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NOVEL HIGH-CONVERSION-RATIO HIGH EFFICIENCY ISOLATED
BIDIRECTIONAL DC–DC CONVERTER
By
A
PROJECT REPORT
Submitted to the Department of electronics & communication Engineering in the
FACULTY OF ENGINEERING & TECHNOLOGY
In partial fulfillment of the requirements for the award of the degree
Of
MASTER OF TECHNOLOGY
IN
ELECTRONICS & COMMUNICATION ENGINEERING
APRIL 2016
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CERTIFICATE
Certified that this project report titled “NOVEL HIGH-CONVERSION-RATIO HIGH
EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” is the bonafide
work of Mr. _____________Who carried out the research under my supervision Certified
further, that to the best of my knowledge the work reported herein does not form part of any
other project report or dissertation on the basis of which a degree or award was conferred on an
earlier occasion on this or any other candidate.
Signature of the Guide Signature of the H.O.D
Name Name
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DECLARATION
I hereby declare that the project work entitled “NOVEL HIGH-CONVERSION-RATIO
HIGH EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” Submitted
to BHARATHIDASAN UNIVERSITY in partial fulfillment of the requirement for the award of
the Degree of MASTER OF APPLIED ELECTRONICS is a record of original work done by me
the guidance of Prof.A.Vinayagam M.Sc., M.Phil., M.E., to the best of my knowledge, the
work reported here is not a part of any other thesis or work on the basis of which a degree or
award was conferred on an earlier occasion to me or any other candidate.
(Student Name)
(Reg.No)
Place:
Date:
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ACKNOWLEDGEMENT
I am extremely glad to present my project “NOVEL HIGH-CONVERSION-RATIO HIGH
EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” which is a part of
my curriculum of third semester Master of Science in Computer science. I take this opportunity
to express my sincere gratitude to those who helped me in bringing out this project work.
I would like to express my Director, Dr. K. ANANDAN, M.A.(Eco.), M.Ed., M.Phil.,(Edn.),
PGDCA., CGT., M.A.(Psy.) of who had given me an opportunity to undertake this project.
I am highly indebted to Co-Ordinator Prof. Muniappan Department of Physics and thank from
my deep heart for her valuable comments I received through my project.
I wish to express my deep sense of gratitude to my guide
Prof. A.Vinayagam M.Sc., M.Phil., M.E., for her immense help and encouragement for
successful completion of this project.
I also express my sincere thanks to the all the staff members of Computer science for their kind
advice.
And last, but not the least, I express my deep gratitude to my parents and friends for their
encouragement and support throughout the project.
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ABSTRACT:
This paper proposes a novel high-conversionratio high-efficiency isolated bidirectional
dc–dc converter. The proposed converter is operated in the step-down stage. The dc-blocking
capacitor in the high-voltage side is used to reduce the voltage on the transformer, and the
currentdoubler circuits are used in the low-voltage side to reduce the output current ripple. The
energy stored in the leakage inductance is recycled to the dc-blocking capacitor. When the
proposed converter is operated with a step-up function, dual current-fed circuits on the low-
voltage side are used to reduce the current ripples and conduction losses of the switches in the
low-voltage side. The voltage-doubler circuit in the high-voltage side increases the conversion
ratio. The proposed converter can achieve high conversion with high efficiency. Experimental
results based on a prototype implemented in the laboratory with a high voltage of 200 V, low
voltage of 24 V, and output power of 200 W verify the performance of the proposed converter.
The peak efficiency of the proposed converter in the high-step-down and high-step-up stages is
96.3% and 95.6%, respectively
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INTRODUCTION:
In addition to improvements in the conversion efficiency of green energy, the storage and
reuse of excess energy have become important research topics. Thus, high-step-up/step-down
converters have become important research subjects.
Converters with high conversion ratios can be used in energy storage systems, high-
intensity discharge lamps, high power applications, communication power, solar power, and
uninterruptible power supplies.
These converters are designed by combining switched-capacitor cells, coupled inductor
techniques, and Z source techniques.
The distributed generation system indicates that the bidirectional dc–dc converter plays a
very important role between energy storage device (Battery) and voltage bus. The function of the
bidirectional converter is to transfer energy between the battery and the dc bus.
