  Enhancing existing transmission lines is a useful tool to combat transmission
congestion and guarantee transmission security with increasing demand and
boosting the renewable energy source. This study concerns the selection of
lines whose capacity should be expanded and by how much from the perspective of
independent system operator (ISO) to minimize the system cost with the
consideration of transmission line constraints and electricity generation and
demand balance conditions, and incorporating ramp-up and startup ramp rates,
shutdown ramp rates, ramp-down rate limits and minimum up and minimum down
times. For that purpose, we develop the ISO unit commitment and economic
dispatch model and show it as a right-hand side uncertainty multiple parametric
analysis for the mixed integer linear programming (MILP) problem. We first
relax the binary variable to continuous variables and employ the Lagrange
method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal
decision variables and objective function) and critical regions associated with
active and inactive constraints. Further, we extend the traditional branch and
bound method for the large-scale MILP problem by determining the upper bound of
the problem at each node, then comparing the difference between the upper and
lower bounds and reaching the approximate optimal solution within the decision
makers' tolerated error range. In additional, the objective function's first
derivative on the parameters of each line is used to inform the selection of
lines to ease congestion and maximize social welfare. Finally, the amount of
capacity upgrade will be chosen by balancing the cost-reduction rate of the
objective function on parameters and the cost of the line upgrade. Our findings
are supported by numerical simulation and provide transmission line planners
with decision-making guidance.
