakage vector ACKNOWEDGMENT Financial supports from the following organizations are greatly acknowlege: Ministry of Science an Technology (Thailan), Office of Higher Eucation of Thailan uner NRU project an Suranaree University of Technology. 85
Res. J. App. Sci. Eng. Technol., 4(7): 846-85, REFERENCES Cavallaro, C., A.O. Ditommaso, R. Miceti, G.R. Galluzzo an M. Trapanese, 5. Efficiency enhancement of permanent-magnet synchronous motor rives by online loss minimization approaches. IEEE T. Inus. Electr., 5: 5-6. Fernanez-bernal, F., A. Garcia-cerraa an R. Faure,. Determination of parameter in interior permanent magnet synchronous motors with iron losses without torque measurement. IEEE T. Inus. Appl., 7: 65-7. Fransua, A. an R. Magureanu, 984. Electrical Machines an Drive Systems. Technical Press, Romania. Krishnan, R.,. Permanent Magnet Synchronous an Brushless DC Motor Drives. CRC Press, US. in, C.K., T.H. iu an C.H. o, 9. Sensorless interior permanent magnet synchronous motor rive system with a wie ajustable spee range. IET Electric Power Applications, (): -46. Monajemy, R. an R. Krishnan,. Control an ynamics of constant-power-loss-base operation of permanent magnet synchronous motor rive system. IEEE T. Inus. Electr., 48(4): 89-844. Morimoto, S., Y. Tong, Y. Takea an T. Hirasa, 994. oss minimization control of permanent magnet synchronous motor rives. IEEE T. Inus. Electr., 4(5): 5-57. Ong, C.M., 998. Dynamic Simulation of Electric Machinery. Prentice Hall, US. Pillay, P. an R. Krishnan, 989. Moeling, simulation an analysis of permanent-magnet motor rives, part II: The brushless DC motor rives. IEEE T. Inus. Appli., 5(): 74-79. 85