Analysis, Design, Implementation of Sensorless V/f control in a Surface Mounted PMSM without damper winding

Analysis, Design, Implementation of Sensorless V/f control in a Surface Mounted PMSM without damper winding Sourabh Paitandi 1, Mainak Sengupta 2 Dept. of Electrical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711103, W.B., India E-mail: 1 sourabh350@gmail.com, 2 msg@ee.iiests.ac.in Abstract This paper presents a reliable and efficient V/f control of permanent magnet synchronous motor(pmsm) without damper winding in the rotor. In absence of damper winding open loop V/f control of SM is inherently unstable, particularly, at high speeds. Stabilisation can be done with proper stator frequency modulation in accordance with the change in rotor speed to provide for effect of damping which has been implemented here. The change in rotor speed is observed from power perturbation. This eliminates the need for using a speed sensor in the drive. Here, the efficiency of the drive is increased with proper control of the power factor irrespective of load and frequency variations. Simulated and experimental results are presented of both open loop and proposed V/f control. These results establish the accuracy of the design of the proposed V/f control and precision of hardware implementation. Keywords Surface mounted PMSM, V/f control, sensor-less control, stabilisation of PMSM, efficiency optimisation. INTRODUCTION Use of PMSM based drives is increasing in several applications due its well known advantages. Different control techniques such as vector control, direct torque control, V/f control with or without position/speed sensor are being used in PMSM drive. Although, the vector control and direct torque control give fast dynamics, the V/f control is one of the simplest control techniques where the speed of the PMSM can be controlled by varying the supply frequency. Use of V/f control first started for IM that does not require very fast dynamic response. Various techniques were reported for improvement of V/f control based IM drive [1], [2]. The use of V/f control for PMSM has been reported first in [3]. However, the open loop V/f control of PMSM without damper winding is inherently unstable after a certain frequency range which has been discussed later. Different stabilisation techniques[4] with an additional speed sensor [5], rotor position estimation using stator voltage and current has also been reported in literature. The stabilisation can be done by provide for effect of damping torque using appropriate control strategy during speed transients of the rotor[6]. An additional speed sensor or position sensor as used in many cases, increases the cost and reduces the reliability. V/f control can be used for the line start PMSM with damper winding in rotor. However, due to different design complexity and to have cost reduction, most of the PMSMs dont have damper winding[7]. For stable V/f operation of these PMSMs the damping torque is provided by controlling the torque angle(δ) during speed transients[8]. Present paper discuss and implements a sensor-less satabilisation technique. The efficiency of the drive has been increased by controlling the terminal power factor ( internal power factor, since δ is small) of the PMSM by controlling the reactive power. The proposed V/f control scheme is shown in Fig.1. Fig. 1. Block diagram proposed V/f controller with stabilisation and power factor control The proposed V/f control PMSM drive has been designed, implemented and tested on a laboratory prototype surface mounted PMSM. The PMSM has been designed and fabricated by the authors with the help of a small machine manufacturer with imported magnets.([10], [11]). The PMSM is coupled with a DC generator for loading

purpose. The ratings and other important parameter of the system is given in the Appendix. Control algorithm has been implemented on FPGA platform. I. MODELLING OF PMSM[9] For the surface mounted PMSM used here, L d = L q = L. The PMSM equation is given by, [ ] vd v q = [ R + pl ωl ] [ id ωl R + pl iq ] + [ 0 ωψ 0 ] J dωr = T e Bω T L (2) where, ω r = mechanical speed in elec. rad/sec, ω = stator frequency in elec. rad/sec and ψ 0 = no load flux linkage. All other symbols have their usual significance. From, (1) The state space model of the PMSM can be obtained by rearranging (1) to (5). However these equations contain non-linear terms. Therefore it is necessary to linearise the equations. The non-linear model can be linearized