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Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method

Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method Hindawi Publishing Corporation Advances in Power Electronics Volume 2012, Article ID 635715, 6 pages doi:10.1155/2012/635715 Research Article Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method 1 2 Sivananda Reddy Thondapu, Mangesh B. Borage, 1 1 Yashwant D. Wanmode, and Purushottam Shrivastava Pulse High Power Microwave Section, Raja Ramanna Centre for Advanced Technology, Indore 452013, India Power Supplies and Industrial Accelerator Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India Correspondence should be addressed to Sivananda Reddy Thondapu, sivananda@rrcat.gov.in Received 31 December 2011; Revised 13 April 2012; Accepted 29 April 2012 Academic Editor: Pavol Bauer Copyright © 2012 Sivananda Reddy Thondapu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper proposes a simpler and more accurate expression for estimation of leakage inductance in E core transformer, which is the most widely used transformer structure. The derived expression for leakage inductance accounts for the flux extending into air. The finite element method (FEM) analysis is made on the secondary shorted transformer to observe the H-field pattern. The results obtained from FEM analysis are used for approximating the field that is extending into air to derive an expression for leakage inductance. This expression is experimentally validated on prototype transformers of different core dimensions. 1. Introduction In energy method, the energy stored in magnetic field of the secondary shorted transformer is calculated and equated Transformer is one of the basic building blocks of many 2 to (1/2)L I where L is the leakage inductance of the leak leak power converters. The following are some of the cases where transformer when referred to primary, and I is current accurate estimation of leakage inductance is required. flowing through primary. The H-profile inside the coil is calculated using Ampere’s (i) Different resonant converter topologies, discussed in law. The energy stored in magnetic field is calculated by [1–5], use parasitics of transformer as a part of reso- evaluating the volume integral in (1): nant tank network. For designing power converter with such topologies, one requires accurate estima- 1 2 2 E = H dv = L I . (1) stored leak tion of leakage inductance. 2 2 The expression derived for leakage inductance using (ii) In hard switched converters, in every cycle the energy energy method is independent of frequency. Hence, it does stored in the parasitics appears as loss in converter. In not consider any frequency-dependent effects on leakage estimation of efficiency of such converters, one needs inductance. The energy method is used for comparing leak- to estimate leakage inductance before hand. age inductance, in different winding configurations. (iii) For designing snubber circuits to limit device voltage On the other hand, method of mutual fluxes uses Max- during turn-off transients [6–8], one needs to esti- well’s equations to predict the leakage inductance more mate leakage inductance. These turn-off transients accurately at high frequencies. As this method accounts for mainly occur due to energy stored in the leakage frequency-dependent effects like eddy current losses and inductance of the transformer. altered flux pattern due to eddy currents, it gives more Methods that are usually employed for estimation of accurate results, particularly at high frequencies. In [14], a leakage inductance are (i) energy method [8–13] and (ii) frequency-dependent formula is presented to find leakage method of mutual fluxes. inductance in a toroidal core transformers. 