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Research Papers

Extremum Seeking for Plants With a Time-Varying Disturbance: Application to Photovoltaic Maximum Power Point Tracking

[+] Author and Article Information
Michelle A. Kehs

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: mak5497@psu.edu

Hosam K. Fathy

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: hkf2@engr.psu.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 4, 2017; final manuscript received August 22, 2018; published online September 26, 2018. Assoc. Editor: Junmin Wang.

J. Dyn. Sys., Meas., Control 141(1), 011011 (Sep 26, 2018) (10 pages) Paper No: DS-17-1399; doi: 10.1115/1.4041297 History: Received August 04, 2017; Revised August 22, 2018

This paper presents an extremum seeking controller for photovoltaic maximum power point tracking (MPPT). The controller belongs to the broad family of “perturb and observe” algorithms, where the terminal voltage of a photovoltaic system is adjusted to maximize its output power. One critical challenge with these algorithms is that it can be difficult to distinguish between changes in photovoltaic power resulting from changes in irradiation versus the control input. With regard to this challenge, we develop an extremum seeking algorithm that uses least-squares estimation to explicitly separate the effect of the control input from the effect of time-varying disturbances. While the use of least-squares estimation in the context of extremum seeking is not new, our separation of time-varying effects is. In addition, our formulation retains much of the structure of traditional extremum seeking, thereby allowing us to perform a stability analysis comparable to the existing literature. This stability analysis assumes the time-varying disturbance to be slow, but we test the controller beyond this limit in simulation for photovoltaic MPPT. We compare our controller to two benchmarks (a similar controller that does not separate time-varying effects and a traditional extremum seeking controller), and our controller outperforms both.

