Indirect Rotor Field Orientation Vector Control for Induction Motor Drives in the Absence of Current Sensors

Transcription

1 Indirect Rotor Field Orientation Vector Control for Induction Motor Drives in the Absence of Current Sensors Z. S. WANG *, S. L. HO ** * College of Electrical Engineering, Zhejiang University, Hangzhou , China ** Electrical Engineering Deartment of Hong Kong Polytechnic University, Hong Kong zjuwzs@hotmail.com, eeslho@inet.olyu.edu.hk Abstract This aer rooses a simlified vector control imlementation strategy that can be realized in the absence of current sensors. In order to decoule the torque and flux in the determination of the three-hase voltage reference commands of the SPWM inverter, both stator and rotor currents in the stationary and rotating frames can be derived from the corresonding rotor flux-oriented vector control requirements and motor dynamic equations. A sensitivity analysis to study the effect of arameter deviation or mismatch is also investigated. Simulation results are resented to demonstrate the feasibility and erformance of the roosed methodology. Keywords- vector control; induction motor control; motor drives I. INTRODUCTION The indirect field orientation control (IFOC) strategy is widely used for imlementing high erformance induction motor drive systems, and has been increasingly adoted as the standard industry solution [1-3]. In this scheme, current sensors are used to measure the motor currents, and two current controllers have to be designed to regulate the motor currents and to infer the M/T-axis voltage reference command. These sensors and controllers not only increase the overall system s cost, but also increase the design comlexity in terms of drift comensation and gain correction, articularly if the scheme is to be alicable over the whole seed and torque load ranges. Conventional sli frequency control scheme does not use voltage and current sensors [4]. However, essentially, it is scalar control. Inevitably, its dynamic erformance is oor due to the couling effect between torque and flux. Yamamura S. etc. integrated the scalar scheme with vector control, and roosed the sli frequency vector control strategy to get good dynamic resonds [5]. But in this method, current sensors and their corresonding controllers have to be designed to regulate the motor currents. This aer resents a novel IFOC imlementation method for induction motor drives without the need to use voltage and current sensors. It also eliminates two current feedback loos and their associated controllers, resulting in overall design simlicity and cost reduction for vector controllers. In order to realize the decouled control between the torque and flux, the stator current is searated into two orthogonal comonents for torque current and flux magnetizing current, and these comonents are then regulated indeendently. Furthermore, it can be shown that if the rotor currents are known values, the voltage alied to the motor can be determined using motor equations. Nevertheless the rotor current cannot be measured directly in induction motors. However, for rotor field orientation drives, one could calculate the rotor current based on the vector control scheme and motor dynamic equations. Thus, the voltage alied to the motor can be controlled recisely. On the other hand, one has to note that as there are no voltage and current feedbacks, the erformance of the drive might deteriorate due to arameter deviations/mismatch and disturbances in the inut DC link voltage. It is shown from the simulation results that even though there are large value mismatching in arameters, the roosed algorithm could, with the excetion of very low seeds, roduce good dynamic and steady state erformances over a wide range of seed. The effect of DC link voltage disturbance can be neglected in many actual ractical alication cases. II. INDUCTION MOTOR MODEL AND THE PROPOSED CONTROL METHODOLOGY According to the rotor field orientation vector control theory [4] [6], the stator current of squirrel-cage induction motor can be decomosed into two orthogonal comonents in the synchronous rotating rotor fluxoriented reference frame (M-T frame) which are, namely, the torque current i TS, which is to generate the electromagnetic torque, and the magnetizing current i MS, which is to excite the motor flux. These two current comonents are searated indeendently and decouled each other. Their magnitudes can be calculated according the electromagnetic torque ( T e ) and rotor flux level ( λ r ), and are governed by the following equations [6] /06/$ IEEE IPEMC 2006

