An efficient four-level programming model for optimizing tri-stage adaptive robust transmission expansion planning

Abstract

Two-stage adaptive robust optimization (RO) has been widely used to formulate the transmission expansion planning (TEP) problem. The goal is to acquire an optimal least-cost expansion plan that is robust against any future realization of the uncertain parameters. The existing models are constructed based on a tri-level min-max-min optimization problem solved using a decomposition-based column-and-constraint generation (CCG) algorithm. These approaches assume that the peak load and generation capacity lie in a prespecified uncertainty set by fixing minimum (lower) and maximum (upper) amounts. However, the minimum and maximum values fixed in these models are assumed to be fully known, while they are uncertain with unknown probability density functions (PDFs), if any. This paper aims to fill this gap by establishing an RO-based model using four-level (min-max-max-min) programming rather than tri-level programming. The presented tri-stage methodological framework is solved by a nested CCG (NCCG). The first stage determines the optimal investment decision, while the second stage specifies the worst-case scenario over an uncertainty set of lower and upper bounds. Then, the third stage identifies the worst-case operation cost over an uncertainty set of peak load and generation capacity. Simulation results indicate the effectiveness of the developed method.