Abstract
This study examines the robust stability of a power system, which is based on proportional-integral-derivative load frequency control and involves uncertain parameters and time delays. The model of the system is firstly established, following which the system is transformed into a closed-loop system with feedback control. On this basis, a new augmented Lyapunov-Krasovskii (LK) functional is established for using the new Bessel-Legendre inequality to estimate the derivative of the functional, which can provide a maximum lower bound. A stability criterion is then derived by employing the LK functional and Bessel-Legendre inequality. Finally, numerical examples are used to demonstrate the validity and superiority of the proposed method.
Highlights
This study examines the robust stability of a power system, which is based on proportional-integral-derivative load frequency control and involves uncertain parameters and time delays
The development of an intelligent power grid requires that the power system frequency operate safely within a small range of its equilibrium value, and the load frequency control[1] (LFC) can meet this requirement
The stability margin of the system is obtained by employing the linear matrix inequality (LMI) toolbox
Summary
The development of an intelligent power grid requires that the power system frequency operate safely within a small range of its equilibrium value, and the load frequency control[1] (LFC) can meet this requirement. In the process of data transmission, time delays are inevitable and uncertain[2] The existence of these factors is likely to affect the stability of the power system. Studying the robust stability of power systems with time delays and uncertain parameters is of tremendous value. The stability margin of the system is obtained by employing the linear matrix inequality (LMI) toolbox. This study aims to improve the upper bound of the time delay of the system by proposing an augmented LK functional and using the Bessel-Legendre inequality to estimate the derivative of the functional. A time-varying delay power system model is established with uncertain parameters based on proportional-integral-derivative (PID) load frequency control. The robust stability criterion of the system is obtained by employing the Bessel-Legendre inequality discussed in Ref. The variables used in this study are defined as follows: Rn and Rn×m denote n-dimensional vectors and n × m dimensional matrices in the real number domain, respectively; RT and R-1 represent the transpose and inverse of a matrix, respectively; I and 0 are identity and zero matrices, respectively; P>0 means that the matrix P is symmetric and positive; Sym{X}=X+XT; ‘*’ represents symmetric terms in a symmetric matrix; and diag{···} denotes a diagonal matrix
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