Convex Hull Pricing via An Explicit Formulation for the Lagrangian Dual of the Network-constrained Unit Commitment

Convex hull pricing (CHP) is a pivotal approach to enhance market transparency by minimizing uplift costs. This pa per revisits the mathematical foundation of CHP and provides an explicit formulation of the Lagrangian dual formulation for network-constrained unit commitment (NCUC), further defining the CHP. Here, a convex hull model for single-unit commitment (1UC) problems is established with ramping constraints and minimum on/off time, making this explicit formulation implementable and further delivering the optimal Lagrangian dual solution via two linear programming (LP) models. The first LP reformulates the NCUC by replacing mixed-integer constraints with convex hull relaxations, while the second, obtained by fixing the inner variables in the Lagrangian dual problem of the NCUC to their optimal val ues from the first LP, generates the optimal Lagrangian dual solution. Numerical experiments on the IEEE-118 and Polish-2383 sys tems validate the superiority of CHP in reducing uplift costs and of this proposed pricing method in computational efficiency.