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Voltage Clamped Dc-Dc Convertor with Reduced Reverse Recovery Current And Stability Analysis


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  • 1. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 Voltage Clamped Dc-Dc Convertor with Reduced Reverse Recovery Current And Stability Analysis Dharamalla. ChadraSekhar, 1 D. Jagan, 2 1, 2 Assistant Professor /GATE Engineering College / JNTU, Hyderabad/ AP /INDIA.Abstract: this paper in vest gates a high-efficiency soft switching. In [8] and [9], coupled inductors wereclamped-voltage dc–dc converter with reduced reverse- employed to provide ea high step-up ratio and to reduce therecovery current And switch-voltage stress. In the circuit switch-voltage stress substantially, and the reverse-recoverytopology, it is designed by way of the combination of in duct problem of the output diode was also alleviated efficiently.or and transformer to increase the corresponding voltage In this case, the leakage energy of the coupledgain. Moreover, one additional inductor provides the inductor is another problem as the main switch was turnedreverse-current path of the transformer to enhance the OFF. It will result in a high voltage ripple a cross the mainutility rate of magnetic core. In addition, the voltage- switch due to the resonant phenomenon induced by theclamped technology issued to reduce the switch-voltage leakage current. In order to protect the switch devices, eitherstress so that it can select the Scotty diode in the output a high-voltage-rated device with higher RDS (ON) or aterminal for all aviating the reverse recovery current and snubber circuit is usually adopted to deplete the leakagedecreasing the witching and conduction losses. Fur the energy. Consequently, the power-conversion efficiency willmore; the closed-loop control methodology is utilization the be degraded. Zhao and Lee [10] introduced a family of high-proposed scheme to overcome the voltage-drift problem of efficiency high-step-up dc–dc converters by only adding onepower source under the variation of loads. Thus, the addition diode and a small capacitor. It can recycle theproposed converter topology has a favor able voltage- leakage energy anclamped effect and superior conversion efficiency. Someexperimental results via an example of a proton exchangemembrane fuel cell (PEMFC) power source with a 250-Wnominal rating are given to demonstrate the effectiveness ofthe proposed power-conversion strategy.Index Terms: Converter, fuel cell, proton-exchangemembrane (PEM), reverse recovery, voltage clamped. I. INTRODUCTION INRECENT years, dc–dc converter switch steepvoltage ratio are usually require din many industrialapplications, e.g., the front-end stage for clean energysources, the dc backup energy system for an uninterruptiblepower supply (UPS),high-intensity discharge (HID) lamps Fig. 1. System configuration of a high -efficiencyfor automobile head lamps, And the telecommunication voltage-clamped dc–dc converter.industry[ 1]–[3].The conventional boost converters cannotprovide such a high dc-voltage ratio due to the losses Alleviate the reverse-recovery problem. However,associated with the inductor, filter capacitor, main switch, a snubber circuit is still required in the output diode terminaland output diode. Even for an extreme duty cycle, It will with extra energy losses.result in serious reverse-recovery problems and increase The Nowadays, fuel cells are in the news because theyrating of the output diode. As a result, the conversion appear to be one of the most efficient and effective solutionsefficiency is degraded, and the electromagnetic interference to the environmental pollution problem [11]–[17]. A fuel(EMI) problem is severe under this situation [4].In order to cell is an energy conversion device that produces electricityincrease the conversion efficiency and voltage gain, many by electrochemically combining fuel (hydrogen) and oxidantmodified boost converter topologies have been investigated (oxygen from the air) gases through electrodes, across anin the past decade[5]–[10]. ion conduction electrolyte. This process produces much Although voltage-clamped techniques are higher conversion efficiency than any conventional thermal-manipulated in the converter design to overcome the severe mechanical system, because it operates without combustionreverse-recovery problem of the