Daily scheduling of generating units with natural-gas market constraints

We address the daily scheduling of generating units (unit commitment) in a system whose production mix includes a large number of natural-gas-fired units. We assume that the natural-gas system, operating under market conditions, does its best to supply the natural-gas for electricity production required by the power system. We formulate this problem as a bi-level model whose upper-level problem represents the scheduling of generating units under a second-order conic relaxation of the AC network constraints, and whose lower-level one represents the clearing of the natural-gas market. The upper-level problem is mixed-integer second-order conic, while the lower-level one is second-order conic as well, but continuous. We replace the lower-level problem by its optimality conditions in the form of primal constraints, dual constraints, and strong duality equality, which results in a single-level nonconvex mixed-integer nonlinear optimization problem. To improve the computational tractability of such formulation, we derive a mixed-integer second-order conic relaxation of the single-level nonconvex mixed-integer nonlinear optimization problem. Such problem is solved using a Benders-type outer-approximation decomposition framework with a master mixed-integer linear problem and two subproblems that are nonlinear but convex. The communication between the master problem and the subproblems is enhanced by incorporating into the master problem linearized information pertaining to the subproblems and valid linear inequalities. The benefits of the proposed model and the effectiveness of the solution procedure are illustrated using the IEEE 24-bus test system coupled with a 20-node natural-gas system and the Central Illinois 200-bus power system coupled with a 48-node natural-gas system.