Adaptive Robust Optimization Models for DER Planning in Distribution Networks under Long- and Short-Term Uncertainties

TL;DR

This work develops adaptive robust optimization (ARO) and adaptive robust stochastic optimization (ARSO) formulations for the optimal sizing and placement of DERs in distribution networks under dual-time-scale uncertainty, explicitly separating long-term demand uncertainty from short-term PV variability via budgeted uncertainty sets and scenario modeling. An adapted Benders decomposition framework solves the resulting tri-level problems efficiently, with ARSO incorporating both LT robustness and ST PV scenarios to reduce conservatism relative to ARO and SRO while staying close to the perfect-information benchmark. Case studies on a modified IEEE 33-bus network demonstrate that ARSO provides better investment decisions, achieving near-optimal DER capacities and higher autonomy with manageable computational effort. The findings support a practical planning methodology for DER integration that leverages LT/ST uncertainty differentiation and budgeted robustness, and point to future work on relaxing network losses, adding market dynamics, multi-energy carriers, and data-driven uncertainty sets.

Abstract

This study introduces adaptive robust optimization (ARO) and adaptive robust stochastic optimization (ARSO) approaches to address long- and short-term uncertainties in the optimal sizing and placement of distributed energy resources in distribution networks. ARO models uncertainty using a Budget of Uncertainty (BoU), while ARSO distinguishes long-term (LT) demand (via BoU) and short-term (ST) photovoltaics generation (via scenarios). Adapted Benders cutting plane algorithms are presented to tackle the tri-level optimization challenges. The experiments consider a modified version of the IEEE 33 bus system to test these two approaches and also compare them with traditional robust and stochastic optimization models. The results indicate that distinguishing between LT and ST uncertainties using a hybrid formulation such ARSO yields a solution closer to the optimal solution under perfect information than ARO.

Figures (4)

• Figure 1: PV Boundary set and scenarios
• Figure 2: Boundary set and scenarios of electricity demand
• Figure 3: Comparison of the installed capacities of PV and BESS across different approaches and the BoU, relative to PI.
• Figure 4: Stochastic and robust approaches versus perfect information