2 Advances in Power Electronics z x (a) Perspective (b) Front view y xxx (c) Top view (d) Side view Figure 1: Simulation result of FEM analysis. In this paper, an expression for leakage inductance is excluding the volume of the core. The flux extends into derived using energy method. Expression derived accounts air shown in Figure 5. The volume shown in Figure 4 is for the flux that extends into air in a secondary shorted trans- divided into four parts, whose top view is shown in Figure 3. former, which is not considered earlier [8, 10, 11]. Therefore, Theprofileof H-field is calculated using Ampere’s law, the the estimated leakage inductance using this expression has same profile is observed in FEM analysis. The H-profile is better accuracy. expressed mathematically in (2): 2. Estimation of Leakage Inductance on H 0 <z <h , ⎪ m 1 ⎪ h E Core Transformer H h <z <h + t, H(z) = m 1 1 ⎪ h + h + t − z FEM analysis on secondary shorted transformer is made ⎪ 1 2 H h + t< z < h + h + t. m 1 1 2 using CST Ver 2008.5 (with magneto-static solver). The 2 (2) simulation result of FEM analysis is shown in Figure 1.The simulation result is the H-field pattern of secondary shorted E core transformer. This gives an idea of profile of H-field Using H-profile given in (2) to evaluate volume integral from the surface of the core to the outer surface of the whole givenin(1), we get expression of the leakage inductance: winding. The profile of H-field of a E core transformer and its winding configuration is shown in Figures 2 and 3,respec- 1 µ N tively. (3) L = (h +2t)[FC + B(E +2h)], leak 3 F Energy stored in the magnetic field in the secondary shorted transformer is equated to energy stored in leakage inductor, which is given in (1). where h = h + h + t is total thickness of the winding 1 2 The volume represented with purple color in Figure 4 is measured from the surface of the core to the outer surface of considered for volume integration. This constitutes (i) the the outer winding, t is total thickness of the insulation used volume occupied by the coils and (ii) the volume formed between the layers. B, C, E, F is are the dimensions of the E by extrusion of the coils along the centre limb of the core, core shown in Figure 6. Advances in Power Electronics 3 h h 1 2 H (z) Figure 2: Profile of H(z) from the surface of the core. Part 3 Center limb of the core Secondary winding (S) Primary winding (P) Part 1 Part 2 Interwinding insulation Part 4 Figure 3: Top view of E core transformer with windings. 15.4 13.5 11.5 9.61 7.69 5.77 3.84 1.92 Figure 5: Scaled side view to show the flux that extends into air. Figure 4: Volume around the core considered for integration. (A/m) 4 Advances in Power Electronics Table 1: EE core transformer with interwinding insulation. Sample no. 1 2 Core type EE42/21/15 EE65/38/13 F 14.45 mm 22.65 mm C 15.20 mm 13.45 mm B 21.10 mm 32.59 mm E 12.05 mm 19.77 mm h thickness of primary 3.20 mm 3.81 mm h thickness of secondary 1.90 mm 1.55 mm t thickness of insulation 1.27 mm 2.00 mm N 34 48 N 17 24 Winding configuration h h 1 2 Photograph P S Leakage inductance L from (5) 11.91 µH 22.52 µH leak,earlier Leakage inductance L from (3) 15.32 µH 28.21 µH leak Leakage inductance L at 10 kHz measured 14.13 µH 26.76 µH exp % deviation of L from calculated L 15.71% 15.84% exp leak,earlier % deviation of L from calculated L 8.38% 5.12% exp leak 3. Experimental Results Three different samples are made to validate the derived expression. The results are compared with the expressions availableinliterature. Theexpression givenin[8, 10, 11]is E D replaced with the dimensions of the core (shown in Figure 6) and the dimensions of windings will give (5): 1 µ N L = (h +2t)F(C + E +2h). (5) leak,earlier 2 2 3p F F C Sample no. 1 is made with E core (EE42/21/15) wound with stranded conductor made with three conductors of 24 SWG. With interwinding insulation of thickness 1.27 mm is Figure 6: E core dimensions given in data sheets. used. Standard winding configuration as shown in Table 1 is used to wind primary and secondary. Sample no. 2 is made with E core (EE65/38/13) wound with stranded conductor made with three conductors of 24 It is seen in [8, 11–13], by sandwiching the windings, SWG. With interwinding insulation of thickness 2.00 mm. leakage inductance reduces by p times, where p is the num- Standard winding configuration as shown in Table 1 is used ber of interfaces between primary and secondary [8]: to wind primary and secondary. Sample no. 3 is made with E core (EE42/21/15) wound with stranded conductor made with two conductors of µ N 1 24 SWG. With total interwinding insulation of thickness o 1 L = (h +2t)[FC + B(E +2h)]. (4) leak 2 2 0.46 mm + 0.26 mm = 0.72 mm is used. Sandwiched winding 3p F Advances in Power Electronics 5 Table 2: EE core transformer with sandwiched winding (P/2, S, P/2). Sample no. 3 Core type EE42/21/15 F 14.45 mm C 15.20 mm B 21.10 mm E 12.05 mm h thickness of primary half 1.41 mm h thickness of secondary 2.93 mm h thickness of primary half 1.52 mm t thickness of insulation 0.46 mm t thickness of insulation 0.26 mm N 46 N 44 Winding configuration h 2 h 1 3 Photograph P/2 S P/2 t t 1 2 Leakage inductance L from (5)4.94 µH leak,earlier Leakage inductance L from (4)6.37 µH leak Leakage inductance L at 10 kHz measured 5.91 µH exp % deviation of L from calculated L 16.41% exp leak,earlier % deviation of L from calculated L 7.82% exp leak configuration as shown in Table 2 is used to wind primary References and secondary. [1] S. D. Johnson, A. F. Witulski, and R. W. Erickson, “Compar- All the measurements for leakage inductance are made ison of resonant topologies in high-voltage dc applications,” by shorting the secondary. The measurements are made with IEEE Transactions on Aerospace and Electronic Systems, vol. 24, LCR meter (make: Gw instek Model: LCR-8101) at 10 kHz. no. 3, pp. 263–274, 1988. Tables 1 and 2 tabulate experimentally measured values, [2] A.K.S.Bhat, A. Biswas,and B. S. R. Iyengar, “Analysisand estimated values using the expression derived in this paper design of (LC)(LC)-type series-parallel resonant converter,” and expression derived earlier for leakage inductance and IEEE Transactions on Aerospace and Electronic Systems, vol. 31, their corresponding errors when compared with the exper- no. 3, pp. 1186–1193, 1995. imentally measured values. [3] B. Yang, F. C. Lee, A. J. Zhang, and G. Huang, “LLC resonant converter for front end DC/DC conversion,” in Proceedings of the 17th Annual IEEE on Applied Power Electronics Conference 4. Conclusion and Exposition Conference (APEC ’02), vol. 2, pp. 1108–1112, Institute of Electrical and Electronics Engineers, 2002. In this paper an improved expression for leakage inductance [4] J. A. Sabate, V. Vlatkovic, R. B. Ridley, F. C. Lee, and B. H. has been derived, using energy method. To observe the Cho, “Design considerations for high-voltage high-power full- H-field pattern, FEM analysis has been carried out on a bridge zero-voltage-switched pwm converter,” in Proceedings secondary shorted transformer, with primary excited. Exper- of the 5th Annual Applied Power Electronics Conference and imental results show that the formula derived in this paper Exposition (APEC ’90), pp. 275–284, Institute of Electrical and has better accuracy. It is observed that the leakage inductance Electronics Engineers, 1990. estimated using improved expression L haslessdeviation leak [5] J. F. Lazar and R. Martinelli, “Steady-state analysis of the LLC from L when compared with leakage inductance estimated exp series resonant converter,” in Proceedings of the 16th Annual from earlier expression L . The accuracy of the leak,earlier Applied Power Electronics Conference and Exposition (APEC estimated value is improved due to consideration of flux that ’01), vol. 2, pp. 728–735, Institute of Electrical and Electronics is extending into air. Engineers, 2001. 6 Advances in Power Electronics [6] P. C. Todd, “Snubber circuits: theory, design and application,” in Unitrode-Power Supply Design Seminar, 1993. [7] William McMurray, “Selection of snubbers and clamps to optimize the design of transistor switching converters,” IEEE Transactions on Industry Applications,vol. IA-16, no.4,pp. 513–523, 1980. [8] N.Mohan,T.M.Undeland, andW.P.Robbins, Power Elec- tronics: Converters, Applications, and Design, vol. 1, John Wiley & Sons, New York, NY, USA, 2003. [9] R. Doebbelin, M. Benecke, and A. Lindemann, “Calculation of leakage inductance of core-type transformers for power elec- tronic circuits,” in Proceedings