  Synthetic power grids enable secure, real-world energy system simulations and
are crucial for algorithm testing, resilience assessment, and policy
formulation. We propose a novel method for the generation of synthetic
transmission power grids using Exponential Random Graph (ERG) models. Our two
main contributions are: (1) the formulation of an ERG model tailored
specifically for capturing the topological nuances of power grids, and (2) a
general procedure for estimating the parameters of such a model conditioned on
working with connected graphs. From a modeling perspective, we identify the
edge counts per bus type and $k$-triangles as crucial topological
characteristics for synthetic power grid generation. From a technical
perspective, we develop a rigorous methodology to estimate the parameters of an
ERG constrained to the space of connected graphs. The proposed model is
flexible, easy to implement, and successfully captures the desired topological
properties of power grids.
