Adaptive Robust Transmission Network Expansion Planning using Structural Reliability and Decomposition Techniques

Structural reliability and decomposition techniques have recently proved to be appropriate tools for solving robust uncertain mixed-integer linear programs using ellipsoidal uncertainty sets. In fact, its computational performance makes this type of problem to be an alternative method in terms of tractability with respect to robust problems based on cardinality constrained uncertainty sets. This paper extends the use of these techniques for solving an adaptive robust optimization (ARO) problem, i.e. the adaptive robust solution of the transmission network expansion planning for energy systems. The formulation of this type of problem materializes on a three-level mixedinteger optimization formulation, which based on structural reliability methods, can be solved using an ad-hoc decomposition technique. The method allows the use of the correlation structure of the uncertain variables involved by means of their variance-covariance matrix, and besides, it provides a new interpretation of the robust problem based on quantile optimization. We also compare results with respect to robust optimization methods that consider cardinality constrained uncertainty sets. Numerical results on an illustrative example, the IEEE-24 and IEEE 118-bus test systems demonstrate that the algorithm is comparable in terms of computational performance with respect to existing robust methods with the additional advantage that the correlation structure of the uncertain variables involved can be incorporated ∗Corresponding author: [email protected], tlfn.: 00 34 926810046 Preprint submitted to European Journal of Operational Research January 28, 2015