of the 13th Power Electronics and Motion Control Conference (EPE-PEMC ’08), pp. 1280–1286, September 2008. [10] A. A. Dauhajre, Modelling and estimation of leakage phenom- ena in magnetic circuits, Ph.D. thesis, California Institute of Technology, Pasadena, Calif, USA, 1986. [11] W. T. McLyman and C. W. T. McLyman, Transformer and Inductor Design Handbook, Marcel Dekker, New York, NY, USA, 2004. [12] Z. Ouyang, O. C. Thomsen, and M. Andersen, “The analysis and comparison of leakage inductance in different winding arrangements for planar transformer,” in Proceedings of the International Conference on Power Electronics and Drive Sys- tems (PEDS ’09), pp. 1143–1148, November 2009. [13] R. Doebbelin, R. Herms, C. Teichert, W. Schaetzing, and A. Lindemann, “Analysis methods and design of transformers with low leakage inductance for pulsed power applications,” in Proceedings of the European Conference on Power Electronics and Applications, pp. 1–7, September 2007. [14] W. G. Hurley and D. J. Wilcox, “Calculation of leakage induc- tance in transformer windings,” IEEE Transactions on Power Electronics, vol. 9, no. 1, pp. 121–126, 1994. International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Power Electronics Hindawi Publishing Corporation

Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method

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Publisher
Hindawi Publishing Corporation
Copyright
Copyright © 2012 Sivananda Reddy Thondapu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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2090-181X
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10.1155/2012/635715
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Abstract

Hindawi Publishing Corporation Advances in Power Electronics Volume 2012, Article ID 635715, 6 pages doi:10.1155/2012/635715 Research Article Improved Expression for Estimation of Leakage Inductance in E Core Transformer Using Energy Method 1 2 Sivananda Reddy Thondapu, Mangesh B. Borage, 1 1 Yashwant D. Wanmode, and Purushottam Shrivastava Pulse High Power Microwave Section, Raja Ramanna Centre for Advanced Technology, Indore 452013, India Power Supplies and Industrial Accelerator Division, Raja Ramanna Centre for Advanced Technology, Indore 452013, India Correspondence should be addressed to Sivananda Reddy Thondapu, sivananda@rrcat.gov.in Received 31 December 2011; Revised 13 April 2012; Accepted 29 April 2012 Academic Editor: Pavol Bauer Copyright © 2012 Sivananda Reddy Thondapu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper proposes a simpler and more accurate expression for estimation of leakage inductance in E core transformer, which is the most widely used transformer structure. The derived expression for leakage inductance accounts for the flux extending into air. The finite element method (FEM) analysis is made on the secondary shorted transformer to observe the H-field pattern. The results obtained from FEM analysis are used for approximating the field that is extending into air to derive an expression for leakage inductance. This expression is experimentally validated on prototype transformers of different core dimensions. 1. Introduction In energy method, the energy stored in magnetic field of the secondary shorted transformer is calculated and equated Transformer is one of the basic building blocks of many 2 to (1/2)L I where L is the leakage inductance of the leak leak power converters. The following are some of the cases where transformer when referred to primary, and I is current accurate estimation of leakage inductance is required. flowing through primary. The H-profile inside the coil is calculated using Ampere’s (i) Different resonant converter topologies, discussed in law. The energy stored in magnetic field is calculated by [1–5], use parasitics of transformer as a part of reso- evaluating the volume integral in (1): nant tank network. For designing power converter with such topologies, one requires accurate estima- 1 2 2 E = H dv = L I . (1) stored leak tion of leakage inductance. 