output diode in high-level and extracts more electricity from the same amount of fuel.voltage applications, there still exist over large switch- This system has the merits of high efficiency, energyvoltage stresses, and the voltage gain is limited by the turn- security, reliability, pollution free, and quiet operations. FuelON time of the auxiliary switch [5], [6].da Silva et al. [7] cells have been known to science for more than 160 yearspresented a boost soft-single-switch converter, which has and have recently become the subject of intense researchonly one single active switch. It is able to operate with soft and development. Up to the present, many demonstrationswitching in a pulse width modulation (PWM) way without projects have shown fuel-cell systems to be feasible forhigh voltage and current stresses. Unfortunately, the voltage portable power, transportation, utility power and on-sitegain is limited below four in order to achieve the function of power generation in a variety of building applications. 4273 | Page
  • 2. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 For portable power, a fuel cell with a fuel container transformer is modeled as an ideal transformer with acan offer a higher-energy density and more convenience secondary leakage inductor (Lk). The turn’s ratio of thisthan conventional battery systems. Moreover, portable ideal transformer is defined aspower packs using fuel cells can be lighter and smaller involume for an equivalent amount of energy. In (1)transportation applications, fuel cells offer higher efficiency Where N1 and N2 are the primary and secondaryand better part-load performance than conventional engines. winding turns. The additional inductor (L) is located inIn stationary power applications, low emissions permit fuel parallel with the primary side of the transformer. Moreover,cells to be located in high-power requirement areas, where the rectifier diodes (D1, D2, D3, and D4) are connectedthey can supplement the existing utility grid. Using fuel between the primary and secondary sides of the transformer.cells and hydrogen technology, electrical power can be The voltages across the additional inductor, the main switch,delivered cleanly, efficiently and sustainability where and the ideal transformer primary and secondary winding, thewhen required. The greatest research interests throughout secondary leakage inductor, the balanced capacitor, and thethe world have focused on proton-exchange membrane output diode are vL, vDS, vLp , vLs , vLk , vCs , and vDo, (PEM) and solid oxide cell stacks. Specially, PEM respectively. The clamped capacitor Cc is assumed to befuel cell (PEMFC) has promising characteristics as follows: large enough to be viewed as a constant voltage source, VCc1) the by-product waste is water; 2) low-temperature . The conductive voltage drops of the main switchoperation; and 3) they use a solid polymer as the electrolyte (S) And all diodes (D1, D2, D3, D4, and Do) arethat reduces concerns related to construction, transportation, neglected to simplify the circuit analyses. The characteristicand safety issues [16]. Thus, it seems to be a good waveforms of the proposed high-efficiency converter arealternative source for distributed generation systems. depicted in Fig. 3. In addition, Fig. 4 illustrates the The aim of this study is to design a high-efficiency operational modes in one switching cycle, and the detailedvoltage clamped dc–dc converter with reduced reverse- operation stages are described as follows.recovery current and switch-voltage stress to provide astable constant dc voltage. To achieve this goal, themanipulation of inductor and transformer is adopted toincrease the voltage gain and to enhance the utility rate ofthe magnetic core. Moreover, the voltage-clampedtechnology is used for reducing the switch voltage stress andsolving the reverse-recovery problem. In addition, theclosed-loop control methodology is utilized in the proposedconverter to overcome the voltage-drift problem of powersource under the variation of loads. The prototype isdeveloped for a PEMFC application requiring an outputpower of 310 W, an output voltage of 200 V, and an inputvoltage varying from 27 to 37.5 V. The remainder of thisstudy is organized as follows. Section II presents theconverter design and analyses in detail. Experimental resultsfor a PEMFC power source with a 250-W nominal rating areprovided to validate the effectiveness of the proposed powerconversion system in Section III. Conclusions are drawn in Fig. 2. Equivalent circuit.Section IV. II. CONVERTER DESIGN AND ANALYSES: A newly designed converter topology is depicted inFig. 