0
Research Papers

Dynamic Model-Based Fuzzy Controller for Maximum Power Point Tracking of Photovoltaic Systems: A Linear Matrix Inequality Approach

[+] Author and Article Information
Navid Vafamand

School of Electrical and Computer Engineering,
Shiraz University,
Shiraz 71946, Fars, Iran
e-mail: n.vafamand@shirazu.ac.ir

Mohsen Rakhshan

Department of Electrical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: mrakhsha@nd.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 2, 2016; final manuscript received November 11, 2016; published online March 16, 2017. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 139(5), 051010 (Mar 16, 2017) (6 pages) Paper No: DS-16-1375; doi: 10.1115/1.4035240 History: Received August 02, 2016; Revised November 11, 2016

In this paper, a new systematic approach for stability analysis and controller design of nonlinear solar photovoltaic (PV) power system is proposed. Based on a nonquadratic Lyapunov function (NQLF), a model-based dynamic nonparallel-distributed compensation (non-PDC) controller and descriptor representation, the problem of the output tracking is formulated in terms of linear matrix inequalities (LMIs). Furthermore, some slack LMI variables are introduced in the problem formulation which lead to more relaxed conditions. Finally, to illustrate the merits of the proposed approach, it is applied to a PV power system in which the reference voltage is calculated from the maximum power point tracking (MPPT) method.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Jacobson, M. Z. , and Delucchi, M. A. , 2011, “ Providing All Global Energy With Wind, Water, and Solar Power, Part I: Technologies, Energy Resources, Quantities and Areas of Infrastructure, and Materials,” Energy Policy, 39(3), pp. 1154–1169. [CrossRef]
Fthenakis, V. , Mason, J. E. , and Zweibel, K. , 2009, “ The Technical, Geographical, and Economic Feasibility for Solar Energy to Supply the Energy Needs of the US,” Energy Policy, 37(2), pp. 387–399. [CrossRef]
Zeinalzadeh, A. , Ghorbani, R. , and Yee, J. , 2016, “ Stochastic Model of Voltage Variations in the Presence of Photovoltaic Systems,” American Control Conference (ACC), July 6–8, pp. 5032–5037.
Sharma, A. , 2011, “ A Comprehensive Study of Solar Power in India and World,” Renewable Sustainable Energy Rev., 15(4), pp. 1767–1776. [CrossRef]
Finley, M., 2011, “ BP Statistical Review of World Energy (2007),” BP, London, accessed Mar. 2015, www.bp.com
E. P. I. Association, 2012, “ Solar Photovoltaics Competing in the Energy Sector, on the Road to Competitiveness,” European Photovoltaic Industry Association, Brussels, Belgium.
E. P. I. Association, 2012, “ Solar Generation 6 Solar Photovoltaic Electricity Empowering the World,” European Photovoltaic Industry Association, Brussels, Belgium.
Subudhi, B. , and Pradhan, R. , 2013, “ A Comparative Study on Maximum Power Point Tracking Techniques for Photovoltaic Power Systems,” IEEE Trans. Sustainable Energy, 4(1), pp. 89–98. [CrossRef]
Rahim, N. A. , Che Soh, A. , Radzi, M. A. M. , and Zainuri, M. A. A. M. , 2014, “ Development of Adaptive Perturb and Observe-Fuzzy Control Maximum Power Point Tracking for Photovoltaic Boost dc–dc Converter,” IET Renewable Power Gener., 8(2), pp. 183–194. [CrossRef]