2 2 The expression derived for leakage inductance using (ii) In hard switched converters, in every cycle the energy energy method is independent of frequency. Hence, it does stored in the parasitics appears as loss in converter. In not consider any frequency-dependent effects on leakage estimation of efficiency of such converters, one needs inductance. The energy method is used for comparing leak- to estimate leakage inductance before hand. age inductance, in different winding configurations. (iii) For designing snubber circuits to limit device voltage On the other hand, method of mutual fluxes uses Max- during turn-off transients [6–8], one needs to esti- well’s equations to predict the leakage inductance more mate leakage inductance. These turn-off transients accurately at high frequencies. As this method accounts for mainly occur due to energy stored in the leakage frequency-dependent effects like eddy current losses and inductance of the transformer. altered flux pattern due to eddy currents, it gives more Methods that are usually employed for estimation of accurate results, particularly at high frequencies. In [14], a leakage inductance are (i) energy method [8–13] and (ii) frequency-dependent formula is presented to find leakage method of mutual fluxes. inductance in a toroidal core transformers. 2 Advances in Power Electronics z x (a) Perspective (b) Front view y xxx (c) Top view (d) Side view Figure 1: Simulation result of FEM analysis. In this paper, an expression for leakage inductance is excluding the volume of the core. The flux extends into derived using energy method. Expression derived accounts air shown in Figure 5. The volume shown in Figure 4 is for the flux that extends into air in a secondary shorted trans- divided into four parts, whose top view is shown in Figure 3. former, which is not considered earlier [8, 10, 11]. Therefore, Theprofileof H-field is calculated using Ampere’s law, the the estimated leakage inductance using this expression has same profile is observed in FEM analysis. The H-profile is better accuracy. expressed mathematically in (2): 2. Estimation of Leakage Inductance on H 0 <z <h , ⎪ m 1 ⎪ h E Core Transformer H h <z <h + t, H(z) = m 1 1 ⎪ h + h + t − z FEM analysis on secondary shorted transformer is made ⎪ 1 2 H h + t< z < h + h + t. m 1 1 2 using CST Ver 2008.5 (with magneto-static solver). The 2 (2) simulation result of FEM analysis is shown in Figure 1.The simulation result is the H-field pattern of secondary shorted E core transformer. This gives an idea of profile of H-field Using H-profile given in (2) to evaluate volume integral from the surface of the core to the outer surface of the whole givenin(1), we get expression of the leakage inductance: winding. The profile of H-field of a E core transformer and its winding configuration is shown in Figures 2 and 3,respec- 1 µ N tively. (3) L = (h +2t)[FC + B(E +2h)], leak 3 F Energy stored in the magnetic field in the secondary shorted transformer is equated to energy stored in leakage inductor, which is given in (1). where h = h + h + t is total thickness of the winding 1 2 The volume represented with purple color in Figure 4 is measured from the surface of the core to the outer surface of considered for volume integration. This constitutes (i) the the outer winding, t is total thickness of the insulation used volume occupied by the coils and (ii) the volume formed between the layers. B, C, E, F is are the dimensions of the E by extrusion of the coils along the centre limb of the core, core shown in Figure 6. Advances in Power Electronics 3 h h 1 2 H (z) Figure 2: Profile of H(z) from the surface of the core. Part 3 Center limb of the core Secondary winding (S) Primary winding (P) Part 1 Part 2 Interwinding insulation Part 4 Figure 3: Top view of E core transformer with windings. 