Characterization of Cutsets in Networks With Application to Transient Stability Analysis of Power Systems

A cutset is a concept of importance in both graph theory and many engineering problems. In this paper, cutset properties are studied and applied to transient stability problems in power systems. First, we reveal that cutsets are intrinsically linked to cycles, another important concept in the graph theory. The main theoretical results include that any pair of edges in a cutset are concyclic (i.e., contained in the same cycle), and any edge together with some of its concyclic edges can form a cutset. Then, with the cycle constraint for the bus angles in power networks, we give a theoretical explanation of a common phenomenon in transient stability that the loss of synchronism initiates from the angle separation across the critical cutset in the underlying power network. This phenomenon is frequently observed but no proof has been presented yet. Moreover, an improved cutset index (ICI) is proposed based on these cutset properties. This index can better identify the vulnerable cutset and help to estimate the cutset-relevant unstable equilibrium points and critical energy for stability region determination. Numerical studies on two IEEE test systems show that the formation of critical cutset coincides with the explanation, and the ICI has better performance than the conventional cutset index especially in heavy-load cases.