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Multisided Linear Induction Generator, Analytical Modeling, 3-D Finite Element Analysis and Experimental Test

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Multisided Linear Induction Generator, Analytical Modeling, 3-D Finite Element Analysis and Experimental Test http://dx.doi.org/10.5755/j01.eee.19.8.2100 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 19, NO. 8, 2013 Multisided Linear Induction Generator, Analytical Modeling, 3-D Finite Element Analysis and Experimental Test M. Hosseini Aliabadi1, S. H. Hosseinian2, S. J. Moghani2, M. Abedi2 1 Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 2 Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran [email protected] Abstract—In this paper, a new generator for converting of of mechanical equipment interface such as gear box and lube sea wave energy to electrical energy is proposed. At the by unrolling a rotating induction generator with a radial emi- beginning, analytical model of generator is extracted and then plane and winding to obtain tubular linear induction 3-D and 2-D finite element analysis (FEA) have been developed generator illustrated in Fig. 1. and implemented on the dodecahedron tubular linear induction motor/generator. The generator have been studied in normal The main advantage of the TLIGs is: they are rugged and and heavy weather condition in Persian Gulf and sensitivity easy to construct [12]. The former is assembled in (four, six analysis of the generator against sea wave period and height on to twelve) separate cores and may be considered as several the voltage, efficiency and thrust is studied. The results verify flat LIGs. So, it is more difficult to build than a flat linear the accuracy of self–excited tubular linear induction generator induction generator. The thrust on the moving part of a (SETLIG) model and show that tubular linear induction TLIG is generated by the electromagnetic interaction generator can be used as a powerful tool for converting of wave energy to electrical energy. between the radial oriented translating magnetic field and the circular induced current on the moving part. Index Terms—Linear induction motor, linear induction generator, wave energy, sensitivity analysis. I. INTRODUCTION A serious effort to make an effective technology began from midst of the 1970 and the proposed programs for extraction of energy from sea and ocean waves are sponsored by many countries. Different types of generators are mostly used in wave energy extraction system. Permanent magnet synchronous generators (PMSG) are investigated in [1]–[10]. Demagnetization of permanent magnet and not to be any control on field is the main Fig. 1. Longitudinally-laminated TLIG: (a) front view of generator, (b) stator lamination. drawbacks of PMSG. Air core generators have been developed in [11]. In spite of simple structure and low Many researches magnetically analyzed the operation of construction cost of this generator, its efficiency is very low linear induction machine [13]–[16], but in standstill and thereby it is not suitable choice for wave energy application, it is not developed very well. In this paper the conversion. analytical and numerical approximation of a force imposed Due to aforementioned drawbacks regarding permanent on conducting section of motor/generator is developed. A magnet and air core generators, induction generators shall be theoretical approach of the system is presented. Finite taken into consideration for conversion of wave and tidal element model and related simulations of system are energy into electrical energy. The noticeable advantages of described. Experimental tests are arranged and comparisons induction generator are: 1) low maintenance cost; 2) rigid among empirical data, analytical model and finite element structure; 3) easy construction; 4) wide range application. methods have been presented. Among the induction generators, linear induction generators are preferred to the rotary type due to elimination II. SYSTEM MODELLING A. System’s configuration Figure 2 shows how the sea energy can be achieved using Manuscript received August 7, 2012; accepted Febraury 1, 2013. This research was supported by Islamic Azad university, science and linear generators. This configuration consists of a buoy research branch. coupled by a rope, directly to the piston. The piston is 8 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 19, NO. 8, 2013 connected via spring to concrete foundation