1, where it contains five parts including a dc-inputcircuit, a primary-side circuit, a secondary-side circuit, a dc-output circuit, and a feedback-control mechanism. Themajor symbol representations are summarized as follows. Viand Ii denote the dc-input voltage and current, and Ci is theinput filter capacitor in the dc-input circuit. Lp representsthe primary inductor of the transformer; L is the additionalinductor in the primary-side circuit; and S is the mainswitch. Ls denote the secondary inductor of the transformer;Cs and Cc are the balanced capacitor and clamped capacitorin the secondary-side circuit; and D1, D2, D3, and D4 arethe rectifier diodes. Vo and Io describe the output voltageand current; Ro is the output load; Do, and Co are the outputdiode and filter capacitor in the output circuit. Vcom and TSare the output-voltage command and switch-driving signal Fig. 3. Characteristic the feedback-control mechanism, respectively. The equivalent circuit and state definition of the A. Mode 1 (t0 − t1) [Fig. 4(a)]newly designed converter is depicted in Fig. 2, where the 4274 | Page
  • 3. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 At time t = t0, the main switch (S) is turned ON. Atthe sametime, the diodes (D1 and D4) become conducted,and other diodes (D2, D3, and Do) are reverse biased. Theadditional inductor (L) and clamped capacitor (Cc) arelinearly charged by the input-voltage source (Vi) through thetransformer. Applying Kirchhoff’s law [4], the voltages ofvL, vLp , vLs , and vLk during this period can be expressedas vL =vLp =Vi (2) vLs =nVi (3) vLk =VCc− nVi − vCs . (4)According to (2)–(4), the rate of change of the additionalinductor current (iL), the primary-side current (iLp ), and thesecondary-side current (iLs ) of the transformer can berepresented as Fig.4.Operational modes: (a) mode 1 [t0 − t1]; (b) mode 2 [t1 − t2];(c) mode 3 [t2 − t3]; (d) mode 4 [t3 − t4].B. Mode 2 (t1 − t2) [Fig. 4(b)] At time t = t1, the main switch (S) is turned OFF.At this time, the diodes (D2, D3, and Do) become forwardbiased to start conducting, and other diodes (D1 and D4) arereverse biased. The stored energy of the additional inductor(L) and clamped capacitor (Cc) in Mode 1 is released tooutput loads. Moreover, the transformer can be operated at Where iDo is the current of the output diode Do;four quadrants to enhance the utility rate of the magnetic iCc is the current of the clamped capacitor Cc. According tocore and to keep the clamped voltage (VCc), since the (11), the cutoff voltage of the main switch (S) is clamped atadditional inductor (L) sup supplies energy to the output Vo − VCc. Moreover, the main switch (S) with low-voltage-terminal by way of the transformer. Applying Kirchhoff’s rated capacity can be selected since the switch-voltage stresslaw [4], the voltage and current relations of each element (vDS) is smaller than the output voltage (Vo). The selectionduring this mode can be described by of a low-voltagerated device with lower RDS (ON) is useful for improving the conversion efficiency. Referring to (8)– (10), the rate of change of iL, iLp and iLs is given by C. Mode 3 (t2 − t3) [Fig. 4(c)] 4275 | Page
  • 4. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 switch-voltage stress (vDS) can be calculated(11),and (22) as Where d is the duty cycle of the main switch (S). Continuously, the main switch (S) is turned ON at time t = t4 to begin the next switching cycle. By analyzing (24), the switch-voltage stress (vDS) is not related to the dc-input voltage (Vi) and duty cycle (d) if the values of the output voltage (Vo) and the turns ratio (n) are fixed. Thus, it can ensure that the sustainable voltage of the main switch (S) is constant. As long as the dc-input voltage is not higher than the rated voltage of the main switch, the high-efficiency voltage clamped dc–dc converter can be applied well to the low-voltage power sources even with large voltage variations, e.g., fuel cell, solar cell, etc. Fuel-cell generation systems have been receiving more attention in the last years due to the advantages of high-conversion efficiency, low aggression to the environment, no moving parts, and superior reliability