assuming[4], x i = X i + x i where x i is the variable, X i is the steady state value and x i is a perturbation. Using (1) to (5) and after the linearisation, the state equations of the V/f controlled drive, we get (6). px = Ax + Bu (6) Where,x= [ i d i q ω r δ ] x = [ i d i q ω r δ ] T u = [ ] v s ω T T l R/L ω r0 I q Vs cos δ 0 L A = ω r0 R/L ψ 0/L Vs sin δ 0 L 0 (p/2) 2 ψ 0 B/J 0 0 0 1 0 sin δ 0 L 0 0 cos δ B = 0 L 0 0 0 0 p/2j 0 0 0 Fig. 2. Phasor diagram of PMSM. Fig.2, V q = V s cos δ and V d = -V s sin δ. Here, δ is the load angle. It will be worthwhile to mention that the electromagnetic torque developed[9] in the motor, T e = p 2 [(L d L q )i d i q + ψ 0 i q ] = p 2 ψ 0i q (as, L d = L q ) Hence, J dω r = ( p 2 )2 ψ 0 i q Bω r T L (3) For transient analysis of PMSM it is also important to consider this load angle. Fig.3 shows the torque angle δ during steady and transient state. Now, The stability analysis can be verified by the eigen values of matrix A. At steady state, v s = 0 and ω = 0. For simplicity, it is assumed that motor is running under no-load which implies, I q = 0. Table I shows the eigen-values of matrix A at different values of ω r0 (stator frequency). It can be seen from the table that the eigenvalues λ 3 and λ 4 has positive real parts after a stator frequency = 230 rad/sec (35Hz) which establishes the instability of open loop V/f drive. Fig.4 shows machine speed when speed reference is ramping from 0 to 475 r.p.m. under open loop V/f control. It can be seen that the machine is stable at this speed. Fig.5 shows that the machine becomes unstable when speed reference is changed to 550 r.p.m. under open loop V/f control. Fig. 3. Power angle change of PMSM during transients θ = ω t δ (4) if, t 0, θ t = ω r, ω r = ω dδ (5) Fig. 4. Upper trace: speed referance ramping upto 475 r.p.m, lower trace: speed of machine under open loop V/f control

Now, torque in a PMSM with a damper winding is given by[9], J dω r = ( p 2 )2 ψ 0 i q + Bω + D(ω ω r ) T l (10) (10) can be linearised as discussed earlier and the block diagram of Fig.7 can be obtained from it. The corresponding characteristic equation with ω=0 is given by, Fig. 5. Upper trace: spped referance ramping to 750rpm, lower trace: speed of machine under open loop V/f control TABLE I EIGENVALUES OF SYSYTEM MATRIX UNDER OPEN LOOP V/F CONTROL AT DIFFERENT STATOR FREQUENCY ω (rad/s) λ 1 λ 2 λ 3 λ 4 105-61+j327-61-j327-48+j99-48-j99 220-107+j324-107-j324-2.2+j233-2.2-j233 230-112+j328-112-j328 3.4+j240 3.4-j240 314-130+j378-130-j378 21+j269 21-j269 s 2 + ( B J + pk d 2J )s + pk e 2J = 0 (11) Comparing Fig.6, Fig.7 and (9), (11), it can be observed that an additional damping term proportional to the speed difference between of stator and rotor mmf provide for the necessary damping torque during transients and ensures the stability of the drive. This can be done by modulating the stator frequency in such a way that, dω r ω = sk d ω r ω = K d (12) This modifies the overall system block diagram which is shown in Fig.8. The characteristic equation for the II. SIMPLIFIED ANALYSIS AND STABILISATION OF V/F CONTROL DRIVE The ctable above is for the open loop system. However it is easy to appreciate that, associated electrical time constant is much lesser than the mechanical time constant. Thus we can simplify (6) to (7) as, ( ) ( ωr J p = B 0 ) ( ) ( ) ( ) ωr 0 p + 2J ω δ 1 0 δ 1 0 T l (7) for a small delta delta, sin δ δ.thus, restoring torque T e is given by, T e = K e δ (8) Fig. 7. Block diagram of simplified small signal model of PMSM with damper winding under V/f control Fig. 8. Block diagram of simplified small signal model of PMSM without damper winding with controlled frequency modulation modified system is given by, Fig. 6. Block diagram of simplified small signal model of PMSM without damper winding under V/f control The block diagram of the system described in (7) is shown in Fig.6. For constant frequency operation under steady state condition, ω=0. Hence, the characteristic equation of the system in Fig.6 is given by, s 2 + B J s + pk e 2J = 0 (9) s 2 + ( B J + pkk e 2J )s + pk e 2J = 0 (13) Comparing (11) and (13), it is evident that modified system has similar characteristics with PMSM with damper winding and hence, can provide necessary damping with a proper selection of K. Although, a speed sensor is required to calculate ω r. However, the same can be calculated from power perturbation without any speed or position sensor which is described in the next section.

