Mathematical Model of Asynchronous
Machine in MATLAB Simulink
1
A A Ansari, 2 D M Deshpande
(1Research Scholar, 2Presently working in M.A.National Institute of Technology, Bhopal,India)
Abstract— Different mathematical models have been used over the years to examine different problems associated with induction motors. These range from the simple equivalent circuit models to more complex d,q models and abc models which allow the inclusion of various forms of impedance and/or voltage unbalance. Recently, hybrid models have been developed which allow the inclusion of supply side unbalance but with the computational economy of the d,q models. This paper presents these models with typical results and provides guidelines for their use The dynamic simulation of small power induction motor based on mathematical modelling is proposed in this paper. The dynamic simulation is one of the key steps in the validation of the design process of the motor drive systems and it is needed for eliminating inadvertent design mistakes and the resulting error in the prototype construction and testing. This paper demonstrates the simulation of steady-state performance of induction motor by MATLAB Program Three phase induction motor is modeled and simulated with SIMULINK model.
Keywords—Squirrel cage induction motor, modeling and simulation, MATLAB software, torque, speed.
1. INTRODUCTION
In recent years the control of high-performance induction motor drives for general industry applications and production automation has received widespread research interests. Induction machine modeling has continuously attracted the attention of researchers not only because such machines are made and used in largest numbers but also due to their varied modes of operation both under steady and dynamic states. In an electric drive system the machine is a part of the control system elements. To be able to control the dynamics of the drive system, dynamic behavior of the machine need to be considered. The dynamic behavior of IM can be described using dynamic model of IM. The dynamic model considers the instantaneous effects of varying voltages/currents, stator frequency and torque disturbance. In this paper the dynamic model of IM is derived by using d and q variables in a synchronously rotating reference frame.
Induction motor is simply an electric transformer whose magnetic circuit is separated by an air gap into two relatively movable portions, one carrying the primary and the other the secondary winding. Alternating current supplied to the primary winding from an electric power system induces an opposing current in the secondary winding, when the latter is short-circuited or closed through external impedance. Relative motion between the primary and secondary structure is produced by the electromagnetic forces corresponding to the power thus transferred across the air gap by induction. The essential features which distinguish the induction machine from other type of electric motors is that the secondary currents are created solely by induction, as in a transformer instead of being supplied by a dc exciter or other external power sources, as in synchronous and dc machines.
2. Equivalent circuit- The parameters of equivalent circuit of Induction Machines are crucial when considering advanced control techniques (i.e.Vector Control). Accidentally these are also uncertain parameters when the machine is released from production. The most common ways, to manually determine induction motor Parameters are to test motor under no-load and locked rotor conditions.
2.1 NO-LOAD TEST
Values measured during this test are current and it’s angle with respect to Known voltage. From this we can calculate total power supplied to the machine.
2.2 LOCKED ROTOR TEST
The locked rotor test, like short circuit test on a transformer, provides the information about leakage impedances and rotor resistance. Rotor is at the stand still, while low voltage is applied to stator windings to circulate rated current. Measure the voltage and power to the phase. Since there is no rotation slip, s=1 which gives us following equivalent circuit.
3 Dqo transformation
Simplified calculations can then be carried out on these imaginary DC quantities before performing the inverse transform to recover the actual phase AC results. It is often used in order to simplify the analysis of three-phase synchronous machines or to simplify calculations for the control of three-three-phase inverters. The dqo transform presented here is exceedingly similar to the transform first proposed in 1929 by R.H. Park. In fact, the dqo transform is often referred to as Park’s transformation.
The dqo transform applied to three-phase currents is shown below in matrix form:
The inverse transform is:
4. DESCRIPTION OF POWER SYSTEM BLOCKSET
Matlab/Simulink is a systems simulator and unable to direct simulate electrical circuits Therefore for simulation of electrical circuits power system block sets are used which incorporates libraries of electrical blocks and analysis tools which are used to convert electrical circuits into Simulink diagrams. The electrical blocks are electrical models such as electrical machines, current and voltage sources, and different electric elements, power electronic switches, connectors, and sensors for measurement purpose. When the simulation starts Simulink use the Pm Blockset and transfers the electrical circuit into a state–space representation with the initial conditions of state variables. The actual simulation starts after this initial conversion, this allows the use of a wide variety of fixed step and variable step algorithms available in Simulink. As variable time step algorithms are faster than fixed time step method because the number of steps are less so these algorithms are used for small- and medium-size systems, And for large systems containing a more number of states and/or power switches, a fixed time step algorithm is used. A Simulink scopes can be used to display the Simulation results or these results can be sent to workspace during the simulation. The variety of MATLAB functions and toolboxes are present for processing and plotting of waveforms from stored data.
5. INDUCTION MOTOR MODEL IN SIMULINK
A generalized dynamic model of the induction motor consists of an electrical sub-model to implement the three-phase to two-axis (3/2) transformation of stator voltage and current calculation, a torque sub-model to calculate the developed electromagnetic torque, and a mechanical sub-model to yield the rotor speed.
