Power Converter Solutions for Industrial PV Applications—A Review
Abstract
:1. Introduction
 
 Maximum power point tracking;
 
 Energy storage and balancing;
 
 Electric parameter transformation and stabilization.
 
 Continuous low ripple input current I;
 
 High efficiency in a wide power range.
 
 Boost converters (G > 1), if R_{SB}_{(max)} < R_{L};
 
 Buck/boost converters (G = G_{(min)}…1…G_{(max)}), if R_{SB}_{(min)} < R_{L} < R_{SB}_{(max)};
 
 Buck converters (G < 1), if R_{SB}_{(min)} > R_{L}.
 The multifunctional purpose of the power converters is:
 
 
 Advanced schematic and control algorithms:
 
 For energy balancing and stable generation, often for AC gridconnected applications, electric batteries with bidirectional chargers are connected [23], as shown in Figure 5c. To make sure that electricity has the right dynamics and quality, you need to use advanced control algorithms with multiloop and predictive control [24].
 
 Special issues in converter design:
 
 For high voltage DC and AC ongrid systems, specialized converters adapted for PV applications are being developed [26];
 
 Hybrid systems provide parallel operation of several alternative power supplies connected to the power grid and load that in general may be considered a multiport power system [27]. As a result, a reducedcomponent multiport power system can be made instead of having a lot of separate power converters that do the same thing [28].
 
 System type (standalone or gridon, DC or AC);
 
 Voltage and power level (low, middle, or high);
 
 The relationship between the voltage of the solar battery and the grid;
 
 Additional requirements on power factor value and power stability.
2. Materials and Methods
3. AC Grid on PV Applications
 
 Boosting DC voltage;
 
 Decreasing k_{C} and P_{con}* to allow for a wider range of input/output voltage operations;
 
 Inconsistency of power grid and solar battery voltages.
 
 Voltage conversion and power grid synchronization;
 
 Disconnection and antiislanding protection when power grid fault appears; Correction of the power factor of the input current.
4. Energy Storage Applications
 
 Load shifting occurs when renewable energy mostly charges the energy storage during the day, and the energy storage is discharged in the late hours of peak power demand [69];
 
 Shutdown protection in smart distributed power grids that allows supplying endusers when loss of power arises [70];
 
 Energy quality control (voltage, frequency, reactive power compensation, high harmonic reduction) [71].
5. High Voltage Gain Converters
6. Hybrid PV Applications
7. Discussion
 
 In buck converters, the output voltage maximum value U_{L}_{(max)} is fixed to the input voltage U_{in}, U_{L}_{(max)} = U_{in} that corresponds to D_{max} = 1;
 
 In boost converters, the output voltage minimum value U_{L}_{(min)} is fixed to the input voltage U_{in}, U_{L}_{(min)} = U_{in} that corresponds to D_{min} = 0;
 
 In buckboost converters, the lowest values of k_{c} and P_{con}* are achieved in the middle of the duty cycle range, D = 0.5. Therefore, for the proper definition of D_{min} < 0.5 and D_{max} > 0.5, one of the following equations is solved:
8. Conclusions
 
 Basic DC–DC buck and boost topologies, as well as fullbridge topologies for DCAC applications, have lower cost and power loss factors, whereas more complex interleaved or softswitching topologies may decrease power loss by increasing the converter total cost;
 
 For DC–AC applications with a low or medium voltage range, it is advisable to use singlestage DC–AC converters, whereas for wide voltage range applications, twostage converters have better cost and power loss factors;
 
 High voltage gain applications suffer from high transistor voltage stress. Therefore, specialized power converter topologies with reduced voltage stress, such as Cockcroft–Walton and Dickson multiplierbased boost converters, boost derived MIESC SCcell converters, and boost 3SSC cell converters, have the advantage over their counterparts;
 
 Hybrid converters have approximately the same power loss and cost as power converters with common topologies because of the same number of power transistors;
 
