MATHEMATICAL MODELING AND SPEED TORQUE ANALYSIS OF THREE PHASE SQUIRREL CAGE INDUCTION MOTOR BY USING MATLAB/SIMULINK

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1 MATHEMATICAL MODELING AND SPEED TORQUE ANALYSIS OF THREE PHASE SQUIRREL CAGE INDUCTION MOTOR BY USING MATLAB/SIMULINK Muhammad Umair Abid, Tahir Sajjad,NaiemArif, Saqib Zafar, Muhammad Tayyab, Engr.Majid Ali Dept. Electrical engineering and Technology (Sharif College of Engineering and Technology) Abstract: Induction motors have an extensive use all over the world, we use different methods to troubleshoot problems arise in induction motors. In this research paper we will emphasize the use of different software s such as MATLAB (SIMULINK) to solve problems of Squirrel cage induction motors. Performing the experiment of squirrel cage induction motor we have to overcome with different type of speed and torque relationships which are to be calculated when experiment is to be done by different methods. We can understand characteristics of three phase induction motor by the curves, but to find response of circuit at any instant of time we use SIMULINK models. We can make these simulations step by step to check results at any instant and to make a comparison between experimental and SIMULINK results. By using different methods regarding machines we can find short circuit current, power factor, starting torque, speed, magnetizing reactance windage, core and friction losses etc., Models on SIMULINK are key to solve different problems of torque and speed for three phase squirrel cage induction motor. By these techniques one is capable to find all of electric machines parameters from very small scale to industry usage electrical drives, because drives in industry require detailed transient dynamic analysis. By using these calculations one can design different motors from small level to industry scales and errors can be reduced. This research is to provide a strong knowledge about squirrel cage induction motor or others, by using different kind of software s. Because they are applicable for both of small scale and industrial scales. One can easily do all of the experiments to calculate transient response and other parameters. Key Words Squirrel Cage Induction Motor, Modeling and Simulation, MATLAB Software. I. Introduction In this era of technology different techniques of study are being developed. Now a days besides of laboratory tasks different new software s are inducted into labs. These software s are a key to perform different tasks relating to experiments. These are a source for a student to compare both of results at a same time both experimentally and theoretically. Developers have design these software such as to be compatible with most of the experiments done in lab and related to daily usage.doing lab while studying Machines there are different software s which are necessary to compute results theoretically and experimentally such as Matlab, Protious and Multisim etc. Experimenting Induction Motor include different type of tests. We can do them experimentally on work stations, while having more knowledge of its components and new techniques we can use SIMULINK (MATLAB) or some other software s. In this software all of the components regarding Induction Motor are available. Different methods have been developed for different test of machines. In experimenting induction motor we have to overcome with different type of speed and torque relationships which are to be calculated when experiment is to be done by different methods. All of these methods are according to IEEE defined rules and regulations. We can understand characteristics of three phase squirrel cage motor by the curves which can be obtained by using SIMULINK models. We will make these simulations step by step to check results at every instant and to make a comparison between experimental and SIMULINK results. Need