Hussein, K. H. , Muta, I. , Hoshino, T. , and Osakada, M. , 1995, “ Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Condition,” Inst. Electron. Eng. Proc. Gener. Transm. Distrib., 142(1), pp. 59–64. [CrossRef]
Lalouni, S. , Rekioua, D. , Rekioua, T. , and Matagne, E. , 2009, “ Fuzzy Logic Control of Stand-Alone Photovoltaic System With Battery Storage,” J. Power Sources, 193(2), pp. 899–907. [CrossRef]
El Khateb, A. , Rahim, N. A. , Selvaraj, J. , and Uddin, M. N. , 2014, “ Fuzzy-Logic-Controller-Based SEPIC Converter for Maximum Power Point Tracking,” IEEE Trans. Ind. Appl., 50(4), pp. 2349–2358. [CrossRef]
Veerachary, M. , Senjyu, T. , and Uezato, K. , 2003, “ Neural-Network-Based Maximum-Power-Point Tracking of Coupled-Inductor Interleaved Boost-Converter-Supplied PV System Using Fuzzy Controller,” IEEE Trans. Ind. Electron., 50(4), pp. 749–758. [CrossRef]
Koutroulis, E. , Kalaitzakis, K. , and Voulgaris, N. C. , 2001, “ Development of a Microcontroller-Based, Photovoltaic Maximum Power Point Tracking Control System,” IEEE Trans. Power Electron., 16(1), pp. 46–54. [CrossRef]
Valenciaga, F. , Puleston, P. F. , and Battaiotto, P. E. , 2001, “ Power Control of a Photovoltaic Array in a Hybrid Electric Generation System Using Sliding Mode Techniques,” Inst. Electron. Eng. Proc. Control Theory Appl., 148(6), pp. 448–455. [CrossRef]
Patcharaprakiti, N. , Premrudeepreechacharnb, S. , and Sriuthaisiriwong, Y. , 2005, “ Maximum Power Point Tracking Using Adaptive Fuzzy Logic Control for Grid-Connected Photovoltaic System,” Renewable Energy, 30(11), pp. 1771–1788. [CrossRef]
Solodovnik, E. V. , Liu, S. , and Dougal, R. A. , 2004, “ Power Controller Design for Maximum Power Tracking in Solar Installations,” IEEE Trans. Power Electron., 19(5), pp. 1295–1304. [CrossRef]
Sha Sadeghi, M. , Vafamand, N. , and Babaei, M. S. , 2014, “ Non-Quadratic Exponential Stabilisation of Non-Linear Hyperbolic Partial Differential Equation Systems,” IET Sci. Meas. Technol., 8(6), pp. 537–545. [CrossRef]
Sadeghi, M. S. , Vafamand, N. , and Khooban, M. H. , 2016, “ LMI-Based Stability Analysis and Robust Controller Design for a Class of Nonlinear Chaotic Power Systems,” J. Frankl. Inst., 353(13), pp. 2835–2858. [CrossRef]
Khooban, M. H. , Vafamand, N. , and Niknam, T. , 2016, “ T–S Fuzzy Model Predictive Speed Control of Electrical Vehicles,” ISA Trans., 64(1), pp. 231–240. [CrossRef] [PubMed]
Asemani, M. H. , and Vatankhah, R. , 2016, “ Tracking Control of Chaotic Spinning Disks Via Nonlinear Dynamic Output Feedback With Input Constraints,” Complexity, 21(S1), pp. 148–159. [CrossRef]
Rakhshan, M. , Vafamand, N. , Sha Sadeghi, M. , Dabbaghjamanesh, M. , and Meeini, A. , “ Design of Networked Polynomial Control Systems With Random Delays: Sum of Squares Approach,” Int. J. Autom. Control, 10(1), pp. 73–86. [CrossRef]
Safarinejadian, B. , Gharibzadeh, M. , and Rakhshan, M. , 2014, “ An Optimized Model of Electricity Price Forecasting in the Electricity Market Based on Fuzzy Timeseries,” Syst. Sci. Control Eng., 2(1), pp. 677–683. [CrossRef]
