Transmission Expansion Planning Considering Resistance Variations of Overhead Lines Using Minimum-Volume Covering Ellipsoid

Reliable planning of electricity networks is a crucial challenge to maintain the continuous power supply. This can be ensured through careful planning which requires a number of parameters as inputs such as electricity demand, generation capacity, fuel price, renewable intermittent generation, among others. The uncertain behaviors of such parameters have been well studied in literature. Another important parameter which is a vital requirement for reliable planning is the resistance of overhead transmission lines. Traditionally, the current models ignore to consider the resistance variations due to Joule heating and ambient temperature changes in transmission expansion planning (TEP) problem. In this sense, this paper presents an adaptive robust optimization (ARO) framework for TEP to model the uncertain resistance through ellipsoidal uncertainty set. Moreover, a data-driven selection of the ellipsoidal uncertainty set is proposed. In this regard, Khachiyans algorithm (KA) is used to identify the minimum-volume covering ellipsoid (MVCE) that contains all uncertain parameters. A case study based on IEEE 118-bus power system is presented to demonstrate the effectiveness of the proposed method. Simulation results show that resistance uncertainty is of serious concern in the TEP problem since the solutions are highly sensitive to fluctuations in the line resistances.