Analysis of Direct Torque Control of PMSM Drive Using Different Inverter Topologies

Analysis of Direct Torque Control of PMSM Drive Using Different Inverter Topologies Atul Sood 1, Dr. Anil Kumar Rai 2, Ritesh Sharma 3 and K. K. Prajapat 4 1,2,3 Department of Electrical and Electronics Engineering, Ajay Kumar Garg Engineering College, PO Adhyatmic Nagar, Ghaziabad 201009 UP 4 Department of Electrical Engineering, Sri Balaji College of Engineering and Technology, Jaipur-302012, Rajasthan sudatul@gmail.com, anilkrai@yahoo.com, call_ritesh@yahoo.com, kkparajapat2004@rediffmail.com Abstract -- Permanent Magnet Synchronous Motor (PMSM) drive is being preferred in industrial automation due to high efficiency, compact structure, and high torque to weight ratio and so on. PMSM have been widely used in variable speed drives. The direct torque control (DTC) technique for a PMSM motor is receiving increasing attention due to the important advantages as the elimination of the current controllers and the low dependence on motor parameters when compared with other motor control techniques. The basic theory of operation for the control technique is presented. A mathematical model for the proposed DTC of the PMSM topology is developed. A simulation mode developed in MATLAB/SIMULINK is used to compare the performance of the PMSM drive using different inverter topologies. Keywords: Direct Torque Control, Permanent Magnet Synchronous Motor, Two -level inverter. I. INTRODUCTION PERMANENT Magnet Synchronous Motor has gained popularity especially in the automation sector due to its compact size, high efficiency, and faster response [9]. As reliability and cost of modern PMSM drives are of importance, advanced control techniques have been developed. The PMSM is very similar to the standard wound rotor synchronous machine except that the PMSM has no damper windings and excitation is provided by a permanent magnet instead of a field winding. The elimination of field coil, dc supply and slip rings reduce the motor loss and complexity [1]. It is now recognized that the two high-performance control strategies for PMSM drives are vector control (VC) and direct torque control (DTC) [1], [2]. These control strategies are different in their operating principles but their objectives are the same. They both aim to control effectively the motor torque and flux in order to force the motor to accurately track the speed and torque references regardless of the machine and load parameter variation [5]. Direct Torque control technique is proving a viable control strategy for PMSM drive. This technique eliminates the current controller and reduces the dependence on motor parameters. It is mathematically proven that the increase of electromagnetic torque in a permanent magnet motor is proportional to the increase of the angle between the stator and rotor flux linkages, and, therefore, the fast torque response can be obtained by adjusting the rotating speed of the stator flux linkage as fast as possible. This is achieved by using direct torque control (DTC) technique. In direct torque control technique, the stator voltage vectors are selected according to the difference between the reference value and actual value of torque and stator flux linkages in order to reduce the torque and flux errors within the prefixed band limits [2]. In this paper, a mathematical model of PMSM has been developed first. Then, a simulation model of DTC of PMSM using different inverter topologies is simulated using MATLAB/SIMULINK. II. THE MATHEMATICAL MODEL OF PMSM DRIVE The well known stator flux linkage, voltage, and electromagnetic torque equations in dq reference frame are as follows: λd = Li d d + λ f λ = Li v v q q q = Ri dλd ωλ + = Ri dλq + ωλ + d s d r q q s q r d Where ë f is the flux linkage of rotor permanent magnet; L d, L q are inductances of d and q axis, respectively; p is the pole pairs; ë d, ë q, i d, i q, v d, v q are flux linkage, current and voltage in d and q axis, respectively [6]. (1) (2) The developed motor torque is being given by 3 Te = p( λdiq λqid) (3) 2 The mechanical torque equation is dω T T B J m e = L + ωm + (4) 23

