Column-Generation for Capacity-Expansion Planning of Electricity Distribution Networks

We present a stochastic model for capacity-expansion planning of electricity distribution networks subject to uncertain demand (CEP). We formulate CEP as a multistage stochastic mixed-integer program with a scenario-tree representation of uncertainty. At each node of the scenario-tree, the model determines capacity-expansions, operating con guration, and power ows. A “super-arc” representation signi cantly reduces the number of binary variables and provides a tighter linear-programming relaxation. Dantzig-Wolfe decomposition leads to (a) a master problem containing binary capacity-expansion and high-level operating decisions; and (b) column-generating subproblems which are mixed-integer programs representing single-period, deterministic capacity-expansion models. Solution times for column generation applied to these models are signi cantly better than those for CPLEX applied to the original stochastic integer programs.