2 of such kind of software s arise one someone has to find behavior of machine for a very short interval of time. Simulations for squirrel cage induction motor can be carried out when the rotor is in stationary state and synchronous reference time frame. Doing experiments when we study machines often steady state of electrical drives is use but we all know that response of drives for short interval is also very important. So if some person is interested to look over behavior for a very short interval of time the techniques like SIMULINK are very good to use. To use such kind of methods we only use equations and built in functions. Software s like that of Simulink are capable to solve all of the models step by step by using different integral and differential techniques. By these techniques from one is capable of find all of electric machines parameters from very small scale to industry usage electrical drives, because drives in industry require detailed transient dynamic analysis. II. Squirrel Cage Induction Motor We can make rotor of induction motor as wound rotor or a squirrel cage rotor. In majority of the cases industrial scale applications involve the use of threephase squirrel-cage induction motors. Field windings in stator of squirrel induction motor is set up by rotating magnetic field with help of rotor. The motion between field and rotation of rotor result into induced electric current in bars. The conductors react with the magnetic field of the motor to generate force acting at a tangent to the rotor, resulting torque to turn the shaft.by its effect the rotor is carried around with the magnetic field but with slower rate of rotation.the rotor core is a cylindrical laminated iron core, with slots around core carrying rotor conductors. Steel laminations are provided on the rotor core.stator in motor is similar for both kind of three phase induction motors. Stator is non rotating part made up of high quality alloy steel. The core of stator carry alternating flux which produce hysteresis and eddy current. The conductors in induction motor are often skew slightly along length of the rotor because by this noise become to reduce and motor runs smoothlywithout torque fluctuations this will result at some speeds due to interactions with the number of pole pieces on the stator. Number of bars on the squirrel cage induction motor determines at what extent the induced currents are fed back to the stator coils. That constructions offer the least feedback employ prime numbers of bars. Iron core present in motor serves to carry the magnetic field through the rotor conductors. As the magnetic field in the rotor is alternating with respect to time, the core uses in construction is similar to a core use in transformer to reduce core energy losses. The slots on rotor windings are either of semi-closed type or of totally closed type. Advantage of this kind of slots is that the effective cross sectional area of the air gap is increased, thus reducing magnetizing currents. Disadvantages of such slots is that due to higher inductance provided by them, power factor p.f is reduced and lowers the starting and breakdown torques. Since the rotor winding is permanently short circuited in cage construction, so there is no possibility of adding any external resistance in the rotor circuit. III. Objective Objective for this project is to Find machine parameters Build SIMULINK block diagram for motor Torque-Speed characteristics from SIMULINK Equivalent circuit for induction motor will be R1 150R L1 100nH L2 100nH Fig.1 IV. Full Load Characteristics L5 100nH R2 150R

3 No load test is done for measurement of losses like rotational losses of motor which explains us about the magnetizing current. We attach transformer as same value of three phases and no voltage fluctuation. Now we attach load thah will be according to the value of resistor connected with DC shunt generator.we will change load after intervals and at each load we will measure the line to line voltage and line currents and will take their average values as follows: And v(l l) = I(l l) = v1 + v2 + v i1 + i2 + i [1] [2] As we calculate the losses at no load same as we will calculate here at each load by noting power and then measuring the stator copper losses, Copper losses will be changing as the line current is changing with change in load. We can calculate the -phase squirrel cage induction motor speed by the use of following formula: Ns = 120 f [] p Slip which is the difference of synchronous speed and actual speed can be calculated as: Ns N S = [4] Ns Input power of rotor can be calculated by subtracting Cu losses from the total input power. Total losses can be calculated by using following equation: The output torque will be lower as depend on power out which will be less than mechanical power becauseof friction and windage losses. V. Full Load parameters calculations for Induction Motor S.N SPECIFICATIONS values 1 Full load Line Voltage 2 Full load Phase Voltage 64 V ohms Full load Current 2.6 A 4 Full load Impedance ohms 5 Full load Power 169 W 6 Full load Power factor Power factor angle degree 8 Full load Impedance i ohm 9 Rotor resistance 4.8 ohms 10 Approximate X ohms Table.1 VI. No Load Characteristics No load test is done for measurement of losses like rotational losses of motor which explains us about the magnetizing current. We attach transformer as same value of three phases and no voltage fluctuation. We can calculate line to line voltage and line current with meter so their average values can be given as: And Vo = Io = v1 + v2 + v i1 + i2 + i [5] [6] VII. No load parameters calculations for Induction Motor S. No Parameters Values 1 Stator Resistance.5 ohm 2 Line to Line 20 V voltage No load current 2.5 A 4 No load input 106 W power 5 Phase voltage at No V load 6 No load impedance ohms 7 No load power factor 8 Power factor angle degree 9 Magnetizing V branch volt 10 Current through A

Xm,Im 11 Current through Rc 0.26608 A.Ic 12 Magnetizing 49.8997 ohms Reactance 1 Core Resistance 466.1721 ohms 14 Magnitizing Impedance.28082+49.44i ohms 15 Approximate.

