Photovoltaic generation is a non-controllable energy source, hence a high share of distributed PV installations in low-voltage networks may lead to over-voltage and lines or transformer overloading. To avoid these, the Distribution System Operator can curtail (or peak-shave), reinforce the grid infrastructure or implement optimally storage utilities. This study investigates an approach for determining optimal system operating conditions for a LV residential grid equipped with batteries of varying capacities and PV generation systems. A study case of one specific day demonstrates the performance improvement thanks to the controllability of batteries. A profitability assessment of grid investment strategy is proposed, with simulations run over a period of one year (2016, time steps of 15 minutes) with typical solar irradiance and load profiles. The optimization model determines the share of PV generation that needs to be curtailed and the optimal battery profile to avoid violated grid constraints. For a given intervention duration ratio, the economical comparison is proposed between the loss of the curtailed power and the cost of the reinforcement of the grid to reach a safe operation of the network. Optimization results show a very clear profitability of power curtailment over grid infrastructure reinforcement, with more than 2 orders of magnitude difference in the related costs.