The energy generated from the renewable source(s) will be transferred to the dc voltage
bus. Load(s) may be connected with dc voltage bus and ac utility grid. Battery is used to provide
energy to dc voltage bus when the grid voltage outage and renewable energy sources cannot
provide enough energy to the load connected with dc voltage bus
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EXISTING SYSTEM:
In bidirectional DC-DC converter topology, the energy flow from the low to the high
voltage side, the boost converter (L) is controlled and the high side converter (H) is not
controlled but operates as a rectifier .To the energy flow into the opposite side the buck converter
(H) is controlled and the low side converter (L) operates as a rectifier. The main problem of this
solution is the use of the same resonant circuit elements for the both directions of the energy
flow. An additional capacitor must be used when the system operates in the buck mode
OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD
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PROPOSED SYSTEM:
The circuit includes high voltage VHV; high-voltage capacitor C1 and dc-blocking
capacitor C2; four active switches S1, S2, S3, and S4; a transformer T1; two inductors L1 and L2;
a low-voltage capacitor C3; and low voltage VLV. The gate signals of S1 and S2 in the high-step-
down stage are interlaced by a phase shift of 180◦, and S3 and S4 are synchronous rectifiers. In
the high-step-up mode, the gate signals of S3 and S4 are greater than 50% and are controlled by a
phase shift of 180◦.
The gate signals of S1 and S2 are smaller than 50% and are controlled by a phase shift of
180◦ with synchronous rectifiers. The function of the proposed bidirectional converter is like the
“double voltage step-down” instead of mode. (When S1 is turned on, the voltage on the primary
winding is reduced by half because of the capacitor C2. Thus, the voltage gain can be reduced by
half by adding C2 in series with the half-bridge converter.)
This converter is controlled with duty control on frequency control so that the effect of
leakage inductance can be neglected. The proposed cannot achieve zero-voltage switching (ZVS)
on the high voltage side power switches but the low voltage side synchronous rectifier can
achieve ZVS
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ADVANTAGES:
 It meets the safety standards of galvanic isolation.
 The size of the transformer can be reduced.
 The energy in the leakage inductance of the transformer can be recycled.
 It has a high conversion ratio.
OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD
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BLOCK DIAGRAM:
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TOOLS AND SOFTWARE USED:
 MPLAB – microcontroller programming.
 ORCAD – circuit layout.
 MATLAB/Simulink – Simulation
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APPLICATIONS:
 Solar and wind energy.
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CONCLUSION:
In this paper, a high-efficiency and high-conversion-ratio isolated bidirectional dc–dc
converter with a low transformer turns ratio has been presented. The size of the capacitor on the
voltage side can be decreased by using current-doubler circuits with low current ripples. The
synchronous-rectifier circuit can achieve ZVS and improve system efficiency. The operating
principles, steady-state analysis, and experimental results are discussed in detail. The efficiencies
of the proposed converter with synchronous rectifiers and antiparallel diodes are compared in the
experimental results. The full-load efficiency in the step-down and step-up stages is near 96.3%
and 95.6%, respectively.
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ECWAY TECHNOLOGIES
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REFERENCES:
[1] Z. Dong, “Nonlinear adaptive power-level control for modular high temperature gas cooled
reactors,” IEEE Trans. Nucl. Sci., vol. 60, no. 2, pp. 1332–1345, Apr. 2013.
[2] T. J. Liang, J. H. Lee, S. M. Chen, and L. S. Yang, “Novel isolated highstep- up DC–DC
converter with voltage lift,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1483–1491, Apr.
2013.
[3] A. Koran, T. Labella, and J. S. Lai, “High efficiency photovoltaic source simulator with fast
response time for solar power conditioning systems evaluation,” IEEE Trans. Power Electron.,
vol. 29, no. 3, pp. 1285–1297, Mar. 2014.
[4] M. Trifkovic, M. Sheikhzadeh, K. Nigim, and P. Daoutidis, “Modeling and control of a
renewable hybrid energy system with hydrogen storage,” IEEE Trans. Control Syst. Technol.,
vol. 22, no. 1, pp. 169–179, Jan. 2014.
[5] Y. K. Lo, H. J. Chiu, T. P. Lee, I. Purnama, and J. M.Wang, “Analysis and design of a
photovoltaic system DC connected to the utility with a power factor corrector,” IEEE Trans.
Power Electron., vol. 56, no. 11, pp. 4354– 4362, Nov. 2009.