 For clear analysis of different types of converters, it is better to represent cost and power loss factors in the space of gain factor and analyze the impact of the environment on gain factor probability distribution during operation.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
 Qazi, A.; Hussain, F.; Rahim, N.A.; Hardaker, G.; Alghazzawi, D.; Shaban, K.; Haruna, K. Towards Sustainable Energy: A Systematic Review of Renewable Energy Sources, Technologies, and Public Opinions. IEEE Access 2019, 7, 63837–63851. [Google Scholar] [CrossRef]
 Statistical Review of World Energy 2021, 70th ed. Available online: https://www.bp.com/content/dam/bp/businesssites/en/global/corporate/pdfs/energyeconomics/statisticalreview/bpstatsreview2021fullreport.pdf (accessed on 30 August 2021).
 Shubbak, M.H. Advances in solar photovoltaics: Technology review and patent trends. Renew. Sustain. Energy Rev. 2019, 115, 109383. [Google Scholar] [CrossRef]
 Mehra, V.; Amatya, R.; Ram, R.J. Estimating the value of demandside management in lowcost, solar microgrids. Energy 2018, 163, 74–87. [Google Scholar] [CrossRef]
 Romashko, V.J.; Verbitsky, I.V.; Kyrychik, I.I. Energy losses analyze in solar battery maximum power picking system. Tech. Electrodyn. 2014, 4, 55–57. [Google Scholar]
 Clauser, C.; Ewert, M. The renewables cost challenge: Levelized cost of geothermal electric energy compared to other sources of primary energy–Review and case study. Renew. Sustain. Energy Rev. 2018, 82, 3683–3693. [Google Scholar] [CrossRef]
 Tummuru, N.R.; Mishra, M.K.; Srinivas, S. Integration of PV/battery hybrid energy conversion system to the grid with power quality improvement features. In Proceedings of the IEEE International Conference on Industrial Technology (ICIT), Cape Town, South Africa, 25–28 February 2013. [Google Scholar] [CrossRef]
 Hua, C.C.; Fang, Y.H.; Wong, C.J. Improved solar system with maximum power point tracking. IET Renew. Power Gener. 2018, 12, 806–814. [Google Scholar] [CrossRef]
 Darvishzadeh, P.; Redzwan, G.; Ahmadi, R.; Gorji, N.E. Modeling the degradation/recovery of shortcircuit current density in perovskite and thin film photovoltaics. Org. Electron. 2017, 43, 247–252. [Google Scholar] [CrossRef]
 Hussaian Basha, C.H.; Rani, C. Performance Analysis of MPPT Techniques for Dynamic Irradiation Condition of Solar PV. Int. J. Fuzzy Syst. 2020, 22, 2577–2598. [Google Scholar] [CrossRef]
 Zhuo, S.; Gaillard, A.; Li, Q.; MA, R.; Paire, D.; Gao, F. Current Ripple Optimization of FourPhase Floating Interleaved DCDC Boost Converter under Switch Fault. IEEE Trans. Ind. Appl. 2020, 56, 4214–4224. [Google Scholar] [CrossRef]
 Raghavendra, K.V.G.; Zeb, K.; Muthusamy, A.; Krishna, T.N.V.; Kumar, S.V.S.V.P.; Kim, D.H.; Kim, M.S.; Cho, H.G.; Kim, H.J. A Comprehensive Review of DC–DC Converter Topologies and Modulation Strategies with Recent Advances in Solar Photovoltaic Systems. Electronics 2020, 9, 31. [Google Scholar] [CrossRef] [Green Version]
 Vinnikov, D.; Chub, A.; Korkh, O.; Liivik, E.; Blaabjerg, F.; Kouro, S. MPPT performance enhancement of lowcost PV microconverters. Sol. Energy 2019, 187, 156–166. [Google Scholar] [CrossRef]
 Kolsi, S.; Samet, H.; Amar, M.B. Design Analysis of DCDC Converters Connected to a Photovoltaic Generator and Controlled by MPPT for Optimal Energy Transfer throughout a Clear Day. J. Power Energy Eng. 2014, 2, 27–34. [Google Scholar] [CrossRef] [Green Version]
 Bukar, A.L.; Tan, C.W.A. Review on Standalone PhotovoltaicWind Energy System with Fuel Cell: System Optimization and Energy Management Strategy. J. Clean. Prod. 2019, 221, 73–88. [Google Scholar] [CrossRef]
 Bonkile, M.P.; Ramadesigan, V. Power management control strategy using physicsbased battery models in standalone PVbattery hybrid systems. J. Energy Storage 2019, 23, 258–268. [Google Scholar] [CrossRef]
 Kumar, A.; Gupta, N.; Gupta, V. A Comprehensive Review on GridTied Solar Photovoltaic System. J. Green Eng. 2017, 7, 213–254. [Google Scholar] [CrossRef]
 Ali Khan, M.Y.; Liu, H.; Yang, Z.; Yuan, X. A Comprehensive Review on Grid Connected Photovoltaic Inverters, Their Modulation Techniques, and Control Strategies. Energies 2020, 13, 4185. [Google Scholar] [CrossRef]
 Mahmood, H.; Michaelson, D.; Jiang, J. A Power Management Strategy for PV/Battery Hybrid Systems in Islanded Microgrids. IEEE J. Emerg. Sel. Top. Power Electron. 2014, 2, 870–882. [Google Scholar] [CrossRef]
 Mira, M.C.; Zhang, Z.; Knott, A.; Andersen, M.A.E. Analysis, Design, Modeling, and Control of an InterleavedBoost FullBridge ThreePort Converter for Hybrid Renewable Energy Systems. IEEE Trans. Power Electron. 2017, 32, 1138–1155. [Google Scholar] [CrossRef] [Green Version]
 Bhattacharjee, A.; Samanta, H.; Banerjee, N.; Saha, H. Development and validation of a realtime flow control integrated MPPT charger for solar PV applications of vanadium redox flow battery. Energy Convers. Manag. 2018, 171, 1449–1462. [Google Scholar] [CrossRef]
 El Aroudi, A.; Haroun, R.; AlNumay, M.; Huang, M. MultipleLoop Control Design for a SingleStage PVFed GridTied Differential Boost Inverter. Appl. Sci. 2020, 10, 4808. [Google Scholar] [CrossRef]
 Nassary, M.; Orabi, M.; Ghoneima, M.; ElNemr, M.K. SinglePhase Isolated Bidirectional ACDC Battery Charger for Electric Vehicle–Review. In Proceedings of the International Conference on Innovative Trends in Computer Engineering (ITCE), Aswan, Egypt, 2–4 February 2019. [Google Scholar] [CrossRef]
 Sultana, W.R.; Sahoo, S.K.; Sukchai, S.; Yamuna, S.; Venkatesh, D. A review on state of art development of model predictive control for renewable energy applications. Renew. Sustain. Energy Rev. 2017, 76, 391–406. [Google Scholar] [CrossRef]
 Deng, W.; Pei, W.; Li, N.; Zhang, G.; Ding, L.; Kong, L. AC/DC Hybrid Renewable Energy System Coordinated Control and Test Platform. In Proceedings of the 2021 3rd Asia Energy and Electrical Engineering Symposium (AEEES), Chengdu, China, 26–29 March 2021. [Google Scholar] [CrossRef]
 Amir, A.; Amir, A.; Che, H.S.; El Khateb, A.; Rahim, N.A. Comparative Analysis of High Voltage Gain DCDC Converter Topologies for Photovoltaic Systems. Renew. Energy 2018, 136, 1147–1163. [Google Scholar] [CrossRef] [Green Version]
 Rahman, S.; Khan, I.; Rahman, K.; Al Otaibi, S.; Alkhammash, H.I.; Iqbal, A. Scalable Multiport Converter Structure for Easy Grid Integration of Alternate Energy Sources for Generation of Isolated Voltage Sources for MMC. Electronics 2021, 10, 1779. [Google Scholar] [CrossRef]
 Chen, G.; Liu, Y.; Qing, X.; Wang, F. Synthesis of Integrated MultiPort DCDC Converters with Reduced Switches. IEEE Trans. Ind. Electron. 2019, 67, 4536–4546. [Google Scholar] [CrossRef]
 Başoğlu, M.E.; Çakır, B. Comparisons of MPPT performances of isolated and nonisolated DC–DC converters by using a new approach. Renew. Sustain. Energy Rev. 2016, 60, 1100–1113. [Google Scholar] [CrossRef]
 Gorji, S.A.; Sahebi, H.G.; Ektesabi, M.; Rad, A.B. Topologies and Control Schemes of Bidirectional DC–DC Power Converters: An Overview. IEEE Access 2019, 7, 117997–118019. [Google Scholar] [CrossRef]
 Moghassemi, A.; Padmanaban, S. Dynamic Voltage Restorer (DVR): A Comprehensive Review of Topologies, Power Converters, Control Methods, and Modified Configurations. Energies 2020, 13, 4152. [Google Scholar] [CrossRef]
 Ansari, S.; Chandel, A.; Tariq, M. A Comprehensive Review on Power Converters Control and Control Strategies of AC/DC Microgrid. IEEE Access 2020, 9, 17998–18015. [Google Scholar] [CrossRef]
 Undeland, M.N.; Robbins, W.P.; Mohan, N. Power Electronics. In Converters, Applications, and Design, 3rd ed.; John Whiley & Sons: Hoboken, NJ, USA, 1995. [Google Scholar]
 Ha, K.; Lee, C.; Kim, J.; Krishnan, R.; Oh, S.G. Design and development of brushless variable speed motor drive for low cost and high efficiency. Proc. IAS Conf. 2006, 4, 1649–1656. [Google Scholar] [CrossRef]
 IEC 617301; Photovoltaic (PV) Module Safety QualificationPart 1: Requirements for Construction. CENELEC: Brussels, Belgium, 2018.
 IEC 617302; Photovoltaic (PV) Module safety QualificationPart 2: Requirements for Testing. CENELEC: Brussels, Belgium, 2018.
 IEC 621091; Safety of Power Converters for Use in Photovoltaic Power Systems–Part 1: General Requirements. CENELEC: Brussels, Belgium, 2010.
 IEC 621092; Safety of power Converters for Use in Photovoltaic Power SystemsPart 2: Particular Requirements for Inverters. CENELEC: Brussels, Belgium, 2011.
 Wang, G.; Wang, F.; Magai, G.; Lei, Y.; Huang, A.; Das, M. Performance comparison of 1200V 100A SiC MOSFET and 1200V 100A silicon IGBT. In Proceedings of the 2013 IEEE Energy Conversion Congress and Exposition, Denver, CO, USA, 15–19 September 2013. [Google Scholar] [CrossRef] [Green Version]
 Datasheet of the Transistor C2M0080170P. Available online: https://cms.wolfspeed.com/app/uploads/2020/12/C2M0080170P.pdf (accessed on 9 October 2021).
 Erickson, R.; Maksimovic, D. Fundamentals of Power Electronics, Ser. Power Electronics; Springer: Berlin/Heidelberg, Germany, 2001. [Google Scholar]
 Datasheet of the diode C5D25170H. Available online: https://cms.wolfspeed.com/app/uploads/2020/12/C5D25170H.pdf (accessed on 9 October 2021).
