The battery energy storage systems (BESS) are most promising solution for increasing efficiency and flexibility of distribution networks (DNs) with significant penetration level of photovoltaic (PV) systems. There are various issues related to the optimal operation of DNs with integrated PV sys-tems and BESS that need to be addressed to maximize DN performance. This paper deals with the day-ahead optimal active-reactive power dispatching in unbalanced DNs with integrated sin-gle-phase PV generation and BESSs. The objectives are the minimization of cost for electricity, en-ergy losses in the DN and voltage unbalance at three-phase load buses by optimal managing of active and reactive power flows. To solve this highly constrained nonlinear optimization problem, a hybrid particle swarm optimization with sigmoid-based acceleration coefficients (PSOS) and cha-otic gravitational search algorithm (CGSA), called PSOS-CGSA algorithm, is proposed. A scenario based approach encompassing the Monte Carlo simulation (MCS) method with the simultaneous backward reduction algorithm is used for the probabilistic assessment of the uncertainty of PV generation and power of loads. The effectiveness of the proposed procedure is evaluated through the series test cases in a modified IEEE 13-bus feeder.