Energy and Reserve Scheduling Under a Joint Generation and Transmission Security Criterion: An Adjustable Robust Optimization Approach

This paper presents a new approach for energy and reserve scheduling in electricity markets subject to transmission flow limits. Security is imposed by guaranteeing power balance under each contingency state including both generation and transmission assets. The model is general enough to embody a joint generation and transmission n-K security criterion and its variants. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing total costs of energy and reserves while ensuring that the system is able to withstand each contingency. The middle-level problem identifies, for a given pre-contingency schedule, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency by minimizing the system power imbalance. The proposed trilevel problem is solved by a Benders decomposition approach. For computation purposes, a tighter formulation for the master problem is presented. Our approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models.