Robust transmission network expansion planning in energy systems: Improving computational performance

In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem tractable in realistic systems. Different sources of uncertainty have been considered, mainly related to the capacity and availability of generation facilities and demand, and making use of adaptive robust optimization models. The mathematical formulations for these models give rise to three-level mixed-integer optimization problems, which are solved using different strategies. Although it is true that these robust methods are more efficient than their stochastic counterparts, it is also correct that solution times for mixed-integer linear programming problems increase exponentially with respect to the size of the problem. Because of this, practitioners and system operators need to use computationally efficient methods when solving this type of problem. In this paper the issue of improving computational performance by taking different features from existing algorithms is addressed. In particular, we replace the lower-level problem with a dual one, and solve the resulting bi-level problem using a primal cutting plane algorithm within a decomposition scheme. By using this alternative and simple approach, the computing time for solving transmission expansion planning problems has been reduced drastically. Numerical results in an illustrative example, the IEEE-24 and IEEE 118-bus test systems demonstrate that the algorithm is superior in terms of computational performance with respect to the existing methods.