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Novel high conversion-ratio high-efficiency isolated bidirectional dc–dc converter

  • 1. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT NOVEL HIGH-CONVERSION-RATIO HIGH EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER By A PROJECT REPORT Submitted to the Department of electronics & communication Engineering in the FACULTY OF ENGINEERING & TECHNOLOGY In partial fulfillment of the requirements for the award of the degree Of MASTER OF TECHNOLOGY IN ELECTRONICS & COMMUNICATION ENGINEERING APRIL 2016
  • 2. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT CERTIFICATE Certified that this project report titled “NOVEL HIGH-CONVERSION-RATIO HIGH EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” is the bonafide work of Mr. _____________Who carried out the research under my supervision Certified further, that to the best of my knowledge the work reported herein does not form part of any other project report or dissertation on the basis of which a degree or award was conferred on an earlier occasion on this or any other candidate. Signature of the Guide Signature of the H.O.D Name Name
  • 3. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT DECLARATION I hereby declare that the project work entitled “NOVEL HIGH-CONVERSION-RATIO HIGH EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” Submitted to BHARATHIDASAN UNIVERSITY in partial fulfillment of the requirement for the award of the Degree of MASTER OF APPLIED ELECTRONICS is a record of original work done by me the guidance of Prof.A.Vinayagam M.Sc., M.Phil., M.E., to the best of my knowledge, the work reported here is not a part of any other thesis or work on the basis of which a degree or award was conferred on an earlier occasion to me or any other candidate. (Student Name) (Reg.No) Place: Date:
  • 4. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT ACKNOWLEDGEMENT I am extremely glad to present my project “NOVEL HIGH-CONVERSION-RATIO HIGH EFFICIENCY ISOLATED BIDIRECTIONAL DC–DC CONVERTER” which is a part of my curriculum of third semester Master of Science in Computer science. I take this opportunity to express my sincere gratitude to those who helped me in bringing out this project work. I would like to express my Director, Dr. K. ANANDAN, M.A.(Eco.), M.Ed., M.Phil.,(Edn.), PGDCA., CGT., M.A.(Psy.) of who had given me an opportunity to undertake this project. I am highly indebted to Co-Ordinator Prof. Muniappan Department of Physics and thank from my deep heart for her valuable comments I received through my project. I wish to express my deep sense of gratitude to my guide Prof. A.Vinayagam M.Sc., M.Phil., M.E., for her immense help and encouragement for successful completion of this project. I also express my sincere thanks to the all the staff members of Computer science for their kind advice. And last, but not the least, I express my deep gratitude to my parents and friends for their encouragement and support throughout the project.
  • 5. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT ABSTRACT: This paper proposes a novel high-conversionratio high-efficiency isolated bidirectional dc–dc converter. The proposed converter is operated in the step-down stage. The dc-blocking capacitor in the high-voltage side is used to reduce the voltage on the transformer, and the currentdoubler circuits are used in the low-voltage side to reduce the output current ripple. The energy stored in the leakage inductance is recycled to the dc-blocking capacitor. When the proposed converter is operated with a step-up function, dual current-fed circuits on the low- voltage side are used to reduce the current ripples and conduction losses of the switches in the low-voltage side. The voltage-doubler circuit in the high-voltage side increases the conversion ratio. The proposed converter can achieve high conversion with high efficiency. Experimental results based on a prototype implemented in the laboratory with a high voltage of 200 V, low voltage of 24 V, and output power of 200 W verify the performance of the proposed converter. The peak efficiency of the proposed converter in the high-step-down and high-step-up stages is 96.3% and 95.6%, respectively
  • 6. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT INTRODUCTION: In addition to improvements in the conversion efficiency of green energy, the storage and reuse of excess energy have become important research topics. Thus, high-step-up/step-down converters have become important research subjects. Converters with high conversion ratios can be used in energy storage systems, high- intensity discharge lamps, high power applications, communication power, solar power, and uninterruptible power supplies. These converters are designed by combining switched-capacitor cells, coupled inductor techniques, and Z source techniques. The distributed generation system indicates that the bidirectional dc–dc converter plays a very important role between energy storage device (Battery) and voltage bus. The function of the bidirectional converter is to transfer energy between the battery and the dc bus. The energy generated from the renewable source(s) will be transferred to the dc voltage bus. Load(s) may be connected with dc voltage bus and ac utility grid. Battery is used to provide energy to dc voltage bus when the grid voltage outage and renewable energy sources cannot provide enough energy to the load connected with dc voltage bus
