Abstract
Among several types of fuel cells available in the market, proton exchange membrane fuel cell (PEMFC) is characterized by low operating temperature, high efficiency and long lifetime. These advantages have prompted the PEM fuel cell to enter into several applications such as vehicle power sources, portable power and backup power applications. However, the PEM fuel cell faces several challenges due to the dependency of the output power on the operating condition like cell temperature and membrane water content. Under changing operating conditions, there is only one unique operating point for the fuel cell system with maximum output. Therefore, for better operation and optimal exploitation, the extraction of maximum power from PEM fuel cell is indispensable. This paper deals with the development golden section search (GSS)-based maximum power point tracking (MPPT) controller for PEMFC power system. To our knowledge, this paper is a first, if modest, attempt to develop a fuel cell MPPT controller based on golden section algorithm. The proposed GSS-based MPPT has been implemented and validated on fuel cell power system composed of 7 kW PEMFC supplying a resistive load via a DC/DC boost converter controlled using the proposed MPPT. Simulation results obtained using MATLAB/Simulink show that the proposed GSS MPPT outperforms the variable step size incremental conductance one in all test cases including cell temperature and membrane water content variations in terms of static as well as dynamic performances regarding all used metrics reducing by the way the response time by 34.33%, the overshoot and ripple by around 100% and with neglect oscillation around MPP improving as a consequence the fuel cell efficiency.
Similar content being viewed by others
Abbreviations
- ANN:
-
Artificial neural networks
- DC:
-
Direct current
- ESC:
-
Extremum seeking control
- ES:
-
Eagle strategy
- FO-HPF:
-
Fractional-order high-pass filter
- FOINC:
-
Fractional-order incremental conductance
- FC:
-
Fuel cell
- FLC:
-
Fuzzy logic controller
- IPSO:
-
Improved particle swarm optimization
- IC:
-
Incremental conductance
- IO-I:
-
Integer order integrator
- LPF:
-
Low-pass filter
- MFC:
-
Microbial fuel cell
- MPP:
-
Maximum power point
- MPPT:
-
Maximum power point tracking
- PSO:
-
Particle swarm optimization
- PSOTVAC:
-
Particle swarm optimization with time-varying acceleration coefficients
- P&O:
-
Perturbation and observation
- PID:
-
Proportional integral derivative
- PEM:
-
Proton exchange membrane
- QPSO:
-
Quantum particle swarm optimization
- RBFN:
-
Radial basis function network
- SMC:
-
Sliding mode control
- STA:
-
Supertwisting algorithm
- VEPSO:
-
Vector evaluated particle swarm optimization
- VOA:
-
Voltage overshoot avoidance
- μ act :
-
Activation voltage
- C :
-
Capacitance
- \(C_{{{\text{O}}_{2} }}\) :
-
Concentration of dissolved oxygen
- μ con :
-
Concentration voltage
- I :
-
Current
- α :
-
Duty cycle
- F :
-
Faraday’s constant
- I FC :
-
Fuel cell current
- υ FC :
-
Fuel cell voltage
- \(P_{{{\text{H}}_{2} }}\) :
-
Hydrogen pressure
- L :
-
Inductance
- ΔI L :
-
Inductor current ripple
- I max :
-
Maximum current density
- δ :
-
Membrane active area
- R M :
-
Membrane resistance
- φ :
-
Membrane water content
- E nernst :
-
Nernst voltage
- \(\kappa\) :
-
Number of electrons
- μ ohm :
-
Ohmic voltage
- Δυ 0 :
-
Output voltage ripple
- \(P_{{{\text{O}}_{2} }}\) :
-
Oxygen pressure
- λ i=1–4 :
-
Parametric coefficients
- P :
-
Power
- R c :
-
Contact resistance
- f s :
-
Switching frequency
- T :
-
Temperature
- \(\ell\) :
-
Thickness of membrane
- R :
-
Universal gas constant
- dI :
-
Current variation
- dP :
-
Power variation
- dV :
-
Voltage variation
- V :
-
Voltage
- Γ:
-
The interval length
- Γ1 :
-
The length of the larger segment
- Γ2 :
-
The length of the smaller segment
- ξ :
-
The golden ration
- ρ :
-
The golden section ratio
- ε :
-
The current precision
References
Mostafaeipour A, Qolipour M, Rezaei M, Babaee-Tirkolaee E (2019) Investigation of off-grid photovoltaic systems for a reverse osmosis desalination system: a case study. Desalination 454:91–103
