energies Article Using Generalized Generation Distribution Factors in a MILP Model to Solve the Transmission-Constrained Unit Commitment Problem Guillermo Gutierrez-Alcaraz 1, * and Victor H. Hinojosa 2, * ID 1 Department of Electrical Engineering, Tecnológico Nacional de México/I.T. Morelia, Morelia 58020, Michoacán, México 2 Department of Electrical Engineering, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile * Correspondence: ggutier@itmorelia.edu.mx (G.G.-A); victor.hinojosa@usm.cl (V.H.H.) Received: 9 August 2018; Accepted: 24 August 2018; Published: 26 August 2018   Abstract: This study proposes a mixed-integer linear programming (MILP) model to figure out the transmission-constrained direct current (DC)-based unit commitment (UC) problem using the generalized generation distribution factors (GGDF) for modeling the transmission network constraints. The UC problem has been reformulated using these linear distribution factors without sacrificing optimality. Several test power systems (PJM 5-bus, IEEE-24, and 118-bus) have been used to validate the introduced formulation. Results demonstrate that the proposed approach is more compact and less computationally burdensome than the classical DC-based formulation, which is commonly employed in the technical literature to carry out the transmission network constraints. Therefore, there is a potential applicability of the accomplished methodology to carry out the UC problem applied to medium and large-scale electrical power systems. Keywords: DC optimal power flow; power transfer distribution factors; generalized generation distribution factors; unit commitment 1. Introduction The unit commitment (UC) optimization problem is the conventional formulation used by regulated companies and power pools to schedule the power generation units for supplying the load demand over a multi-hour to multi-day timeframe [1]. The UC problem consists of deciding which thermoelectric power units need to operate at each time period (1 h) in order to minimize the generation costs (fuel cost, startup, and shutdown costs), and to satisfy the operational technical constraints for the entire power system (spinning reserve and load), as well as for each power generation unit (minimum up/down times, minimum and maximum power, and load ramps) [2]. 1.1. Literature Review It is critical that transmission power flow constraints will be incorporated in the UC formulation, because most power grids are operating close to their security electrical margins [3]. Different linear transmission network formulations have been apply to model the transmission capacity limits in the UC optimization problem. However, most researchers use the classical DC-based power flow formulation [4–13], where the active power unit generation and the voltage phase angles are the decision variables used to carry out the operational problem. This problem consists of two analyses: (1) the nodal power balance equality constraints; and (2) the maximum transmission power flow inequality constraints. Based on the classical DC-based formulation and incorporating the transmission power flow constraints in the optimization problem, it is significantly increased the problem size becoming computationally more complex when it is applied to large-scale electrical power systems. Energies 2018, 11, 2232; doi:10.3390/en11092232 www.mdpi.com/journal/energies