A modified Branch and Bound algorithm to solve the transmission expansion planning problem

In this paper a novel Branch and Bound (B&B) algorithm to solve the transmission expansion planning which is a non-convex mixed integer nonlinear programming problem (MINLP) is presented. Based on defining the options of the separating variables and makes a search in breadth, we call this algorithm a B&BML algorithm. The proposed algorithm is implemented in AMPL and an open source Ipopt solver is used to solve the nonlinear programming (NLP) problems of all candidates in the B&B tree. Strategies have been developed to address the problem of non-linearity and non-convexity of the search region. The proposed algorithm is applied to the problem of long-term transmission expansion planning modeled as an MINLP problem. The proposed algorithm has carried out on five commonly used test systems such as Garver 6-Bus, IEEE 24-Bus, 46-Bus South Brazilian test systems, Bolivian 57-Bus, and Colombian 93-Bus. Results show that the proposed methodology not only can find the best known solution but it also yields a large reduction between 24% to 77.6% in the number of NLP problems regarding to the size of the systems.