Two-stage approach for the predispatch problem with uncertain demand using splitting variables in interior-point methods

The stochastic predispatch optimal power flow problem aims to minimize generation costs and
transmission losses subject to network constraints under demand uncertainty. We formulate it as
a two-stage stochastic quadratic optimization problem with fixed recourse, in which hydroelectric
generation constitutes the here-and-now decision, while thermal generation and transmission flows
are recourse decisions. Using a splitting-variable reformulation, we cast the extensive form into a
block-angular structure and solve the resulting problem with a specialized interior-point method
(implemented in the academic solver BlockIP), which combines direct and iterative methods for
computing the Newton direction. On a benchmark of seven networks from 30 to 9 241 buses with
up to 100 demand scenarios, the method returns an optimal solution on every instance, including
a large-scale case with millions of variables on which the commercial solvers CPLEX and Gurobi
and the open-source solver HiPO-HiGHS all fail to return a solution (CPLEX and Gurobi exhaust
the available memory, while HiPO-HiGHS terminates with a solver error). We further quantify the
economic value of the stochastic solution through the VSS and EVPI metrics, characterizing the
regimes in which the stochastic model yields the largest benefit over its deterministic counterpart.

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