Where Vas, Vbs, and Vcs are the three-phase stator voltages, while Vds and Vqs are the two-axis components of the stator voltage vector .Fig shows torque sub-model of induction motor In the two-axis
stator reference frame, the electromagnetic T is
given
by
Mechanical sub-model of induction motor from the torque balance equations and neglecting viscous friction, the rotor speed ωo may be obtained as follows
Where J is the moment of inertia of the rotor and load and TL is the load torque
Stator current output sub-model
6. SIMULATION RESULTS
The induction motor chosen for the simulation studies has the following parameters: Rs=1.5 ohm Rr=0.7ohm L s=0.012 H Lm=0.1118 H
L r=0.1122 H J=0.054 kg m2 P=2 Ts=0.0546 nm Tr=0.160 nm
Torque developed
Speed RPM
Speed RPM
Ird
Irq
5. CONCLUSIONS
SIMULINK is a powerful software package for the study of dynamic and nonlinear systems. Using SIMULINK, the simulation model can be built up systematically starting from simple sub-models. The induction motor model developed may be used alone, as in the direct-on-line starting example presented, or it can be incorporated in an advanced motor drive system, e.g. field oriented control. The authors believe that SIMULINK will soon become an indispensable tool for the teaching and research of electrical machine drives.
6. REFERENCES
[6] P.C. Krause, “Electric machines” , prentice Hall, 1985. Hoang Le-Huy..‘Modeling and Simulation of Electrical Drives using MATLAB/Simulink and Power System Blockset’. IEcon’01: The 27th Annual Conference of the IEEE Industrial Electronics Society.
[7] Czeslaw T. Kowalski, Jacek Lis, Teresa Orlowska- Kowalska,. ‘FPGA implementation of DTC Control Method for the Induction Motor Drive’. EUROCON 2007 : The International Conference on “Computer as a Tool” Warsaw, Sept. 9-12,2007
[8] R.K.Rajput, “Electrical Machines,” first edition, New York: McGraw- Hill, 1993, pp. 352-353
[9] R.Krishnan, “Electric Motor Drives Modeling, Analysis and Control”, first edition, 2001Prentice-Hall International, Inc. Upper Saddle River, New Jersey 07458.
[10] Krause, P. C., ‘Simulation of symmetrical induction machinery’, IEEE T rans. Power apparatus Systems, Vol. PAS-84, No. 11, pp. 1038– 1053 (1965)
[11] Ghani, S. N., ‘Digital computer simulation of three-phase induction machine dynamics a generalized approach’, IEEE T rans Industry Appl., Vol. 24, No. 1, pp. 106–114 (1988)
[12] Wade, S., Dunnigan, M. W. and Williams, B. W., ‘Modeling and simulation of induction machine vector control and rotor resistance identification’, IEEE Trans. Power Electronics, Vol. 12, No. 3, pp. 495–505 (1997)
[13]. R. Krishnan, Electric Motor Drives Modeling, Analysis, and Control, Prentice Hall 2001 [14]. P. C. Sen, Principles of Electric Machines & Power Electronics, Wiley 1999
[15] Shi, K. L., Chan, T. F. and Wong, Y. K., ‘Modelling of the three-phase induction motor using SIMULINK’, Record of the 1997 IEEE International Electric Machines and Drives Conference, USA, pp. WB3-6 (1997)
[16] Shi, K. L., Chan, T. F. and Wong, Y. K., ‘Modelling and simulation of direct self control system’, IASTED International Conference: Modelling and Simulation, Pittsburgh, USA, pp.231–235 (May 1998)
[16] Trzynadlowski, A. M., T he Field Orientation Principle in Control of Induction Motors Kluwer (1994) [17] Using SIMUL INK, Dynamic System Simulation for MAT L AB, The Mathworks Inc. (1997) [18] Krause, P. C., Wasynczuk, O. and Sudhoff, S. D., Analysis of Electric Machinery, IEEE (1995)
[19] P. Krause and C. Thomas,"Simulation of symmetrical induction machinery," I€ff Trans. PAS-84, 1965, pp.1038-1053.
[20]. J.E. Brown, W. Drury, B.L. Jones and P. Vas, "Analysis of the periodic transient slate of a static Kramer drive," Proc lff, ~01.133, Pt.B. no 1, Jan 1 !386, pp.21-30.
[21]. P. Pillay and IL. Refoufi,"Calculation of slip energy recoveryinduction motor drive behavior using the equivalent circuit," /€ff Trans. lnd. Appl., vo1.30, no.1,Jan/Feb 1994, pp. 154-1 63.
[22]. D.G.O. Morris,"!;ome tests of an exact practical theory of the induction motor," F'roc. Iff, vol. 97, Pt.11, pp. 767-778. [23]. P. Krause, "Analysis of electric machinery," McGraw-Hi//, 1986.
[24]. R. Lee, P. Pillay and R. Harley, "D,Q reference frames for the simulation of induction motors," fPSR Journal, vo1.8. October
[25]. T. Higgins, P. Young, W. Snider, H. Holley, "Report on bus transfer studies,'"IEEE Trans. Energy Conversion, vo1.5, no.3, September 1990, pp. 470-484.
