Tight convex relaxation for TEP problem: A multiparametric disaggregation approach

In recent years, there has been an increasing interest in using AC power flow equations for the transmission expansion planning (TEP) studies. The AC power flow equations are quadratic and hence the TEP problem can be formulated as a mixed-integer quadratically constrained programme. Therefore, the complexity of the TEP problem lies in the non-convexity of AC power flow equations in which the global optimal solution is not guaranteed to be found. This study aims at proposing a tight convex relaxation for the TEP problem. In this context, first, the TEP problem is formulated as a mixed-integer bilinear problem by representing the complex bus voltage in its rectangular coordinates. Second, the multiparametric disaggregation technique (MDT) and piecewise McCormick relaxation are employed to generate a mixed-integer linear relaxation. MDT is based on the discretisation of the domain of one of the variables in every bilinear term. The method presented is much more precise compared with the DC or other linearisation approaches, while the optimal solution is of high quality. The results of the case studies show the tractability and exactness of the proposed model as well as its superiority over the state-of-the-art schemes.