Transient Stability Conditions Assessment in Smart Grids via New Lyapunov Approaches

In recent years, due to the significant increase in power demand, stability issue has been considered as a remarkable challenge in power networks. In view of this fact, it could be mentioned that the presentation of accurate and definitive conditions to associate the stability of power system with related parameters and graph-theoretical characteristics of the underlying network, has been the main concern of control engineers. In this paper, utilizing the non-uniform model of the second-order Kuramoto oscillators, the stability conditions of smart grids with arbitrary interconnection topology and uncertain input power to generating units have been presented based on the explicit functions of physical characteristics of oscillators and network graph topology. The stability conditions have been obtained by two separate methods: the LaSalle's invariance principle and contraction property. The validity and the practical applicability of the developed transient stability conditions have been confirmed through the numerical simulations on the IEEE 39-bus system.