Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach
This paper presents a novel mathematical framework for modelling and optimizing Phase-Locked Loop (PLL) dynamics in grid-connected systems using a hybrid optimization approach. The proposed model combines a state-space representation of PLL dynamics with an innovative dual-optimization algorithm int...
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| Format: | Article |
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Taylor & Francis Group
2025-12-01
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| Series: | Systems Science & Control Engineering |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/21642583.2024.2448636 |
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| author | Mrinal Kanti Rajak Rajen Pudur |
| author_facet | Mrinal Kanti Rajak Rajen Pudur |
| author_sort | Mrinal Kanti Rajak |
| collection | DOAJ |
| description | This paper presents a novel mathematical framework for modelling and optimizing Phase-Locked Loop (PLL) dynamics in grid-connected systems using a hybrid optimization approach. The proposed model combines a state-space representation of PLL dynamics with an innovative dual-optimization algorithm integrating Particle Swarm Optimization (PSO) and Gradient Descent (GD). A comprehensive mathematical model is developed, incorporating the nonlinear dynamics of the PLL system through differential equations and transfer functions. The hybrid optimization framework is formulated as a constrained optimization problem, where PSO provides global search capabilities while GD ensures local convergence. Numerical simulations demonstrate the model's superior performance compared to conventional approaches including SRF-PLL, DDSRF-PLL, and MSOGI-PLL, achieving 40% faster convergence and maintaining phase tracking errors below 3 degrees during severe grid disturbances. The framework offers a systematic method for analyzing and optimizing dynamical systems in power electronics. |
| format | Article |
| id | doaj-art-0a7c4b6a69734a008f5c263b3c772fce |
| institution | Kabale University |
| issn | 2164-2583 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Systems Science & Control Engineering |
| spelling | doaj-art-0a7c4b6a69734a008f5c263b3c772fce2025-01-08T19:19:56ZengTaylor & Francis GroupSystems Science & Control Engineering2164-25832025-12-0113110.1080/21642583.2024.2448636Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approachMrinal Kanti Rajak0Rajen Pudur1Department of Electrical Engineering, National Institute of Technology Arunachal Pradesh, Jote, Arunachal Pradesh, IndiaDepartment of Electrical Engineering, National Institute of Technology Arunachal Pradesh, Jote, Arunachal Pradesh, IndiaThis paper presents a novel mathematical framework for modelling and optimizing Phase-Locked Loop (PLL) dynamics in grid-connected systems using a hybrid optimization approach. The proposed model combines a state-space representation of PLL dynamics with an innovative dual-optimization algorithm integrating Particle Swarm Optimization (PSO) and Gradient Descent (GD). A comprehensive mathematical model is developed, incorporating the nonlinear dynamics of the PLL system through differential equations and transfer functions. The hybrid optimization framework is formulated as a constrained optimization problem, where PSO provides global search capabilities while GD ensures local convergence. Numerical simulations demonstrate the model's superior performance compared to conventional approaches including SRF-PLL, DDSRF-PLL, and MSOGI-PLL, achieving 40% faster convergence and maintaining phase tracking errors below 3 degrees during severe grid disturbances. The framework offers a systematic method for analyzing and optimizing dynamical systems in power electronics.https://www.tandfonline.com/doi/10.1080/21642583.2024.2448636Dynamical systems modellinghybrid optimization and power system dynamics |
| spellingShingle | Mrinal Kanti Rajak Rajen Pudur Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach Systems Science & Control Engineering Dynamical systems modelling hybrid optimization and power system dynamics |
| title | Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach |
| title_full | Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach |
| title_fullStr | Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach |
| title_full_unstemmed | Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach |
| title_short | Mathematical modelling and dynamic optimization of phase-locked loop systems using hybrid PSO-gradient descent approach |
| title_sort | mathematical modelling and dynamic optimization of phase locked loop systems using hybrid pso gradient descent approach |
| topic | Dynamical systems modelling hybrid optimization and power system dynamics |
| url | https://www.tandfonline.com/doi/10.1080/21642583.2024.2448636 |
| work_keys_str_mv | AT mrinalkantirajak mathematicalmodellinganddynamicoptimizationofphaselockedloopsystemsusinghybridpsogradientdescentapproach AT rajenpudur mathematicalmodellinganddynamicoptimizationofphaselockedloopsystemsusinghybridpsogradientdescentapproach |