Power-based transmission constrained unit commitment formulation with energy-based reserve

Staircase transmission constrained unit commitment (TCUC) formulations have been used for decades and are considered as energy-based TCUC formulations (EbUC). Recently, it has been reported that EbUC formulations may result in undeliverable energy schedules. Some power-based TCUC formulations (PbUC) have been proposed to address this problem. However, exact continuous time-based power outputs of units are usually approximated in these PbUC formulations and ramp-rate capacities of units are not accurately modelled. Besides, the implicit coupling between ramp-rate constraints and spinning reserves is neglected in both EbUC and PbUC formulations, which may cause that scheduled spinning reserve levels are unavailable in some time periods. To address these problems, a new PbUC formulation is proposed in this study with continuous time-based power outputs. It is found that the formulation can be transformed into an equivalent mathematical program and a Lagrangian relaxation-based approach is presented. Numerical testing is performed for a 10-unit system and an IEEE 24-bus system. Results show that the model and the solution algorithm in this study are effective.