The increasing share of photovoltaic (PV) power in the global energy mix presents a great challenge to power grid operators. In particular, PV powers intermittency caused by varying weather conditions can cause mismatches between energy production and expectation. Battery Energy Storage Systems (BESS) are often put forward as a good technological solution to these problems, as they are able to mitigate PV power forecast errors. However, the investment cost for such systems is high, which makes their use in operational contexts difficult. In this paper, we compare several strategies to manage a PV power plant coupled with a BESS in a market environment. They are obtained by stochastic optimization using a Model Predictive Control (MPC) approach. This paper proposes an approach that takes into account the ageing of the BESS, both at the day-ahead level and in the real-time control of the BESS, by modeling the cost associated with BESS usage. As a result, the BESS arbitrates between compensating forecast errors and preserving its own life expectancy, based on both PV production and price scenarios derived from probabilistic forecasts. A sensitivity analysis is also carried out to provide guidelines on the optimal sizing of the BESS capacity, depending on market characteristics and BESS prospective costs.