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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.


Related in: MedlinePlus

Open loop responses of hydrogen and oxygen partial pressures for a step change in SOFC reference current
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Fig3: Open loop responses of hydrogen and oxygen partial pressures for a step change in SOFC reference current

Mentions: Eigenvalue based study and the time domain based simulation results for the open loop response of the SOFC linearized dynamic model is reported here. Numerical data used for these studies are listed in the “Appendix”. Open loop eigenvalues are listed in Table 1 and the corresponding time domain simulations are shown in Figs. 3 and 4 for step change  = 30 A applied at 5 s. Observation of Table 1 reveals that all eigenvalues of the studied SOFC stand-alone system are real in nature and do not possess any oscillating frequency. Thus, once disturbed, the controllable system states, i.e. the partial pressures of oxygen and hydrogen show sluggish responses. This fact is presented in Fig. 3 where it is found that the system dynamics for these states are stable under this disturbance but the variables settle to new steady state values after long duration owing to large time constants. Specifically, the settling times for the hydrogen and oxygen partial pressures are more than 70 and 20 s, respectively. The participation factor (Sanchez-Gasca et al. 2007) column of Table 1 reveals the fact that all the states are completely decoupled and introduction of control in one of the states will have minimal or no impact on the others. So, if it is desired that the changes in the partial pressures of oxygen and hydrogen are to be tracked by the controllers, status of the other states are going to be mostly unchanged. Figure 4 shows the responses of the remaining three state variables where it is observed that all of them are stable in nature. The water vapor partial pressure and SOFC temperature increases and settles to a new value after a long duration whereas the SOFC current reaches the new equilibrium after 29.76 s. The water vapor partial pressure is measured at the outlet of the SOFC in practice and explicit regulators are not present there. Independent temperature controller is required for proper control of the temperature dynamics but is out of the scope of this work and hence not included.Table 1


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)

Open loop responses of hydrogen and oxygen partial pressures for a step change in SOFC reference current
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig3: Open loop responses of hydrogen and oxygen partial pressures for a step change in SOFC reference current
Mentions: Eigenvalue based study and the time domain based simulation results for the open loop response of the SOFC linearized dynamic model is reported here. Numerical data used for these studies are listed in the “Appendix”. Open loop eigenvalues are listed in Table 1 and the corresponding time domain simulations are shown in Figs. 3 and 4 for step change  = 30 A applied at 5 s. Observation of Table 1 reveals that all eigenvalues of the studied SOFC stand-alone system are real in nature and do not possess any oscillating frequency. Thus, once disturbed, the controllable system states, i.e. the partial pressures of oxygen and hydrogen show sluggish responses. This fact is presented in Fig. 3 where it is found that the system dynamics for these states are stable under this disturbance but the variables settle to new steady state values after long duration owing to large time constants. Specifically, the settling times for the hydrogen and oxygen partial pressures are more than 70 and 20 s, respectively. The participation factor (Sanchez-Gasca et al. 2007) column of Table 1 reveals the fact that all the states are completely decoupled and introduction of control in one of the states will have minimal or no impact on the others. So, if it is desired that the changes in the partial pressures of oxygen and hydrogen are to be tracked by the controllers, status of the other states are going to be mostly unchanged. Figure 4 shows the responses of the remaining three state variables where it is observed that all of them are stable in nature. The water vapor partial pressure and SOFC temperature increases and settles to a new value after a long duration whereas the SOFC current reaches the new equilibrium after 29.76 s. The water vapor partial pressure is measured at the outlet of the SOFC in practice and explicit regulators are not present there. Independent temperature controller is required for proper control of the temperature dynamics but is out of the scope of this work and hence not included.Table 1

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