Convex optimization of PV-battery system sizing and operation with non-linear loss models

To mitigate climate change, households are increasingly incentivized to install PV systems in combination with battery energy storage systems to increase their self-sufficiency and flexibility as well as to relieve the stress caused by the high penetration of distributed generation on the grid. This paper aims to assess the need for non-linear loss models as opposed to linear loss models found in the literature when optimizing the sizing and operation of PV-battery systems. Therefore, an optimization model is presented which implements non-linear, convex and linear converter and battery loss model formulations. The relaxed convex formulation is equivalent to the original non-linear formulation and can be solved more efficiently, decreasing the run time by a factor of 4. The impact of non-linear as opposed to linear loss models on the optimal solution is illustrated for a residential DC-coupled PV-battery system. The linear loss model is shown to result in an underestimation of the cost by 14.7% and the battery size by 12.4%. Further, the battery utilization is underestimated by a third. The proposed method is useful to accurately model the losses when optimizing the sizing and operation of a PV-battery system 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.