 Jain, S.; Agarwal, V. A SingleStage GridConnected Inverter Topology for Solar PV Systems with Maximum Power Point Tracking. IEEE Trans. Power Electron. 2007, 22, 1928–1940. [Google Scholar] [CrossRef] [Green Version]
 Altin, N.; Ozdemir, S.; Komurcugil, H.; Sefa, I.; Biricik, S. Twostage gridconnected inverter for PV systems. In Proceedings of the 2018 IEEE 12th International Conference on Compatibility, Power Electronics and Power Engineering, Doha, Qatar, 10–12 April 2018. [Google Scholar] [CrossRef]
 Zebarjadi, M.; Askarzadeh, A. Optimization of a reliable gridconnected PVbased power plant with/without energy storage system by a heuristic approach. Sol. Energy 2016, 125, 12–21. [Google Scholar] [CrossRef]
 Xiao, W.; El Moursi, M.S.; Khan, O.; Infield, D. Review of gridtied converter topologies used in photovoltaic systems. IET Renew. Power Gener. 2016, 10, 1543–1551. [Google Scholar] [CrossRef] [Green Version]
 Zhang, Y..; Sen, P.C. A new softswitching technique for buck, boost, and buck~boost converters. IEEE Trans. Ind. Appl. 2003, 39, 1775–1782. [Google Scholar] [CrossRef]
 Verbytskyi, I.; Bondarenko, O.; Liivik, E. Control features of multi celltype current regulator for resistance welding. In Proceedings of the 2017 IEEE 58th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Doha, Qatar, 10–12 April 2018. [Google Scholar] [CrossRef]
 Jyotheeswara Reddy, K.; Sudhakar, N. High Voltage Gain Interleaved Boost Converter With Neural Network Based MPPT Controller for Fuel Cell Based Electric Vehicle Applications. IEEE Access 2018, 6, 3899–3908. [Google Scholar] [CrossRef]
 Zeb, K.; Uddin, W.; Khan, M.A.; Ali, Z.; Ali, M.U.; Christofides, N.; Kim, H.J. A comprehensive review on inverter topologies and control strategies for grid connected photovoltaic system. Renew. Sustain. Energy Rev. 2018, 94, 1120–1141. [Google Scholar] [CrossRef]
 Keyhani, H.; Toliyat, H.A. SingleStage Multi string PV Inverter With an Isolated HighFrequency Link and SoftSwitching Operation. IEEE Trans. Power Electron. 2014, 29, 3919–3929. [Google Scholar] [CrossRef]
 Khodabandeh, M.; Afshari, E.; Amirabadi, M. A SingleStage SoftSwitching HighFrequency ACLink PV Inverter: Design, Analysis, and Evaluation of Sibased and SiCbased Prototypes. IEEE Trans. Power Electron. 2018, 34, 2312–2326. [Google Scholar] [CrossRef]
 Lopez, O.; Freijedo, F.D.; Yepes, A.G.; FernandezComesana, P.; Malvar, J.; Teodorescu, R.; DovalGandoy, J. Eliminating ground current in a transformerless photovoltaic application. IEEE Trans. Energy Convers. 2010, 25, 140–147. [Google Scholar] [CrossRef]
 Xiao, H.; Xie, S. Leakage current analytical model and application in singlephase transformerless photovoltaic gridconnected inverter. IEEE Trans. Electromagn Compat. 2010, 52, 902–913. [Google Scholar] [CrossRef]
 Zhang, L.; Sun, K.; Xing, Y.; Xing, M. H6 Transformerless FullBridge PV GridTied Inverters. IEEE Trans. Power Electron. 2014, 29, 1229–1238. [Google Scholar] [CrossRef]
 Ahmed, M.H.; Wang, M.; Hassan, M.A.S.; Ullah, I. Power Loss Model and Efficiency Analysis of Threephase Inverter Based on SiC MOSFETs for PV Applications. IEEE Access 2019, 7, 75768–75781. [Google Scholar] [CrossRef]
 Escobar, G.; MartinezRodriguez, P.R.; Pool, E.I.; PenaQuintal, A.E.; Vazquez, G.; Sosa, J.M. A modelbased controller of a threelevel stackedcell grid connected converter. In Proceedings of the IECON 201541st Annual Conference of the IEEE Industrial Electronics Society, Yokohama, Japan, 9–12 November 2015. [Google Scholar] [CrossRef]
 Mamadaminov, U.M. Advanced Inverters and Their Functionalities for Distributed Solar Generation; Energy Engineering III, Spring; Oregon Institute of Technology: Wilsonville, OR, USA, 2014. [Google Scholar]
 Hidalgo, R.; Abbey, C. Integrating distributed generation with Smart Grid enabling technologies. In Proceedings of the IEEE PES Conference on Innovative Smart Grid Technologies Latin America SGT LA, Medellin, Colombia, 19–21 October 2011. [Google Scholar] [CrossRef]
 Talha, M.; Amir, A.; Raihan, S.R.S.; Abd Rahim, N. Gridconnected photovoltaic inverters with lowvoltage ride through for a residentialscale system: A review. Int. Trans. Electr. Energy Syst. 2020, 31, e12630. [Google Scholar] [CrossRef]
 Taul, M.G.; Wang, X.; Davari, P.; Blaabjerg, F. An Overview of Assessment Methods for Synchronization Stability of GridConnected Converters Under Severe Symmetrical Grid Faults. IEEE Trans. Power Electron. 2019, 34, 9655–9670. [Google Scholar] [CrossRef] [Green Version]
 Geddada, N.; Karanki, S.B.; Mishra, M.K. Synchronous reference frame based current controller with SPWM switching strategy for DSTATCOM applications. In Proceedings of the 2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Bengaluru, India, 16–19 December 2012. [Google Scholar] [CrossRef]
 Chappa, H.; Thakur, T. Voltage instability detection using synchrophasor measurements: A review. Int. Trans. Electr. Energy Syst. 2020, 30, 12343. [Google Scholar] [CrossRef]
 Calleja, H.; Jimenez, H. Performance of a grid connected PV system used as active filter. Energy Convers. Manag. 2004, 45, 2417–2428. [Google Scholar] [CrossRef]
 Verbytskyi, Y.V. Double Fourier series using for calculating modulating signals spectrum. Tekhnichna Elektrodynamika 2014, 4, 96–98. [Google Scholar]
 Adewuyi, O.B.; Shigenobu, R.; Ooya, K.; Senjyu, T.; Howlader, A.M. Static voltage stability improvement with battery energy storage considering optimal control of active and reactive power injection. Electr. Power Syst. Res. 2019, 172, 303–312. [Google Scholar] [CrossRef]
 Pinnangudi, B.; Kuykendal, M.; Bhadra, S. Smart Grid Energy Storage. Power Grid 2017, 93–135. [Google Scholar] [CrossRef]
 Liu, S.; Xie, X.; Yang, L. Analysis, Modeling and Implementation of a Switching Bidirectional BuckBoost Converter Based on Electric Vehicle Hybrid Energy Storage for V2G System. IEEE Access 2020, 8, 65868–65879. [Google Scholar] [CrossRef]
 Pakkiraiah, B.; Sukumar, G.D. Research Survey on Various MPPT Performance Issues to Improve the Solar PV System Efficiency. J. Sol. Energy 2016, 2016, 8012432. [Google Scholar] [CrossRef] [Green Version]
 Yang, J.H.; Jeong, K.I.; Kwon, J.M. Energy storage system with PV generation and online UPS functions. In Proceedings of the 2014 IEEE 36th International Telecommunications Energy Conference (INTELEC), Vancouver, BC, Canada, 28 September–2 October 2014. [Google Scholar] [CrossRef]
 Li, K.; Zhao, J.; Ma, Q.; Xu, H. Hierarchy control of power quality for wind–battery energy storage system. IET Power Electron. 2014, 7, 2123–2132. [Google Scholar] [CrossRef]
 Li, X.; Wang, S. A review on energy management, operation control and application methods for grid battery energy storage systems. CSEE J. Power Energy Syst. 2019, 7, 1026–1040. [Google Scholar] [CrossRef]
 Hannan, M.A.; Hoque, M.M.; Hussain, A.; Yusof, Y.; Ker, P.J. StateoftheArt and Energy Management System of LithiumIon Batteries in Electric Vehicle Applications: Issues and Recommendations. IEEE Access 2018, 6, 19362–19378. [Google Scholar] [CrossRef]
 Ortúzar, M.; Dixon, J.; Moreno, J. UltracapacitorBased Auxiliary Energy System for an Electric Vehicle: Implementation and Evaluation. IEEE Trans. Ind. Electron. 2007, 54, 2147–2156. [Google Scholar] [CrossRef]
 Fernandez, G. A Bidirectional Buffered Charging Unit for EV’s (BBCU). In Proceedings of the International Power Electronics Conference (IPECNiigata 2018ECCE Asia), Niigata, Japan, 20–24 May 2018. [Google Scholar] [CrossRef]
 Schupbachj, R.M.; Bald, C. Comparing DCDC Converters for Power Management in Hybrid Electric Vehicles. In Proceedings of the IEEE International Electric Machines and Drives Conference, Madison, WI, USA, 1–4 June 2003; Volume 3, pp. 1369–1374. [Google Scholar] [CrossRef]
 Czogalla, J.; Li, J.; Sullivan, C.R. Automotive Application of MultiPhase CoupledInductor DCDC Converter. In Proceedings of the IEEE Industry Applications Conference, Salt Lake City, UT, USA, 12–16 October 2003; Volume 3, pp. 1524–1529. [Google Scholar] [CrossRef]
 Farhangi, B.; Toliyat, H.A. Modeling and Analyzing Multiport Isolation Transformer Capacitive Components for Onboard Vehicular Power Conditioners. IEEE Trans. Ind. Electron. 2015, 62, 3134–3142. [Google Scholar] [CrossRef]
 Inoue, S.; Akagi, H. A BiDirectional DC/DC Converter for an Energy Storage System. In Proceedings of the APEC 07TwentySecond Annual IEEE Applied Power Electronics Conference and Exposition, Anaheim, CA, USA, 25 February–1 March 2007. [Google Scholar] [CrossRef]
 Xu, X.; Khambadkone, A.M.; Oruganti, R. A SoftSwitched BacktoBack Bidirectional DC/DC Converter with an FPGA based Digital Control for Automotive applications. In Proceedings of the IECON 200733rd Annual Conference of the IEEE Industrial Electronics Society, Taipei, Taiwan, 5–8 November 2007. [Google Scholar] [CrossRef]
 Jang, S.J.; Lee, T.W.; Lee, W.C.; Won, C.Y. Bidirectional DC to DC Converters for Fuel Cell Generation System. Power Electron. Spec. Conf. 2004, 6, 4722–4728. [Google Scholar] [CrossRef]
 Lin, B.R.; Hung, T.L. Singlephase halfbridge converter topology for power quality compensation. Electr. Power Appl. IEE Proc. 2002, 149, 351–359. [Google Scholar] [CrossRef]