that is fixed in TABLE I.TUBULAR LINEAR INDUCTION GENERATOR the bottom of the sea. The tension of the rope will be PARAMETERS balanced with the above mentioned spring. The piston will Parameter Quantity move up and down approximately with the wave and tidal Number of phases 3 speed. Number of coil/phase/pole 1 Number of turns/coil 90 Pole pitch 84 mm Coil-pitch 84 mm Current supply 14.6 A (r.m.s) Rotor aluminum thickness 3 mm Rotor iron thickness 1.6 mm Coil thickness 23 mm Teeth thickness 5 mm Inner stator diameter 114 mm Fig. 2. General outline of direct drive energy extraction system. Number of poles 6 A cross sectional view of a TLIG used as sea wave energy Length of generator 510 mm convertor is shown in Fig. 3. Using this fact that flux density is zero in z direction and current density is zero in x and y directions, the force density will have x and y components and is zero in z direction. Force density distribution in the conductor is obtained by (2)–(4): f= j × b, (2) f= j × b =( jy b z − j z b y)()u x + j z b x − j x b zu y + %((&((' %((&((' F Fx y +( jx b y − j y b x),u z (3) a) %((&((' Fz f= −()()jz b y u x + j z b x u y = F x u x + F y u y, (4) where b is magnetic flux density and x,y,z are Cartesian Axis’s direction. The magnetic vector potential A can be employed to obtain the electromagnetic equations needed for a complete description of the system. The distribution of the magnetic vector potential is given by (5) 2 2 b) ∂AAAAz ∂ z∂ z ∂ z + −µσvx − µσ = 0. (5) Fig. 3. Tubular linear induction generator: (a) cross section, (b) three- ∂x2 ∂ y 2 ∂x ∂ t dimensional model. III. STANDSTILL OPERATION ANALYSIS The solution of (5) is given by (6) The induction machine imposes a sliding linear current j() wt− kx density defined by (1) [12] AAz (,,)().x y t= y e (6) j() wt− kx Substituting (5) in (6) results following differential JJe= me , (1) equation where J , w and k are current density, angular frequency 2 and machine wave constant respectively. The system d A 2 parameters have been driven from the laboratorial prototype. −[k + jµσ w ]A = 0. (7) dy2 The related parameters of the TLIG are listed in Table I. B. Bi dimensional analysis Therefore A )y( is Considering the Fig. 3(a), the z component of the flux density is zero ( b = 0 ) and the current density has only the βy− β y z Α()y= C1 e + C 2 e , (8) z component ( jx= j y = 0 ). 9 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 19, NO. 8, 2013 2 2 where β=k2 + j µσ w , µ , σ are permeability and ()k − β βy− β y j() wt − kx jz =(C1 e + C 2 e). e (16) conductivity constants, C1, C2 , β are equation constants µ respectively. Eventually A is obtained from (9) So second equation of CC1, 2 is A =(C eβy + C e− β y). e j() wt − kx u (9) 1 2 z µ j [C ( eβh− 1) − C ( e− β h − 1) = m . (17) 1 2 β Using two boundary conditions, equation (9) can be solved. First condition is obtained by neglecting the air gap Using (13) and (17), C1 and C2 will be presented by: between stator and conductor for simplicity Fig. 4. j e−β h Copper conductor µ m b c C1 = , (18) y=0 β()eβh− e− β h β h dL d µ jme a a C2 = . (19) Current sheet Stator β ()eβh− e− β h a) Back iron This formula can be used to obtain the magnetic vector b c potential distribution, magnetic field density and current Copper h density: y=0 β()()y− h β h − y a d µ jm()e+ e j() wt− kx A = e uz , (20) x=0 βh− β h Current Stator β(e− e ) b) β()()y− h β h − y Fig. 4. First boundary condition at y=0 (a); second boundary condition j ()e− e H = m e j() wt− kx u including the current density in the conductor from y = 0 to y = h (b). h h x β(eβ− e− β ) From (9) and with considering the fact that the contour β()()y− h β h − y j (e+ e ) j() wt− kx can be chosen small enough, the magnetic field does not + jm e u , (21) βh− β h y vary appreciably over its length. Based on Fig. 4(a) at y=0, β(e− e ) magnetic field intensity is obtained by (10) 2 2 β()()y− h β h − y jm( k− β )( e+ e ) j() wt− kx j = e uz. (22) b c d a b β(eβh− e− β h) ∫Hxdx+ ∫ H y dy + ∫ H x dx + ∫ H y dy = ∫ j e dx, (10) a b c d a Based on (4), force can be calculated as follows Hx= − j e, (11) ∂A 2 2β (y− h ) β ( h − y ) b z j at y 2 (k−β )( e + e ) x= = −µ e = 0. (12) f= −kµ jm Re[ × ∂y β()eβh− e− β h (eβ()()y− h+ e β h − y ) Substituting (9) in latter equation from (6), the subsequent ×ej() wt− kx ] × Re[ j × formula is derived β()eβh− e− β h 2 2β (y− h ) β ( h − y ) j( wt− kx ) 2 (k−β )( e + e ) µ jm ×e ]ux + µ j m Re[ × CC− = .
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