Convex Hull Pricing Via Ramp-Constrained Network-Flow Unit Commitment Models

This work presents a Convex Hull Pricing framework based on a network-flow formulation of the Unit Commitment problem, incorporating generation ramp constraints directly in the model. The inclusion of ramp constraints directly impacts the feasible solution polyhedron, which no longer exhibits total unimodularity (TU). As a consequence, subproblems can no longer be solved using shortest-path algorithms for network flow problems. Instead, MIP solvers must be used which, due to their preprocessing capabilities, significantly reduce the number of variables and constraints, thereby improving computational efficiency. The solution approach relaxes the system power balance constraint and applies a primal-dual Bienstock-Zuckerberg (BZ) algorithm. Through an iterative process, the method generates partitions of the arc variables associated with generating units, effectively approximating the feasible solution space and enhancing computational performance over successive iterations. Computational experiments on instances from the California and FERC systems (without transmission network). The proposed method is benchmarked against two state-of-the-art approaches: the Dantzig-Wolfe (DW) decomposition and the Level Method (LM). The results show that the BZ algorithm outperforms the DW and LM approaches, reducing the average computational times by 40 % and 18 % for the CA system compared to LM and DW, respectively. For the FERC system, the reductions are 17 % (LM) and 9% (DW). In addition, the proposed approach exhibits a lower standard deviation across the simulated instances, which indicates more robust performance. Moreover, with a 0.5 % gap, BZ achieved the lowest normalized uplift on both instances (California and FERC), outperforming LM and DW, which indicates that, given the prescribed gap, the proposed methodology attains a solution closer to the global optimum.