 Lin, B.R.; Hung, T.L.; Huang, C.H. Bidirectional singlephase halfbridge rectifier for power quality compensation. Electr. Power Appl. IEE Proc. 2003, 150, 397–406. [Google Scholar] [CrossRef]
 Korkh, O.; Blinov, A.; Vinnikov, D. Analysis of Oscillation Suppression Methods in the ACAC Stage of High Frequency Link Converters. In Proceedings of the IEEE 60th International Scientific Conference on Power and Electrical Engineering of Riga Technical University (RTUCON), Riga, Latvia, 7–9 October 2019. [Google Scholar] [CrossRef]
 Bilgin, B.; Emadi, A.; Krishnamurthy, M. Universal input battery charger circuit for PHEV applications with the simplified controller. In Proceedings of the Applied Power Electronics Conference and Exposition (APEC), Fort Worth, TX, USA, 6–11 March 2011; pp. 815–820. [Google Scholar] [CrossRef]
 Segaran, D.; Holmes, D.G.; McGrath, B.P. High performance bidirectional ACDC converters for PHEV with minimized DC bus capacitance. In Proceedings of the IECON 37th Annual Conference on IEEE Industrial Electronics Society, Melbourne, Australia, 7–10 November 2011; pp. 3620–3625. [Google Scholar] [CrossRef]
 Odamov, U.O.; Kamilov, M.M.; Niyazov, S.K.; Song, K. Research of the efficiency of the solar battery operations in real exploitation conditions. Sci. Rep. Bukhara State Univ. 2021, 5, 2–17. [Google Scholar] [CrossRef]
 Saidi, A.S.; Slimene, M.B.; Khlifi, M.A. Transient stability analysis of photovoltaic system with experimental shading effects. Eng. Technol. Appl. Sci. Res. 2018, 8, 3592–3597. [Google Scholar] [CrossRef]
 Araujo, S.V.; TorricoBascope, R.P.; TorricoBascope, G.V.; Menezes, L. Stepup converter with high voltage gain employing threestate switching cell and voltage multiplier. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 2271–2277. [Google Scholar] [CrossRef]
 Ahmad, J.; Pervez, I.; Sarwar, A.; Tariq, M.; Fahad, M.; Chakrabortty, R.K.; Ryan, M.J. Performance Analysis and HardwareintheLoop (HIL) Validation of Single Switch High Voltage Gain DCDC Converters for MPP Tracking in Solar PV System. IEEE Access 2021, 9, 48811–48830. [Google Scholar] [CrossRef]
 Arunkumari, T.; Indragandhi, V. An overview of high voltage conversion ratio DCDC converter configurations used in DC microgrid architectures. Renew. Sustain. Energy Rev. 2017, 77, 670–687. [Google Scholar] [CrossRef]
 Blinov, A.; Verbytskyi, I.; Zinchenko, D.; Vinnikov, D.; Galkin, I. Modular Battery Charger for Light Electric Vehicles. Energies 2020, 13, 774. [Google Scholar] [CrossRef] [Green Version]
 Norrga, S. Experimental Study of a SoftSwitched Isolated Bidirectional AC DC Converter Without Auxiliary Circuit. IEEE Trans. Power Electron. 2006, 21, 1580–1587. [Google Scholar] [CrossRef]
 Kummari, N.; Chakraborty, S.; Chattopadhyay, S. An Isolated HighFrequency Link Microinverter Operated with SecondarySide Modulation for Efficiency Improvement. IEEE Trans. Power Electron. 2018, 33, 2187–2200. [Google Scholar] [CrossRef]
 Nayak, P.; Rajashekara, K.; Pramanick, S. SoftSwitched Modulation Technique for a SingleStage MatrixType Isolated DC–AC Converter. IEEE Trans. Ind. Appl. 2019, 55, 7642–7656. [Google Scholar] [CrossRef]
 Tibola, G.; Lemmen, E.; Duarte, J.L.; Barbi, I. Passive Regenerative and Dissipative Snubber Cells for Isolated SEPIC Converters: Analysis, Design, and Comparison. IEEE Trans. Power Electron. 2017, 32, 9210–9222. [Google Scholar] [CrossRef] [Green Version]
 Blinov, A.; Verbytskyi, I.; Peftitsis, D.; Vinnikov, D. Regenerative Passive Snubber Circuit for HighFrequency Link Converters. IEEE J. Emerg. Sel. Top. Ind. Electron. 2021, 3, 252–257. [Google Scholar] [CrossRef]
 Blinov, A.; Kosenko, R.; Chub, A.; Vinnikov, D. Snubberless boost fullbridge converters: Analysis of softswitching performance and limitations. Int. J. Circ. Theor. Appl. 2019, 47, 884–908. [Google Scholar] [CrossRef]
 Luo, F.L.; Ye, H. Positive output superlift converters. IEEE Trans. Power Electron. 2003, 18, 105–113. [Google Scholar] [CrossRef]
 Zhang, S.; Xu, J.; Yang, P. A singleswitch high gain quadratic boost converter based on voltagelift technique. In Proceedings of the 10th International Power & Energy Conference (IPEC), Ho Chi Minh City, Vietnam, 12–14 December 2012; pp. 71–75. [Google Scholar] [CrossRef]
 Axelrod, B.; Berkovich, Y.; Shenkman, A.; Golan, G. Diodecapacitor voltage multipliers combined with boostconverters: Topologies and characteristics. IET Power Electron. 2012, 5, 873–884. [Google Scholar] [CrossRef]
 Wu, G.; Ruan, X.; Ye, Z. Nonisolated High StepUp DCDC Converters Adopting SwitchedCapacitor Cell. IEEE Trans. Ind. Electron. 2015, 62, 383–393. [Google Scholar] [CrossRef]
 Tofoli, F.L.; de Souza Oliveira, D.; TorricoBascopé, R.P.; Alcazar, Y.J.A. Novel Nonisolated HighVoltage Gain DC–DC Converters Based on 3SSC and VMC. IEEE Trans. Power Electron. 2012, 27, 3897–3907. [Google Scholar] [CrossRef]
 Zhang, J.; Huang, L.; Shu, J.; Wang, H.; Ding, J. Energy Management of PVdieselbattery Hybrid Power System for Island Standalone Microgrid. Energy Procedia 2017, 105, 2201–2206. [Google Scholar] [CrossRef]
 Cano, A.; Jurado, F.; Sánchez, H.; Fernández, L.M.; Castañeda, M. Optimal sizing of standalone hybrid systems based on PV/WT/FC by using several methodologies. J. Energy Inst. 2014, 87, 330–340. [Google Scholar] [CrossRef]
 Ghaffari, A.; Askarzadeh, A. Design optimization of a hybrid system subject to reliability level and renewable energy penetration. Energy 2020, 193, 116754. [Google Scholar] [CrossRef]
 Noshahr, J.B.; Mohamadi, B.; Kermani, M.; Kermani, M. Operational Planning of Inverter Control in a gridconnected Microgrid with hybrid PV and BESS. In Proceedings of the 2020 IEEE International Conference on Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe (EEEIC/I & CPS Europe), Madrid, Spain, 9–12 June 2020. [Google Scholar] [CrossRef]
 Vahid, S.; ELRefaie, A. A Novel Topology for an Extendable Isolated DCDC Multiport Power Converter with a Multipurpose Hybrid Energy Storage System. In Proceedings of the 2020 IEEE Energy Conversion Congress and Exposition (ECCE), Detroit, MI, USA, 11–15 October 2020. [Google Scholar] [CrossRef]
 Pereira, T.; Hoffmann, F.; Zhu, R.; Liserre, M. A Comprehensive Assessment of Multiwinding TransformerBased DCDC Converters. IEEE Trans. Power Electron. 2021, 36, 10020–10036. [Google Scholar] [CrossRef]
 Wu, H.; Xing, Y.; Xia, Y.; Sun, K. A family of nonisolated threeport converters for standalone renewable power systems. In Proceedings of the IECON 201137th Annual Conference of the IEEE Industrial Electronics Society, Melbourne, Australia, 7–10 November 2011. [Google Scholar] [CrossRef]
 Zhang, M.; Xing, Y.; Wu, H.; Lu, Y.; Sun, K. Performance evaluation of a nonisolated bidirectional threeport power converter for energy storage applications. In Proceedings of the 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMCECCE Asia), Hefei, China, 22–26 May 2016; pp. 2703–2708. [Google Scholar] [CrossRef]
 Sato, Y.; Uno, M.; Nagata, H. Nonisolated Multiport Converters Based on Integration of PWM Converter and PhaseShift SwitchedCapacitor Converter. IEEE Trans. Power Electron. 2019, 35, 455–470. [Google Scholar] [CrossRef]
 Faraji, R.; Farzanehfard, H. Fully Soft Switched MultiPort DCDC Converter with High Integration. IEEE Trans. Power Electron. 2020, 36, 1901–1908. [Google Scholar] [CrossRef]
 Kwasinski, A. Identification of Feasible Topologies for MultipleInput DCDC Converters. IEEE Trans. Power Electron. 2009, 24, 856–861. [Google Scholar] [CrossRef]
 Balaji, C.; Chellammal, N.; Sanjeevikumar, P.; Bhaskar, M.S.; HolmNielsen, J.B.; Leonowicz, Z.; Masebinu, S.O. NonIsolated HighGain Triple Port DCDC BuckBoost Converter with Positive Output Voltage for Photovoltaic Application. IEEE Access 2020, 2020, 3003192. [Google Scholar] [CrossRef]
 Thang, T.V.; Ahmed, A.; Kim, C.I.; Park, J.H. The flexible system architecture of standalone PV power generation with the energy storage device. IEEE Trans. Energy Convers. 2015, 30, 1386–1396. [Google Scholar] [CrossRef]
 Amirabadi, M.; Toliyat, H.A.; Alexander, W.C. A multiport ac link PV inverter with reduced size and weight for a standalone application. IEEE Trans. Ind. Appl. 2013, 49, 2217–2228. [Google Scholar] [CrossRef]
 Hassan, S.Z.; Mumtaz, S.; Kamal, T.; Khan, L. Performance of gridintegrated photovoltaic/fuel cell/ electrolyzer/battery hybrid power system. In Proceedings of the 2015 Power Generation Systems and Renewable Energy Technologies, PGSRET, Islamabad, Pakistan, 10–11 June 2015. [Google Scholar] [CrossRef]
 Jayasinghe, S.D.; Vilathgamuwa, D.M.; Madawala, U.K. Diodeclamped threelevel inverterbased battery/supercapacitor direct integration scheme for renewable energy systems. IEEE Trans. Power Electron. 2011, 26, 3720–3729. [Google Scholar] [CrossRef]
 Rangu, S.K.; Lolla, P.R.; Dhenuvakonda, K.R.; Singh, A.R. Recent trends in power management strategies for optimal operation of distributed energy resources in microgrids: A comprehensive review. Int. J. Energy Res. 2020, 44, 9889–9911. [Google Scholar] [CrossRef]
 David, F. Probability and Statistics for Computer Science; Springer International Publishing: Berlin/Heidelberg, Germany, 2018; p. 367. [Google Scholar] [CrossRef]
PV Application  Modifications 

