Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications
Abstract
:1. Introduction
2. Existence of Periodic Solutions
- (i)
- implies ;
- (ii)
- is compact and continuous;
- (iii)
- is a contraction mapping.
3. Asymptotic Stability
4. Application in Smart Grid Optimization
- Dynamic Load Demand: Fluctuations in electricity consumption require advanced models to maintain stability and efficiency [36].
4.1. Problem Statement
- Periodic and nonlinear variations in voltage and power flow.
- The impact of transmission delays on grid stability.
- The long-term asymptotic behavior of voltage fluctuations in the presence of nonlinearities.
4.2. Application of Theoretical Results
- represents the voltage at a node in the network.
- models the periodic power input from renewable sources.
- accounts for delays due to transmission distances.
- and describe nonlinear load characteristics.
- The nonlinear behavior of loads and power sources.
- Delayed feedback due to communication or signal propagation.
- Periodic variations in power generation and consumption.
4.3. Simulation of Voltage Dynamics
- T: Period of the system, .
- : Delay term, defined as .
- : Periodic coefficient, defined as .
- : Periodic coefficient, defined as .
- : Periodic power input, defined as .
- : Periodic coefficient, defined as .
- : Nonlinear function, defined as .
- : Nonlinear function, defined as .
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Mesmouli, M.B.; Ardjouni, A.; Popa, I.-L.; Saber, H.; Damag, F.H.; Madani, Y.A.; Hassan, T.S. Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications. Axioms 2025, 14, 269. https://doi.org/10.3390/axioms14040269
Mesmouli MB, Ardjouni A, Popa I-L, Saber H, Damag FH, Madani YA, Hassan TS. Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications. Axioms. 2025; 14(4):269. https://doi.org/10.3390/axioms14040269
Chicago/Turabian StyleMesmouli, Mouataz Billah, Abdelouaheb Ardjouni, Ioan-Lucian Popa, Hicham Saber, Faten H. Damag, Yasir A. Madani, and Taher S. Hassan. 2025. "Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications" Axioms 14, no. 4: 269. https://doi.org/10.3390/axioms14040269
APA StyleMesmouli, M. B., Ardjouni, A., Popa, I.-L., Saber, H., Damag, F. H., Madani, Y. A., & Hassan, T. S. (2025). Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications. Axioms, 14(4), 269. https://doi.org/10.3390/axioms14040269