The dynamic modeling of three phase squirrel cage induction motor is done by using SIMULINK designed model for three phase induction motor fed by PWM inverter.

4 Xm,Im 11 Current through Rc A.Ic 12 Magnetizing ohms Reactance 1 Core Resistance ohms 14 Magnitizing Impedance i ohms 15 Approximate.2166 ohms Reactance 16 Stator Copper W Losses 17 Rotational Losses W Table.2 VIII. Modeling of Squirrel Cage Induction Motor for Speed Torque analysis Fig. The dynamic modeling of three phase squirrel cage induction motor is done by using SIMULINK designed model for three phase induction motor fed by PWM inverter Torque speed curve of induction motor Pull out Torque IX. Simulation Results The simulation results for induction motor in Electrical Machines lab are shown as follow Torque induced N.m Starting Torque at R=5,p=6, Pin=120 2 Smax Rotor Speed (rpm) Fig.4 Torque speed curve of induction motor 9 Pull out Torque 8 7 Fig.2 This result show that with increase in rotor speed value of torque also increase. Torque induced N.m 6 5 at R1=5 ohm Starting Torque Smax Rotor Speed (rpm) Fig.5

5 X. Conclusion In this paper we have represented different parameters of induction motor with the help of software, each and every modal of machines can be generate by using Simiulink on Matlab. The results compiled on software sare manually and experimentally same to one another.the machines simulated on SIMULINKhave given a satisfactory response in terms of full load, no load andtorque, speed characteristics. So by using different techniques on software s one can be able to generate SIMLINK models for large machines also.this research provides a complete relationship between hardware and software understanding of three phase induction motor. This concludes that the Matlab/SIMULINK is a reliable and completely accordingthe way to analyze and predict the behavior of induction. XI. References [1]. ns/sqmovies.html [2]. []. ree-phase-induction-motor-workingsquirrel-cage.html [4]. [5]. ISR-University of Coimbra, Motors Study Group, "Actions to Promote Energy- Efficient [6]. Electric Motors", DGXVII, European Commission, October [7]. Bose, Bimal K., "Power Electronics and Variable Frequency Drives", Technology and Applications, IEEE Press, USA, [8]. Nasar S. A.; Boldea, Ion: "Electric Drives", CRC Press LLC, Florida, [9]. Electric Motors and Drives", Springer- Verlag, Berlin, [10]. Frank J. Bartos, "Reliability, Ease of Use Widen AC Drives' Application Harizons", Control [11]. NEMA Publication # MG 1, ref MG , table 12.6B. [12]. Eaton Dynamatic Electric Drive Applications Guide page M-7. [1]. Induction Motors with Solid-State Motor Design using Simulated Annealing Algorithm, Electric Power Components and Systems, Vol., 2005 [14]. A.E. Fitzgerald, C. Kingsly, Jr., and S.D. Umans, Electrical Machines, 5th edition, McGraw-Hill New York, [15]. M.G. Say, The Performance and Design of Alternating current Machines, third edition, CBS Publishers and Distributors, New Delhi. [16]. D.P. Kothari, I.J. Nagrath, Electrical Machines, Tata McGraw-Hill, [17]. Chapman, S. J. (Ed.). (2005). Electric Machinery Fundamentals (fourth ed.): McGraw Hill. [18]. Adjustable Frequency Controllers", IEEE Transactions. [19]. Industry Applications, Vol 1A-20, no. 1, January/February [20]. John B. Mitchell, "Inverter Power Factor and Noise", Power Transmission Designmagazine. [21]. R.Bhuvaneswari, S. Subramanian, Optimization of Three-Phase Induction motor.

SIMULINK Based Model for Determination of Different Design Parameters of a Three Phase Delta Connected Squirrel Cage Induction Motor

IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-issn: 2278-1676,p-ISSN: 2320-3331, Volume 7, Issue 4 (Sep. - Oct. 2013), PP 25-32 SIMULINK Based Model for Determination of Different