III. STABILISATION USING POWER PERTURBATION Electrical energy input of the machine consists of field storage, losses and energy for mechanical work. For small perturbation about equilibrium point, change in motor losses are negligible. Also, the stored magnetic energy is almost constant over a cycle. During small rotor perturbation, the perturbation in average power primarily consists of accelerating power and change in load power. Power balance equation can be written as, p e = P e + p e = Losses + dw fe + ( 2 ) 2 dω 2 p J r + ( 2 2 p) Bω 2 r + 2 p ω r T l Neglecting change in losses and stored magnetic field energy, p e = ( 2 ) 2 d ω r p 2Jω0 + 2 p T l0 ω r (14) Comparing (12) and (14) it can be written that, ω = K p e = K ( ( 2 p ) 2 2Jω0 d ω r + 2 p T l0 ω r ) (15) This modifies the system in Fig.8 into system drawn Fig. 10. Block diagram showing power perturbation calculation machine. Here, the cut off frequency is 3.5Hz (chosen through iterations). Fig.11 and Fig.12 show the speed response during sudden loading of the the motor with the cut off frequency 3.5 Hz. Fig.13 shows the speed response of the drive with cut off frequency 7 Hz. It can be seen that the system is under-damped and speed is slight oscillatory during sudden load change. Very low cut-off frequency makes the speed transients more sluggish. Fig. 9. Block diagram of simplified small signal model of PMSM without damper winding with controlled frequency modulation Fig. 11. Simulated result: Speed reference, actual speed, load current during sudden loading of 30Nm with 3.5 Hz cut off frequency (scale: X-axis: 0.5 sec/div, y-axis: 10rad/sec/div or 10A/div) in Fig.9. The characteristic equation for the modified system is given by, s 2 + s( B 2J + 4KK eω r ) + k 2 p 2J (p + KT l0) = 0 (16) Additional Damping can be provided by proper selection of K. Here K = 0.5 has been used. A. Measurement of power perturbation Input power in any machine/3-phase circuit can be calculated as, P = V α I α + V β I β (17) Input power of the PMSM can be calculated using (17) with the help of reference voltages generated for sine PWM and sensed phase current for any pre-fixed DClink voltage of the inverter. Active power perturbations can be measured using a high pass filter which is shown in Fig.10. The cut-off frequency of the high pass filter is determined from mechanical time constant of the Fig. 12. Experimental result: Speed reference, actual speed, load current during sudden loading of 30Nm with 3.5 Hz cut off frequency IV. POWER FACTOR CONTROL AND EFFICIENCY OPTIMISATION For a surface mounted PMSM maximum efficiency operation is possible when, I d = 0. Hence, I a =I q. It can be understood from Fig.14 that maximum efficiency operation is possible by minimising the stator copper loss

(power factor) is almost unity. This gives maximum output power per ampere at any particular speed. Fig. 13. Simulated result: Speed reference, actual speed, load current during sudden loading of 30Nm with 7 Hz cut off frequency (scale: X-axis: 1 sec/div, y-axis: 10rad/sec/div or 10A/div) Fig. 15. Block diagram of reactive power controller Fig. 14. Energy flow diagram in PMSM as all other losses are constant. The PMSM used here (actually all the Surface mounted PMSM) has very low inductance (L d =L q =5.5mH) which gives full load torque angle very low (here full load torque angle δ=10 0 ). This particular characteristics of SPMSM lead to the fact that external power factor (V a and I a are in phase) and internal power factor (E and I a are in phase) are almost same for this machines (Fig.2). Unity external power factor gives internal power factor of 0.985 (cos 10 0 ) at full load. In a V/f control drive, the back emf is not available since rotor position is not estimated to make the control more simple. However, the terminal voltage (voltages used for sine PWM) and current are known. This gives the calculation of input reactive power as, Q = V β I α V α I β It is necessary to make Q=0 to maintain external u.p.f. during entire operation of drive. It is also well known that reactive power (power factor) of any PMSM can be controlled by controlling the terminal voltage. Here the terminal voltage is maintained to desired value corresponds to u.p.f by measuring Q and maintaining Q=0 by a PI controller. The schematic is given in Fig.15. Fig.16 and Fig.17 show the reactive power transients during sudden loading of the machine. Fig.18 and Fig.19 shows that the steady state external displacement factor Fig. 16. Simulated Result: Upper trace active power (scale: x-axis 0.2sec/div, y-axis: 200W/div) and lower trace reactive