1. Standalone PV applications [15,16] 

2. Ongrid PV applications [17,18]  
3. Hybrid PV applications [19,20] 
Power Loss Type  Converter Type  

HardSwitching  SoftSwitching  Resonant  
Transistor static power loss, P_{Tst}*  $\frac{D}{3}{k}_{Tst(k)}{}^{2}{\left(\frac{{U}_{k\mathrm{max}}}{{U}_{\mathrm{max}}}\right)}^{2}$  $\frac{D}{3}{k}_{Tst(k)}{}^{2}{\left(\frac{{U}_{k\mathrm{max}}}{{U}_{\mathrm{max}}}\right)}^{2}$  $\frac{{\pi}^{2}D}{8}{k}_{Tst(k)}{}^{2}{\left(\frac{{U}_{k\mathrm{max}}}{{U}_{\mathrm{max}}}\right)}^{2}$ 
Transistor dynamic power loss, P_{Td}*  $\frac{0.5{U}_{Tk}{I}_{Tk}}{{U}_{\mathrm{max}}{I}_{DC}}$  0  0 
Diode static power loss, P_{Dst}*  $\frac{0.8{k}_{Dst(k)}{U}_{k\mathrm{max}}(1D)}{{U}_{\mathrm{max}}}$  $\frac{0.8{k}_{Dst(k)}{U}_{k\mathrm{max}}(1D)}{{U}_{\mathrm{max}}}$  $\frac{0.8{k}_{Dst(k)}\pi {U}_{k\mathrm{max}}(1D)}{2\sqrt{2}{U}_{\mathrm{max}}}$ 
Diode dynamic power loss, P_{Dd}*  $\frac{0.5{U}_{Dk}{I}_{Dk}}{{U}_{\mathrm{max}}{I}_{DC}}$  0  0 
Converter Topology  k_{C}  P_{con} * 