andAt time t = t2, the residual energy of the clamped capacitor durability. Owing to the electrochemical reaction, fuel cell(Cc) is discharged entirely, i.e., iCc (t2) = 0. Immediately, has the power quality of low voltage and high current.the clamped capacitor (Cc) is charged by the energy of the However, the fuel-cell stack with high output voltage isadditional inductor (L) through the transformer, and the rate difficult to fabricate and it may be failure when any singleof change of the clamped-capacitor current (iCc) can be cell is inactive. Besides, the output voltage is varied easilydenoted as Moreover, the stored energy of the additional with respect to the load variations. In order to satisfy theinductor (L) is released continuously to the output terminal requirement of high-voltage demand, a stable boostby way of the transformer. The rate of charge of iDo is converter with high voltage gain and superior conversiongiven by efficiency is necessary to utilize the fuel-cell energy more efficiently. The validity of the proposed converter is verified by the following experimental results via an example of a PEMFC power source. III. EXPERIMENTAL RESULTS In order to verify the effectiveness of the designed converter topology, the clean energy of a PEMFC system is utilized for the low-voltage power source in the proposedD. Mode 4 (t3 − t4) [Fig. 4(d)] high-efficiency voltage-clamped dc–dc converter, and its At time t = t3, the clamped-capacitor current (iCc ) application circuit is depicted in Fig. 5. The PEMFC systemequals to the secondary-side current (iLs ) of the used in this study is the PowerPEMTM-PS250transformer, and the output diode current (iDo ) decays to 0, manufactured by the H power Company. It is a dc poweri.e., iDo (t3) = 0. During this period, the voltage of the source with 250-W dc nominal power rating.output diode (vDo ) Maintains the zero status until the main The system operates on an ambient air and cleanswitch (S) is turned ON. Moreover, the magnitude of the pressurized hydrogen fuel. The fuel-cell system consists of aadditional inductor current (iL) is equal to the one of the (40) cell stack of the PEM type, mechanical auxiliaries, andprimary-side current (iLp ). According to (13) and (14), the electronic control module. In experimentation, the high-rate of change of iLp and iLs can be represented as Since the efficiency voltage-clamped dc–dc converter is designed tosecondary leakage inductor (Lk) and the change rate of iLs operate from the fuel-cell variability dc input, Vi = 27−37.5in the transformer are very small, the voltage of the V, to deliver a constant dc output, Vo = 200 V, with thesecondary leakage inductor (vLk ) can be neglected. maximal capability of output power, Po,max = 330 W. If theAccording to the concept of the zero average voltage across maximal value of main switch voltage (vDS) is arranged forthe inductor over one period [4], the voltages of vCs , VCc , clamping at 50 V, the turns ratio can be determined as n =and Vo for steady state operation can be described via (2), (2Vo/vDS(max)) − 2 = 6 according to (24). As can be seen(4), (8), and (10) as. from Figs. 3 and 4, the voltage stress of the output diode Since the voltage difference may be caused by the (vDo ) is the same as the switch-voltage stress. In addition,secondary inductor of the transformer, as d = 0.5, the major the voltage stresses of rectifier diodes (vD1, vD2, vD3, andfunction of the balanced capacitor (Cc) is used for keeping vD4) can be calculated via (21) and (23) as nvDS/2 = 150 V.the cutoff voltages of the rectifier diodes (D1, D2, D3, and For conservative consideration, the main switch (FQI90N08,D4) balanced. Moreover, it also can avoid the overlarge 80 V), the output diode (Schottky diode SR20100, 100 V),current that passed through the rectifier diodes. According to and the rectifier diodes (Schottky diode SR20200, 200 V)(22), the voltage gain can be tuned by regulating the turn’s are adopted in the experimental converter.ratio (n) in the transformer to overcome the boost- ratio In order to solve the problem of the fuel-cell output voltagelimitation of the conventional converter. In addition, the varied with the variations of loads, the proposed converter with dc-voltage feedback control is utilized to ensure the system stability, and a PWM control IC TL494 is adopted to 4276 | Page