2 4Te its 3Pλr (1) 1+ ( Lr ) λr The subscrit s and r indicate the stator and rotor variables, M,T reresent the variables in the rotor field orientation rotating reference frame. R r, L M, L S and Lr are the motor rotor resistance, mutual inductance, stator inductance and rotor inductance, resectively. λ r and T e are the resective rotor flux and electromagnetic torque. P is the number of ole airs. is the d / dt oerator. In most cases, the flux magnitude should be ket at some constant level, articularly when the motor runs below its base seed. So, (1) can be rewritten as 4Te its 3Pλr (2) λr The current angle θ 2 in M-T axis is its θ 2 arctg (3) On the other hand, the sli frequency is [4] RriTS ω s (4) Lr The rotor flux angle in stationary reference frame can be exressed as θ 1 ( ω r + ωs )dt (5) where ωr is the rotor mechanical seed. Thus, the stator current can be exressed in the stationary reference frame as: i i αs βs cosθ1 sinθ1 - sinθ1 i cosθ 1 i MS TS On the hand, in the rotor flux-orientated reference frame, the rotor side voltage-current equations of squirrel-cage induction motor can be described as [6] where i 0 0 ωs Mr, i Tr 0 0 its + Rr + Lr Lrω S 0 R r imr itr are rotor current comonents in M-T axis. The first row of (7) can be rewritten as 0 RriMr + ( ims + LriMr ) RriMr + λmr (6) (7) (8) In the rotor field orientation control, λ r λmr,λtr 0. In most cases, flux magnitude should be ket at some constant levels: λ r const., or λ r 0. Base on these requirements and the flux definition, the rotor current comonents in M-T axis, i, i, can be obtained as [6] Mr imr λmr λr 0 itr ( λtr LmiTs ) / Lr ( 0 / Lr ) its (9) ( / Lr ) its Using coordinate transformation, the rotor current can be exressed in the stationary reference as iα r cosθ1 sinθ1 imr (10) r sinθ1 cosθ1 itr The hasor diagram of the stator and rotor current ( i s, i r ) in α β axis and M-T axis is shown in Fig. 1. Tr Fig.1 Phasor diagram of stator and rotor current Based on the motor voltage-current equations in stationary reference frame which are shown below, uα s RS + LS uβ s iα s R S + LS s 0 iα r r (11) where R s, L s are stator resistance and inductance. Using the 2-hase to 3-hase coordinate transformation, the three hase reference command voltage signal can finally be determined. Thus, the final stator voltage, including frequency, hase and magnitude, can be directly derived from the motor dynamic equations just according to the seed and flux requirements (reference). Any voltage current sensors, signal feedback loos, and corresonding controllers do not need. Moreover, this method does not require comlicated algorithm [5][6], and time-consuming arameter online identification technique [6]. So, the roosed control scheme can greatly simlify the system design, and reduce overall cost.

3 Fig.2 Configuration o the roosed vector control method III. SIMULATION RESULTS Digital simulation research is carried out to validate the roosed control method. Fig. 2 shows the system configuration of the vector control: a 2.2 kw induction motor is driven by a SPWM voltage-tye inverter, and the three-hase voltage reference command alied to the inverter is derived from the flux and torque references. The simulation investigation is focused on the motor erformance with decouled torque and flux, a sensitivity study to evaluate arameter mismatch or deviation, and the tracking ability of the motor in detuned cases. The motor arameters are R S 3 Ω, R r 3. 23Ω, L M 210mH, LS Lr 223mH, P2. A. Performance of the Proosed IFO Conreoller Detailed simulation tests are carried out to assess the roosed control method. Figs. 3 and 4 show the torque and flux decouled erformance of the motor. In Fig. 3, the motor is running at a seed of 1000 rm. It can be seen that as the load torque is suddenly changed from 5.5 Nm to 10.5 Nm (trace a), the rotor flux level hardly changes (trace b, c), although there is a small seed di but then it is restored quickly (trace d). Fig. 4 shows a different case in that the flux level is suddenly changed at t5 s by the maniulators (trace a, c), however the torque can be restored to its original level quickly (trace b). Fig. 5 shows the tracking erformance of the motor following a traezoidal seed reference (trace a). Trace b is the seed error, and trace c is the rotor flux in the α axis. It can be seen that the flux level can be ket constant in different seed regions. The M-axis and the T-axis fluxes in trace d illustrate the effect of the rotor field-oriented control: λ T r 0, λ M r const. The seed tracking exeriment is in a constant load condition (10Nm). This traezoidal test can be used to evaluate the driver running in bi-direction oeration, constant /variable seed and motoring/generative modes. Fig. 6 shows the seed transient and ste torque change resonses (trace a). The load torque is roortional to the rotor seed in this case. There are seed reference and load torque ste changes at time t3 s and at t3.5 s (trace a, c) resectively. Trace d and b show the corresonding flux magnitude and α axis flux. Because there are no voltage and current feedbacks in this control method, arameter mismatching or detuned running is a major roblem. The following tests are designed to evaluate this erformance. In Fig.7, the DC link voltage, which is alied to the inverter, is set to have a ± 20% deviation from the rated voltages (the rated voltage is 500V) (trace a). It shows that the steady state torque is not changed (trace c), but the flux level is changed by as much as about ± 20%. This is still an accetable result because in ractical alications, most motors have their own inut voltage ranges and their corresonding flux levels. Moreover, many new generation drivers use ower factor correction (PFC) circuits in the first stage, so that their DC link voltage can be maintained at a constant level, and therefore one does not need to take into account this influence. Fig. 8 shows the flux sensitivity with resect to the inductor arameters ( L M,LS, Lr ) and mismatching in low-seed (100rm, traces a, b) and high-seed (1200 rm, trace c, d) running. During t2s to 3s, Lˆ MSR L * MSR. During t3s to 4s, Lˆ MSR 2L * MSR. During t4s to 5s: Lˆ MSR 0. 5L * MSR, where L * MSR means the actual motor L M, L S, Lr arameters, and Lˆ MSR means the corresonding mismatched arameters used in the controller. These mismatching has a slight influence uon the motor erformance at high-seed running only, the influence is much more ronounced at low-seeds. The resistance mismatching influence is shown in Fig.9, similarly, it exlains the flux level versus different stator and rotor resistances in low-seed (100rm in trace a, b) and high-seed (1200 rm in trace in trace d, e) regions. During t2s to 3s, Rˆ * s r R s r. During t3s to 4s, Rˆ * s r 2R s r. During t4s to 5s, Rˆ * s r 0. 5R s r, where R * s r means the actual arameters, and Rˆ s r means the mismatched arameters used in the controller. One can

