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"Sharpening Skills..... Serving Nation" International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014) International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA. Methodology to Estimate The D-Q Axis Model Parameter For Three Phase Induction Motor Using MATLAB Mugdha Mishra1, Nitin Saxena2, Amit Singhal3, Sandeep Nain4 Moradabad Institute of Technology, Moradabad (U.P., INDIA) [email protected],[email protected],[email protected], [email protected] Abstract— This paper addresses a d-q model of three phase induction motor. It is the objective of this paper to derive and explain induction motor model in relatively simple terms by using the concept of d-q variables. This method reduces the three-phase system to a two-phase system. Using MATLAB programming we have modeled three-phase induction motor and obtained its direct and quadrature axis parameters. The basic purpose of using d-q model approach is to control the motor parameters independently i.e. torque of induction motor. Index Terms— d-axis, d-q transformation. induction motor, q-axis. I. INTRODUCTION By the help of Clarke and park transforms, three-phase induction motor can be modeled in an arbitrary two axis (d & q-axis) rotating reference frame. It will be shown that when we choose a synchronous reference frame in which rotor flux lies on the d-axis, this model can estimate the stator current along the direction of two-reference axis as shown in fig.1 along D & Q axis. In the rotating frame of reference the frame of reference in regard to the phase A is named the d-axis (for direct axis) and the other axis is named the q-axis (for quadrature axis). fig.1: Two reference model for rotating machine In many cases, analysis of induction motors with space vector model is complicated due to the fact that we have to deal with variables of complex numbers. When induction motors are controlled by a vector drive, control computation is often done in the synchronous frame. Since actual stator variables either to be generated or to be measured are all in stationary a-b-c frame, frame transform should be executed in the control. The most popular transform is between stationary a-b-c frame quantities to synchronously rotating d-q quantities. What remains is to define a method for performing the phase transformations to the rotating frame of reference. The transformation is done by defining a transformation-matrix for the systems as, f dq Tabcdq f abc Where, f denote currents, voltages, flux-linkage, etc. The dynamic model of the induction motor is necessary for understanding and analyzing the three-phase inductor motor for the purpose of speed control. In this paper induction motor has been modeled by MATLAB program. II. MATHEMATICAL MODELING OF THREE-PHASE INDUCTION MOTOR There are a number of AC induction motor models. The three-phase induction is modeled into a two-phase model. We can look at the motor as a 2-phase machine. Utilizing of the 2-phase motor model reduces the number of equations and simplifies the control design. The model used for vector control design can be obtained by utilizing space-vector theory. Such a model is valid for any instantaneous variation of voltage and current, and adequately describes the performance of the machine under both steady-state and transient operations. Complex space vectors can be described using only two orthogonal axes. For the demonstration of the analysis of an induction motor in the phase frame let us consider the power rating, slip, stator and rotor impedances and voltage rating. Firstly we have to develop the positive and negative sequence network for the machine in which the value of load impedances is only the difference. Forward rotating magnetic field treated as positive sequence and has slip s1 given by (1) And backward rotating magnetic field is treated as negative sequence and has slip s2 given by, (2) The positive sequence load impedance is, Lord Krishna College of Engineering (An ISO 9001:2008 Certified Institute) Ghaziabad, Uttar Pradesh, INDIA. Page 85 "Sharpening Skills..... Serving Nation" International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014) International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA. Three-phase line-to-neutral voltages, (3) The negative sequence load impedance is, [ ] [ ] (4) Input complex power to the motor, The net input positive sequence impedances of the network is, ( ) ( (5) ) The net input negative sequence impedances of the network is, ( ) ( (6) ) ∑ (14) Input power to motor =| | power factor of the motor, = cos( ( )) (15) For rotor currents and voltage evaluation we have to obtain the ABCD parameters of the machine, From Eq.5 & 6 we can evaluate the input sequence admittances as, (16) (17) (7) (18) and and (8) (19) Now the sequence admittance matrix will be formed as, [ ] (9) This sequence matrix will be transformed into the phase