Battery energy storage systems (BESSs) have been used in AC Microgrids (AMGs) for frequency control (FC) and energy management (EM). AMGs with low inertia might suffer large frequency deviations with high rates without the required reserve power for FC. This paper proposes a linear model for the optimal operation of grid-connected AMGs considering frequency security constraints. BESS and photovoltaic systems both participate in primary FC (PFC) and EM. PVSs can decrease their generation in power surplus conditions. They can release the energy of their DC-link capacitors in power shortage conditions. Through coordinated use of BESS and PVSs, the required BESS power for PFC decreases considerably, which allows the BESS to participate in EM more effectively and hence reduces the AMG operational cost. Frequency simulation studies show that PVSs can considerably assist BESS for PFC. Moreover, the optimization results show that without PVSs' support, load shedding is unavoidable which increases the AMG operation cost significantly. In this regard, deterministic and stochastic optimization show that PVSs' participation in PFC results in 24 % and 24.2 % reduction in the AMG operation cost compared to those when BESS is only used for PFC. Therefore, the PVSs' assist in PFC, even though short, has large impact on the optimal operation of the AMG.