Photovoltaic (PV) energy generation in microgrids (MGs) is increasing. Battery energy storage systems (BESSs) reduce the fluctuations in PV outputs caused by the intermittent availability of solar energy. Although BESSs are advantageous for stable MG operation, they are still relatively expensive. By remaining within the operational limits during normal and contingency operation, optimal sizing of BESS is required to maintain security considering cost of MG system. This paper proposes a BESS sizing optimization approach for MGs by solving the security constrained optimal power flow (SCOPF), considering the stochastic errors in forecasting the PV outputs. The degree of compensation for the solar energy forecasting error is firstly configured. To address these errors, the combined PV and BESS operation system is modeled by applying a control strategy to smooth PV fluctuations and minimize battery life degradation. BESS sizing optimization, under a certain degree of compensation, minimizes the PV penalty cost and BESS operation cost. The optimal BESS capacity and schedule are then obtained for the MG. To enhance the convergence and computational efficiency, decomposed-probabilistic security constrained optimal power flow (D-PSCOPF) is proposed. It efficiently solves the problem by dividing it into a master problem and a slave problem. The base case solution is computed in the slave problem, which induces the partial optimal size of BESS. By adding the feasibility cut through the violation of the slave problem, the master problem derives the optimal BESS capacity. Different case studies were analyzed, confirming the superiority and computational efficiency of the proposed approach. shutdown 𝐶 𝑡𝑠0 𝐶 𝑡𝑠𝑐 𝐶 𝑡𝑠𝑑 Weighted price vectors summarizing contributi ons to the value of terminal storage 𝛾 𝑡 Probability of making it to period t without branch off the central path in a contingency in periods 𝑃 𝑃𝑉,𝑎𝑐𝑡𝑢𝑎𝑙 Actual power output of PV 𝑃 𝑃𝑉,𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 Forecasted power output of PV 𝑃 𝑟𝑎𝑡𝑒 Required rated power of the BESS 𝑃 𝐵𝐸𝑆𝑆 Actual charging and discharging power of the B ESS 𝐸 Energy fluctuation of BESS at the sampling tim e relative to the initial state 𝐸 𝑟𝑎𝑡𝑒 Rated capacity of the BESS 𝑄 𝑐𝑦𝑐𝑙𝑒 Capacity loss at the time instants 𝑃 𝐺