Understanding the structural properties of the power grids under different disruptive event scenarios is the key towards improvement of the security, reliability, and efficiency of modern power systems. The most widely explored characteristics of power grid resilience in the complex network context are node degree distribution and its functions that primarily address a global network topology. However, the robustness of power grids is also intrinsically connected to local higher-order network features. In this study, the concepts of network motifs and topological data analysis, particularly, persistent homology, are used to derive a new metric for resilience of power grid networks. These methods are demonstrated on electricity transmission networks of European countries and a simulated version of the Texas power grid network.