A transmission topology control (TC) framework for production cost reduction based on a shift factor (SF) representation of line flows is proposed. The framework can model topology changes endogenously while maintaining linearity in the overall Mixed Integer Linear Programming (MILP) formulation of the problem. In large power systems it is standard practice to optimize operations considering few but representative contingency constraints. Under these conditions and when tractably small switchable sets are analyzed, the shift factor framework has significant computational advantages compared to the standard Bθ alternative used so far in TC research. These claims are supported and elaborated by numerical results on full models of PJM with over 13,000 buses. We finally present analytical investigations on locational marginal price (LMP) computation in our shift factor TC framework and their relation to LMPs computed for problems without TC. Also, we discuss practical implementation choices such as sufficient conditions on lower bounds that allow selection of large numbers employed in the MILP formulation. NOMENCLATURE Scalars are indicated by lower case italic, vectors by lower case bold, matrices by upper case bold, and sets by upper case script characters, indexed appropriately. Upper limits are indicated by an over-bar, and lower limits by an under-bar. Optimal solutions of the problem without topology control are denoted by an asterisk. Sensitivities are indicated with Greek characters.
Indices m, nBuses. k, ℓLines. i ℓ From bus of line ℓ. j ℓ To bus of line ℓ. τ Contingency topology.
Sets and FunctionsL n+ Branches whose to node is n.