Abstract
In this study, the solution of a variational problem that allows determining the input voltage form that provides the maximum power factor of the battery charging process in the RLC circuit and the change character of the charging current for constant R, L, C and charging time has been examined. The defined problem is obtained and solved in the form of a linear integro-differential equation. A quadratic voltage criterion is proposed to analyze the convergence of the power factor to its maximum value for various modes of charging the battery.
References
- Jiang, C., Wang, S., Wu, B., Fernandez, C., Xiong, X., & Coffie-Ken, J. (2021). A state-of-charge estimation method of the power lithium-ion battery in complex conditions based on adaptive square root extended Kalman filter. Energy, 219, 119603.
- Perez, H. E., Hu, X., Dey, S., & Moura, S. J. (2017). Optimal charging of Li-ion batteries with coupled electro-thermal-aging dynamics. IEEE Transactions on Vehicular Technology, 66 (9), 7761-7770.
- Pontryagin L.S., Boltianski V., Gamkrelidze R., and. Mitchtchenko E. (1962). The Mathematical Theory of Optimal Processes, John Wiley and Sons, New York.
- Mumford, D. B., & Shah, J. (1989). Optimal approximations by piecewise smooth functions and associated variational problems. Communications on pure and applied mathematics.
- Sethi S. P., and Thompson G. L. (2000). Optimal Control Theory: Applications to Management Science and Economics, Kluwer, Boston, 2nd edition.
- Sotskov A.I., Kolesnik G.V. (2002). Optimal Control: Problems and Solutions. Moscow, New Econ.School,58 p.
- Jost, J.; Li-Jost, X. (2003) Calculus of Variations. Cambridge University Press.
- Troutman, J. L. (2012). Variational calculus with elementary convexity. Springer Science & Business Media.
- Alisoy, H. Z., Alisoy, G. T., Keleş, C., Deniz, F. N., Işık, İ., & İçel, Y. (2013).Darbe generatörünün maksimum enerjisi hakkında varyasyonel problem. İnönü Üniversitesi Malatya.TOK.
- Clarke F. (2013) Functional Analysis, Calculus of Variations and Optimal Control. Springer.
- Noton, A. R. M. (2013). Introduction to variational methods in control engineering. Elsevier.
Abstract
Bu çalışmada, sabit R, L, C ve şarj süresi için, R L C devresindeki batarya şarj işleminin maksimum güç faktörünü sağlayan giriş voltajı formunu ve şarj akımının değişim karakterini belirlemeye olanak sağlayan bir varyasyonel problemin çözümü incelenmiştir. Tanımlanan problem, lineer bir integro-diferansiyel denklem biçiminde elde edilir ve çözülür. Bataryanın şarj etmenin çeşitli modları için, güç faktörünün maksimum değerine yakınsamasının analizi için ikinci dereceden bir voltaj kriteri önerilmiştir.
References
- Jiang, C., Wang, S., Wu, B., Fernandez, C., Xiong, X., & Coffie-Ken, J. (2021). A state-of-charge estimation method of the power lithium-ion battery in complex conditions based on adaptive square root extended Kalman filter. Energy, 219, 119603.
- Perez, H. E., Hu, X., Dey, S., & Moura, S. J. (2017). Optimal charging of Li-ion batteries with coupled electro-thermal-aging dynamics. IEEE Transactions on Vehicular Technology, 66 (9), 7761-7770.
- Pontryagin L.S., Boltianski V., Gamkrelidze R., and. Mitchtchenko E. (1962). The Mathematical Theory of Optimal Processes, John Wiley and Sons, New York.
- Mumford, D. B., & Shah, J. (1989). Optimal approximations by piecewise smooth functions and associated variational problems. Communications on pure and applied mathematics.
- Sethi S. P., and Thompson G. L. (2000). Optimal Control Theory: Applications to Management Science and Economics, Kluwer, Boston, 2nd edition.
- Sotskov A.I., Kolesnik G.V. (2002). Optimal Control: Problems and Solutions. Moscow, New Econ.School,58 p.
- Jost, J.; Li-Jost, X. (2003) Calculus of Variations. Cambridge University Press.
- Troutman, J. L. (2012). Variational calculus with elementary convexity. Springer Science & Business Media.
- Alisoy, H. Z., Alisoy, G. T., Keleş, C., Deniz, F. N., Işık, İ., & İçel, Y. (2013).Darbe generatörünün maksimum enerjisi hakkında varyasyonel problem. İnönü Üniversitesi Malatya.TOK.
- Clarke F. (2013) Functional Analysis, Calculus of Variations and Optimal Control. Springer.
- Noton, A. R. M. (2013). Introduction to variational methods in control engineering. Elsevier.
Details
| Primary Language | English |
|---|---|
| Subjects | Control Theoryand Applications |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | December 30, 2023 |
| Publication Date | December 31, 2023 |
| Submission Date | October 12, 2023 |
| Acceptance Date | November 21, 2023 |
| Published in Issue | Year 2023 |