Sensitivity-based approaches for handling discrete variables in optimal power flow computations

This paper proposes and compares three iterative approaches for handling discrete variables in optimal power flow (OPF) computations. The first two approaches rely on the sensitivities of the objective and inequality constraints with respect to discrete variables. They set the discrete variables values either by solving a mixed-integer linear programming (MILP) problem or by using a simple procedure based on a merit function. The third approach relies on the use of Lagrange multipliers corresponding to the discrete variables bound constraints at the OPF solution. The classical round-off technique and a progressive round-off approach have been also used as a basis of comparison. We provide extensive numerical results with these approaches on four test systems with up to 1203 buses, and for two OPF problems: loss minimization and generation cost minimization, respectively. These results show that the sensitivity-based approach combined with the merit function clearly outperforms the other approaches in terms of: objective function quality, reliability, and computational times. Furthermore, the objective value obtained with this approach has been very close to that provided by the continuous relaxation OPF. This approach constitutes therefore a viable alternative to other methods dealing with discrete variables in an OPF.