Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics

An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal s...
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Autor*in:	Ji'Ang Zhang [verfasserIn] Zonghang Han [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions

Übergeordnetes Werk:	In: IEEE Access - IEEE, 2014, 8(2020), Seite 129878-129888
Übergeordnetes Werk:	volume:8 ; year:2020 ; pages:129878-129888

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1109/ACCESS.2020.3009258

Katalog-ID:	DOAJ053350022

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520			\|a An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.
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allfields	10.1109/ACCESS.2020.3009258 doi (DE-627)DOAJ053350022 (DE-599)DOAJa5aee4abfa3547b3a9a50fbf54eb068c DE-627 ger DE-627 rakwb eng TK1-9971 Ji'Ang Zhang verfasserin aut Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time. Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering Zonghang Han verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 129878-129888 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:129878-129888 https://doi.org/10.1109/ACCESS.2020.3009258 kostenfrei https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c kostenfrei https://ieeexplore.ieee.org/document/9139956/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 129878-129888
spelling	10.1109/ACCESS.2020.3009258 doi (DE-627)DOAJ053350022 (DE-599)DOAJa5aee4abfa3547b3a9a50fbf54eb068c DE-627 ger DE-627 rakwb eng TK1-9971 Ji'Ang Zhang verfasserin aut Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time. Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering Zonghang Han verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 129878-129888 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:129878-129888 https://doi.org/10.1109/ACCESS.2020.3009258 kostenfrei https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c kostenfrei https://ieeexplore.ieee.org/document/9139956/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 129878-129888
allfields_unstemmed	10.1109/ACCESS.2020.3009258 doi (DE-627)DOAJ053350022 (DE-599)DOAJa5aee4abfa3547b3a9a50fbf54eb068c DE-627 ger DE-627 rakwb eng TK1-9971 Ji'Ang Zhang verfasserin aut Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time. Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering Zonghang Han verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 129878-129888 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:129878-129888 https://doi.org/10.1109/ACCESS.2020.3009258 kostenfrei https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c kostenfrei https://ieeexplore.ieee.org/document/9139956/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 129878-129888
allfieldsGer	10.1109/ACCESS.2020.3009258 doi (DE-627)DOAJ053350022 (DE-599)DOAJa5aee4abfa3547b3a9a50fbf54eb068c DE-627 ger DE-627 rakwb eng TK1-9971 Ji'Ang Zhang verfasserin aut Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time. Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering Zonghang Han verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 129878-129888 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:129878-129888 https://doi.org/10.1109/ACCESS.2020.3009258 kostenfrei https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c kostenfrei https://ieeexplore.ieee.org/document/9139956/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 129878-129888
allfieldsSound	10.1109/ACCESS.2020.3009258 doi (DE-627)DOAJ053350022 (DE-599)DOAJa5aee4abfa3547b3a9a50fbf54eb068c DE-627 ger DE-627 rakwb eng TK1-9971 Ji'Ang Zhang verfasserin aut Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time. Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering Zonghang Han verfasserin aut In IEEE Access IEEE, 2014 8(2020), Seite 129878-129888 (DE-627)728440385 (DE-600)2687964-5 21693536 nnns volume:8 year:2020 pages:129878-129888 https://doi.org/10.1109/ACCESS.2020.3009258 kostenfrei https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c kostenfrei https://ieeexplore.ieee.org/document/9139956/ kostenfrei https://doaj.org/toc/2169-3536 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2020 129878-129888
language	English
source	In IEEE Access 8(2020), Seite 129878-129888 volume:8 year:2020 pages:129878-129888
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topic_facet	Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions Electrical engineering. Electronics. Nuclear engineering
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authorswithroles_txt_mv	Ji'Ang Zhang @@aut@@ Zonghang Han @@aut@@
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callnumber-first	T - Technology
author	Ji'Ang Zhang
spellingShingle	Ji'Ang Zhang misc TK1-9971 misc Global optimization misc nonlinear dynamics misc multiple solutions for OPF misc KKT conditions misc Electrical engineering. Electronics. Nuclear engineering Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics
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topic_title	TK1-9971 Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics Global optimization nonlinear dynamics multiple solutions for OPF KKT conditions
topic	misc TK1-9971 misc Global optimization misc nonlinear dynamics misc multiple solutions for OPF misc KKT conditions misc Electrical engineering. Electronics. Nuclear engineering
topic_unstemmed	misc TK1-9971 misc Global optimization misc nonlinear dynamics misc multiple solutions for OPF misc KKT conditions misc Electrical engineering. Electronics. Nuclear engineering
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title	Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics
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title_full	Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics
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title_sort	identifying multiple local optima for optimal power flow based on nonlinear dynamics
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title_auth	Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics
abstract	An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.
abstractGer	An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.
abstract_unstemmed	An optimal power flow (OPF) problem of power systems can have multiple local optimal solutions, which is worthwhile studying both in theory and practice. Based on the existing nonlinear dynamic systems, this paper proposes an efficient deterministic algorithm to solve multiple or all local optimal solutions of OPF, which takes some numerical improving measures to enhance the numerical convergence for integration process of dynamics and adapt to OPF problem. The steps of this algorithm are as follows: 1. The reflected gradient system (RGS) is used to calculate the decomposition points to locate different feasible components. 2. The quotient gradient system (QGS) is used to calculate feasible points in different feasible components, and we numerically integrate projected gradient system (PGS) with these feasible points as initial points forward until the trajectories approach the local optima. 3. Slack variable perturbation method (SVPM) is proposed to help escape from the saddle points to the adjacent local optima when the trajectories fall into saddle points. Compared with the interior point method (IPM) with random initialization, multiple IEEE test cases show that the proposed algorithm can identify much more local optimal solutions, and meanwhile, significantly reduce the calculation time.
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title_short	Identifying Multiple Local Optima for Optimal Power Flow Based on Nonlinear Dynamics
url	https://doi.org/10.1109/ACCESS.2020.3009258 https://doaj.org/article/a5aee4abfa3547b3a9a50fbf54eb068c https://ieeexplore.ieee.org/document/9139956/ https://doaj.org/toc/2169-3536
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