AKGEC INTERNATIONAL JOURNAL OF TECHNOLOGY, Vol. 3, No. 1 III. SYSTEM IMPLEMENTATION FOR PMSM DRIVE At present, the control techniques normally employed in ac drives are: vector control and Direct Torque control. Direct Torque control, as the name suggest, control the electromagnetic torque and flux linkage directly and independently by the use of six or eight voltage space vectors [2]. The voltage vector selection for controlling the stator flux linkage and amplitude is normally done by diving voltage vector plane into eight regions. Stator flux estimation method: The stator flux is estimated using the following equation ( ) λ s = Vs Rsis (5) Using the above equation, the amplitude of the flux and the region where the flux is present, can be estimated. If the resistance term in the stator flux estimation is neglected, the variation of the stator flux linkage will only depend on the applied voltage vector as shown in Fig. 1. For a short interval of time, namely the sampling time, Ts = Ä t, the stator flux linkage, ës position and amplitude can be changed by applying the stator voltage vector, Vs. The position change of the stator flux linkage vector, ës, will affect the torque. In each region two adjacent voltage vectors, which give the minimum switching frequency, are selected to increase or decrease the amplitude of stator flux linkage, respectively. For example, according to the Table I, when the voltage vector V2, is applied in Sector 1, then the amplitude of the stator flux increases when the flux vector rotates counter-clockwise. If V3, is selected then stator flux linkage amplitude decreases. Torque estimation method: Electromagnetic torque is estimated using stator linking flux components and measured stator currents using the following equations: 3P Te = ( λdiq λqid ) (6) 4 The magnitude of stator flux and electromagnetic torque are compared with their reference values using the corresponding hysteresis controller. Hysteresis controllers are employed to maintain the torque and stator flux within a prescribed limit. The output of these controllers, in addition to the location of stator linkage flux in particular sector is fed to a switching table to select a voltage vector producing desired torque. Fig. 1 shows the DTC system incorporating the flux and torque estimators, flux and torque hysteresis controllers, switching table and Two Level inverter. [6] Figure 1. Incremental stator flux linkage space vector representation in the DQ-plane. During the sampling interval time or switching interval, one out of the six voltage vectors is applied. The goal of controlling the flux in DTC is to keep its amplitude within a pre-defined hysteresis band. By applying a required voltage vector stator flux linkage amplitude can be controlled [3]. To select the voltage vectors for controlling the amplitude of the stator flux linkage the voltage plane is divided into six regions, as shown in Fig. 3. Figure 2. Block Diagram of DTC. To determine the proper applied voltage vectors, information from the torque and flux hysteresis outputs, as well as stator flux vector position, are used so that circular stator flux vector trajectory is divided into six symmetrical sections according to the non zero voltage vectors as shown in Fig. 3 [2]. The switching table for controlling both the amplitude and rotating direction of the stator flux linkage is given in Table I. [4] 24

determined by the status of the three switches, S a, S b and S c. If the switch is at state 0 that means the phase is connected to the negative and if it is at 1 it means that the phase is connected to the positive leg. Figure 3. Voltage Space Vectors. Table I SWITCHING TABLE Figure 4. VSI connected to the R-L load. The output of the torque hysteresis comparator is denoted as ô, the output of the flux hysteresis comparator as ø and the flux linkage sector is denoted as è. The torque hysteresis comparator is a two valued comparator; ô = 0 means that the actual value of the torque is above the reference and out of the hysteresis limit and ô = 1 means that the actual value is below the reference and out of the hysteresis limit. The flux hysteresis comparator is a two valued comparator as well where ø = 1 means that the actual value of the flux linkage is below the reference and out of the hysteresis limit and ø = 0 means that the actual value of the flux linkage is above the reference and out of the hysteresis limit. We