  • 5. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645achieve this goal of feedback control. The prototype with According to Fig. 10, the converter output voltage, Vo = 200the following V, is insensitive to the variation of loads due to the closed- Specifications are designed in this section to loop control, and the output current ripple is also slightlyillustrate the design procedure given in Section II: extreme as a result of the high switching frequency. Fig. 11Switching frequency fs = 100 kHz; summarizes the conversion efficiency of the proposedTurns ratio n = 6; converter and the PEMFC output voltage under differentAdditional inductor L = 5.9 μH; output powers. From the experimental results, the measurePrimary inductor of transformer Lp = 213.6 μH of efficiency of the proposed converter operating at 310-WSecondary inductor of transformer Ls = 7689.6 μH; output power is 95.6%, and the maximal efficiency is 96.5%Secondary leakage inductor Lk = 0.6 μH; at 190-W output power. The above experimental resultsBalanced capacitor Cs = 4× 6.8 μF; agree well with those obtained from the design procedureClamped capacitor Cc = 6× 4.7 μF; given in Section II. However, slight differences in theseInput filter capacitor Ci = 3300 μF; results are attributed to the factor of system uncertainties inOutput filter capacitor Co = 3× 4.7 μF; practical applications.Main switch S: FQI90N08 (80 V,RDS (ON) = 16 mΩ);Output diode Do: Schottky diodeSR20100 (100 V, 20 A);Rectifier diodes D1, D2, D3, D4:Scotty diode SR20200 (200 V, 20 A). Fig. 5 depicts the experimental voltage and currentcurves of the main switch (S) at 310-W output power. Ascan be seen from this figure, the shaken switch voltage atthe beginning is caused by the line inductor when the switch Fig 5 (a)output voltageis turned OFF. Fortunately, the steady state of this switch-voltage stress is about 50 V due to the utilization of voltage-clamped technique, and it is much smaller than the outputvoltage, Vo = 200 V. It has the merit of selecting a low-voltage-rated device in order to reduce the conduction lossof the switch. The experimental current waveforms of theadditional inductor (L), in parallel with the transformer,primary inductor of transformer (Lp), and secondaryinductor of transformer (Ls) at 310-W output power, aredepicted in Fig. 5(c). By observing the currents of iLp and Fig 5 (b)output current:iLs, it is obvious that the transformer is manipulated duringthe four-quadrant operation so that the utility rate of themagnetic core is improved to exhibit the transformercharacteristics completely. The experimental voltage andcurrent responses of the diodes (Do, D3, and D4) at 310-Woutput power are depicted in Fig. 5. From these results, thereverse-recovery currents in these diodes are small to givethe credit to the utilization of Schottky diodes withextremely low switching and conduction losses. Thus, it canalleviate the reverse-recovery problem for further raising theconversion efficiency. As can been seen from Fig. 5(a) and Fig 5 (c) clamped capacitor voltage(b), The balanced capacitor (Cs) can be used forbalancing the current and cutoff voltage of the diodes (D3and D4) when the condition of d _= 0.5 holds. For verifyingthe voltage-clamped property, the experimental voltageresponses of the output voltage (Vo), clamped capacitor(Cc), output diode (Do), and main switch (S) at 310-Woutput power are depicted. As can be seen from this figure,the output voltage, Vo = 200 V, is strode mainly across theclamped capacitor in the secondary-side circuit (i.e., VCc =150 V). Thus, the switch-voltage stress and the cutoffvoltage of the output diode are clamped at about 50 V. In Fig 5 (d) clamped capacitor currentorder to examine the robust performance of the proposedconverter scheme, the experimental results of the converteroutput voltage (Vo), output current (Io), and the PEMFCoutput current (Ii) under the step load variation between noload (0 W) and full load (310 W) are depicted Fig. 10. 4277 | Page
