Robustness and fault detection in power systems based on parameter-dependent Lyapunov functions

In power systems, it is inevitable for faults and disturbances to happen, and the robust fault detection of power systems has become the focus of researchers in recent years. Since power systems do not generally have only one typical operating condition, the polytopic model provides a description of the uncertain system operation with a better physical meaning. To this end, the present study investigates the fault detection problem for uncertain polytopic power system model. In order to reduce the conservativeness of existing conditions, we present an efficient algorithm by generating homogeneous polynomial parameter-dependent Lyapunov functions of arbitrary degree on the uncertain parameters, which includes as special cases existing conditions for RFDF design. It can be established that as the degree of the polynomial increases, the number of LMIs and free variables increases and the test becomes less conservative. The methodology proposed can possibly be applied to relevant aspects such as improving the dynamic stability and robustness of power systems.