Mohammed A, Pasupuleti J, Khatib T, Elmenreich W (2015) A review of process and operational system control of hybrid photovoltaic/diesel generator systems. Renew Sustain Energy Rev 44:436–446
Nagpal M, Kakkar R (2018) An evolving energy solution: intermediate hydrogen storage. Int J Hydrog Energy 43:12168–12188
Sorgulu F, Dincer I (2018) A renewable source based hydrogen energy system for residential applications. Int J Hydrog Energy 43:5842–5851
Mekhilef S, Saidur R, Safari A (2012) Comparative study of different fuel cell technologies. Renew Sustain Energy Rev 16:981–989
Inci M, Türksoy O (2019) Review of fuel cells to grid interface: configurations, technical challenges and trends. J Clean Prod 213:1353–1370
Abderezzak B, Rekioua D, Binns R, Busawon K, Hinaje M, Douine B, Guilbert D (2018) Technical feasibility assessment of a PEM fuel cell refrigerator system. Int J Hydrog Energy. https://doi.org/10.1016/j.ijhydene.2018.04.060
Sankar K, Jana AK (2018) Nonlinear multivariable sliding mode control of a reversible PEM fuel cell integrated system. Energy Convers Manag 171:541–565
Wang T, Li Q, Yin L, Chen W (2018) Hydrogen consumption minimization method based on the online identification for multi-stack PEMFCs system. Int J Hydrog Energy 44:5074–5081
Wang C, Nehrir MH, Shaw SR (2005) Dynamic models and model validation for PEMFC using electrical circuits. IEEE Trans Energy Convers 20(2):442–451
Mann RF, Amphlett JC, Hooper MAI, Jensen HM, Peppley BA, Roberge PR (2000) Development and application of a generalized steady-state electrochemical model for a PEMFC. J Power Sources 86:173–180
Fathabadi H (2016) Novel highly accurate universal maximum power point tracker for maximum power extraction from hybrid fuel cell/photovoltaic/wind power generation systems. Energy 116:402–416
Karami N, Moubayed N, Outbib R (2017) General review and classification of different MPPT techniques. Renew Sustain Energy Rev 68:1–18
Karami N (2013) Control of a hybrid system based PEMFC and photovoltaic panels. Ph.D. thesis. Aix-Marseille University, France
Zhi-dan Z, Hai-bo H, **n-jian Z, Guang-yi C, Yuan R (2008) Adaptive maximum power point tracking control of fuel cell power plants. J Power Sources 176:259–269
Dargahi M, Rouhi J, Rezanejad M, Shakeri M (2009) Maximum power point tracking for fuel cell in fuel cell/battery hybrid power systems. Eur J Sci Res 25:538–548
Becherif M, Hissel D (2010) MPPT of a PEMFC based on air supply control of the motocompressor group. Int J Hydrog Energy 35:2521–2530
Benyahia N, Denoun H, Badji A, Zaouia M, Rekioua T, Benamrouche N, Rekioua D (2014) MPPT controller for an interleaved boost DC–DC converter used in fuel cell electric vehicles. Int J Hydrog Energy 39:15196–15205
Karami N, El Khoury L, Khoury G, Moubayed N (2014) Comparative study between P&O and incremental conductance for fuel cell MPPT. In: 2nd renewable energy of develo** countries (REDEC), pp 17–22
Harrag A, Messalti S (2017) Variable step size IC MPPT controller for PEMFC power system improving static and dynamic performances. Fuel Cells 17(6):816–824
Chen P, Yu K, Yau H, Li J, Liao C (2017) A novel variable step size fractional order incremental conductance algorithm to maximize power tracking of fuel cells. Appl Math Model 45:1067–1075
Rezanejad M, Sarvi M (2014) A particle swarm optimization based maximum power point tracking for fuel cell compared with P&O algorithm. Int J Enhanced Res Sci Technol Eng 2(1):33–39
Soltani I, Sarvi M, Marefatjou H (2013) An intelligent, fast and robust maximum power point tracking for proton exchange membrane fuel cell. World Appl Program 3:264–281
Ahmadi S, Abdi S, Kakavand M (2017) Maximum power point tracking of a proton exchange membrane fuel cell system using PSO-PID controller. Int J Hydrog Energy 42:20430–20443
Romdlony MZ, Trilaksono BR, Ortega R (2012) Experimental study of extremum seeking control for maximum power point tracking of PEM fuel cell. In: International conference on system engineering and technology, Bandung, Indonesia, p 345
Liu J, Zhao T, Chen Y (2017) Maximum power point tracking with fractional order high pass filter for proton exchange membrane fuel cell. J. Autom Sin 4:70
