MODELING SIMULATION AND HARMONIC ANALYSIS OF A SERIES RESONANT INVERTER FEEDING RL LOAD: CONSIDERING TRANSFORMER PARAMETERS

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1 Abtrat Journal of Reearh in Engineering and Applied Siene MODEING SIMUATION AND HARMONI ANAYSIS OF A SERIES RESONANT INVERTER FEEDING R OAD: ONSIDERING TRANSFORMER PARAMETERS R K Kehri and A. B. hattopadhyay, Aitant Profeor, Department of Eletrial Engineering VNIT, Nagpur, India Profeor, Departement of Eletrial Engineering, BITS, Pilani Dubai { ritehkehri@gmail.om, ab_8857@yahoo.o.in} Serie Reonant Inverter (SRI) i a oure of very high frequeny energy and i ued for high frequeny appliation, uh a Indution heating, Metal and thin film plati urfae treatment, ommuniation and A power flow area (HVD and HVA) et. SRI are linked with the load through high frequeny tranformer to improve the urrent gain. Inluion of tranformer and R load lead to higher frequeny harmoni omponent in the load voltage. The preent paper inlude the harmoni analyi of a bai SRI (la A), feeding R load with the onideration of tranformer parameter. Sytem i modeled firt in ontinuou time domain and then harmoni analyi i arried out uing MATAB/SIMUINK whih i extended to the filtering out the higher frequeny harmoni omponent uing Butterworth IIR filter. Keyword: Serie Reonant Inverter, Modeling, High frequeny tranformer, Harmoni analyi, Butterworth filter.. Introdution SERIES reonant inverter are defined a oure of high frequeny energy in power eletroni. Reonant inverter have drawn attention of reearher [-]. Mot of the work are foued on uggeting different topologie for the improvement of withing ation, redution of harmoni due to withing and different type of load [-], implementation to variou area like UPS, low temperature plama generator [8], thin film urfae treatment [], ynhronou retifier [7] et., onidering tranformer a ideal one to link load with the. Problem Formulation Sytem onidered for analyi i MHz, kw high frequeny high power erie reonant inverter: for inverter and finally the reult were ompared with the real data. In the preent work we have onentrated ourelve onto analyzing the effet on the load voltage if tranformer parameter are onidered. Sytem i firt modeled and tranfer funtion i obtained. Sytem i repreented in term of blok diagram and imulated uing MATAB/SIMUINK. Further uing the tool available in MATAB harmoni analyi and filtering of higher order frequeny omponent ha been arried out. low temperature plama generator [8]. iruit i hown in Fig.. S S 3 i o i l V v o i I S S 4 Fig. iruit diagram for MHz kw high-frequeny high-power erie reonant inverter: for low temperature plama generator 3 Vol., Iue, January 6

2 A our aim i to analyze the effet on the load voltage, when tranformer parameter are onidered. Thi an be done by onidering a bai SRI (la A) in plae of la D [5], [9] or la E Serie reonant inverter [8]. ater on the analyi an be extended to la D or la E inverter without the lo of generality a here for our analyi we are onerned with output of the reonant inverter being fed to tranformer onneted in parallel with the apaitor for urrent gain a hown in Figure a. la A Serie reonant inverter in the hown iruit onidered and orreponding waveform i hown below in Figure b. It ha been onidered that output frequeny f and reonant frequeny fr i ame. Operation of the onidered iruit i hown below in Fig. 3 S V d D p N: HF Tranformer Fig. a la A Serie Reonant Inverter iruit - V V () i i p on D on O t t v (t) V O O T r = fr T o = fo Fig. b Wave form of primary urrent and voltage aro apaitor t When with i ON att= V a l p N: V (I) V D (I) HF Tranformer (a) 4 Vol., Iue, January 6