4 Fig.3 Flux erformance under torque ste changing Fig.4 Torque erformance under flux ste changing Fig.5 Traezoidal tracking running Fig. 6 Transient erformance under ste seed and load Fig. 7.Dc link voltage mismatching Fig.8 Inductor mismatching

5 Fig.9 Resistance mismatching see that noticeable influence only aears in case of low seed running. For the roosed control method, it will have a general tolerance to oerate with arameters mismatching to a certain extent. A transient erformance with arameter mismatching is shown in Fig. 10. The mismatched arameters are: R * s r 2 Rˆ s r, L* MSR 1. 5Lˆ MSR. The load is set to be roortional to the rotor seed. One can see that although the transient time is increased a bit, the steady state flux and torque (seed) are still stable with very small riles. B. Dynamic Resonds Comarison with Conventional Vector Control The roosed control algorithm is derived form the basic rincile of rotor field orientation control. Consequently, so it is still vector control method. It should be noted that the urose of this control method is aimed to reduce the money cost in hardware, and simlify the control design. Fig.11 shows the dynamic resonds of conventional vector control and roosed control scheme in case of no load ( (a)) and 10 Nm load (Trace (b)). Fig. 11 Ste resonds of roosed control method and conventional vector control. (a). no load running, (b). running in 10 Nm load Fig. 10 Synthetic arameter mismatching Both trace (a) and (b) show that the roosed control scheme shares comarable good dynamic resonds erformance with conventional vector controller using current sensors no matter running in no load or in a heavy load. IV. CONCLUSIONS A vector control strategy for induction motor drives, which does not use current sensor, is roosed and tested. This scheme can reduce the system cost and simlify the control design. The current feedback loo and controller can be eliminated. It exhibits the decouled effect between the flux and torque. Sensitivity to the arameter mismatching is evaluated by simulation, and it shows that the roosed algorithm works well over most seed ranges with the excetion of low seeds. Moreover, the roosed system can oerate stably with significant arameters mismatching as well. REFERENCES [1] A. Consoli, G. Scarcella, and A. Testa, Seed-and Current- Sensorless Field-Oriented Induction Motor Drive Oeration at Low Stator Frequencies, IEEE Trans. Industry Alications, Vol.40, No. 1, , Jan./Feb., [2] Fang-Zheng Peng, and T. Fukao, Robust Seed Identification for Seed-sensorless Vector Control of Induction Motors, IEEE Trans. Industry Al., Vol.30, No. 5, , Set./Oct., [3] R. Gabriel, W. Leonard, C. Nordby, Field Oriented Control of a Standard AC Motor Using Micro-rocessors, IEEE Trans. Industry Alications, Vol.IA-16, No. 2, , [4] Andrzej M. Trzynadlowski, The Field Orientation Princile in Control of Induction Motors, Kluwer Academic Publishers, U.S.A. [5] Yamamura S., Siral Vector Theory of AC Motor Analysis and Control, IEEE Industry Alications Society Annual Meeting, 1991, Conference Record of 1991, [6] Bose B. K., Modern Power Electronics and AC Drivers, Prentice- Hall, Englewood Cliffs, New Jersey, 1986.