Piecewise-linear approximations for a non-linear transmission expansion planning problem

Abstract

This study proposes a new approach to solve the transmission expansion planning (TEP) problem considering that the network is represented by a non-linear model. Non-linear constraints are approximated with piecewise-linear (PWL) functions, which renders TEP a mixed-integer linear programming (MILP) problem. This study presents MILP formulations obtained from the PWL approximation using the incremental, special ordered sets of type 2 (SOS2) and the logarithmic convex combination (Log) model. Three test systems are used to assess the effectiveness of the formulations. The computational analysis encompasses a baseline formulation, which accounts for the costs on line installation and transmission losses, and a variation of this formulation which minimises the operating costs rather than transmission losses. The results obtained by the MILP models are compared with those of a transmission planning model based on the DC representation of the network. The analysis of the results showed that expansion plans obtained from the MILP formulations are feasible, whereas the plans derived from the DC model are infeasible with respect to system constraints.