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

Abstract

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.

Modelling and region stability analysis of wind turbines with battery energy storage system based on switched system with multi-equilibriums

“…Fig. 9(c) shows the plots of wind turbine rotor speed, which demonstrates the proposed results (the solid red line) is better than other results (the dotted black line) (Palejiya et al, 2013) which is based on the single equilibrium analysis (Palejiya et al, 2013). Finally, it can be seen from Figures 10 and 11 that the proposed schedule method of battery energy can keep the SOC with the expected range and smooth the output power of WT/BESS effectively.…”

“…To analyze the stability for wind turbine, the method of linearization as follows is often used (Palejiya et al, 2013, Lin Z et al, 2018…”

“…Considering a practical WT/BESS given in (Palejiya et al, 2013), where the rotor radius Assume the average wind speed is 12m/s, and by following the design procedure presented in Section 3, the PI controller and the corresponding stable region are obtained.…”

Kharitonov Theorem Based Robust Stability Analysis of a Wind Turbine Pitch Control System

“…As explained in the work of Behr et al [21], the Lyapunov Equation is the symmetric version of the general Sylvester Equation, so they are usually considered to be part of the same criterion. The application of the Lyapunov criterion to the control system of a horizontal axis wind turbines can be found in the works of Palejiya et al [22,23]. In those papers, the stability of a control algorithm proposed for the transitions of the wind turbine between the under rated and the rated operations is analyzed by means of the Lyapunov criterion.…”

Almost Sure Stability of Switching Markov Jump Linear Systems

“…For example, in renewable power generation industry, the performance of a wind turbines can be described by a Markov model considering the component reliability and the effect of wind speed [16]. In this area, various complicated switching controls are essential for stable and optimised operation [17].…”