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References

Villalva, M. G. , Gazoli, J. R. , and Filho, E. R. , 2009, “ Comprehensive Approach to Modeling and Simulation of Photovoltaic Arrays,” IEEE Trans. Power Electron., 24(5), pp. 1198–1208. [CrossRef]
Esram, T. , and Chapman, P. L. , 2007, “ Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques,” IEEE Trans. Energy Convers., 22(2), pp. 439–449. [CrossRef]
Salas, V. , Olías, E. , Barrado, A. , and Lázaro, A. , 2006, “ Review of the Maximum Power Point Tracking Algorithms for Stand-Alone Photovoltaic Systems,” Sol. Energy Mater. Sol. Cells, 90(11), pp. 1555–1578. [CrossRef]
Docimo, D. J. , Ghanaatpishe, M. , and Mamun, A. , 2017, “ Extended Kalman Filtering to Estimate Temperature and Irradiation for Maximum Power Point Tracking of a Photovoltaic Module,” Energy, 120, pp. 47–57. [CrossRef]
Hussein, K. H. , Muta, I. , Hoshino, T. , and Osakada, M. , 1995, “ Maximum Photovoltaic Power Tracking: An Algorithm for Rapidly Changing Atmospheric Conditions,” IEE Proc. Gener., Transm., Distrib., 142(1), pp. 59–64. [CrossRef]
Azevedo, G. M. S. , Cavalcanti, M. C. , Oliveira, K. C. , Neves, F. A. S. , and Lins, Z. D. , 2009, “ Comparative Evaluation of Maximum Power Point Tracking Methods for Photovoltaic Systems,” ASME J. Sol. Energy Eng., 131(3), p. 031006. [CrossRef]
Femia, N. , Patrone, G. , Spagnuolo, G. , and Vitelli, M. , 2005, “ Optimization of Perturb and Observe Maximum Power Point Tracking Method,” IEEE Trans. Power Electron., 20(4), pp. 963–973. [CrossRef]
Piegari, L. , and Rizzo, R. , 2010, “ Adaptive Perturb and Observe Algorithm for Photovoltaic Maximum Power Point Tracking,” IET Renewable Power Gener., 4(4), pp. 317–328. [CrossRef]
Levya, R. , Alonso, C. , Queinnec, I. , Cid-Pastor, A. , Lagrange, D. , and Martínez, S. L. , 2006, “ MPPT of Photovoltaic Systems Using Extremum-Seeking Control,” IEEE Trans. Aerosp. Electron. Syst., 42(1), pp. 249–258. [CrossRef]
Brunton, S. L. , Rowley, C. W. , Kulkarni, S. R. , and Clarkson, C. , 2010, “ Maximum Power Point Tracking for Photovoltaic Optimization Using Ripple-Based Extremum Seeking Control,” IEEE Trans. Power Electron., 25(10), pp. 2531–2540. [CrossRef]
Moura, S. J. , and Chang, Y. A. , 2013, “ Lyapunov-Based Switched Extremum Seeking for Photovoltaic Power Maximization,” Control Eng. Pract., 21(7), pp. 971–980. [CrossRef]
Ariyur, K. , and Krstić, M. , 2003, Real-Time Optimization by Extremum Seeking Control, Wiley, Hoboken, NJ.
Tan, Y. , Moase, W. H. , Manzie, C. , Nešić, D. , and Mareels, I. M. Y. , 2010, “ Extremum Seeking From 1922 to 2010,” 29th Chinese Control Conference, Beijing, China, July 29–31, pp. 14–26. https://ieeexplore.ieee.org/document/5572972/
Manzie, C. , and Krstić, M. , 2009, “ Extremum Seeking With Stochastic Perturbations,” IEEE Trans. Autom. Control, 54(3), pp. 580–585. [CrossRef]
Zhang, C. , and Oróñez, R. , 2007, “ Numerical Optimization-Based Extremum Seeking Control With Application to Abs Design,” IEEE Trans. Autom. Control, 52(3), pp. 454–467. [CrossRef]
Zhang, C. , and Ordóñez, R. , 2009, “ Robust and Adaptive Design of Numerical Optimization-Based Extremum Seeking Control,” Automatica, 45(3), pp. 634–646. [CrossRef]
Carnevale, D. , Astolfi, A. , Centioli, C. , Podda, S. , Vitale, V. , and Zaccarian, L. , 2009, “ A New Extremum Seeking Technique and Its Application to Maximize RF Heating on FTU,” Fusion Eng. Des., 84(2–6), pp. 554–558. [CrossRef]
Drakunov, S. , Özgüner, U. , Dix, P. , and Ashrafi, B. , 1995, “ ABS Control Using Optimum Search Via Sliding Modes,” IEEE Trans. Control Syst. Technol., 3(1), pp. 79–85. [CrossRef]
Yin, C. , Chen, Y. , and Zhong, S. , 2014, “ Fractional-Order Sliding Mode Based Extremum Seeking Control of a Class of Nonlinear Systems,” Automatica, 50(12), pp. 3173–3181. [CrossRef]
Nešić, D. , Tan, Y. , Moase, W. H. , and Manzie, C. , 2010, “ A Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives,” 49th IEEE Conference on Decision and Control, Atlanta, GA, Dec. 15–17, pp. 4625–4630.
Mohammadi, A. , Manzie, C. , and Nešić, D. , 2014, “ Online Optimization of Spark Advance in Alternative Fueled Engines Using Extremum Seeking Control,” Control Eng. Pract., 29, pp. 201–211. [CrossRef]
Nešić, D. , Mohammadi, A. , and Manzie, C. , 2013, “ Framework for Extremum Seeking Control of Systems With Parameter Uncertainties,” IEEE Trans. Autom. Control, 58(2), pp. 435–448. [CrossRef]
Chioua, M. , Srinivasan, B. , Guay, M. , and Perrier, M. , 2016, “ Performance Improvement of Extremum Seeking Control Using Recursive Least Square Estimation With Forgetting Factor,” IFAC-PapersOnLine, 49(7), pp. 424–429. [CrossRef]
Pan, Y. , and Özgüner, U. , 2002, “ Discrete-Time Extremum Seeking Algorithms,” American Control Conference, Anchorage, AK, May 8–10, pp. 3147–3152.
Guay, M. , and Dochain, D. , 2015, “ A Time-Varying Extremum-Seeking Control Approach,” Automatica, 51, pp. 356–363. [CrossRef]
Hunnekens, B. G. B. , Haring, M. A. M. , van de Wouw, N. , and Nijmeijer, H. , 2014, “ A Dither-Free Extremum-Seeking Control Approach Using 1st-Order Least-Squares Fits for Gradient Estimation,” IEEE Conference on Decision and Control, Los Angeles, CA, Dec. 15–17, pp. 2679–2684.
Ryan, J. J. , and Speyer, J. L. , 2010, “ Peak-Seeking Control Using Gradient and Hessian Estimates,” American Control Conference, Baltimore, MD, June 30–July 2, pp. 611–616.
Krstić, M. , and Wang, H. , 2000, “ Stability of Extremum Seeking Feedback for General Nonlinear Dynamic Systems,” Automatica, 36(4), pp. 595–601. [CrossRef]
Jones, A. D. , and Underwood, C. P. , 2001, “ A Thermal Model for Photovoltaic Systems,” Sol. Energy, 70(4), pp. 349–359. [CrossRef]
Abdelsalem, A. K. , Massoud, A. M. , Ahmed, S. , and Enjeti, P. N. , 2011, “ High-Performance Adaptive Perturb and Observe MPPT Techniques for Photovoltaic-Based Microgrids,” IEEE Trans. Power Electron., 26(4), pp. 1010–1021. [CrossRef]
Jager, D. , and Andreas, A. , 1996, “ NREL National Wind Technology Center (NWTC): M2 Tower; Boulder, Colorado (Data),” National Renewable Energy Laboratory, Golden, CO, Report No. DA-5500-56489.
Khalil, H. K. , 1996, Nonlinear Systems, 2nd ed., Prentice Hall, Upper Saddle River, NJ.

Figures

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Fig. 1

A photovoltaic array's current–voltage and power–voltage curves with varying irradiation [1]. An X marks the MPP.

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Fig. 2

Current–voltage and power–voltage curves for different temperatures and constant irradiation of 600 W/m2; model from Ref. [1]. An X marks the MPP.

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Fig. 3

Block diagram of the extremum seeking controller

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Fig. 4

Simulation results for a constant 600 W/m2 irradiation

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Fig. 5

Simulation results using real irradiation data from Mar. 10, 2017

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Fig. 6

Simulation results using real irradiation data from Mar. 12, 2017

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Fig. 7

Simulation results for power measurement corrupted by noise; constant 600 W/m2 irradiation

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Fig. 8

Block diagram of benchmark 1

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Fig. 9

Block diagram of benchmark 2

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Fig. 10

Comparison to benchmark 1 for a constant 600 W/m2 irradiation

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Fig. 11

Comparison to benchmark 1 for a step change in irradiation

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Fig. 12

Comparison to benchmark 1 for real irradiation data from Mar. 10, 2017

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Fig. 13

Comparison to benchmark 2 for a constant 600 W/m2 irradiation

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Fig. 14

Comparison to benchmark 2 for a step change in irradiation

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Fig. 15

Comparison to benchmark 2 for real irradiation data from Mar. 10, 2017 (Data adapted from Ref. [31])

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