3 V d io D N: V a Va V o (I) HF Tranformer Fig.3 b Operation of bai Serie reonant inverter S D i i V (t) R V i (t) (a) N: r r i i R v (t) m Fig. 4 Bai erie reonant inverter feeding R load and equivalent diagram of the tranformer (b) A. Bai formulation of the iruit di dt ) i dt v ( v V For initially relaxed ytem v () =, i ( ) = olution of the above differential equation i For the preent work we have onidered that the R- load i onneted to inverter through high frequeny tranformer and the turn ratio of the tranformer i :. All the parameter of the tranformer are onidered in per v ( t) V ( o t ) For an ideal tranformer onidered eondary voltage (output voltage) r v ( t) v ( t) V ( o ) rt r Reonant frequeny of the iruit. unit ytem. The ytem to be analyzed with the onideration and equivalent diagram of the tranformer i hown in Fig Vol., Iue, January 6

4 Referring to the iruit hown in Fig. 4, with the onideration that the turn ratio i : voltage balane equation of primary and eondary winding of the tranformer in time domain an be written a: di di ri v ( t) (3.) dt dt r di di v ( ) (3.) dt dt i t di and v( t) Ri l (3.3) dt By taking aplae tranform and olving the above equation and with the onideration that ytem i initially relaxed, tranfer funtion relating input voltage to tranformer, primary urrent, eondary urrent and load voltage i obtained and given below I ( ) G ( ) V ( ) (3.4) I ) G ( ) I ( ) (3.5) ( V V( ) (3.6) ( ) V ) ( R ) I ( ) G ( ) G ( ) V ( ) (3.7) l ( l l I ( ) a G ( ) V a a a ( ) (3.8) 3 4 I ( ) a (3.9) I a G ( ) ( ) From the Mathematial modeling of the ytem, tranfer funtion model i obtained; model i hown below in Fig. 5. V (S) a a a3a4 I () a a I () R V () G () G () Fig. 5 Tranfer funtion model of the erie reonant inverter feeding R- load through high frequeny tranformer Expreion for the load voltage and urrent in domain are given below V l( ) ( R l) G ( ) G ( ) V( ) kr k Vl ( ) a a a a a a l l ( 4 ) 3 4 k I ( ) a a ( a a ) a a Where, a a ( ) a3 r a a4 r a Parameter of the ytem onidered in per unit and alulated oeffiient of the tranfer funtion are hown in Table. k a V a l a R r l Table : iruit parameter and oeffiient of tranfer funtion G () and G () r r V ù k = a V ù a R l l oad Impedane a a a a 3 a Vol., Iue, January 6

5 3. Matlab Simulation Fig. 7a and 7b are the teady tate and tranient voltage aro the load onidered. Voltage aro the load would have been ame if tranformer i not onidered. From the wave form of the load voltage it i lear that higher frequeny omponent are injeted due to tranformer. Fig. 7a Steady State teady tate repone a obtained from the Matlab imulation Fig. 7b Tranient repone a obtained from the Matab imulation 7 Vol., Iue, January 6

6 A. Harmoni analyi of the load voltage Harmoni analyi on the load voltage an be arried out uing FFT tool available in Matlab. Reult obtained are hown in Figure 8. Higher frequeny omponent in the load voltage due to the onideration of tranformer parameter and R nd load are filtered out uing order Butterworth IIR filter. Filtered load voltage i hown in figure 9. Figure 9a how the load voltage with and without filter inluding the tranient and Figure 9b how the load voltage during teady tate without and with filter. FFT window4 of 398 yle eleted ingal oad voltage Time () Fundamental (.59Hz) =.9, THD =.5% (a).5 Mag (% of Fundamental).5 Fig. 8 Harmoni ontent of the load voltage a obtained from the FFT analyi of the load voltage Sampling time Sample per yle Fundamental Harmoni order (b) Table : Perentage Harmoni ontent Of The oad Voltage e (Peak).843 rm Total Harmoni Ditortion (thd).5% Harmoni order (D) frequeny % (Hz) ( relative to fundmental ) Table detail the harmoni analyi on load voltage uing FFT tool available in Matlab. Filtering out the high frequeny omponent from the load voltage uing Butterworth IIR filter Fig. 9 Harmoni ontent of the load voltage a obtained from the FFT analyi of the load voltage Table 3 : Perentage Harmoni ontent Of The oad Voltage With Filter Sampling time Sample per yle Fundamental e (Peak).6575 rm Total Harmoni Ditortion (thd).% % harmoni order frequeny (Hz) ( relative to fundmental ) (D) onluion Effet of onidering tranformer parameter on the load voltage of a erie reonant inverter have been analyzed uing obtained tranfer funtion model. From the harmoni analyi uing FFT it i lear that ignifiant amount of harmoni ontent are injeted in the load voltage due to tranformer and R load. From the table II and III it i lear that by uing Butterworth IIR filter unwanted harmoni ontent are redued up to muh extent. The analyi arried out an be extended to la D and la E erie reonant inverter and the onideration of tranformer parameter may redue the error between experimental reult and that obtained from the model ued for the analyi and filter deign. 8 Vol., Iue, January 6

