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Design, Analysis of Linear Induction Motor Based on Harmony Search Algorithm and Finite Element Method

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Design, Analysis of Linear Induction Motor Based on Harmony Search Algorithm and Finite Element Method JOURNAL OF Journal of Engineering Science and Technology Review 9 (6) (2016) 189 - 195 Engineering Science and estr Technology Review J Research Article www.jestr.org Design, Analysis of Linear Induction Motor based on Harmony Search Algorithm and Finite Element Method Ch. V. N. Raja and K. Rama Sudha Department of Electrical Engineering, A.U. College of Engineering (A)Visakhapatnam, India Received 16 August 2016; Accepted 29 December 2016 ___________________________________________________________________________________________ Abstract Linear Induction motors (LIM) are used extensively in industrial applications, especially in transportation systems. These applications need high efficiency with high power factor. Mainly LIM suffer from two major drawbacks, low power factor and low efficiency. These drawbacks cause high energy consumption and high input current. In this paper, a novel Harmony Search optimization algorithm is proposed to meet required efficiency and power factor in the design of a Linear Induction Motor. Finite Element Method is adopted to analyze the flux density in LIM with the parameters obtained using HSA. Keywords: : Linear Induction motor, Harmonic search Algorithm and FEM analysis __________________________________________________________________________________________ 1. Introduction Ugur Hasirci [11] discussed about design, execution and nonlinear velocity tracking control of a novel maglev system Linear Induction motor (LIM), is basically an advanced for maglev trains. A. Shiri [12] derived analytical expression version of motor that is in use to achieve rectilinear motion for braking force of LIM based on iron saturation, transverse instead of rotational motion as in ordinary conventional edge effect, longitudinal end effect and skin effect. A.A. motors. The stator is cut axially and spread out flat. The LIM Pourmoosa [13] introduced imperialist competitive is broadly applicable in variety of applications such as algorithm (ICA) to equivalent Linear Induction motor based military, transportation, actuators, robot base movers on coupled-circuit model. elevators and etc., [1] due to easy maintenance, high Maurizio Cirrincione [14] implemented an adaptive acceleration/deceleration and no need of transformation neural network based model reference system (NNMRAS) system from rotary to translational motion. for low speed LIM drives. Adil Hameed Ahmed [15] Roma Rinkevicien [2] discussed application of linear suggested indirect field oriented voltage control to improve induction motor in mechatronic systems. Dal-HoIm [3] Linear Induction Motor Performance. Xu Qiwei [16] describes an optimization problem using the Interior Point implemented Sliding mode observer to LIM in order to algorithm (IPA) to meet desired specifications. Yoon [4], reduce the steady state error and suppress the integral optimization is performed to LIM based on starting thrust saturation. Hsin - Han Chiang [17] proposed an optimized and output power input volt–ampere ratio. Rong - Jong Wai adaptive tracking control for a LIM drive by considering the [5] developed nonlinear control strategy from lyapunov’s uncertainties like friction force, unknown end effects and principle to control LIM servo drive for periodic motion. payload. Hadi Zayandehroodi [18] introduced a multi- Mehmet Cunkas [6] developed Genetic Algorithm (GA) objective cuckoo optimization algorithm (COA) enhanced to program package to meet required torque efficiency and improve both efficiency and power factor. cost. This paper is organized as follows; section II describes A. Hassanpour Isfahani [7] proposed a multi-objective Equivalent Circuit and dynamical model of LIM, section III genetic algorithm optimization method to improve both describes Identification of LIM parameters using HSA, motor power factor and efficiency. Liu Ai-min [8] discussed section IV describes FEM Analysis for LIM and section V on a Neighborhood Topology algorithm (NTA) to maintain describes the computer simulations results. high starting thrust and high reliability for high-voltage circuit breaker. Ismail Khalil Bousserhane [9] intended an Adaptive Backstepping controller for LIM to achieve a 2. Machine Modelling position and flux tracking objective under disturbance of load torque and parameter uncertainties. A. Zare Bazghaleh 2.1. Equivalent Circuit model of LIM [10] proposed particle swarm optimization (PSO) to evaluate Fig. 1. shows the architecture of the single sided LIM. It intensity of end effect with help of equivalent circuit contains a three-phase primary and an aluminium laid sheet method. on the secondary back iron [7]. In 1983, J. Duncan implemented the equivalent