Alaraj M, Radenkovic M, Park J (2017) Intelligent energy harvesting scheme for microbial fuel cells: maximum power point tracking and voltage overshoot avoidance. J Power Sources 342:726–732
Bizon N (2010) On tracking robustness in adaptive extremum seeking control of the fuel cell power plants. Appl Energy 87:3115–3130
Bizon N (2013) FC energy harvesting using the MPP tracking based on advanced extremum seeking control. Int J Hydrog Energy 38:1952–1966
Bizon N (2013) Energy harvesting from the FC stack that operates using the MPP tracking based on modified extremum seeking control. Appl Energy 104:326–336
Abdi S, Afshar K, Bigdeli N, Ahmadi S (2012) A novel approach for robust maximum power point tracking of PEM fuel cell generator using sliding mode control approach. Int J Electrochem Sci 7:4192–4209
Jiao J, Cui X (2013) Adaptive control of MPPT for fuel cell power system. J Converg Inf Technol 8(4):1–10
Inthamoussou AF, Mantz RJ, Battista HD (2012) Flexible power control of fuel cells using sliding mode techniques. J Power Sources 205:281–289
Derbeli M, Farhat M, Barambones O, Sbita L (2017) Control of PEM fuel cell power system using sliding mode and super-twisting algorithms. Int J Hydrog Energy 42:8833–8844
Venkateshkumar M, Sarathkumar G, Britto S (2013) Intelligent control based MPPT method for fuel cell power system. In: Proceedings international conference on renewable energy and sustainable energy (ICRESE), pp 253–257
Jiao J (2014) Maximum power point tracking of fuel cell power system using fuzzy logic control. Electroteh Electron Autom 62:45–52
Harrag A, Messalti S (2017) How fuzzy logic can improve PEM fuel cell MPPT performances? Int J Hydrog Energy 43:537–550
Luta ND, Raji AK (2019) Comparing fuzzy rule-based MPPT techniques for fuel cell stack applications. Energy Proc 156:177–182
Benchouia NE, Derghal A, Mahmah B, Madi B, Khochemane L, Aoul EH (2015) An adaptive fuzzy logic controller (AFLC) for PEMFC fuel cell. Int J Hydrog Energy 40:3806–3819
Sarvi M, Parpaei M, Soltani I, Taghikhani MA (2015) Eagle strategy based maximum power point tracker for fuel cell system. Int J Eng 28:529–536
Sisworahardjo NS, Yalcinoz T, El-Sharkh MY, Alam MS (2010) Neural network model of 100 W portable PEM fuel cell and experimental verification. Int J Hydrog Energy 35(17):9104–9105
Damour C, Benne M, Lebreton C, Deseure J, Grondin-Perez B (2014) Real-time implementation of a neural model-based self-tuning PID strategy for oxygen stoichiometry control in PEM fuel cell. Int J Eng 39:12819–12825
Abbaspour A, Khalilnejad A, Chen Z (2016) Robust adaptive neural network control for PEM fuel cell. Int J Hydrog Energy 41(44):20385–20395
Harrag A, Bahri H (2017) Novel neural network IC-based variable step size fuel cell MPPT controller, performance, efficiency and lifetime improvement. Int J Eng 42:3549–3563
Reddy KJ, Sudhakar N (2018) A new RBFN based MPPT controller for grid-connected PEMFC system with high step-up three-phase IBC. Int J Eng 43:17835–17848
Kim M, Choe J, Lim JW, Lee DG (2015) Manufacturing of the carbon/phenol composite bipolar plates for PEMFC with continuous hot rolling process. Compos Struct 132:1122–1128
Brouzgou A, Song SQ, Tsiakaras P (2012) Low and non-platinum electrocatalysts for PEMFCs: current status, challenges and prospects. Appl Catal B 127:371–388
Sundarabalan CK, Selvi K (2015) Compensation of voltage disturbances using PEMFC supported dynamic voltage restorer. Electr Power Energy Syst 71:77–92
Sun Z, Wang N, Bi Y, Srinivasan D (2015) Parameter identification of PEMFC model based on hybrid adaptive differential evolution algorithm. Energy 90:1334–1341
Benchouia NE, Elias HA, Khochemane L, Mahmah B (2014) Bond graph modeling approach development for fuel cell PEMFC systems. Int J Hydrog Energy 39:15224–15231
Bigdeli N (2015) Optimal management of hybrid PV/fuel cell/battery power system: a comparison of optimal hybrid approaches. Renew Sustain Energy Rev 42:377–393
Mosaad MI, Ramadan HS (2018) Power quality enhancement of grid-connected fuel cell using evolutionary computing techniques. Int J Hydrog Energy 43:11568–11582