define ø and ô to be the outputs of the hysteresis controllers for flux and torque, respectively, and θ (1) -θ (6) as the sector numbers to be used in defining the stator flux linkage positions. In Table I, if ø = 1, then the actual flux linkage is smaller than the reference value. On the other hand, if ø = 0, then the actual flux linkage is greater than the reference value. The same is true for the torque. IV. GENERATION OF VOLTAGE SPACE VECTOR The estimation of the stator flux linkage components requires the stator terminal voltages. In a DTC scheme it is possible to reconstruct those voltages from the DC link voltage, Vdc, and the switching states (S a, S b, S c ) of a six-step voltage-source inverter [2]. When the primary windings are fed by an inverter, as shown in Fig. 3, the primary voltages va, vb and vc are For example, va is connected to Vdc if Sa is one, otherwise va is connected to zero. This is similar for vb and vc. The voltage vectors that are obtained this way are shown in Fig.2. There are six non-zero voltage vectors: V 1 (100), V 2 (110), and V6(101) and two zero voltage vectors: V7(000) and V8(111).The six nonzero voltage vectors are 60 degree apart from each other as in Fig. 2. V. VOLTAGE VECTOR SELECTION IN DTC OF PMSM DRIVE Control strategy adopted for selection of appropriate voltage vector is based on the Table II. On the basis of the sector è (è=1, 2... 6) in which the stator flux linkage lies and of the magnitude of the errors of the torque and flux, a voltage space vector V i (with i = l, 2,.. 6 ) is generated as shown in the fig. 4. Figure 5. Voltage vector selection when the stator flux vector is located in sector i. 25

AKGEC INTERNATIONAL JOURNAL OF TECHNOLOGY, Vol. 3, No. 1 As shown in Fig. 5, while the stator flux vector is situated in sector i, voltage vectors V i+1 and V i-1 have positive direct components, increasing the stator flux amplitude, and V i+2 and V i-2 have negative direct components, decreasing the stator flux amplitude.fig.5 Voltage vector selection when the stator flux vector is located in sector I Moreover, V i+1 and V i+2 have positive indirect components, increasing the torque response, and V i-1 and V i-2 have negative indirect components, decreasing the torque response. In other words, applying V i+1 increases both torque and flux but applying i+1 increases torque and decreases flux amplitude. constant = 0.476wb, Motor Moment of Inertia = 0.000423 kgm 2, Damping coefficient =.0004012 kg-m 2 /s. The command signal for the torque is taken as a step change changing from 1N-m to 2N-m at 0.1s. The simulation is performed using the actual values of the stator flux and torque and then comparing it in the respective hysteresis comparator. As shown in fig.6, the output of these two comparators, in addition to the sector selector is then applied to the switching table to obtain the best possible voltage vector. VI. SIMULATION AND RESULTS MATLAB/Simulink model of the permanent magnet synchronous motor is developed using two-level inverter. The 2 pole motor parameters used for simulation are Stator resistance (R S ) = 9.76 Ù, Direct axis self inductance (Lsd) = 92 mh, Quadrature axis self inductance (Lsq) = 126mH, Rotor flux Figure 8. Flux Trajectory. Figure 6. Flux trajectory. Figure 7. Harmonic Spectrum of stator current for two level inverter. Figure 9. Harmonic spectrum of Stator current for three level inverter. 26

Matlab implementation Direct Torque Control Technique with both 2-level and 3-level inverter are done and results for both the cases are presented. The stator current i a spectrum for three level inverter is shown. The spectrum when compared with the spectrum of i a with two level inverter the THD% has been reduced to 20.97% and also the fundamental component has been increased to 1.109.Hence simulation results prove that the use of 3-level inverter instead of 2-level inverter in DTC technique results in lower ripple content in torque, stator flux and stator currents. VII. REFERENCES [1] M. Depenbrock, Direct Self Control (DSC) of Inverter Fed Induction Machine, IEEE Trans. Power Electronics, Vol. 3, No 4, October 1988. [2] Enrique L. Carrillo Arroyo Modeling and Simulation of Permanent Magnet Synchronous Motor Drive system, Ph.D thesis, University of Puerto Rico Mayagüez campus. 