circuit model of LIM. The per- ______________ phase equivalent circuit model of SLIM is shown in Fig. 2. • E-mail address: [email protected] ISSN: 1791-2377 © 2016 Eastern Macedonia and Thrace Institute of Technology. All rights reserved. Ch. V. N. Raja and K. Rama Sudha/Journal of Engineering Science and Technology Review 9 (6) (2016) 189-195 gap; wse is the equivalent stator width; ρr is the volume resistivity of the rotor conductor outer layer and fl is primary frequency. To maintain air gap flux density below 0.5 T, then the iron losses is negligible and the thrust, the efficiency and the power factor will be given by 2 mI1Rr Fs = (7) Fig. 1. Architecture of a single sided LIM ⎡ ⎤ 1 ⎢ 1⎥ sV ⎢ 2 + ⎥ s ⎢ sG ⎥ ⎣( ) ⎦ F 2τ f (1− s) η = s 1 (8) F 2τ f +3I2R s 1 1 Fig. 2. Equivalent circuit of a LIM F 2τ f +3I2R cosϕ = s 1 1 (9) ρ l 3VI Per-phase stator resistance R = w w (1) s A wt Hassanpour Isfahani A, et. al., 2008 explained effect of Per-phase stator-slot leakage reactance different parameters on efficiency and power factor and hence it is necessary to employ an optimization method to ⎡⎛ ⎛ 3⎞ ⎞ W ⎤ achieve required specifications. Table 1 describes design 2 1 s I N 2 µ0 ⎢⎜ λs ⎜ + ⎟ + λd ⎟ + λe ce ⎥ variables of optimization problems for LIM. ⎢⎝ ⎝ p⎠ ⎠ q ⎥ X = ⎣ ⎦ (2) s p Table 1. Design variables of optimization problem Parameter Symbol Unit Max. Min. Slot, differential and end connection permeance are Value Value Maximum thrust s -- 0.1 0.3 slip h (1+3k ) s p Pole Pitch τ mm 40 60 λs = 12ws Aluminium d mm 3 6 thickness ⎛ ge ⎞ 2 5⎜ ⎟ Primary current J A/mm 1 3 ⎝ w ⎠ λ = s (3) Density d ⎛ ⎞ Efficiency η -- 0.7 -- g0 5+4⎜ ⎟ Power Factor cosϕ -- 0.7 -- w ⎝ s ⎠ λ = 0.3(3k −1) 2.2. Dynamical Modelling of LIM e p The dynamic model of the LIM is modified from traditional model of a three-phase, Y-connected LIM and can be Magnetizing Reactance per phase expressed in the d-q synchronously rotating frame as [9] 24µ π fw K N 2τ X = 0 se W l (4) ⎛ ⎛ 2 ⎞ ⎞ m 2 ⎛ L ⎞ π pg ⎜ ⎜ m ⎟ ⎟ e − Rs + ⎜ ⎟ Rr i + ⎜ ⎜ ⎝ L ⎠ ⎟ ds ⎟ ⎜ ⎝ r ⎠ ⎟ X ⎜ ⎟ Per-phase rotor resistance R m (5) di 1 π L R = ds = ⎜ +σ L v i + m r ϕ +⎟ (10) r G dt L ⎜ s e qs 2 dr ⎟ σ s τ Lr ⎜ ⎟ ⎜ PL π ⎟ 2µ f τ 2 + m ϕ v + V 0 l ⎜ qr r ds ⎟ Goodness factor G = (6) ⎜ Lrτ ⎟ ⎛ ρ ⎞ r g ⎝ ⎠ π ⎜ ⎟ e ⎝ d ⎠ Where, ρw is the volume resistivity of the copper wire used in the stator winding; lw is the copper wire length per phase; Awt is the cross sectional area of the wire; kp is the pitch factor; kw is the winding factor; ge is the equivalent air 190 Ch. V. N. Raja and K. Rama Sudha/Journal of Engineering Science and Technology Review 9 (6) (2016) 189-195 ⎛ ⎛ 2 ⎞ ⎞ optimization. When power factor is more important, choose π ⎛ L ⎞ k =0, k = 1 and when efficiency is more important than ⎜ L v i ⎜ R m R ⎟ i ⎟ 1 2 −σ s e ds − s + ⎜ ⎟ r qs − power factor, choose k =1, k = 0. By considering k =k = 1, diqs 1 ⎜ τ ⎜ ⎝ Lr ⎠ ⎟ ⎟ 1 2 1 2 = ⎜ ⎝ ⎠ ⎟ (11) optimized simultaneously to meet desired efficiency and dt σ L ⎜ ⎟ s PL π L R power factor. ⎜ − m ϕ v + m r ϕ + V ⎟ ⎜ dr r 2 qr qs ⎟ Harmony Search Algorithm (HSA) is an optimization ⎝ Lrτ L ⎠ r algorithm developed by Xiaolei Wang in 2015. HSA is an advanced process control and optimization for industrial scale systems. HSA is based on the musical process where d ϕdr LmRr Rr ⎛ π π ⎞ music players manage the pitches of their instruments to find = i − ϕ + ve−P vr ϕqr (12) necessary harmony. Steps involved in the process of HSA dt L ds L dr ⎝⎜ τ τ ⎠⎟ r r are as follows: dϕqr L R ⎛ π π ⎞ R Step 1: Assign the number of parameters to be identified = m r i − v −P v ϕ − r ϕ dt L qs ⎜ τ e τ r ⎟ dr L qr for a LIM r ⎝ ⎠ r (13) Step 2: Initialize the HSO parameters such as harmony memory (HM), harmony memory considering rate (HMCR), • pitch adjusting rate (PAR), bandwidth (BW) and maximum Fe = K ϕ iqs −ϕqri = Mvr + D vr + F L (14) f ( dr ds ) number of iterations for convergence. Step 3: Define the multi objective function as Secondary time constant L f1= η(s, τ, d, J) = η(x1, x2, x3, x4) and τ = r r R r f2 = pf(s, τ, d, J) = pf(x1, x2, x3, x4) ....... (16) ⎛ 2 ⎞ Step 4: Defined the range of values for the function Lm Leakage coefficient σ = 1− ⎜ ⎟ and force variables. ⎝ (LsLr )⎠ Step 5: Obtain functional value of initial Harmony 3PπL constant K = m memory. f (2τLr ) Step 6: Set iteration counter t=0. Step 7: Increment the iteration counter t=t+1. Where Lm is the magnetizing inductance per phase; Ls and Lr be primary and secondary inductance per phase; vr is Step 8: Starting of Harmony Search, if generated the mover linear velocity; τ is the pole pitch; P is the number random value > HMCR. Then select the value of parameter of pole pairs; φ and φ are q-axis and d-axis secondary qr dr randomly as, flux; iqs and ids and are q-axis and d-axis primary current; Vds and Vqs are d-axis and q-axis primary voltage; Where, External force disturbance be FL, electromagnetic force be xinew = xold + rand(0,1) * BW ...
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