Geodesic
On the generalized Gardner problem for phase-locked loops in electrical grids
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 71-75.

Voir la notice de l'article provenant de la source Math-Net.Ru

Methods of nonlinear analysis and synthesis of synchronization control systems for electrical grids have been developed. The use of averaging methods and Lyapunov-type stability criteria for the cylindrical phase space have made it possible for the first time in the Gardner problem to obtain analytical estimates of the system parameters to ensure acceptable values of phase errors and to take into account changes in the reference signal amplitude.
Keywords: phase-locked loop, tunable lock-in range, Lyapunov function, Gardner problem, electrical grids. 
@article{DANMA_2021_498_a13,
     author = {N. Kuznetsov and M. Yu. Lobachev and M. V. Yuldashev and R. V. Yuldashev and S. I. Volskiy and D. A. Sorokin},
     title = {On the generalized {Gardner} problem for phase-locked loops in electrical grids},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {71--75},
     publisher = {mathdoc},
     volume = {498},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/}
}
TY  - JOUR
AU  - N. Kuznetsov
AU  - M. Yu. Lobachev
AU  - M. V. Yuldashev
AU  - R. V. Yuldashev
AU  - S. I. Volskiy
AU  - D. A. Sorokin
TI  - On the generalized Gardner problem for phase-locked loops in electrical grids
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 71
EP  - 75
VL  - 498
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/
LA  - ru
ID  - DANMA_2021_498_a13
ER  - 
%0 Journal Article
%A N. Kuznetsov
%A M. Yu. Lobachev
%A M. V. Yuldashev
%A R. V. Yuldashev
%A S. I. Volskiy
%A D. A. Sorokin
%T On the generalized Gardner problem for phase-locked loops in electrical grids
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 71-75
%V 498
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/
%G ru
%F DANMA_2021_498_a13
N. Kuznetsov; M. Yu. Lobachev; M. V. Yuldashev; R. V. Yuldashev; S. I. Volskiy; D. A. Sorokin. On the generalized Gardner problem for phase-locked loops in electrical grids. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 71-75. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a13/

[1] Shakhgildyan V.V., Lyakhovkin A.A., Fazovaya avtopodstroika chastoty, Svyaz, M., 1966

[2] Viterbi A., Principles of coherent communications, McGraw-Hill, N.Y., 1966

[3] Best R.E., Phase-Locked Loops: Design, Simulation and Application, 6th ed., McGraw-Hill, N.Y., 2007 | MR

[4] Karimi-Ghartemani M., Enhanced phase-locked loop structures for power and energy applications, John Wiley Sons, 2014

[5] Golestan S., Guerrero J., Vasquez J., “Single-phase PLLs: A review of recent advances”, IEEE Transactions on Power Electronics, 32:12 (2017), 9013–9030 | DOI

[6] Burton T., Jenkins N., Sharpe D., Bossanyi E., Wind energy handbook, John Wiley Sons, 2011

[7] Kuznetsov N.V., Volskiy S.I., Sorokin D.A., Yuldashev M.V., Yuldashev R.V., “Power supply system for aircraft with electric traction”, 21st Intern. Sci. Conf. on Electric Power Engineering, 2020, 1–5 | MR

[8] Gardner F.M., Phaselock Techniques, 3rd edition, John Wiley Sons, N.Y., 2005

[9] Kuznetsov N.V., Lobachev M.Yu., Yuldashev M.V., Yuldashev R.V., “O probleme Gardnera dlya sistem upravleniya fazovoi avtopodstroikoi chastoty”, DAN, 489:6 (2019), 541–544 | MR | Zbl

[10] Bogolyubov N.N., Mitropolskii Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Gos. izd-vo fiz.-mat. lit-ry, M., 1958 | MR

[11] Matrosov V.M., Malikov A.I., “Razvitie idei A.M. Lyapunova za 100 let: 1892-1992”, Izvestiya vuzov. Matematika, 1993, no. 4, 3–47 | MR

[12] Vasilev S.N., Kozlov R.I., Ulyanov S.A., “Ustoichivost mnogorezhimnykh formatsii”, DAN, 455:3 (2014), 269–274

[13] Leonov G.A., Kuznetsov N.V., Nonlinear mathematical models of phase-locked loops. Stability and oscillations, Cambridge Scientific Publishers, Cambridge, 2014 | MR

[14] Kuznetsov N.V., Leonov G.A., Yuldashev M.V., Yulda-shev R.V., “Hidden attractors in dynamical models of phase-locked loop circuits: limitations of simulation in MATLAB and SPICE”, Communications in Nonlinear Science and Numerical Simulation, 51 (2017), 39–49 | DOI | MR

[15] Kuznetsov N.V., “Teoriya skrytykh kolebanii i ustoichivost sistem upravleniya”, Izvestiya RAN. Teoriya i sistemy upravleniya, 2020, no. 5, 5–27 | DOI | Zbl