15.4 13.5 11.5 9.61 7.69 5.77 3.84 1.92 Figure 5: Scaled side view to show the flux that extends into air. Figure 4: Volume around the core considered for integration. (A/m) 4 Advances in Power Electronics Table 1: EE core transformer with interwinding insulation. Sample no. 1 2 Core type EE42/21/15 EE65/38/13 F 14.45 mm 22.65 mm C 15.20 mm 13.45 mm B 21.10 mm 32.59 mm E 12.05 mm 19.77 mm h thickness of primary 3.20 mm 3.81 mm h thickness of secondary 1.90 mm 1.55 mm t thickness of insulation 1.27 mm 2.00 mm N 34 48 N 17 24 Winding configuration h h 1 2 Photograph P S Leakage inductance L from (5) 11.91 µH 22.52 µH leak,earlier Leakage inductance L from (3) 15.32 µH 28.21 µH leak Leakage inductance L at 10 kHz measured 14.13 µH 26.76 µH exp % deviation of L from calculated L 15.71% 15.84% exp leak,earlier % deviation of L from calculated L 8.38% 5.12% exp leak 3. Experimental Results Three different samples are made to validate the derived expression. The results are compared with the expressions availableinliterature. Theexpression givenin[8, 10, 11]is E D replaced with the dimensions of the core (shown in Figure 6) and the dimensions of windings will give (5): 1 µ N L = (h +2t)F(C + E +2h). (5) leak,earlier 2 2 3p F F C Sample no. 1 is made with E core (EE42/21/15) wound with stranded conductor made with three conductors of 24 SWG. With interwinding insulation of thickness 1.27 mm is Figure 6: E core dimensions given in data sheets. used. Standard winding configuration as shown in Table 1 is used to wind primary and secondary. Sample no. 2 is made with E core (EE65/38/13) wound with stranded conductor made with three conductors of 24 It is seen in [8, 11–13], by sandwiching the windings, SWG. With interwinding insulation of thickness 2.00 mm. leakage inductance reduces by p times, where p is the num- Standard winding configuration as shown in Table 1 is used ber of interfaces between primary and secondary [8]: to wind primary and secondary. Sample no. 3 is made with E core (EE42/21/15) wound with stranded conductor made with two conductors of µ N 1 24 SWG. With total interwinding insulation of thickness o 1 L = (h +2t)[FC + B(E +2h)]. (4) leak 2 2 0.46 mm + 0.26 mm = 0.72 mm is used. Sandwiched winding 3p F Advances in Power Electronics 5 Table 2: EE core transformer with sandwiched winding (P/2, S, P/2). Sample no. 3 Core type EE42/21/15 F 14.45 mm C 15.20 mm B 21.10 mm E 12.05 mm h thickness of primary half 1.41 mm h thickness of secondary 2.93 mm h thickness of primary half 1.52 mm t thickness of insulation 0.46 mm t thickness of insulation 0.26 mm N 46 N 44 Winding configuration h 2 h 1 3 Photograph P/2 S P/2 t t 1 2 Leakage inductance L from (5)4.94 µH leak,earlier Leakage inductance L from (4)6.37 µH leak Leakage inductance L at 10 kHz measured 5.91 µH exp % deviation of L from calculated L 16.41% exp leak,earlier % deviation of L from calculated L 7.82% exp leak configuration as shown in Table 2 is used to wind primary References and secondary. [1] S. D. Johnson, A. F. Witulski, and R. W. Erickson, “Compar- All the measurements for leakage inductance are made ison of resonant topologies in high-voltage dc applications,” by shorting the secondary. The measurements are made with IEEE Transactions on Aerospace and Electronic Systems, vol. 24, LCR meter (make: Gw instek Model: LCR-8101) at 10 kHz. no. 3, pp. 263–274, 1988. Tables 1 and 2 tabulate experimentally measured values, [2] A.K.S.Bhat, A. Biswas,and B. S. R. Iyengar, “Analysisand estimated values using the expression derived in this paper design of (LC)(LC)-type series-parallel resonant converter,” and expression derived earlier for leakage inductance and IEEE Transactions on Aerospace and Electronic Systems, vol. 31, their corresponding errors when compared with the exper- no. 3, pp. 1186–1193, 1995. imentally measured values. [3] B. Yang, F. C. Lee, A. J. Zhang, and G. Huang, “LLC resonant converter for front end DC/DC conversion,” in Proceedings of the 17th Annual IEEE on Applied Power Electronics Conference 4. Conclusion and Exposition Conference (APEC ’02), vol. 2, pp. 1108–1112, Institute of Electrical and Electronics Engineers, 2002. In this paper an improved expression for leakage inductance [4] J. A. Sabate, V. Vlatkovic, R. B. Ridley, F. C. Lee, and B. H. has been derived, using energy method. To observe the Cho, “Design considerations for high-voltage high-power full- H-field pattern, FEM analysis