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Fig 1.

Flowchart for h-ASPSO.

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Fig 2.

Schematic diagram of a basic AVR system.

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Fig 3.

Step response of uncontrolled AVR system.

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Fig 4.

Schematic diagram of a DFIG-based wind turbine system.

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Fig 5.

Step response of uncontrolled DFIG-based wind turbine system.

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Fig 6.

Block diagram of feedback control system with PID controller.

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Fig 7.

Implementation of the proposed design approach for optimizing AVR and DFIG-based wind turbine systems.

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Fig 8.

Convergence curves of ASO and h-ASPSO algorithms for AVR system.

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Table 1.

Statistical metrics of objective function for AVR system.

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Table 1 Expand

Table 2.

The obtained PID parameters for AVR system.

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Table 2 Expand

Table 3.

Closed-loop transfer functions of optimization methods for AVR system.

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Table 3 Expand

Fig 9.

Step responses of PID controlled AVR system tuned by various algorithms.

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Fig 9 Expand

Table 4.

Numerical values of time-domain performance indicators for AVR system.

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Table 4 Expand

Fig 10.

Bode plot of h-ASPSO optimized AVR system.

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Fig 11.

Convergence curves of ASO and h-ASPSO algorithms for DFIG-based wind turbine system.

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Fig 11 Expand

Table 5.

Statistical metrics of objective function for DFIG-based wind turbine system.

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Table 5 Expand

Table 6.

The obtained PID parameters for DFIG-based wind turbine system.

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Table 6 Expand

Table 7.

Closed-loop transfer functions of optimization methods for DFIG-based wind turbine system.

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Table 7 Expand

Fig 12.

Step responses of PID controlled DFIG-based wind turbine system tuned by various algorithms.

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Fig 12 Expand

Table 8.

Numerical values of time-domain performance indicators for DFIG-based wind turbine system.

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Table 8 Expand

Fig 13.

Bode plot of h-ASPSO optimized DFIG-based wind turbine system.

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Fig 13 Expand