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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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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