  The stable and efficient operation of the transmission network is fundamental
to the power system's ability to deliver electricity reliably and cheaply. As
average temperatures continue to rise, the ability of the transmission network
to meet demand is diminished. Higher temperatures lead to congestion by
reducing thermal limits of lines while simultaneously reducing generation
potential. Due to prohibitive costs and limited real estate for building new
lines, it is necessary to consider capacity expansion as well to improve the
functioning and efficiency of the grid. Optimal control, however, requires many
discrete choices, rendering fully accurate models intractable. Furthermore,
temperature changes will impact different regions and climate differently. As
such, it is necessary to model both temperature changes and transmission flows
with high spatial resolution. This work proposes a case study of the
transmission grid centered in Arizona, using a DC optimal power flow
mathematical formulation to plan for future transmission expansion and capacity
expansion to efficiently meet demand. The effects of rising temperatures on
transmission and generation are modeled at the regional level. Several classes
of valid inequalities are employed to speed up the solution process. Multiple
experiments considering different temperature and demand trends are considered
which include each of the above technologies.