admittance matrix, [ ] [ ][ ][ ] 1 1 1 2 α= A= 1 1 2 , [ ] (11) ][ ] (12) The stator phase voltages can be evaluated from ,[ ] [ ][ [ [ ] [ ] [ ] [ ] ] [ [ The stator phase current is calculated as, ] ] ] (20) (21) (22) and Let Vab, Vbc and Vca are the three phase voltages, line-to-line voltages will be, [ [ (10) Where, [ We can form sequence ABCD parameters as, ] (13) ] (23) We have to transform these sequence ABCD parameters into a-b-c phase parameters, [ ] [ ][ ][ ] (24) [ ] [ ][ ][ ] (25) [ ] [ ][ ][ ] (26) ] [ ][ ][ ] (27) and [ Rotor phase voltage and current can be evaluated as, Lord Krishna College of Engineering (An ISO 9001:2008 Certified Institute) Ghaziabad, Uttar Pradesh, INDIA. Page 86 "Sharpening Skills..... Serving Nation" International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014) International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA. [ ] [ ][ [ ] [ ][ ] [ ][ ] (28) [ ][ ] (29) 250 200 Shaft power, ∑ 150 three-phase supply voltage ] (30) 100 50 0 -50 -100 -150 -200 -250 To convert three-phase voltages into two-phase synchronously rotating frame, they are first converted into two-phase stationary frame using the formula given below, 0 0.2 0.4 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.2 three-phase supply voltage 150 100 [ ] [ ][ √ ] (31) stator voltages 50 0 -50 √ -100 and then from the stationary frame to the synchronously rotating frame it is converted to give two-phase voltages, -150 0 0.2 0.4 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.3 stator three-phase voltages (32) 400 (33) 300 200 stator current Where, s denotes stationary reference frame and 100 0 -100 ∫ -200 -300 0 0.2 stator angular electrical frequency 0.4 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.4 stator three-phase currents We can obtain d-axis and q-axis currents from voltages, 150 (34) 100 rotor voltage 50 (35) 0 -50 √ -100 [ ] [ [ √ ] -150 0 0.2 0.4 ] 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.5 rotor voltages III. RESULTS 150 100 50 rotor voltage The basic purpose of this paper is to understand the exact mathematical model used for induction motor for finding the direct-axis and quadrature axis components of voltage and current. Using MATLAB programming we have modeled three-phase induction motor into two-phase machine. The quadrature and direct axis voltage components of modeled three-phase induction motor are shown in fig.7. 0 -50 -100 -150 0 0.2 0.4 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.6 rotor currents Lord Krishna College of Engineering (An ISO 9001:2008 Certified Institute) Ghaziabad, Uttar Pradesh, INDIA. Page 87 "Sharpening Skills..... Serving Nation" International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459 (Online), Volume 4, Special Issue 1, February 2014) International Conference on Advanced Developments in Engineering and Technology (ICADET-14), INDIA. Nomenclature 150 (d,q) : Rs, Xs : Rr, Xr : Vqr & Vdr : Vqs & Vds : 100 Vqs & Vds 50 0 -50 -100 -150 0 0.2 0.4 0.6 0.8 1 time t 1.2 1.4 1.6 1.8 2 fig.7 voltage components of q-axis and d-axis IV. CONCLUSION In this paper a two-phase model of three-phase induction motor has been modeled. By the help of two-phase modeled the analysis of three-phase induction motor becomes simple as well as this model is helpful for the speed and torque control of induction motor. This model is also essential when developing high performance control techniques for the asynchronous motor drives such as vector control or direct control (DTC) drives. APPENDIX Induction Motor Data Specifications of Induction Motor Power rating: 25 HP Supply : 240V, 50Hz Stator impedance: 0.0774+j0.1843 ohm Reactance of core: j4.8384 ohm Rotor impedance: 0.0908+j0.1843 ohm Slip: 0.035 direct & quadrature axis stator resistance and reactance rotor resistance and reactance d-axis & q-axis components of rotor voltage Vr d-axis & q-axis components of stator voltage Vs REFERENCES [1 ] Wiliam H.Kersting, Distribution System Modeling and Analysis, CRC press, Second Edition 2007. [2 ] Burak Ozpineci, Leon M.Tolbert, “Simulink Implementation of Induction Machine Model-A Modular Approach” [3 ] M. G. Morshad, “Direct Torque Control in Induction Motor”, IEEMA Journal of Electrical Engineering, Nov 2011. [4 ] Sifat Shah, A. Rashid, and M.K.L Bhatti, “ Direct Quadrate (D-Q) Modeling of 3-phase Induction Motor Using MATLAB Simulink”, Canadian Journal on Electrical and Electronics Engineering , vol. 3, no. 5, May 2012. [5 ] Power System Stability and Control, Pranha Kundur, TMH, Fifth Edition, 2008. [6 ] M. L. de Aguiar, M. M. Cad, “The concept of complex transfer functions applied to the modeling of induction motors,” Power [7 ] Engineering Society Winter Meeting, pp. 387–391, 2000. [8 ] [7] P. C. Krause, Analysis of Electric Machinery, McGraw-Hill Book Company, 1986. Lord Krishna College of Engineering (An ISO 9001:2008 Certified Institute) Ghaziabad, Uttar Pradesh, INDIA. Page 88