Robust optimization for day-ahead market participation of smart-home aggregators

This paper proposes an optimization model to participate in day-ahead energy markets when PV generation, thermal and electro-chemical storage devices are aggregated at the residential level. The model includes uncertainty in energy prices, PV and load; and adjustable robust optimization is used to determine a tractable counterpart of the problem. By means of robust control parameters, solutions with different levels of conservatism can be found and analyzed. In addition, the presented model includes explicit representation of battery degradation by means of special ordered sets. This equivalent cycling aging calculation takes into account the non-linear relation between depth of discharge and total life cycles of the battery by piecewise linearization. Performance analysis shows the advantage of the proposed approach when compared to the deterministic solution in terms of average cost and risk. For the analyzed real-life test system, the robust formulation achieves cost reduction of up to 5.7% and standard deviation decreases as much as 36.4%.