2006. [3] Cui Bowen, Zhou Jihua, Ren Zhang, Modeling and Simulation of Permanent Magnet Synchronous Motor Drive Fifth IEEE International Conference on Electrical Machines and Systems, Volume 2, Aug. 2001. [4] B. K. Bose, Power Electronics and AC drives, Prentice Hall Inc., Englewood Cliffs, New Jersey, 1986. [5] Cui Bowen, Zhou Jihua, Ren Zhang Modelling and Simulation of Permanent magnet Synchronous motor Drives, IEEE proceedings 1990. [6] R. Krishnan, Electric Motor Drives: Modelling, Analysis and Control, Prentice-Hall of India Private Limited, New Delhi, 2005. [7] L. Zhong, M. F. Rahman, A Direct Torque Controller for Permanent Magnet Synchronous Motor Drives, IEEE Trans. Energy Conversion, Vol. 14, No.3, September, 1999. [8] S. Dan, F. Weizhong, H. Yikang, Study on the Direct Torque Control of Permanent-Magnet Synchronous Motor Drives, Fourth IEEE International Conference on Power electronics and Drive System, October 22-25, Bali, Indonesia, p. 571-574. [9] L. Zhong, M. F. Rahman, W.Y. Hu, K.W. Lim, Analysis of Direct Torque Control in Permanent Magnet Synchronous Motor Drive, IEEE Trans. Power Electronics, Vol. 12, No.3, May, 1997. [10] Salih Baris Ozturk Modelling, Simulation and Analysis of Low-cost Direct Torque Control of PMSM using HALL- EFFECT sensors, Ph.D thesis, Texas A&M University, December 2005 [11] D.Casadei, Francesco Profumo, Giovanni Serra, Angelo Tanni, FOC and DTC: two viable schemes for Induction Motor Torque control, IEEE Trans. on Power Electronics. 2001. [12] LANG Bao-hua, LIU Wei-guo, ZHOU Xi-wei, LI Rong, Research on Direct Torque Control of Permanent Magnet Synchronous Motor Based on Optimized State Selector, IEEE ISIE Volume 3, 9-13 July 2006. [13] Rahman MF, Zhong L. Voltage switching tables for DTC controlled interior permanent magnet motor, IECON 99, 25th annual Conference June 1999. p. 1445 51. [14] Maurizio Cirrincione, Marcello Pucci, Gianpaolo Vitale A Novel Direct Torque Control of an Induction Motor Drive with a Three-Level Inverter, IEEE Bologna PowerTech Conference, June 23-:26.2003. [15] K. E. B. Quinderé, E. Ruppert F., Milton E. de Oliveira F, Direct torque control of permanent magnet synchronous motor drive with a three-level inverter IEEE Trans. Power Electronics, 18-22 June 2006. Atul Sood obtained B.E.(Electronics and Power) from Nagpur University in 2000.He completed MBA with specialization in Marketing Management in 2005. Since last six years, he is working at Ajay Kumar Garg Engineering College where he is Assistant Professor in the Department of Electrical & Electronics Engineering. He has taught a number of courses namely Electrical Engineering, Electrical Measurement and measuring instruments, Microprocessor, Reliability Engineering. He has published one paper each in national conference and technical journal. Dr. Anil Kumar Rai obtained his B.Sc. Engg. Degree in Electrical Engineering from BCE Bhagalpur in 1991. He obtained his Ph.D. Degree from I I T Delhi in 2007. He has published several research papers in International and National Journals and Conferences. One of his research papers, entitled An Investigation of Mismatch losses in solar cell network published in Elsevier Publication, received 68 citations since 2007. Presently he is working as Professor in the Department of Electrical & Electronics Engineering at Ajay Kumar Garg Engineering College, Ghaziabad. His areas of interest are Renewable Energy systems, Control systems, Electrical Power Quality and so on. Ritesh Sharma obtain B.E.(Electrical Engg.) from MITS Gwalior in 2000. He is pursuing M. Tech from Sri Balaji College of Engg. & Technology in Power system Engg. Cuurently, he is teaching in Ajay Kumar Garg Engineering College Ghaziabad where he is Assistant Professor in the Department of Electrical & Electronics Engineering. He has published one paper each in national conference and technical journal. Kamal Kant Prajapat obtained B.E. in 2006 and M.Tech in 2009 from Govt. Engg. College Kota and ITBHU Varanasi respectively. Since last two years, he is teaching at Sri Balaji College of Technology, where, he is Assistant Professor in the Department of Electrical Engg. He has published various papers in technical journals and conferences. His area of interest is Electrical Machines and drives. 27