Optimal power flow considering line-conductor temperature limits under high penetration of intermittent renewable energy sources

Forecasts of the power generated by intermittent renewable energy (IRE) sources are typically characterized by high uncertainty levels. Hence, recent formulations of the optimal power flow (OPF) problem incorporate the costs associated with the increased risk of generation shortage due to IRE uncertainty. Additionally, IRE generation increases the power flow uncertainty, thereby increasing the possibility of violating the thermal limits of overhead conductors. Real-time monitoring of the thermal statuses of overhead lines has been considered effective in increasing the transmission-system usage; in addition, it can influence IRE scheduling and the associated uncertainty costs. This paper proposes the formulation of an OPF problem incorporating the thermal characteristics of the conductor, calculated from the monitored weather parameters, for a system with significant IRE-source generation. The resulting convex nonlinear optimization problem is solved using a primal-dual interior point solver. A simplified form of the overhead-conductor heat balance equation that expresses the conductor temperature as an explicit function of the current is proposed, simplifying the incorporation of the conductor thermal characteristics in the problem formulation. The application of the proposed formulation is demonstrated using a modified version of the IEEE 30-bus test system with IRE generation.