Bilevel transmission expansion planning using second-order cone programming considering wind investment

This paper presents a new framework for bi-level multi-stage transmission expansion planning (TEP) considering wind investment. In the upper-level problem, the transmission and wind investment decisions are modeled, while in the lower-level problem, the market-clearing problem based on the alternating current-optimal power flow (AC-OPF) is formulated. Since the lower-level optimization problem is nonconvex, the second-order cone programming (SOCP) is applied to convexify this problem. Afterwards, the Karush-Kuhn-Tucker (KKT) optimality conditions are employed in order to convert the bi-level problem into a single-level problem. Due to the convexity of the lower-level problem, the KKT conditions are both necessary and sufficient. The whole problem is then solved by a commercial and powerful solver. To show the effectiveness and applicability of the proposed scheme, it is applied to two power systems, namely, IEEE 24-bus RTS and IEEE 118-bus. The numerical results illustrate the efficient performance of the proposed method. Furthermore, the results obtained from the AC-OPF-based market-clearing problem are compared with those obtained from the direct current-optimal power flow (DC-OPF)-based market-clearing problem, and the comparative analysis indicates that the latter may lead to inaccurate solutions.