Advanced functionalities of the smart grids are possible thanks to a tight integration between power systems and communication networks. Such an integration allows for a more efficient utilization of the grid assists via enhanced control strategies. Towards this objective, optimal allocation of metering and control devices with advanced communication capabilities is a necessity. However, in order to ensure optimal allocation and coverage for such communication devices, spatial information about the smart grid entities must be available. This is mainly due to the fact that the electric loads within the grid exhibit substantial spatial correlations. Unfortunately, the existing grid models such as the IEEE-bus test systems do not reflect such a spatial dimension. The problem is further complicated as the smart grid infrastructure is continuously expanding with time. To address this limitation, we propose in this paper a stochastic geometry based spatio-temporal expanding power grid model that is constructed in a Poissonian city. Such a model can be used as a tool for strategic deployment of communication devices within the smart grid. A thorough comparison with a real power grid shows that our model provides accurate spatial approximation in terms of node degree distribution, betweenness centrality, grid diameter, node clustering, and eigenvalues spread.