  In the literature, when optimizing the sizing and operation of a residential
PV system in combination with a battery energy storage system, the efficiency
of the battery and the converter is generally assumed constant, which
corresponds to a linear loss model that can be readily integrated in an
optimization model. However, this assumption does not always represent the
impact of the losses accurately. For this reason, an approach is presented that
includes non-linear converter and battery loss models by applying convex
relaxations to the non-linear constraints. The relaxed convex formulation is
equivalent to the original non-linear formulation and can be solved more
efficiently. The difference between the optimization model with non-linear loss
models and linear loss models is illustrated for a residential DC-coupled
PV-battery system. The linear loss model is shown to result in an
underestimation of the battery size and cost as well as a lower utilization of
the battery. The proposed method is useful to accurately model the impact of
losses on the optimal sizing and operation in exchange for a slightly higher
computational time compared to linear loss models, though far below that of
solving the non-relaxed non-linear problem.
