A computational comparison of PTDF-based and phase-angle-based formulations of network constraints in distributed unit commitment

In centralized approaches for the network-constrained unit commitment problem, the dominant way to formulate the linearized power flow problem is based on sensitivity factors such as power transfer distribution factors (PTDF formulation), instead of using phase-angle variables (b-theta formulation). The PTDF formulation enables various exploits of the problem structure, and those exploits grow in importance with the problem size. While these exploits exist for centralized approaches, new challenges arise for distributed approaches that are based on regional decomposition. In distributed approaches, additional constraints for tie lines need to be added to the PTDF formulation. At the same time, the advantages of the PTDF formulation diminish, since a distributed approach often solves smaller-sized unit commitment (UC) problems for each region in an iterative manner until convergence is achieved. This paper explores the performance of distributed algorithms for network-constrained UC problems based on two ways of formulating the linearized power flow problem for the power grid: PTDF-based and phase-angle-based. The performance of the two mathematical models is analyzed at different degrees of decomposition. Numerical simulations are performed to solve 24-h unit commitment problems for a Polish 3012-bus system. The results show that when the number of buses in each subproblem is large and binary constraints are enforced, the PTDF formulation performs better. The results also show that partitioning into more regions may take more iterations to reach desired solution quality, although each iteration takes less time. This trade-off need to be considered in the application of distributed unit commitment algorithms.