Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-9
Year of Publication : 2021
Authors : Na Han, Yanhui Zhai
  10.14445/22315373/IJMTT-V67I9P516

MLA

MLA Style: Na Han, Yanhui Zhai."Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model" International Journal of Mathematics Trends and Technology 67.9 (2021):138-145. 

APA Style: Na Han, Yanhui Zhai(2021). Stability and Hopf Bifurcation of PD-Controlled XCP Network Congestion Model  International Journal of Mathematics Trends and Technology, 67(9), 138-145.

Abstract
Based on feedback control and bifurcation theory, a PD controller is proposed to solve the Hopf branch problem of XCP network congested power system. Firstly, α is selected as the branching parameter to obtain the critical value that keeps the original system and the controlled system stable. When the delay value passes the critical value, the system will lose stability at the equilibrium point and Hopf branch will be generated. Then, the addition of PD controller increases the critical value of system branch parameters, expands the stability region, and effectively alleviates the generation of Hopf branches. Finally, the feasibility of theoretical analysis is verified by numerical simulation with mathematical software.

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Keywords : Hopf bifurcation, PD controller, Stability, network congestion