has been carried out on a bridge zero-voltage-switched pwm converter,” in Proceedings secondary shorted transformer, with primary excited. Exper- of the 5th Annual Applied Power Electronics Conference and imental results show that the formula derived in this paper Exposition (APEC ’90), pp. 275–284, Institute of Electrical and has better accuracy. It is observed that the leakage inductance Electronics Engineers, 1990. estimated using improved expression L haslessdeviation leak [5] J. F. Lazar and R. Martinelli, “Steady-state analysis of the LLC from L when compared with leakage inductance estimated exp series resonant converter,” in Proceedings of the 16th Annual from earlier expression L . The accuracy of the leak,earlier Applied Power Electronics Conference and Exposition (APEC estimated value is improved due to consideration of flux that ’01), vol. 2, pp. 728–735, Institute of Electrical and Electronics is extending into air. Engineers, 2001. 6 Advances in Power Electronics [6] P. C. Todd, “Snubber circuits: theory, design and application,” in Unitrode-Power Supply Design Seminar, 1993. [7] William McMurray, “Selection of snubbers and clamps to optimize the design of transistor switching converters,” IEEE Transactions on Industry Applications,vol. IA-16, no.4,pp. 513–523, 1980. [8] N.Mohan,T.M.Undeland, andW.P.Robbins, Power Elec- tronics: Converters, Applications, and Design, vol. 1, John Wiley & Sons, New York, NY, USA, 2003. [9] R. Doebbelin, M. Benecke, and A. Lindemann, “Calculation of leakage inductance of core-type transformers for power elec- tronic circuits,” in Proceedings of the 13th Power Electronics and Motion Control Conference (EPE-PEMC ’08), pp. 1280–1286, September 2008. [10] A. A. Dauhajre, Modelling and estimation of leakage phenom- ena in magnetic circuits, Ph.D. thesis, California Institute of Technology, Pasadena, Calif, USA, 1986. [11] W. T. McLyman and C. W. T. McLyman, Transformer and Inductor Design Handbook, Marcel Dekker, New York, NY, USA, 2004. [12] Z. Ouyang, O. C. Thomsen, and M. Andersen, “The analysis and comparison of leakage inductance in different winding arrangements for planar transformer,” in Proceedings of the International Conference on Power Electronics and Drive Sys- tems (PEDS ’09), pp. 1143–1148, November 2009. [13] R. Doebbelin, R. Herms, C. Teichert, W. Schaetzing, and A. Lindemann, “Analysis methods and design of transformers with low leakage inductance for pulsed power applications,” in Proceedings of the European Conference on Power Electronics and Applications, pp. 1–7, September 2007. [14] W. G. Hurley and D. J. Wilcox, “Calculation of leakage induc- tance in transformer windings,” IEEE Transactions on Power Electronics, vol. 9, no. 1, pp. 121–126, 1994. International Journal of Rotating Machinery International Journal of Journal of The Scientific Journal of Distributed Engineering World Journal Sensors Sensor Networks Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Volume 2014 Journal of Control Science and Engineering Advances in Civil Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 Submit your manuscripts at http://www.hindawi.com Journal of Journal of Electrical and Computer Robotics Engineering Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 VLSI Design Advances in OptoElectronics International Journal of Modelling & Aerospace International Journal of Simulation Navigation and in Engineering Engineering Observation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2010 Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com http://www.hindawi.com Volume 2014 International Journal of Active and Passive International Journal of Antennas and Advances in Chemical Engineering Propagation Electronic Components Shock and Vibration Acoustics and Vibration Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation Hindawi Publishing Corporation http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014 http://www.hindawi.com Volume 2014

Journal

Advances in Power ElectronicsHindawi Publishing Corporation

Published: Aug 9, 2012

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