Fictitious losses in the DCOPF with a piecewise linear approximation of losses

This paper examines the effect of fictitious or non-physical losses on optimal power flow solutions and LMPs. Fictitious losses are created when segments of piecewise linear functions used to approximate real power losses for a DCOPF problem are selected in the wrong order. The segments of a piecewise linear function may be improperly selected when non-positive LMPs occur. Creating fictitious losses at a bus with a negative LMP increases the LMP until it is either zero or until fictitious losses cannot be created any longer. This effect is rigorously examined in this paper, proven theoretically with duality theory and the KKT conditions and illustrated with a numerical example. A MILP formulation to correct for fictitious losses is also discussed.