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Optimal design of proportional-integral controllers for stand-alone solid oxide fuel cell power plant using differential evolution algorithm.

Ahmed A, Ullah MS - Springerplus (2016)

Bottom Line: To test the efficacy of DE over other optimization tools, the results obtained with DE are compared with those obtained by particle swarm optimization (PSO) algorithm and invasive weed optimization (IWO) algorithm.Three different types of load disturbances are considered for the time domain based results to investigate the performances of different optimizers under different sorts of load variations.The presented results suggest the supremacy of DE over PSO and IWO in finding the optimal solution.

View Article: PubMed Central - PubMed

Affiliation: EEE Department, Islamic University of Technology, Boardbazar, Gazipur Bangladesh.

ABSTRACT
This paper proposes the application of differential evolution (DE) algorithm for the optimal tuning of proportional-integral (PI) controller designed to improve the small signal dynamic response of a stand-alone solid oxide fuel cell (SOFC) system. The small signal model of the study system is derived and considered for the controller design as the target here is to track small variations in SOFC load current. Two PI controllers are incorporated in the feedback loops of hydrogen and oxygen partial pressures with an aim to improve the small signal dynamic responses. The controller design problem is formulated as the minimization of an eigenvalue based objective function where the target is to find out the optimal gains of the PI controllers in such a way that the discrepancy of the obtained and desired eigenvalues are minimized. Eigenvalue and time domain simulations are presented for both open-loop and closed loop systems. To test the efficacy of DE over other optimization tools, the results obtained with DE are compared with those obtained by particle swarm optimization (PSO) algorithm and invasive weed optimization (IWO) algorithm. Three different types of load disturbances are considered for the time domain based results to investigate the performances of different optimizers under different sorts of load variations. Moreover, non-parametric statistical analyses, namely, one sample Kolmogorov-Smirnov (KS) test and paired sample t test are used to identify the statistical advantage of one optimizer over the other for the problem under study. The presented results suggest the supremacy of DE over PSO and IWO in finding the optimal solution.

No MeSH data available.


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Flowchart of DE algorithm
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Fig6: Flowchart of DE algorithm

Mentions: In the selection phase a comparison is made between the target vector and trial vector and the ones with the best value is selected and forwarded to the next generation.22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{x}_{i,G + 1} = \left\{ {\begin{array}{*{20}l} {\varvec{u}_{i,G + 1} } \hfill &\quad {if\;J(\varvec{u}_{i,G + 1} ) \le J(\varvec{x}_{i,G} )} \hfill \\ {\varvec{x}_{i,G} } \hfill &\quad {otherwise} \hfill \\ \end{array} } \right.$$\end{document}xi,G+1=ui,G+1ifJ(ui,G+1)≤J(xi,G)xi,GotherwiseThe mutation, recombination and selection phases continue until a pre-specified stopping criterion is fulfilled. The overall working procedure of the DE algorithm is presented in the flowchart of Fig. 6.Fig. 6


Optimal design of proportional-integral controllers for stand-alone solid oxide fuel cell power plant using differential evolution algorithm.

Ahmed A, Ullah MS - Springerplus (2016)

Flowchart of DE algorithm
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4814395&req=5

Fig6: Flowchart of DE algorithm
Mentions: In the selection phase a comparison is made between the target vector and trial vector and the ones with the best value is selected and forwarded to the next generation.22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{x}_{i,G + 1} = \left\{ {\begin{array}{*{20}l} {\varvec{u}_{i,G + 1} } \hfill &\quad {if\;J(\varvec{u}_{i,G + 1} ) \le J(\varvec{x}_{i,G} )} \hfill \\ {\varvec{x}_{i,G} } \hfill &\quad {otherwise} \hfill \\ \end{array} } \right.$$\end{document}xi,G+1=ui,G+1ifJ(ui,G+1)≤J(xi,G)xi,GotherwiseThe mutation, recombination and selection phases continue until a pre-specified stopping criterion is fulfilled. The overall working procedure of the DE algorithm is presented in the flowchart of Fig. 6.Fig. 6

Bottom Line: To test the efficacy of DE over other optimization tools, the results obtained with DE are compared with those obtained by particle swarm optimization (PSO) algorithm and invasive weed optimization (IWO) algorithm.Three different types of load disturbances are considered for the time domain based results to investigate the performances of different optimizers under different sorts of load variations.The presented results suggest the supremacy of DE over PSO and IWO in finding the optimal solution.

View Article: PubMed Central - PubMed

Affiliation: EEE Department, Islamic University of Technology, Boardbazar, Gazipur Bangladesh.

ABSTRACT
This paper proposes the application of differential evolution (DE) algorithm for the optimal tuning of proportional-integral (PI) controller designed to improve the small signal dynamic response of a stand-alone solid oxide fuel cell (SOFC) system. The small signal model of the study system is derived and considered for the controller design as the target here is to track small variations in SOFC load current. Two PI controllers are incorporated in the feedback loops of hydrogen and oxygen partial pressures with an aim to improve the small signal dynamic responses. The controller design problem is formulated as the minimization of an eigenvalue based objective function where the target is to find out the optimal gains of the PI controllers in such a way that the discrepancy of the obtained and desired eigenvalues are minimized. Eigenvalue and time domain simulations are presented for both open-loop and closed loop systems. To test the efficacy of DE over other optimization tools, the results obtained with DE are compared with those obtained by particle swarm optimization (PSO) algorithm and invasive weed optimization (IWO) algorithm. Three different types of load disturbances are considered for the time domain based results to investigate the performances of different optimizers under different sorts of load variations. Moreover, non-parametric statistical analyses, namely, one sample Kolmogorov-Smirnov (KS) test and paired sample t test are used to identify the statistical advantage of one optimizer over the other for the problem under study. The presented results suggest the supremacy of DE over PSO and IWO in finding the optimal solution.

No MeSH data available.


Related in: MedlinePlus