# Robust Transmission Network Expansion Planning Problem Considering Storage Units

## TL;DR

This paper develops a robust optimization framework for transmission network expansion planning that incorporates storage units and addresses uncertainties in demand and generation, introducing binary recourse variables to prevent simultaneous charging and discharging.

## Contribution

It introduces a novel two-stage adaptive robust optimization model with binary recourse variables and a nested column-and-constraint generation algorithm for solving complex discrete problems.

## Key findings

- Algorithm guarantees convergence to the global optimum.
- Effective handling of storage unit operations under uncertainty.
- Validated on Garver's test system.

## Abstract

This paper addresses the transmission network expansion planning problem considering storage units under uncertain demand and generation capacity. A two-stage adaptive robust optimization framework is adopted whereby short- and long-term uncertainties are accounted for. This work differs from previously reported solutions in an important aspect, namely, we include binary recourse variables to avoid the simultaneous charging and discharging of storage units once uncertainty is revealed. Two-stage robust optimization with discrete recourse problems is a challenging task, so we propose using a nested column-and-constraint generation algorithm to solve the resulting problem. This algorithm guarantees convergence to the global optimum in a finite number of iterations. The performance of the proposed algorithm is illustrated using the Garver's test system.