power (scale: x- axis 0.2sec/div, y-axis: 200VAr/div) during sudden loading of 20N-m Fig. 17. Experimental Result: Upper trace active power and lower trace reactive power during sudden loading of 20N-m The values of K p and K i are chosen such a way so that it does not affect transient response of the machine as the control is being done on stator reference frame without any decoupling between d and q-axis. Higher values of K p and K i make the transient reactive power reset to zero faster but results in speed oscillation (Fig.20). CONCLUSIONS Here, closed loop stable V/f control of a surface mounted PMSM has been implemented. The inherent instability of open loop V/f drive has been eliminated with proper frequency modulation with the help of power perturbation. scheme eliminates the need for any shaft mounted speed or position sensor. the proposed scheme

Fig. 18. Experimental Result: V ph and I ph at steady state Fig. 20. Upper trace active power (scale: x-axis 0.5sec/div, y- axis 1kW/div), middle trace speed (scale x-axis 0.5sec/div, y-axis 20rad/sec/div), lower trace reactive power (scale: x-axis 0.5sec/div, y- axis 20VAr/div) during sudden loading of 20N-m with K p=0.2, K i =2 TABLE II RATINGS AND OTHER PARAMETERS OF THE PMSM Fig. 19. Experimental Result: V ph ref and I ph at steady state L d = L q 5.5 mh R 0.7Ω ψ 0 0.76 volts-sec No. of.pole, p 8 Rated speed 750 rpm J 0.01kg-m 2 B 0.015 Nm-sec/rad is found to be unaffected by parameter variations. The efficiency of the motor has maximised by making the reactive power to zero. Simulated results along with basic analysis of the system proves the instability of open loop V/f control above 500 r.pm. However, the PMSM runs smoothly without any instability or sustained oscillation with the closed loop frequency modulation. The simulated and experimental results of the proposed closed loop V/f control has been presented here. Simulated and experimental results are in excellent correlation with each other and in perfect agreement with theoretical analysis. This drive is perhaps more suited to applications where efficiency and simplicity are more important than high dynamic performance, notably in pump, fan, and compressor drives etc. ACKNOWLEDGMENTS The authors would like to express their gratitude for the fund support received from the NaMPET initiative of the Govt. of India, DIT, MCIT. The authors wish to thank GE Motors, Sheoraphully, specially Mr. Kausik Pyne, for the support and in prototype fabrication. The assistance received from the IIEST authorities and research colleagues at the Advanced Power Electronics Laboratory, Dept. of EE, IIEST. APPENDIX REFERENCES [1] F. Fallside and A. T. Wortley, Steady-state oscillation and stabilisation of variable-frequency invertor fed induction motor drives, Proc. IEE, vol. 116, no. 6, pp. 991-999, June 1969. [2] K. Koga, R. Ueda, T Sonoda, Constitution of V/f control for reducing the steady state speed error to zero in induction motor drive system, IEE IAS Annual meeting,vol. 1, pp. 639-646, Oct. 1990. [3] Roy S. Colby, Donald W. Novotny, An Efficiency-Optimizing Permanent-Magnet Synchronous Motor Drive, IEEE Transactions on Industry Application, Vol. 24, pp. 104-112, June 1988. [4] P. D. Chandana Perera, F. Blaabjerg, J. K. Pedersen, and P. Thogersen, A sensorless, stable V/f control method for permanent-magnet synchronous motor drives IEEE Trans. Industry Application, vol. 39, pp. 783-791, Jun. 2003. [5] T. A. Lipo and P. C. Krause, Stability analysis for variable frequency operation of synchronous machines, IEEE Transactions on power application system, Vol. 3, pp. 227-234, 1967. [6] G. C. Verghese, J. H. Lang, and L. F. Casey, Analysis of Instability in Electric Machines, IEEE Truns. Ind. Appl., vol. IA-22, pp. 853-864, Oct. 1986. [7] B.K. Bose, Power electronics and variable frequency drives. Technology and applications. IEEE Press, 1997 [8] S. C. Agarlita, C. E. Coman, I. Boldea,Stable V/f control system with controlled power factor angle for permanent magnet synchronous motor drives, IET Electric Power Application, Vol. 2, PP-278-286, March 2006. [9] D.O Kelly And S.Simmons, Generalized Electrical Machine Theory, McGRAW HILL, 1968. [10] S. paitandi and M.Sengupta, Design, fabrication and parameter evaluation of a surface mounted permanent magnet synchronous motor IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Dec 2014. [11] S. paitandi and M.Sengupta, Design, analysis of a surface mounted permanent magnet synchronous motor and its comparison with a Induction Motor of same nominal rating National Power Electronics conference (NPEC), Dec 2013.