Guerra, T. M. , Bernal, M. , Guelton, K. , and Labiod, S. , 2012, “ Non-Quadratic Local Stabilization for Continuous-Time Takagi–Sugeno Models,” Fuzzy Sets Syst., 201(1), pp. 40–54. [CrossRef]
Dahmane, M. , Bosche, J. , and El-Hajjaji, A. , 2013, “ Robust Control Approach for Photovoltaic Conversion System,” 2013 International Conference on Renewable and Sustainable Energy Conference (IRSEC), Mar. 7–9, pp. 123–129.
Aitouche, A. , and Kamal, E. , 2013, “ Robust Fuzzy Control of PV Systems With Parametric Uncertainties,” IET Conference on Control and Automation 2013: Uniting Problems and Solutions, p. 22.
Ouachani, I. , Rabhi, A. , Tidhaf, B. , Zouggar, S. , and Elhajjaji, A. , 2013, “ Optimization and Control for a Photovoltaic Pumping System,” 2013 International Conference on Renewable Energy Research and Applications (ICRERA), Oct. 20–23, pp. 734–739.
Chiu, C.-S. , 2010, “ T-S Fuzzy Maximum Power Point Tracking Control of Solar Power Generation Systems,” IEEE Trans. Energy Convers., 25(4), pp. 1123–1132. [CrossRef]
Chiu, C.-S. , and Ouyang, Y.-L. , 2011, “ Robust Maximum Power Tracking Control of Uncertain Photovoltaic Systems: A Unified T-S Fuzzy Model-Based Approach,” IEEE Trans. Control Syst. Technol., 19(6), pp. 1516–1526. [CrossRef]
Jafarzadeh, S. , and Fadali, M. S. , “ On the Stability and Control of Continuous-Time TSK Fuzzy Systems,” IEEE Trans. Cybern., 43(3), pp. 1073–1087. [CrossRef] [PubMed]
Sha Sadeghi, M. , and Vafamand, N. , 2014, “ More Relaxed Stability Conditions for Fuzzy TS Control Systems by Optimal Determination of Membership Function Information,” J. Control Eng. Appl. Inform., 16(2), pp. 67–77.
Jafarzadeh, S. , Fadali, M. S. , and Sonbol, A. H. , 2011, “ Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design,” IEEE Trans. Fuzzy Syst., 19(6), pp. 1001–1013. [CrossRef]
Wang, W.-J. , and Sun, C.-H. , “ Relaxed Stability and Stabilization Conditions for a T–S Fuzzy Discrete System,” Fuzzy Sets Syst., 156(2), pp. 208–225. [CrossRef]
Cao, Y.-Y. , Sun, Y.-X. , and Cheng, C. , 1998, “ Delay-Dependent Robust Stabilization of Uncertain Systems With Multiple State Delays,” IEEE Trans. Autom. Control, 43(11), pp. 1608–1612. [CrossRef]
Scherer, C. , and Weiland, S. , 2004, “ Linear Matrix Inequalities in Control,” Dutch Institute for Systems and Control, Delft, The Netherlands.
Mendes, E. M. A. M. , Palhares, R. M. , and Mozelli, L. A. , 2010,“ Equivalent Techniques, Extra Comparisons and Less Conservative Control Design for Takagi–Sugeno (TS) Fuzzy Systems,” IET Control Theory Appl., 4(12), pp. 2813–2822. [CrossRef]
Mahmud, M. A. , Pota, H. R. , and Hossain, M. J. , 2014, “ Nonlinear Current Control Scheme for a Single-Phase Grid-Connected Photovoltaic System,” IEEE Trans. Sustain. Energy, 5(1), pp. 218–227. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

Varying insolation atmosphere

Grahic Jump Location
Fig. 1

PV power control system using a dc/dc buck converter

Grahic Jump Location
Fig. 2

The PV system_ scenario 1: (a) PV array voltage, (b) PV array power, and (c) control effort

Grahic Jump Location
Fig. 4

Power–voltage diagram of PV system_ scenario 2: (a) the proposed approach, (b) PDC controller [28], (c) fuzzy model-free controller [12], and (d) PI controller [14]

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In