Partial stability criterion for a heterogeneous power grid with hub structures

Abstract

One of the priority tasks in studying power grids is to find the conditions of their stable operation. The fundamental requirement is synchronizing all the elements (generators and consumers) of a power grid. However, various disturbances can destroy the synchronization. Moreover, desynchronization occurring in a small part of the grid can lead to severe large-scale power outages (or blackouts) due to numerous cascading failures. Here we consider the model of a heterogeneous power grid with hub structures (subgrids), taking into account arbitrary lengths and impedances of grid’s transmission lines and also their arbitrary amount. Using the auxiliary comparison systems approach, we analyze the dynamics of a hub subgrid. Based on the findings, we develop a novel criterion of partial stability of power grids featuring hub structures. The criterion makes it possible to identify the regions of safe operation of individual hub subgrid elements. First, the criterion allows obtaining parameters’ values that guarantee existence and local stability of either synchronous or quasi-synchronous modes in individual hub subgrid elements, i.e. steady-state stability. Second, the criterion allows obtaining the safe values of abrupt frequency and phase disturbances that eventually vanish, i.e. imply transient stability with respect to state disturbance. Third, the criterion permits determining the safe ranges of parameters’ disturbances that do not lead to catastrophic desynchronizing effects, i.e. imply transient stability with respect to parameters’ disturbance. Also, we discover typical dependences of the safe regions on the parameters of transmission lines. We demonstrate the applicability of the criterion on two test power grids with arbitrary distributions of powers as well as effective lengths and impedances of transmission lines. The results may help optimize stability and contribute to developing new real-time control schemes for smart grids that can automatically recover from failures.