A two-stage adaptive robust optimization (ARO) for optimal sizing and operation of residential solar-photovoltaic (PV) systems coupled with battery units. Uncertainties of PV generation and load are modelled by user defined bounded intervals through polyhedral uncertainty sets. The proposed model determines the optimal size of PV-battery system while minimizing operating costs under the worst-case realization of uncertainties. ARO model is proposed as a tri-level min-max-min optimization problem. The outer min problem characterizes sizing variables as “here-and-now” decisions to be obtained prior to uncertainty realization. The inner max-min problem, however, determines the operation variables in place of “wait-and-see” decisions to be obtained after uncertainty realization. An iterative decomposition methodology is developed by means of column-and constraint technique to recast the tri-level problem into a single-level master problem (the outer min problem) and a bi-level sub-problem (the inner max-min problem). Duality theory and Big-M linearization technique are used to transform the bi-level sub problem into a solvable single-level max problem. The immunization of the model against uncertainties is justified by testing the obtained solutions against 36500 trial uncertainty scenarios in a post-event analysis. The proposed post-event analysis also determines the optimum robustness level of the ARO model to avoid over/under conservative solutions.