  The topological structure of the power grid plays a key role in the reliable
delivery of electricity and price settlement in the electricity market.
Incorporation of new energy sources and loads into the grid over time has led
to its structural and geographical expansion and can affect its stable
operation. This paper presents an intuitive analytical model for the temporal
evolution of large grids and uses it to understand common structural features
observed in grids across America. In particular, key graph parameters like
degree distribution, graph diameter, betweenness centralities, eigen-spread and
clustering coefficients, as well as graph processes like infection propagation
are used to quantify the model's benefits through comparison with the Western
US and ERCOT power grids. The most significant contribution of the developed
model is its analytical tractability, that provides a closed form expression
for the nodal degree distribution observed in large grids. The discussed model
can be used to generate realistic test cases to analyze topological effects on
grid functioning and new grid technologies.
