A computational comparison of 2 mathematical formulations to handle transmission network constraints in the unit commitment problem

Until recently, transmission network constraints have been incorporated into the unit commitment (UC) problem (security-constrained UC [SCUC]) using the classical direct current (DC)-based equation. This paper proposes a new formulation to model network constraints in the UC problem by using the power transfer distribution factor (PTDF). The classical formulation uses the binary commitment status, the power generation, and the voltage-phase angles as decision variables. For the proposed formulation, the nodal balance equality constraints are modeled using one equality constraint, and the transmission network constraints have been modeled using the PTDF and the active power generation (decision variables). The main advantage of this formulation is the reduction of decision variables in the operation problem in comparison with the classical DC formulation. Transmission losses, using a piecewise linear approximation, are included in the SCUC problem as well. Both formulations are validated and tested on the Institute of Electrical and Electronics Engineers (IEEE) 14-bus, the IEEE 30-bus, the IEEE 57-bus, and the IEEE 118-bus. The IEEE 14-bus and IEEE 57-bus systems are used to compare the loss and the lossless models. The results show that the PTDF-based formulation, which requires fewer continuous variables and equality constraints than the classical DC formulation, reduces the simulation time without sacrificing optimality. The results also demonstrate the feasibility of the proposed formulation to address the SCUC problem and its potential applicability to medium-scale and large-scale power systems.