scholarly journals A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope

Automatica ◽  
2019 ◽  
Vol 100 ◽  
pp. 52-60 ◽  
Author(s):  
Amaury Hayat ◽  
Peipei Shang
Keyword(s):  
Lyapunov Function ◽  
Quadratic Lyapunov Function ◽  
Saint Venant Equations

Stability of Wind Turbine Switching Control in an Integrated Wind Turbine and Rechargeable Battery System: A Common Quadratic Lyapunov Function Approach

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Dushyant Palejiya ◽  
John Hall ◽  
Christine Mecklenborg ◽  
Dongmei Chen
Keyword(s):  
Wind Speed ◽  
Lyapunov Function ◽  
Wind Turbine ◽  
Rechargeable Batteries ◽  
System Stability ◽  
Control Mode ◽  
Rechargeable Battery ◽  
Quadratic Lyapunov Function ◽  
Battery System ◽  
Single Output

The power generated by wind turbines varies due to variations in the wind speed. A pack of rechargeable batteries could be used as a reserve power source to alleviate the intermittency in the wind turbine power. An integrated wind turbine and battery storage system is constructed where the wind turbine is electrically connected to a rechargeable battery system. Such a system can operate in two modes depending on the wind speed, power demand, and battery limit. The switching conditions for the wind turbine to operate in multi-input, single-output and single-input, single-output control mode are discussed. Linearized approximations of the closed loop wind turbine system are derived in order to analyze the switching stability between control modes. Common quadratic Lyapunov function (CQLF) is established for both control modes to prove the system stability. Simulation results demonstrating system stability are also presented.

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