Alternative approaches to consider DC-power flow with losses in a linear program for short term hydrothermal scheduling

This paper discusses alternative ways of representing line flow limits constraints and linear approximations for transmission line losses in the short term hydrothermal scheduling problem with a dc model of the electrical network. In the first approach, applied previously by the authors, participation factors for the generations are employed, where in the second approach, proposed in this paper, phase shift angles are represented directly as additional variables of the optimization problem. Although the proposed approach leads to a much higher number of variables for the optimization problem, the sparsity of the line flow and transmission losses expressions as a function of phase angles yields a much smaller number of non-null matrix elements. Numerical results are presented both for an IEEE-118 bus study case and the real Brazilian system with over 4600 buses and 6600 lines, where we show the drastic reduction in CPU time and memory allocation provided by the proposed approach.