Seyezhai R, Mathur BL (2011) Modeling and control of a PEM fuel cell based hybrid multilevel inverter. Int J Hydrog Energy 36:15029–15043
Wang YX, Yu DH, Chen SA, Kim YB (2014) Robust DC/DC converter control for polymer electrolyte membrane fuel cell application. J Power Sources 261:292–305
Mokrani Z, Rekioua D, Mebarki N, Rekioua T, Bacha S (2017) Proposed energy management strategy in electric vehicle for recovering power excess produced by fuel cells. Int J Hydrog Energy 42:19556–19575
Chang KY (2011) The optimal design for PEMFC modeling based on Taguchi method and genetic algorithm neural networks. Int J Hydrog Energy 36:13683–13694
Mokrani Z, Rekioua D, Rekioua T (2014) Modeling, control and power management of hybrid photovoltaic fuel cells with battery bank supplying electric vehicle. Int J Hydrog Energy 39:15178–15187
Bankupalli PT, Ghosh S, Kumar L, Samanta S (2018) Fractional order modeling and two loop control of PEM fuel cell for voltage regulation considering both source and load perturbations. Int J Hydrog Energy 43:6294–6309
Kiefer J (1953) Sequential minimax search for a maximum. Proc Am Math Soc 4:502–506
Korda N, Szörényi B, Li S (2016) Distributed clustering of linear bandits in peer to peer networks. In: Proceedings of the 33rd international conference on international conference on machine learning, vol 48, pp 1301–1309
Li S, Karatzoglou A, Gentile C (2016) Collaborative filtering bandits. In: Proceedings of the 39th international ACM SIGIR conference on research and development in information retrieval, pp 539–548
Kar P, Li S, Narasimhan H, Chawla S, Sebastiani F (2016) Online optimization methods for the quantification problem. In: Proceedings of the 22nd ACM SIGKDD international conference on knowledge discovery and data mining, pp 1625–1634
Hao F, Park DS, Li S, Lee HM (2016) Mining λ-maximal cliques from a fuzzy graph. Sustainability 8(6):1–16
Li S, Chen W, Leung KS (2019) Improved algorithm on online clustering of bandits. In: Proceedings of the twenty-eighth international joint conference on artificial intelligence, Macao, India, pp 2923–2929
Ma J, Man KL, Ting TO, Lee H, Jeong T, Sean J, Guan S (2012) Insight of direct search methods and module-integrated algorithms for maximum power point tracking (MPPT) of stand-alone photovoltaic systems. In: Park JJ, Zomaya A, Yeo SS, Sahni S (eds) Network and parallel computing. NPC 2012. Lecture notes in computer science, vol 7513. Springer, Berlin
Agrawal J, Aware M (2012) Golden section search (GSS) algorithm for maximum power point tracking in photovoltaic system. In: IEEE 5th India international conference on power electronics (IICPE), Delhi, India
Balakishan C, Sandeep N, Aware MV (2015) Design and implementation of three-level DC–DC converter with golden section search based MPPT for the photovoltaic, applications. Adv Power Electron. https://doi.org/10.1155/2015/587197
Gayathri R, Ezhilarasi GA (2018) Golden section search based maximum power point tracking strategy for a dual output DC–DC converter. Ain Shams Eng J 9:2617–2630
Kheldoun A, Bradai R, Boukenoui R, Mellit A (2016) A new golden section method-based maximum power point tracking algorithm for photovoltaic systems. Energy Convers Manag 111:125–136
Djeriou S, Kheldoun A, Mellit A (2018) Efficiency improvement in induction motor-driven solar water pum** system using golden section search algorithm. Arab J Sci Eng 43(6):3199–3211
Andrean V, Chang PC, Lian KL (2018) A review and new problems discovery of four simple decentralized maximum power point tracking algorithms—perturb and observe, incremental conductance, golden section search, and Newton’s quadratic interpolation. Energies 11(11):2966
Acknowledgements
The Algerian Ministry of Higher Education and Scientific Research via DGRSDT supported this research (Research PRFU Project A01L07UN190120180005).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, Abdelghani Harrag states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bahri, H., Harrag, A. Ingenious golden section search MPPT algorithm for PEM fuel cell power system. Neural Comput & Applic 33, 8275–8298 (2021). https://doi.org/10.1007/s00521-020-05581-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-020-05581-4