Copyright © 2018 Authors. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestrict- ed use, distribution, and reproduction in any medium, provided the original work is properly cited. International Journal of Engineering &Technology, 7 (4.24) (2018) 111-114 International Journal of Engineering & Technology Website: www.sciencepubco.com/index.php/IJET Research paper Mathematical Modelling of Linear Induction Motor M.Naga Raju 1 *, M.Sandhya Rani 2 , 1 Assistant professor, Department of Electrical Engineering, VLITS College, Vadlamudi, India 2 Department of Electrical Engineering, VLITS College, Vadlamudi, India *Corresponding author E-mail:nmurikipudi@gmail.com Abstract The Linear Induction Motor is a special purpose electrical machines it produces rectilinear motion in place of rotational motion. By using D-Q axes equivalent circuit the mathematical modelling is done because to distinguish dynamic behavior of LIM, because of the time varying parameters like end effect, saturation of core, and half filled slot the dynamic modelling of LIM is difficult. For simplification hear we are using the two axes modelling because to evade inductances time varying nature it becomes complex in modelling, this also reduces number of variables in the dynamic equation. Modelling is done using MATLAB/SIMULINK. LIM can be controlled by using sliding model control, vector control, and position control. Keywords: longitudinal end effect; transverse edge effect; equivalent circuit; applications; Dynamic performance. Nomenclature Symbols Description V Voltage C Current V dp ,V qp Primary voltage in the d-q axes(V) V dl ,V ql Linor voltage in the d-q axes (V) i dp ,i qp d-q axis primary current (A) i dl ,i ql d-q axis linor current (A) λ dp ,λ qp d-q axis primary flux linkages λ dl ,λ ql d-q axis linor flux linkages R p ,R l primary and linor resistance (A) L lp ,L ll primary and linor leakage inductance(H) L m magnetizing or mutual inductance (H) L p ,L l primary and linor self inductances (H) P no. of poles Τ pole pitch (m) D length of the linor (m) Q factor associated with linor length V velocity (m/s) ω primary angular velocity (rad/sec) ω l linor angular velocity (rad/sec) ω sl slip frequency (rad/sec) 1. Introduction LINEAR INDUCTION MOTOR the name itself says linear so it produces linear motion. In industries these LIM are usually used for automated systems. Because of the occurrence of end effects the dynamic modelling of these kind of motors are complicated to model. For understanding motor behavior during disturbance of load and at normal condition motor modelling is done, by using rotor reference frame, arbitrary reference frame etc. It have many popular performance features, together with high-speed operation, during starting it has high thrust force, mechanical construction is simple, silence operation, Simple structure, and easy maintenance, low cost, it do not require any gear mechanism, good reliability, reduction of mechanical losses. By considering the end effects LIM is simulated in synchronously rotating reference frame, based on our requirement the reference frames are selected. For obtaining easy solution in hybrid comput- er the two-axis modeling is done to evade inductance time varying nature and reduce variables in equations. Compared to AC quanti- ties DC quantities are chosen for controlling of LIM. The DC quintiles will decide the operating point it is simple to model in small signal equation and difficult to model in non- linear equation. The park’s transformation converts 3Φ quantities to 2Φ quantities for mmf equality. For maintaining voltage unbalance and inver- sion of park’s transformation the Zero sequence component which is a new variable is introduced. LIM’s are used in many applications particularly in electrome- chanical conversion units such as Elevators, Baggage handling, Automatic sliding doors, Accelerators, Horizontal conveyance systems, Cranes, Material handling and storage, actuator, transpor- tation, piston pumps, electric traction, automotive control and robotics etc. 2. End effect in LIM When the primary moves, a new flux is always generated at the primary entrey side, while at the exit side flux will be disappears. Ther will be a rapid generation and disappeareance of the magnetic lines produce statically induced currents in the secondary sheet. The air gap flux is affected by the eddey currents. With the increase of speed the losses, and the flux-profile become sever this is called End-Effect in LIM. If velocity increases the primarie’s length decreases this increases end effect which causes reduction of magnetization currents of LIM. For zero velocity the length of the primary is considerd as infinite to reduce the end effect.