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HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems.

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Title: HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems.
Authors: Li, Yaya1 (AUTHOR), Hu, Qing2 (AUTHOR) future0550@cdu.edu.cn, Liu, Xingyue1 (AUTHOR), Jiang, Yu1,2 (AUTHOR), Liao, Xuanqi1 (AUTHOR), Shi, Kaibo1 (AUTHOR)
Source: Energies (19961073). Jun2026, Vol. 19 Issue 12, p2783. 29p.
Subject Terms: *Grey Wolf Optimizer algorithm, *Electric power system control, *Differential evolution, *PID controllers, *Nonlinear systems, *Interconnected power systems, *Time delay systems
Abstract: In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions. [ABSTRACT FROM AUTHOR]
Database: Energy & Power Source
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Header DbId: enr
DbLabel: Energy & Power Source
An: 194909232
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  Label: Title
  Group: Ti
  Data: HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems.
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  Data: <searchLink fieldCode="AR" term="%22Li%2C+Yaya%22">Li, Yaya</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hu%2C+Qing%22">Hu, Qing</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> future0550@cdu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Xingyue%22">Liu, Xingyue</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Jiang%2C+Yu%22">Jiang, Yu</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liao%2C+Xuanqi%22">Liao, Xuanqi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Shi%2C+Kaibo%22">Shi, Kaibo</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Energies+%2819961073%29%22">Energies (19961073)</searchLink>. Jun2026, Vol. 19 Issue 12, p2783. 29p.
– Name: Subject
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  Data: *<searchLink fieldCode="DE" term="%22Grey+Wolf+Optimizer+algorithm%22">Grey Wolf Optimizer algorithm</searchLink><br />*<searchLink fieldCode="DE" term="%22Electric+power+system+control%22">Electric power system control</searchLink><br />*<searchLink fieldCode="DE" term="%22Differential+evolution%22">Differential evolution</searchLink><br />*<searchLink fieldCode="DE" term="%22PID+controllers%22">PID controllers</searchLink><br />*<searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br />*<searchLink fieldCode="DE" term="%22Interconnected+power+systems%22">Interconnected power systems</searchLink><br />*<searchLink fieldCode="DE" term="%22Time+delay+systems%22">Time delay systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions. [ABSTRACT FROM AUTHOR]
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.3390/en19122783
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 29
        StartPage: 2783
    Subjects:
      – SubjectFull: Grey Wolf Optimizer algorithm
        Type: general
      – SubjectFull: Electric power system control
        Type: general
      – SubjectFull: Differential evolution
        Type: general
      – SubjectFull: PID controllers
        Type: general
      – SubjectFull: Nonlinear systems
        Type: general
      – SubjectFull: Interconnected power systems
        Type: general
      – SubjectFull: Time delay systems
        Type: general
    Titles:
      – TitleFull: HDE-CGWO-Based Optimal Load Frequency Control for Nonlinear Power Systems.
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Li, Yaya
      – PersonEntity:
          Name:
            NameFull: Hu, Qing
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            NameFull: Liu, Xingyue
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            NameFull: Jiang, Yu
      – PersonEntity:
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            NameFull: Liao, Xuanqi
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            NameFull: Shi, Kaibo
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            – D: 15
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 19961073
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              Value: 19
            – Type: issue
              Value: 12
          Titles:
            – TitleFull: Energies (19961073)
              Type: main
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