7 Referene [] R. M. Nelm, Harmoni Analyi of a Parallel loaded Reonant onverter, IEEE tranation on power eletroni, Vol 7, No. 4, July, 99. [] Jain, Prveen K. and Dewan, Sahi B., Performane omparion of full and half bridge erie reonant inverter in high frequeny high power appliation, in IEEE Tranation on Indutry Appliation, vol. 6 No., Marh/April 99. [3] Franoeur, B., Viarogue, P. and e-huy, H., Ue of GTO a a zero turn off-time thyritor in a erie reonant inverter,h853-/9/-668 $. 99 IEEE. [4] Jain, Prveen K. and Dewan, Sahi B., Analyi and deign of a high-frequeny high-power erie reonant inverter uing aymmetrial thyritor, in IEEE Tranation on Power Eletroni, vol. 7, No. 4. Otober 99. [5] Kazimierzuk, Marian K. and Meher, Mark J., la-d onverter with half wave regulated ynhronou retifier, $ IEEE. [6] zarkowki, Dariuz and Kazimierzuk, Marian K., ZVS la D Serie Reonant Inverter- Direte time tate pae Simulation and experimental reult, in IEEE Tranation on iruit and Sytem-I: Fundamental Theory and Appliation, vol. 45, no., November 998. [7] hang, hin, hang, Joeph and Bruning, Gert W., Analyi of the Self-Oillating Serie Reonant Inverter for Eletroni Ballat, in IEEE Tranation On Power Eletroni, vol. 4, NO. 3, May 999. [8] Fujiita, Hideaki and Akagi, Hirofumi, A -MHz - kw Voltage-Soure Inverter for ow-temperature Plama Generator: Implementation of Fat Swithing with a Third-Order Reonant iruit, in IEEE Tranation on Indutry Appliation, vol. 35, NO., January/February 999. [9] Wang, hien-ming and Hieh Guan-hyum, Nonlinear-ontrol Strategy for the Half Bridge Serie Reonant Inverter, in IEEE Tranation on Indutrial Eletroni, vol. 5, No., April 3. [] Burdfo, Joe M., Barragan, ui A. Monterde, Fernando, Navarro, Deni and Aero, Jeu, Aymmetrial Voltage anellation ontrol for Full-Bridge Serie Reonant Inverter, in IEEE Tranation on Power Eletroni, vol. 9, No., Marh 4. [] iu, Yong and He, Xiangning, A Serie Reonant Inverter Sytem with PDM and PFM hybrid ontrol for Plati Film Surfae Treatment, IAS 5, /5/$. 5 IEEE. [] Samuel S. M. han, Henry S. H. hung and S. Y. (Ron) Hui, Deign and Analyi of an I-e Self-Oillating Serie Reonant Inverter for Dimmable Eletroni Ballat, in IEEE Tranation on Power Eletroni, Vol., No. 6, November 6. [3] hitode J. S., Digital Signal Proeing & t Appliation, Edition Tehnial Publiation, Pune, India. 9 Vol., Iue, January 6