  The development of algorithms for enhancing the resilience and efficiency of
the power grid requires performance evaluation with real topologies of power
transmission networks. However, due to security reasons, such topologies and
particularly the locations of the substations and the lines are usually not
publicly available. Therefore, we study the structural properties of the North
American grids and present an algorithm for generating synthetic spatially
embedded networks with similar properties to a given grid. The algorithm uses
the Gaussian Mixture Model (GMM) for density estimation of the node positions
and generates a set of nodes with similar spatial distribution to the nodes in
a given network. Then, it uses two procedures, which are inspired by the
historical evolution of the grids, to connect the nodes. The algorithm has
several tunable parameters that allow generating grids similar to any given
grid. Particularly, we apply it to the Western Interconnection (WI) and to
grids that operate under the SERC Reliability Corporation (SERC) and the
Florida Reliability Coordinating Council (FRCC), and show that it generates
grids with similar structural and spatial properties to these grids. To the
best of our knowledge, this is the first attempt to consider the spatial
distribution of the nodes and lines and its importance in generating synthetic
power grids.
