Modeling network losses using quadratic cones

This paper shows that line losses can be accounted for locally in dc optimal power flow (DC-OPF) by adding rotated quadratic cones to a variation of the original linear set of constraints. The result is a conic quadratic optimization problem. A favorable property of this problem is that primal-dual interior-point methods developed for linear programming can be generalized to its solution while maintaining their efficiency. Numerical results using an efficient implementation of an interior-point method are presented.