DC–DC converters  
Buck [12], Figure 9a  $\frac{{I}_{peak}}{D{I}_{Tav}}$  $\frac{4}{3D}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8(1D)}{D}+\frac{{I}_{peak}}{D{I}_{Tav}}$ 
Boost [12], Figure 9b  $\frac{{I}_{peak}}{D(1D){I}_{Tav}}$  $\frac{4D}{3{\left(1D\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{(1D){I}_{Tav}}$ 
Buckboost, SEPIC, Cuk’ [12], Figure 9c–e  $\frac{{I}_{peak}}{D(1D){I}_{Tav}}$  $\frac{4}{3D{\left(1D\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{D}+\frac{{I}_{peak}}{(1D)D{I}_{Tav}}$ 
Softswitching buck [47], Figure 9f  $\frac{2{I}_{peak}}{D{I}_{Tav}}$  $\frac{4}{3D}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8(1D)}{D}$ 
Softswitching boost [47], Figure 9g  $\frac{2{I}_{peak}}{(1D){I}_{Tav}}$  $\frac{4D}{3{\left(1D\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8$ 
Interleaved buck [48], Figure 9h, m cells  $\frac{{I}_{peak}}{D{I}_{Tav}}$  $\frac{4}{3Dm}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8(1D)}{D}+\frac{{I}_{peak}}{Dm{I}_{Tav}}$ 
Interleaved boost [49], Figure 9i, m cells  $\frac{{I}_{peak}}{(1D){I}_{Tav}}$  $\frac{4D}{3{\left(1D\right)}^{2}m}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{(1D)m{I}_{Tav}}$ 
DC–AC converters  
Halfbridge [50],Figure 9j  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\frac{4{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{1.6}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{2{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
Fullbridge [50], Figure 9k  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{3{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
Triplebridge [50], Figure 9l  $\frac{12{I}_{peak(m)}}{\sqrt{3}{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\frac{2\pi}{9{D}_{\mathrm{max}}}\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
H5 [55], Figure 9m  $\frac{10{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{3{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{1.5{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
H6 [55], Figure 9n  $\frac{12{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{1.5{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
HERIC [55],Figure 9o  $\frac{12{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{3{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{1.5{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
3LNPC [56], Figure 9p  $\frac{8{I}_{peak(m)}}{{D}_{1}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{3{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
3LSC [57], Figure 9q  $\frac{10{I}_{peak(m)}}{{D}_{1}{I}_{Tav(m)}}$  $\left(\frac{\pi}{2{D}_{\mathrm{max}}}+\frac{5{\pi}^{2}}{12{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
k_{C}  P_{con} *  

Singlestage application with a fullbridge converter  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{3{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}}{I}_{Tav(m)}}$ 
Twostage application with buck and fullbridge converters  $\frac{{I}_{peak(m)}}{{I}_{Tav(m)}}\left(8+\frac{1}{D}\right)$  $\begin{array}{c}\left(\frac{2\pi}{3}+\frac{{\pi}^{2}}{3}+\frac{4}{3D}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+0.8\left(\frac{\pi}{2}+1\right)+\\ \frac{{I}_{peak(m)}}{{I}_{Tav(m)}}\left(1+\frac{1}{D}\right)+\frac{0.8(1D)}{D}\end{array}$ 
Opportunities for Power Grid Control  Converter Function  Control Strategy 

Reactive power control [58]  Independent reactive and active power generation  Sinusoidal pulse width modulation (SPWM), space vector modulation (SVM) or hysteresis modulation in dq or αβ space 
Voltage stabilization [60,61,62,63,64,65]  Voltage and frequency ride through, voltage sag detection, reactive power generation  For frequency synchronization: zerocrossing method and the phaselockedloop. For sag detection: RMS value estimator, synchronous rotating reference frame, wavelet, and Fourier transform. For power generation: SPWM, SVM or hysteresis modulation in dq or αβ space 
Grid power quality control [62]  Controlled injected current  SPWM or hysteresis modulation, frequency synchronization 
Converter Topology  k_{C}  P_{con} * 

DC–DC converters  
Halfbridge [74], Figure 14a  $\frac{4{I}_{peak}}{{D}_{1}{I}_{Tav}}$  $\frac{4}{3{D}_{1}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{1}}+\frac{{I}_{peak}}{{D}_{1}{I}_{Tav}}$ 
3LNPC [75], Figure 9q  $\frac{4{I}_{peak}}{{D}_{1}{I}_{Tav}}$  $\left(\frac{4}{3{D}_{1}}+\frac{4}{3{D}_{1}^{2}}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8(1{D}_{1})}{{D}_{1}}+\frac{{I}_{peak}}{{D}_{1}{I}_{Tav}}$ 
Cuk’ [76], Figure 14b, SEPIC/Luo [76], Figure 14c  $\frac{2{I}_{peak}}{{D}_{1}(1{D}_{1}){I}_{Tav}}$  $\frac{4}{3{D}_{1}{\left(1{D}_{1}\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.4}{{D}_{1}\left(1{D}_{1}\right)}+\frac{{I}_{peak}}{{D}_{1}(1{D}_{1}){I}_{Tav}}$ 
Interleaved halfbridge [77], Figure 14d  $\frac{2{I}_{peak}}{{D}_{1}{I}_{Tav}}$  $\frac{2}{3m{D}_{1}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{1}}+\frac{{I}_{peak}}{{D}_{1}m{I}_{Tav}}$ 
If U_{BT} > U_{g} → Cascaded halfbridge [78], Figure 14e If U_{BT} < U_{g} →  $\frac{2{I}_{peak}(1+{D}_{1})}{{D}_{1}{I}_{Tav}}$$\frac{2{I}_{peak}(2{D}_{1})}{(1{D}_{1}){I}_{Tav}}$  $\frac{4}{3{D}_{1}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{1}}+\frac{{I}_{peak}}{{D}_{1}(1{D}_{1}){I}_{Tav}}$$\frac{4}{3{(1{D}_{1})}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{1{D}_{1}}+\frac{{I}_{peak}}{{D}_{1}(1{D}_{1}){I}_{Tav}}$ 
DC–AC converters  
Halfbridge, Figure 9j  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$  $\frac{4{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{1.6}{{D}_{\mathrm{max}1}}\left(\frac{\pi}{2}+1\right)+\frac{2{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$ 
Fullbridge, Figure 9k  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$  $\begin{array}{c}\left(\frac{2\pi}{3{D}_{\mathrm{max}1}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\\ \frac{0.8}{{D}_{\mathrm{max}1}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}\end{array}$ 
Halfbridge rectifier with neutral point switch clamped scheme [82], Figure 14f  $\frac{5{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$  $\frac{4{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{3.2}{{D}_{\mathrm{max}1}}\left(\frac{\pi}{2}+1\right)+\frac{2{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$ 
Capacitor clamped threelevel PWM converter [83], Figure 14g  $\frac{8{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$  $\frac{8{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.5{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$ 
Highfrequency link inverter [84], Figure 14h  $\frac{24{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}$  $\left(\frac{2\pi}{{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak(m)}+{I}_{\mathrm{min}(m)})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{3.2}{\pi}$ 
Converter Topology  k_{C}  P_{con} * 

