Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.
Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China.|University of the Chinese Academy of Sciences, Beijing, China.
Jinpeng
J
Ma
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, China.|University of the Chinese Academy of Sciences, Beijing, China.
Yong
Y
Sun
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China.
Xiaoming
X
Yuan
Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany.|Department of Physics, Humboldt University, Berlin, Germany.|Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, United Kingdom.
Jürgen
J
Kurths
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan, China.
Meng
M
Zhan
D000465:Algorithms; D003198:Computer Simulation; D011211:Electric Power Supplies; D004560:Electricity; D004867:Equipment Design; D008956:Models, Chemical; D017711:Nonlinear Dynamics