  • 7. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT EXISTING SYSTEM: In bidirectional DC-DC converter topology, the energy flow from the low to the high voltage side, the boost converter (L) is controlled and the high side converter (H) is not controlled but operates as a rectifier .To the energy flow into the opposite side the buck converter (H) is controlled and the low side converter (L) operates as a rectifier. The main problem of this solution is the use of the same resonant circuit elements for the both directions of the energy flow. An additional capacitor must be used when the system operates in the buck mode
  • 8. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT PROPOSED SYSTEM: The circuit includes high voltage VHV; high-voltage capacitor C1 and dc-blocking capacitor C2; four active switches S1, S2, S3, and S4; a transformer T1; two inductors L1 and L2; a low-voltage capacitor C3; and low voltage VLV. The gate signals of S1 and S2 in the high-step- down stage are interlaced by a phase shift of 180◦, and S3 and S4 are synchronous rectifiers. In the high-step-up mode, the gate signals of S3 and S4 are greater than 50% and are controlled by a phase shift of 180◦. The gate signals of S1 and S2 are smaller than 50% and are controlled by a phase shift of 180◦ with synchronous rectifiers. The function of the proposed bidirectional converter is like the “double voltage step-down” instead of mode. (When S1 is turned on, the voltage on the primary winding is reduced by half because of the capacitor C2. Thus, the voltage gain can be reduced by half by adding C2 in series with the half-bridge converter.) This converter is controlled with duty control on frequency control so that the effect of leakage inductance can be neglected. The proposed cannot achieve zero-voltage switching (ZVS) on the high voltage side power switches but the low voltage side synchronous rectifier can achieve ZVS
  • 9. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT ADVANTAGES:  It meets the safety standards of galvanic isolation.  The size of the transformer can be reduced.  The energy in the leakage inductance of the transformer can be recycled.  It has a high conversion ratio.
  • 10. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT BLOCK DIAGRAM:
  • 11. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT TOOLS AND SOFTWARE USED:  MPLAB – microcontroller programming.  ORCAD – circuit layout.  MATLAB/Simulink – Simulation
  • 12. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT APPLICATIONS:  Solar and wind energy.
  • 13. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT CONCLUSION: In this paper, a high-efficiency and high-conversion-ratio isolated bidirectional dc–dc converter with a low transformer turns ratio has been presented. The size of the capacitor on the voltage side can be decreased by using current-doubler circuits with low current ripples. The synchronous-rectifier circuit can achieve ZVS and improve system efficiency. The operating principles, steady-state analysis, and experimental results are discussed in detail. The efficiencies of the proposed converter with synchronous rectifiers and antiparallel diodes are compared in the experimental results. The full-load efficiency in the step-down and step-up stages is near 96.3% and 95.6%, respectively.
  • 14. OUR OFFICES @CHENNAI/ TRICHY/ KARUR / ERODE / MADURAI / SALEM / COIMBATORE / BANGALORE / HYDRABAD CELL: 9894917187 | 875487 1111 / 2111 / 3111 / 4111 / 5111 / 6111 Visit: www.ecwaytechnologies.com | www.ecwayprojects.com Mail to: ecwaytechnologies@gmail.com ECWAY TECHNOLOGIES IEEE SOFTWARE | EMBEDDED | MECHANICAL | ROBOTICS PROJECTS DEVELOPMENT REFERENCES: [1] Z. Dong, “Nonlinear adaptive power-level control for modular high temperature gas cooled reactors,” IEEE Trans. Nucl. Sci., vol. 60, no. 2, pp. 1332–1345, Apr. 2013. [2] T. J. Liang, J. H. Lee, S. M. Chen, and L. S. Yang, “Novel isolated highstep- up DC–DC converter with voltage lift,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1483–1491, Apr. 2013. [3] A. Koran, T. Labella, and J. S. Lai, “High efficiency photovoltaic source simulator with fast response time for solar power conditioning systems evaluation,” IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1285–1297, Mar. 2014. [4] M. Trifkovic, M. Sheikhzadeh, K. Nigim, and P. Daoutidis, “Modeling and control of a renewable hybrid energy system with hydrogen storage,” IEEE Trans. Control Syst. Technol., vol. 22, no. 1, pp. 169–179, Jan. 2014. [5] Y. K. Lo, H. J. Chiu, T. P. Lee, I. Purnama, and J. M.Wang, “Analysis and design of a photovoltaic system DC connected to the utility with a power factor corrector,” IEEE Trans. Power Electron., vol. 56, no. 11, pp. 4354– 4362, Nov. 2009.