Decomposition of energy function and hierarchical transient stability diagnosis for power networks

In this paper, we consider a power network with multiple synchronous machines (generators and motors) exhibiting multiple collective swing motions and aim at hierarchical diagnosis of transient stability in the network. We decompose an energy function of the entire network into energy functions of the collective motion of coherently clustered machines and of the machines´ motion relative to the collective motions as a main result. This decomposition enables us to extract distinctive behaviors in swing dynamics, and to consider hierarchical stability diagnosis. We also derive a hierarchical sufficient condition of transient stability of the entire network in terms of these energy functions. Finally, we study the diagnosis with a numerical example of a simple power network model.