DC–DC converters  
Dual active bridge, Figure 15a  $\frac{8{I}_{peak}}{{D}_{1}{I}_{Tav}}$  $\frac{4}{3{D}_{1}^{2}}\left(1+{D}_{1}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{1}}+0.8+\frac{3{I}_{peak}}{{D}_{1}{I}_{Tav}}$ 
Dual active bridge softswitching [79], Figure 15b  $\frac{8{I}_{peak}}{{D}_{1}{I}_{Tav}}$  $\frac{4}{3{D}_{1}^{2}}\left(1+{D}_{1}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{1}}+0.8$ 
Converter with two voltagefed halfbridges [80], Figure 15c  $\frac{8{I}_{peak}}{{D}_{1}{I}_{Tav}}$  8 
Combinedvoltage halfbridge and currentfed fullbridge [81], Figure 15d  $\frac{11{I}_{peak}}{(1{D}_{1}){I}_{Tav}}$  $\left(\frac{5+4{D}_{1}}{3{(1{D}_{1})}^{2}}+\frac{8(1{D}_{1})}{3{D}_{1}{}^{2}}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{1{D}_{1}}$ 
DC–AC converters  
Halfbridge and fullbridge [85], Figure 15e  $\begin{array}{c}\frac{{I}_{peak(m)}}{{I}_{Tav(m)}}(\frac{8}{{D}_{\mathrm{max}1}}+\\ \frac{2}{(1{D}_{3})})\end{array}$  $\begin{array}{c}\left(\frac{2\pi}{3{D}_{\mathrm{max}1}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}+\frac{4{D}_{3}}{3{\left(1{D}_{3}\right)}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8}{{D}_{\mathrm{max}1}}\left(\frac{\pi}{2}+1\right)+0.8+\frac{{I}_{peak(m)}}{{I}_{Tav(m)}}\left(\frac{1}{{D}_{\mathrm{max}1}}+\frac{1}{(1{D}_{3})}\right)\end{array}$ 
Fullbridge DC–AC and dual active bridge DC–DC [86], Figure 15f  $\begin{array}{c}\frac{8{I}_{peak(m)}}{{I}_{Tav(m)}}\times \\ \left(\frac{1}{{D}_{\mathrm{max}1}}+\frac{1}{{D}_{3}}\right)\end{array}$  $\begin{array}{c}\left(\frac{2\pi}{3{D}_{\mathrm{max}1}}+\frac{{\pi}^{2}}{3{D}_{\mathrm{max}1}^{2}}+\frac{4}{3{D}_{3}}+\frac{4}{3{D}_{3}{}^{2}}\right)\left(1\frac{{I}_{peak(m)}{I}_{\mathrm{min}(m)}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8}{{D}_{\mathrm{max}1}}\left(\frac{\pi}{2}+1\right)+0.8+\frac{0.8}{{D}_{3}}+\frac{{I}_{peak(m)}}{{D}_{\mathrm{max}1}{I}_{Tav(m)}}\end{array}$ 
Converter Topology  G  k_{C}  P_{con}* 

Isolated fullbridge, Figure 18a  nD  $\frac{8{I}_{peak}}{D{I}_{Tav}}$  $\frac{32}{3D}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{1.6}{D}+\frac{2{I}_{peak}}{D{I}_{Tav}}$ 
Conventional boost converter, Figure 9b  $\frac{1}{1D}$  $\frac{{I}_{peak}}{(1D){I}_{Tav}}$  $\frac{4D}{3{\left(1D\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{(1D){I}_{Tav}}$ 
Cascaded boost converter [90], Figure 18b  $\frac{1}{{(1D)}^{2}}$  $\frac{{I}_{peak}}{{(1D)}^{2}{I}_{Tav}}$  $\begin{array}{c}\frac{4D}{3{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8{D}^{2}}{{(1D)}^{2}}+0.8+\\ \frac{0.8}{1D}+\frac{2{I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
SEPIC [92], Figure 9d, Flyback [92], Figure 18c  $\frac{nD}{1D}$  $\frac{1.5{I}_{peak}}{(1D)D{I}_{Tav}}$  $\frac{3}{D{\left(1D\right)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{D}+\frac{{I}_{peak}}{(1D)D{I}_{Tav}}$ 
LC parallel current source converter with voltage doubler [98], Figure 18d  $\frac{2n}{1D}$  $\frac{1.1{I}_{peak}}{(1D){I}_{Tav}}$  $\left(\frac{2.42D}{3{(1D)}^{4}}+\frac{8}{3(1D)}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{(1D){I}_{Tav}}$ 
Super lift voltage converter [99], m cells, Figure 18e  ${\left(\frac{2D}{1D}\right)}^{m}$  $\begin{array}{c}({\left(\frac{2D}{1D}\right)}^{m}\\ \begin{array}{c}\\ \end{array}1)\frac{{I}_{peak}}{{I}_{Tav}}\end{array}$  $\begin{array}{c}\frac{4D}{3{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{(1.6(m1)+0.8)D}{(1D)}+\\ 0.8m+\frac{1.5m{I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
Modified voltage lift converter [100], m cells, Figure 18f  ${\left(\frac{2}{1D}\right)}^{m}$  $\begin{array}{c}({\left(\frac{2}{1D}\right)}^{m}\\ \begin{array}{c}\\ \end{array}1)\frac{{I}_{peak}}{{I}_{Tav}}\end{array}$  $\begin{array}{c}\frac{4D}{3{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{(1.6(m1)+0.8)D}{(1D)}+\\ 1.6m+\frac{2m{I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
Cockcroft–Walton and Dickson multiplier based boost converter [101], m cells, Figure 18g,h  $\frac{m+D}{1D}$  $\frac{{I}_{peak}}{(1D){I}_{Tav}}$  $\begin{array}{l}\frac{4D}{3{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8mD}{(1D)}+0.8(m+1)+\frac{(m+0.5){I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
Boost derived MIESC SCcell converter [102], m cells, Figure 18i  ${\left(\frac{2}{1D}\right)}^{m}$  $\frac{{I}_{peak}}{(1D){I}_{Tav}}$  $\begin{array}{c}\frac{4D}{3{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8D}{(1D)}+0.8(m+2)+\frac{0.5(m+4){I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
Buckboost derived MIESC SCcell converter [102], m cells, Figure 18j  ${\left(\frac{1+D}{1D}\right)}^{m}$  $\frac{{I}_{peak}}{D(1D){I}_{Tav}}$  $\begin{array}{c}\frac{4}{3D{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8}{1D}+\frac{0.8(m+2)}{D}+\frac{0.5(m+4){I}_{peak}}{(1D)D{I}_{Tav}}\end{array}$ 
Boost 3SSC cell converter [103], m cells, Figure 18k  $\frac{m+1}{1D}$  $\frac{2{I}_{peak}}{(1D){I}_{Tav}}$  $\begin{array}{c}\left(\frac{2D}{3{(1D)}^{2}}+\frac{4}{3(1D)}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ 1.6+\frac{(m+0.5){I}_{peak}}{(1D){I}_{Tav}}\end{array}$ 
Converter Topology  k_{C}  P_{con} * 