  • 6. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 [4] N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications, and Design. New York: Wiley, 1995. [5] M. M. Jovanovic and Y. Jang, ―A new soft-switched boost converter with isolated active snubber,‖ IEEE Trans. Ind. Appl., vol. 35, no. 2, pp. 496–502, Mar./Apr. 1999. [6] C. M. C. Duarte and I. Barbi, ―An improved family of ZVS-PWM active-clamping DC-to-DC converters,‖ IEEE Trans. Power Electron., Fig 5 (e) Inductor current: vol. 17, no. 1, pp. 1–7, Jan. 2002. [7] E. S. da Silva, L. dos Reis Barbosa, J. B. Vieira, L. C. IV. CONCLUSION de Freitas, and V. J. Farias, ―An improved boost PWM This paper has successfully developed a high- soft-single-switched converter with low voltage andefficiency voltage-clamped dc–dc converter with reduced current stresses,‖ IEEE Trans. Ind. Electron., vol. 48,reverse recovery current and switch-voltage stress, and this no. 6, pp. 1174–1179, Dec. 2001.converter has been applied well to a PEMFC system with a [8] K. Hirachi, M. Yamanaka, K. Kajiyama, and S.power quality of low voltage and high current. According to Isokane, ―Circuit configuration of bidirectionalthe experimental results, the maximal efficiency was DC/DC converter specific for small scale load levelingmeasured to be over 96%, which is comparatively higher system,‖ in Proc. IEE Power Conversion Conf.,than the conventional converter with the same voltage gain. Osaka, Japan, 2002, pp. 603–609.The newly designed converter circuit has the following [9] C. W. Roh, S. H. Han, and M. J. Youn, ―Dual coupledimprovements compared to the previous work. inductor fed isolated boost converter for low input1) It can select the main switch with lower sustainable voltage applications,‖ Electron. Lett., vol. 35, no. 21,voltage for alleviating the switch conduction loss due to the pp. 1791–1792, Oct. 1999.utilization of voltage-clamped technique. [10] Q. Zhao and F. C. Lee, ―High-efficiency, high step-up2) All diodes in this circuit topology are Schottky diodes dc–dc converters,‖ IEEE Trans. Power Electron., vol.with the reduction of switching and conduction losses. 18, no. 1, pp. 65–73, Jan. 2003.3) The additional inductor is used for providing the reverse [11] K. Ro and S. Rahman, ―Two-loop controller forcurrent path of the transformer to raise the utility rate of the maximizing performance of a grid-connectedmagnetic core. photovoltaic-fuel cell hybrid power plant,‖ IEEE4) Additional snubber circuits for absorbing the voltage Trans. Energy Convers., vol. 13, no. 3, pp. 276–281,spikes in the diodes are not required to further cut down the Sep. 1998.manufacture cost. [12] M. D. Lukas, K. Y. Lee, and H. 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The authors would like to express their gratitude to [15] M. W. Ellis, M. R. Von Spakovsky, and D. J. Nelson,the Referees and the Associate Editor for their useful ―Fuel cell systems: Efficient, flexible energycomments and suggestions. conversion for the 21st century,‖ Proc. IEEE, vol. 89, no. 12, pp. 1808–1818, Dec. 2001. REFERENCES [16] J. M. Correa, F. A. Farret, J. R. Gomes, and M. G.[1] I. Barbi and R. Gules, ―Isolated dc–dc converters with Simoes, ―Simulation of fuel-cell stacks using a high-output voltage for TWTA telecommunication computer-controlled power rectifier with the purposes satellite applications,‖ IEEE Trans. Power Electron., of actual high-power injection applications,‖ IEEE vol. 18, no. 4, pp. 975–984, Jul. 2003. Trans. Ind. Appl., vol. 39, no. 4, pp. 1136–1142,[2] O. Abutbul, A. Gherlitz, Y. Berkovich, and A. Jul./Aug. 2003. Ioinovici, ―Step-up switching-mode converter with [17] K. Green and J. C. 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  • 7. International Journal of Modern Engineering Research (IJMER) Vol.2, Issue.6, Nov-Dec. 2012 pp-4273-4279 ISSN: 2249-6645 Dharamalla.ChandraSekhar- wasborn in Andhra Pradesh, INDIA in 1982. He received theB.Tech degree from JNTU Hyderabad in 2004 and M.Techdegree in Power Electronics from JNTU Hyderabad in2010.Since July 2004-Sept 2008 he has been Assistant Professorin the Department of Electrical and Electronics in Hi-TechEngineering College. From October-2008 he was beenworking as a Head of Department of Electrical andElectronics Engineering in GATE Engineering College,JNTUH, AP. His areas of interest are Electrical Machines,Power Electronics and Drives, Control Systems andElectrical Circuits. D Jagan - was born in Andhra Pradesh,INDIA in 1988. He received the B.Tech degree from JNTUHyderabad in 2010, the M.Tech degree in Power Electronicsfrom JNTU Ananthapur I n 2012.Since July 2010-Oct 2012 he has been Assistant Professor inthe Department of Electrical and Electronics in GATEEngineering College, JNTUH, and AP. His areas of interestare Electrical Machines, Power Electronics and Drives,Control Systems and Electrical Circuits. 4279 | Page