Boost threeport converter [110], Figure 20a  $\frac{3}{1D}\frac{{I}_{peak}}{{I}_{Tav}}$  $\frac{16D}{9{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{(1D){I}_{Tav}}$ 
Buck threeport converter [110], Figure 20b  $\left(\frac{2}{D}+1\right)\frac{{I}_{peak}}{{I}_{Tav}}$  $\frac{4}{3D}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)\left(1+\frac{1}{3D}\right)+\frac{0.8(1.33D)}{D}+\frac{{I}_{peak}}{D{I}_{Tav}}$ 
Buckboost threeport converter [110], Figure 20c  $\frac{2}{D(1D)}\frac{{I}_{peak}}{{I}_{Tav}}$  $\begin{array}{c}\frac{4}{3}\left(\frac{1}{D{(1D)}^{2}}+\frac{1}{3(1D)}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8}{D}\frac{0.8}{3}+\frac{{I}_{peak}}{3{I}_{Tav}}\left(\frac{2}{D(1D)}+\frac{1}{D}\right)\end{array}$ 
Bidirectional buckboost converter [111], Figure 20d  $\frac{8{I}_{peak}}{D{I}_{Tav}}$  $\frac{4D}{{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8\cdot (1D)}{3D}+\frac{3.2}{3}+\frac{0.5{I}_{peak}}{3D{I}_{Tav}}$ 
Switched capacitor multiport converter [112], Figure 20e  $\frac{2{I}_{peak}}{D{I}_{Tav}}$  $\frac{1}{3D}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{5\cdot 0.8(1D)}{3D}$ 
Dual active bridge multiport converter [112], Figure 20f  $\frac{4{I}_{peak}}{D{I}_{Tav}}$  $\begin{array}{c}\left(\frac{4}{9D}+\frac{8D}{9{(1D)}^{2}}\left(1+\frac{1}{2D}\right)\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ \frac{0.8}{3D}+\frac{1.6}{3}+\frac{0.8D}{3(1D)}+\frac{{I}_{peak}}{3D{I}_{Tav}}\end{array}$ 
Doublestage with battery boost converter [116], Figure 20g  $\frac{{I}_{peak}}{{I}_{Tav}}\left(\frac{3}{1D}+8\right)$  $\begin{array}{c}\left(\frac{4D}{3{(1D)}^{2}}+\frac{\pi}{3}+\frac{{\pi}^{2}}{6}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ 0.8+0.4\left(\frac{\pi}{2}+1\right)+\frac{0.5{I}_{peak}}{{I}_{Tav}(1D)}+\frac{0.5{I}_{peak}}{{I}_{Tav}}\end{array}$ 
Fully softswitched multiport DCDC converter [113], Figure 20h  $\frac{5{I}_{peak}}{D{I}_{Tav}}$  $\frac{4}{9}\left(\frac{1}{{D}^{2}}+\frac{D+1}{{(1D)}^{2}}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8(1D)}{3D}$ 
Multipleinput SEPIC converter, m cells [114], Figure 20i  $\frac{{I}_{peak}}{D(1D){I}_{Tav}}$  $\frac{4}{3Dm{(1D)}^{2}}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{D}+\frac{0.8}{1D}+\frac{1.5{I}_{peak}}{{I}_{Tav}mD(1D)}$ 
NPC multiport converter [110], Figure 20j  $\frac{8{I}_{peak}}{{D}_{\mathrm{max}}{I}_{Tav}}$  $\left(\frac{2\pi}{9{D}_{\mathrm{max}}}+\frac{{\pi}^{2}}{9{D}_{\mathrm{max}}^{2}}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{0.8}{{D}_{\mathrm{max}}}\left(\frac{\pi}{2}+1\right)+\frac{{I}_{peak}}{{D}_{\mathrm{max}}{I}_{Tav}}$ 
Converter Topology  k_{C}  P_{con}_{(av)} * 

Buck  $\frac{{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\frac{1}{{G}_{\mathrm{max}}{}^{{}^{\ast}}1}\left(\frac{{G}_{\mathrm{max}}{}^{{}^{\ast}2}1}{2}\left(\frac{4}{3}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{{I}_{Tav}}\right)0.8({G}_{\mathrm{max}}{}^{\ast}1)\right)$ 
Boost  $\frac{{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\begin{array}{c}\frac{1}{{G}_{\mathrm{max}}{}^{\ast}1}(\left(\frac{4({G}_{\mathrm{max}}{}^{{}^{\ast}3}1)}{9}\frac{2({G}_{\mathrm{max}}{}^{{}^{\ast}2}1)}{3}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ +0.8({G}_{\mathrm{max}}{}^{\ast}1)+\frac{({G}_{\mathrm{max}}{}^{{}^{\ast}2}1){I}_{peak}}{2{I}_{Tav}})\end{array}$ 
Buckboost, SEPIC, Cuk’  $\frac{{\left(1+\sqrt{{G}_{\mathrm{max}}{}^{\ast}}\right)}^{2}{I}_{peak}}{\sqrt{{G}_{\mathrm{max}}{}^{\ast}}{I}_{Tav}}$  $\begin{array}{c}\frac{1}{{G}_{\mathrm{max}}{}^{\ast}1}(\left(\frac{4}{3}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{{I}_{peak}}{{I}_{Tav}}\right)\times \\ \left(\frac{2}{3}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{3/4}+3{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}+6{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/4}+\frac{1}{2}\mathrm{ln}\left({G}_{\mathrm{max}}{}^{\ast}\right)\frac{29}{3}\right)+\\ +0.8\left({\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}1\right)+0.53\left({\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{3/4}1\right)+\\ 1.6\left({\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/4}\right)+\\ 0.8\left({G}_{\mathrm{max}}{}^{\ast}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}\right)+\left(\frac{4}{3}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\frac{{I}_{peak}}{{I}_{Tav}}\right)\times \\ (2\left({\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{3/2}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{3/4}\right)+\frac{1}{2}\left({G}_{\mathrm{max}}{{}^{\ast}}^{2}{G}_{\mathrm{max}}{}^{\ast}\right)\\ +2\left({\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/4}\right)+3\left({G}_{\mathrm{max}}{}^{\ast}{\left({G}_{\mathrm{max}}{}^{\ast}\right)}^{1/2}\right))\end{array}$ 
Softswitching buck  $\frac{2{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\frac{1}{{G}_{\mathrm{max}}{}^{\ast}1}\left(\frac{{G}_{\mathrm{max}}{}^{{}^{\ast}2}1}{2}\left(\frac{4}{3}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8\right)0.8({G}_{\mathrm{max}}{}^{{}^{\ast}}1)\right)$ 
Softswitching boost  $\frac{2{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\begin{array}{c}\frac{1}{{G}_{\mathrm{max}}{}^{{}^{\ast}}1}(\left(\frac{4({G}_{\mathrm{max}}{}^{{}^{\ast}3}1)}{9}\frac{2({G}_{\mathrm{max}}{}^{{}^{\ast}2}1)}{3}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ +0.8({G}_{\mathrm{max}}{}^{{}^{\ast}}1))\end{array}$ 
Interleaved buck  $\frac{{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\begin{array}{c}\frac{1}{{G}_{\mathrm{max}}{}^{{}^{\ast}}1}\times \\ \left(\frac{{G}_{\mathrm{max}}{}^{{}^{\ast}2}1}{2}\left(\frac{4}{3m}\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+0.8+\frac{{I}_{peak}}{m{I}_{Tav}}\right)0.8({G}_{\mathrm{max}}{}^{{}^{\ast}}1)\right)\end{array}$ 
Interleaved boost  $\frac{{G}_{\mathrm{max}}{}^{\ast}{I}_{peak}}{{I}_{Tav}}$  $\begin{array}{c}\frac{1}{{G}_{\mathrm{max}}{}^{{}^{\ast}}1}(\frac{1}{m}\left(\frac{4({G}_{\mathrm{max}}{}^{{}^{\ast}3}1)}{9}\frac{2({G}_{\mathrm{max}}{}^{{}^{\ast}2}1)}{3}\right)\left(1\frac{{I}_{peak}{I}_{\mathrm{min}}}{{({I}_{peak}+{I}_{\mathrm{min}})}^{2}}\right)+\\ +0.8({G}_{\mathrm{max}}{}^{{}^{\ast}}1)+\frac{({G}_{\mathrm{max}}{}^{{}^{\ast}2}1){I}_{peak}}{2m{I}_{Tav}})\end{array}$ 
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Verbytskyi, I.; Lukianov, M.; Nassereddine, K.; Pakhaliuk, B.; Husev, O.; Strzelecki, R.M. Power Converter Solutions for Industrial PV Applications—A Review. Energies 2022, 15, 3295. https://doi.org/10.3390/en15093295
Verbytskyi I, Lukianov M, Nassereddine K, Pakhaliuk B, Husev O, Strzelecki RM. Power Converter Solutions for Industrial PV Applications—A Review. Energies. 2022; 15(9):3295. https://doi.org/10.3390/en15093295
Chicago/Turabian StyleVerbytskyi, Ievgen, Mykola Lukianov, Kawsar Nassereddine, Bohdan Pakhaliuk, Oleksandr Husev, and Ryszard Michał Strzelecki. 2022. "Power Converter Solutions for Industrial PV Applications—A Review" Energies 15, no. 9: 3295. https://doi.org/10.3390/en15093295